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value | split stringclasses 1
value | row_index int64 0 4.5k | theorem stringlengths 7 81 | file_path stringclasses 723
values | repo_url stringclasses 1
value | repo_commit stringclasses 1
value | tactic stringlengths 3 2.13k | text_state stringlengths 7 2.31k | text_target_state stringlengths 0 4.07k | raw_goal_sexp stringlengths 10 11.8M | raw_hyp_sexps stringlengths 2 15.6M | model_goal_sexp stringlengths 10 2.68M | model_hyp_sexps stringlengths 2 3.62M | source_syntax stringlengths 179 164k | syntax_args stringclasses 256
values | term_ranges stringlengths 2 6.01k | local_context stringlengths 2 10.3k | unit_index int64 3 1.26k | invocation_index int64 0 357 | alignment_kind stringclasses 2
values | target_state_matches_invocation bool 2
classes | pending_goal_count int64 1 1 | hypothesis_count int64 0 77 | hypothesis_names_match bool 2
classes | raw_schema_version int64 4 4 | raw_extractor_version stringclasses 1
value | model_schema_version int64 2 2 | model_normalization stringclasses 1
value | trace_schema_version int64 3 3 | trace_extractor_version stringclasses 1
value | pantograph_commit stringclasses 1
value | model_pantograph_commit stringclasses 1
value | raw_record_sha256 stringlengths 64 64 | state_sha256 stringlengths 64 64 | tactic_sha256 stringlengths 64 64 | target_state_sha256 stringlengths 64 64 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
cat-searcher/leandojo-benchmark-4-random | test | 2,777 | Set.le_edist_of_le_infsep | Mathlib/Topology/MetricSpace/Infsep.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>le_trans</a> hd <a>dist_nonneg</a> | case neg
α : Type u_1
β : Type u_2
inst✝ : PseudoMetricSpace α
x✝ y✝ z : α
s t : Set α
d : ℝ
x : α
hx : x ∈ s
y : α
hy : y ∈ s
hxy : x ≠ y
hd : d ≤ 0
hs : s.Subsingleton
⊢ d ≤ dist x y | ((:c LE.le) (:c Real) (:c Real.instLE) (:fv _uniq.48395) ((:c Dist.dist) (:fv _uniq.48225) ((:c PseudoMetricSpace.toDist) (:fv _uniq.48225) (:fv _uniq.48231)) (:fv _uniq.48396) (:fv _uniq.48398))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c PseudoMetricSpace) (:fv _uniq.48225))"},{"name":"x✝","sexp":"(:fv _uniq.48225)"},{"name":"y✝","sexp":"(:fv _uniq.48225)"},{"name":"z","sexp":"(:fv _uniq.48225)"},{"name":"s","sexp":"((:c Set) (:fv _uniq.48225))... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv FV9)) (:arg :explicit 3 (:app (:c Dist.dist) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Dist) (:arg :explicit 0 (:fv FV0))))) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.48228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"exact","sourceEnd":16696,"sourceStart":16691,"tag":"atom"},{"children":[{"name":"le_trans","semanticRole":"global","source":"le_trans","sourceEnd":16705,"sourceStart":16697,"tag":"identifier"},{"children":[{"contextIndex":15,"semanticRole":"local","source":"hd","sourceEnd":16708,"sourceStart":16... | [] | [{"source":"le_trans hd dist_nonneg","source_end":16720,"source_start":16697,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.48228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 149 | 20 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 09c07b08ac2629aefae2a837bcd897a9a874fbcbe2b32056c7bf686f02dbead7 | 55793150d984d7c1a9385b0a1b73013bcbbbcf48b39fd5f10df18ad18582909b | 1553573defb58fabbf7f9cd5b04f288bb1b87dd4a3f8cdf07a68bef2d9f0c23a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,778 | WeierstrassCurve.Φ_one | Mathlib/AlgebraicGeometry/EllipticCurve/DivisionPolynomial/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | erw [<a>WeierstrassCurve.Φ_ofNat</a>, <a>WeierstrassCurve.preΨ'_one</a>, <a>one_pow</a>, <a>mul_one</a>, <a>mul_one</a>, <a>WeierstrassCurve.preΨ'_zero</a>, <a>MulZeroClass.mul_zero</a>, <a>MulZeroClass.zero_mul</a>, <a>sub_zero</a>] | R : Type r
S : Type s
inst✝¹ : CommRing R
inst✝ : CommRing S
W : WeierstrassCurve R
⊢ W.Φ 1 = X | ((:c Eq) ((:c Polynomial) (:fv _uniq.155987) ((:c CommSemiring.toSemiring) (:fv _uniq.155987) ((:c CommRing.toCommSemiring) (:fv _uniq.155987) (:fv _uniq.155992)))) ((:c WeierstrassCurve.Φ) (:fv _uniq.155987) (:fv _uniq.155992) (:fv _uniq.155998) ((:c OfNat.ofNat) (:c Int) (:lit 1) ((:c instOfNat) (:lit 1)))) ((:c Poly... | [{"name":"R","sexp":"(:sort (+ r 1))"},{"name":"S","sexp":"(:sort (+ s 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.155987))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.155989))"},{"name":"W","sexp":"((:c WeierstrassCurve) (:fv _uniq.155987))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c WeierstrassCurve.Φ) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommRing) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.155987","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.155989","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"source":"erw","sourceEnd":14201,"sourceStart":14198,"tag":"atom"},{"children":[{"source":"[","sourceEnd":14203,"sourceStart":14202,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"WeierstrassCurve.Φ_ofNat","sema... | [] | [{"source":"Φ_ofNat","source_end":14211,"source_start":14203,"syntax_kind":"ident"},{"source":"preΨ'_one","source_end":14223,"source_start":14213,"syntax_kind":"ident"},{"source":"one_pow","source_end":14232,"source_start":14225,"syntax_kind":"ident"},{"source":"mul_one","source_end":14241,"source_start":14234,"syntax_... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.155987","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.155989","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal... | 76 | 2 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6c6370ccf3e53dd3a9587e1b57c979aa95314af93e257f5580c0aed71aca3879 | 0433c0e27c855be477aca7a84daffd14f1b9d03e63b37cbb7d5df67f8e498777 | 0bac5585454e4927cc91ad2a0aba16ed7397e374862c933716fc285a46f6ddab | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,780 | FiniteField.pow_card | Mathlib/FieldTheory/Finite/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Nat.succ_pred_eq_of_pos</a> <a>Fintype.card_pos</a>, <a>pow_succ</a>, <a>Nat.pred_eq_sub_one</a>, <a>FiniteField.pow_card_sub_one_eq_one</a> a h, <a>one_mul</a>] | case neg
K : Type u_1
R : Type u_2
inst✝¹ : GroupWithZero K
inst✝ : Fintype K
a : K
h : ¬a = 0
⊢ a ^ q = a | ((:c Eq) (:fv _uniq.78564) ((:c HPow.hPow) (:fv _uniq.78564) (:c Nat) (:fv _uniq.78564) ((:c instHPow) (:fv _uniq.78564) (:c Nat) ((:c Monoid.toNatPow) (:fv _uniq.78564) ((:c MonoidWithZero.toMonoid) (:fv _uniq.78564) ((:c GroupWithZero.toMonoidWithZero) (:fv _uniq.78564) (:fv _uniq.78570))))) (:fv _uniq.78858) ((:c Fi... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c GroupWithZero) (:fv _uniq.78564))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.78564))"},{"name":"a","sexp":"(:fv _uniq.78564)"},{"name":"h","sexp":"((:c Not) ((:c Eq) (:fv _uniq.78564) (:fv _uniq.78858)... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:fv FV0)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.78564","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.78567","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":9957,"sourceStart":9955,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":9959,"sourceStart":9958,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":9962,"sourceStart":... | [] | [{"source":"Nat.succ_pred_eq_of_pos Fintype.card_pos","source_end":10003,"source_start":9963,"syntax_kind":"Lean.Parser.Term.app"},{"source":"pow_succ","source_end":10013,"source_start":10005,"syntax_kind":"ident"},{"source":"Nat.pred_eq_sub_one","source_end":10034,"source_start":10015,"syntax_kind":"ident"},{"source":... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.78564","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.78567","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 25 | 15 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fd1f0bfa0eea56c28db9b32f52e61813a15be09a4e430df8934ecf5e54c08905 | 99b4d5fb46a0318bddfd2b960a379430bd6a6c5f5b7775dcf00fbd8f4b87d173 | acb73d13b6e9069bd124ccfce0463d90d422498510c1eb93fa1fda6fa9f3bb8c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,781 | FiniteField.pow_card | Mathlib/FieldTheory/Finite/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [h] | case pos
K : Type u_1
R : Type u_2
inst✝¹ : GroupWithZero K
inst✝ : Fintype K
a : K
h : a = 0
⊢ a ^ q = a | case pos
K : Type u_1
R : Type u_2
inst✝¹ : GroupWithZero K
inst✝ : Fintype K
a : K
h : a = 0
⊢ 0 ^ q = 0 | ((:c Eq) (:fv _uniq.78564) ((:c HPow.hPow) (:fv _uniq.78564) (:c Nat) (:fv _uniq.78564) ((:c instHPow) (:fv _uniq.78564) (:c Nat) ((:c Monoid.toNatPow) (:fv _uniq.78564) ((:c MonoidWithZero.toMonoid) (:fv _uniq.78564) ((:c GroupWithZero.toMonoidWithZero) (:fv _uniq.78564) (:fv _uniq.78570))))) (:fv _uniq.78858) ((:c Fi... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c GroupWithZero) (:fv _uniq.78564))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.78564))"},{"name":"a","sexp":"(:fv _uniq.78564)"},{"name":"h","sexp":"((:c Eq) (:fv _uniq.78564) (:fv _uniq.78858) ((:c OfNa... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:fv FV0)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.78564","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.78567","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":9911,"sourceStart":9909,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":9913,"sourceStart":9912,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":6,"semanticRo... | [] | [{"source":"h","source_end":9914,"source_start":9913,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.78564","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.78567","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 25 | 10 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 63902c0106ec57a259c14210b23d5e2616b3d4a0cd94cc2ec4d396ee55b4c8a0 | 529f519aba57034991286a52da598eb63904fd4ed6e0381832d35793a67fa972 | 8e1ff58c9c2ffe38f33c0acb9a280a2097eb986bf9afb4a3b7b955b60bd0b8f6 | 0308100f32531e6448a8de5102b359bf2fa19b7f747e00486c3e31bcb605595e |
cat-searcher/leandojo-benchmark-4-random | test | 2,782 | FiniteField.pow_card | Mathlib/FieldTheory/Finite/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>zero_pow</a> <a>Fintype.card_ne_zero</a> | case pos
K : Type u_1
R : Type u_2
inst✝¹ : GroupWithZero K
inst✝ : Fintype K
a : K
h : a = 0
⊢ 0 ^ q = 0 | ((:c Eq) (:fv _uniq.78564) ((:c HPow.hPow) (:fv _uniq.78564) (:c Nat) (:fv _uniq.78564) ((:c instHPow) (:fv _uniq.78564) (:c Nat) ((:c Monoid.toNatPow) (:fv _uniq.78564) ((:c MonoidWithZero.toMonoid) (:fv _uniq.78564) ((:c GroupWithZero.toMonoidWithZero) (:fv _uniq.78564) (:fv _uniq.78570))))) ((:c OfNat.ofNat) (:fv _u... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c GroupWithZero) (:fv _uniq.78564))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.78564))"},{"name":"a","sexp":"(:fv _uniq.78564)"},{"name":"h","sexp":"((:c Eq) (:fv _uniq.78564) (:fv _uniq.78858) ((:c OfNa... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:fv FV0)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.78564","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.78567","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"apply","sourceEnd":9922,"sourceStart":9917,"tag":"atom"},{"children":[{"name":"zero_pow","semanticRole":"global","source":"zero_pow","sourceEnd":9931,"sourceStart":9923,"tag":"identifier"},{"children":[{"name":"Fintype.card_ne_zero","semanticRole":"global","source":"Fintype.card_ne_zero","source... | [] | [{"source":"zero_pow Fintype.card_ne_zero","source_end":9952,"source_start":9923,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.78564","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.78567","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 25 | 14 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0a706011535802b8cb83c16792b7fe16f32561f7cce2f6a342ecb41434da1f9e | 0308100f32531e6448a8de5102b359bf2fa19b7f747e00486c3e31bcb605595e | 19d0f6a2fc125c305f4a3cb4822608ef4bc07dc51742dc7aa2809347c9d938ea | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,783 | Zsqrtd.nonneg_mul | Mathlib/NumberTheory/Zsqrtd/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>mul_comm</a>] | d : ℕ
a b : ℤ√↑d
ha✝ : a.Nonneg
hb : b.Nonneg
x y z w : ℕ
ha : { re := -↑x, im := ↑y }.Nonneg
x✝ : { re := ↑z, im := ↑w }.Nonneg
⊢ ({ re := -↑x, im := ↑y } * { re := ↑z, im := ↑w }).Nonneg | d : ℕ
a b : ℤ√↑d
ha✝ : a.Nonneg
hb : b.Nonneg
x y z w : ℕ
ha : { re := -↑x, im := ↑y }.Nonneg
x✝ : { re := ↑z, im := ↑w }.Nonneg
⊢ ({ re := ↑z, im := ↑w } * { re := -↑x, im := ↑y }).Nonneg | ((:c Zsqrtd.Nonneg) (:fv _uniq.225509) ((:c HMul.hMul) ((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509))) ((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509))) ((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509))) ((:c instHMul) ((:c Zsqrtd) ((:... | [{"name":"d","sexp":"(:c Nat)"},{"name":"a","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"b","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"ha✝","sexp":"((:c Zsqrtd.Nonneg) (:fv _uniq.225509) (:fv _uniq.225625))"},{"nam... | (:app (:c Zsqrtd.Nonneg) (:arg :implicit 0) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (:c Zsqrtd) (:arg :explicit 0 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c Int)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c Int))))) (:arg :explicit 2 (:fv FV0)))))) (:arg :imp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"name":"d","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"name":"a","sexp":"(:app (:c Zsqrtd) (:arg :explicit 0 (:app (:c Na... | {"children":[{"source":"rw","sourceEnd":30138,"sourceStart":30136,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":30140,"sourceStart":30139,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"mul_comm","seman... | [] | [{"source":"mul_comm","source_end":30148,"source_start":30140,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"user_name":"d"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 246 | 4 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 52a349eef6586cffbf0fba56f1a6577370ebc0172c27a06568e1382ed9720d02 | e1cee5eeb9b4d1d660ca744a81b3a1812ca416316274f8b65953cc4ee06beed7 | b40139e2832d8f817070a6f57dda46abb72fcb05e2a85e2d0d7b1991ae7615d3 | 6f646640647833aa71f71fabec80b2c5ede038e25436f2c7baa6c4fc771fbea9 |
cat-searcher/leandojo-benchmark-4-random | test | 2,784 | Zsqrtd.nonneg_mul | Mathlib/NumberTheory/Zsqrtd/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Zsqrtd.nonneg_mul_lem</a> ha | d : ℕ
a b : ℤ√↑d
ha✝ : a.Nonneg
hb : b.Nonneg
x y z w : ℕ
ha : { re := -↑x, im := ↑y }.Nonneg
x✝ : { re := ↑z, im := ↑w }.Nonneg
⊢ ({ re := ↑z, im := ↑w } * { re := -↑x, im := ↑y }).Nonneg | ((:c Zsqrtd.Nonneg) (:fv _uniq.225509) ((:c HMul.hMul) ((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509))) ((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509))) ((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509))) ((:c instHMul) ((:c Zsqrtd) ((:... | [{"name":"d","sexp":"(:c Nat)"},{"name":"a","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"b","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"ha✝","sexp":"((:c Zsqrtd.Nonneg) (:fv _uniq.225509) (:fv _uniq.225625))"},{"nam... | (:app (:c Zsqrtd.Nonneg) (:arg :implicit 0) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (:c Zsqrtd) (:arg :explicit 0 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c Int)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c Int))))) (:arg :explicit 2 (:fv FV0)))))) (:arg :imp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"name":"d","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"name":"a","sexp":"(:app (:c Zsqrtd) (:arg :explicit 0 (:app (:c Na... | {"children":[{"source":"exact","sourceEnd":30156,"sourceStart":30151,"tag":"atom"},{"children":[{"name":"Zsqrtd.nonneg_mul_lem","semanticRole":"global","source":"nonneg_mul_lem","sourceEnd":30171,"sourceStart":30157,"tag":"identifier"},{"children":[{"contextIndex":10,"semanticRole":"local","source":"ha","sourceEnd":301... | [] | [{"source":"nonneg_mul_lem ha","source_end":30174,"source_start":30157,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"user_name":"d"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 246 | 8 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 98725273293013e55b881a151b80fc69fd7b98f3891a90dd047684b5a5eb12fc | 6f646640647833aa71f71fabec80b2c5ede038e25436f2c7baa6c4fc771fbea9 | 4466026fbdd867e53f0b5434d8895674706b21647a6cccab4b28d21b09b57d70 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,785 | Zsqrtd.nonneg_mul | Mathlib/NumberTheory/Zsqrtd/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>mul_comm</a>] | d : ℕ
a b : ℤ√↑d
ha✝ : a.Nonneg
hb : b.Nonneg
x y z w : ℕ
ha : { re := ↑x, im := -↑y }.Nonneg
x✝ : { re := ↑z, im := ↑w }.Nonneg
⊢ ({ re := ↑x, im := -↑y } * { re := ↑z, im := ↑w }).Nonneg | d : ℕ
a b : ℤ√↑d
ha✝ : a.Nonneg
hb : b.Nonneg
x y z w : ℕ
ha : { re := ↑x, im := -↑y }.Nonneg
x✝ : { re := ↑z, im := ↑w }.Nonneg
⊢ ({ re := ↑z, im := ↑w } * { re := ↑x, im := -↑y }).Nonneg | ((:c Zsqrtd.Nonneg) (:fv _uniq.225509) ((:c HMul.hMul) ((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509))) ((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509))) ((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509))) ((:c instHMul) ((:c Zsqrtd) ((:... | [{"name":"d","sexp":"(:c Nat)"},{"name":"a","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"b","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"ha✝","sexp":"((:c Zsqrtd.Nonneg) (:fv _uniq.225509) (:fv _uniq.225625))"},{"nam... | (:app (:c Zsqrtd.Nonneg) (:arg :implicit 0) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (:c Zsqrtd) (:arg :explicit 0 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c Int)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c Int))))) (:arg :explicit 2 (:fv FV0)))))) (:arg :imp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"name":"d","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"name":"a","sexp":"(:app (:c Zsqrtd) (:arg :explicit 0 (:app (:c Na... | {"children":[{"source":"rw","sourceEnd":30261,"sourceStart":30259,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":30263,"sourceStart":30262,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"mul_comm","seman... | [] | [{"source":"mul_comm","source_end":30271,"source_start":30263,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"user_name":"d"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 246 | 13 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 34c168cff2565eb84e99ab0520d10eeb695bcf8890190383421e572a83cc4134 | fe5e6d5b74fe549963df11febfc234f0974c86ac38417df4c8100e662f9168a3 | b40139e2832d8f817070a6f57dda46abb72fcb05e2a85e2d0d7b1991ae7615d3 | 7c84483ec669fd742a7dfdb0b503c296113ab714daaaff2cdc56543949dfa33c |
cat-searcher/leandojo-benchmark-4-random | test | 2,786 | Zsqrtd.nonneg_mul | Mathlib/NumberTheory/Zsqrtd/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Zsqrtd.nonneg_mul_lem</a> ha | d : ℕ
a b : ℤ√↑d
ha✝ : a.Nonneg
hb : b.Nonneg
x y z w : ℕ
ha : { re := ↑x, im := -↑y }.Nonneg
x✝ : { re := ↑z, im := ↑w }.Nonneg
⊢ ({ re := ↑z, im := ↑w } * { re := ↑x, im := -↑y }).Nonneg | ((:c Zsqrtd.Nonneg) (:fv _uniq.225509) ((:c HMul.hMul) ((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509))) ((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509))) ((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509))) ((:c instHMul) ((:c Zsqrtd) ((:... | [{"name":"d","sexp":"(:c Nat)"},{"name":"a","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"b","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"ha✝","sexp":"((:c Zsqrtd.Nonneg) (:fv _uniq.225509) (:fv _uniq.225625))"},{"nam... | (:app (:c Zsqrtd.Nonneg) (:arg :implicit 0) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (:c Zsqrtd) (:arg :explicit 0 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c Int)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c Int))))) (:arg :explicit 2 (:fv FV0)))))) (:arg :imp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"name":"d","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"name":"a","sexp":"(:app (:c Zsqrtd) (:arg :explicit 0 (:app (:c Na... | {"children":[{"source":"exact","sourceEnd":30279,"sourceStart":30274,"tag":"atom"},{"children":[{"name":"Zsqrtd.nonneg_mul_lem","semanticRole":"global","source":"nonneg_mul_lem","sourceEnd":30294,"sourceStart":30280,"tag":"identifier"},{"children":[{"contextIndex":10,"semanticRole":"local","source":"ha","sourceEnd":302... | [] | [{"source":"nonneg_mul_lem ha","source_end":30297,"source_start":30280,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"user_name":"d"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 246 | 17 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 93b42efe4063c56825e9e53367b8ed0771c7a2ace4bdc0ca0f05f0ad9cb46aed | 7c84483ec669fd742a7dfdb0b503c296113ab714daaaff2cdc56543949dfa33c | 4466026fbdd867e53f0b5434d8895674706b21647a6cccab4b28d21b09b57d70 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,787 | Zsqrtd.nonneg_mul | Mathlib/NumberTheory/Zsqrtd/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [calc (⟨-x, y⟩ * ⟨-z, w⟩ : ℤ√d) = ⟨_, _⟩ := <a>rfl</a> _ = ⟨x * z + d * y * w, -(x * w + y * z)⟩ := by simp [<a>add_comm</a>] ] | d : ℕ
a b : ℤ√↑d
ha✝ : a.Nonneg
hb✝ : b.Nonneg
x y z w : ℕ
ha : { re := -↑x, im := ↑y }.Nonneg
hb : { re := -↑z, im := ↑w }.Nonneg
⊢ ({ re := -↑x, im := ↑y } * { re := -↑z, im := ↑w }).Nonneg | d : ℕ
a b : ℤ√↑d
ha✝ : a.Nonneg
hb✝ : b.Nonneg
x y z w : ℕ
ha : { re := -↑x, im := ↑y }.Nonneg
hb : { re := -↑z, im := ↑w }.Nonneg
⊢ { re := ↑x * ↑z + ↑d * ↑y * ↑w, im := -(↑x * ↑w + ↑y * ↑z) }.Nonneg | ((:c Zsqrtd.Nonneg) (:fv _uniq.225509) ((:c HMul.hMul) ((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509))) ((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509))) ((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509))) ((:c instHMul) ((:c Zsqrtd) ((:... | [{"name":"d","sexp":"(:c Nat)"},{"name":"a","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"b","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"ha✝","sexp":"((:c Zsqrtd.Nonneg) (:fv _uniq.225509) (:fv _uniq.225625))"},{"nam... | (:app (:c Zsqrtd.Nonneg) (:arg :implicit 0) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (:c Zsqrtd) (:arg :explicit 0 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c Int)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c Int))))) (:arg :explicit 2 (:fv FV0)))))) (:arg :imp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"name":"d","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"name":"a","sexp":"(:app (:c Zsqrtd) (:arg :explicit 0 (:app (:c Na... | {"children":[{"source":"rw","sourceEnd":30395,"sourceStart":30393,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":30397,"sourceStart":30396,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"c... | [] | [{"source":"calc\n (⟨-x, y⟩ * ⟨-z, w⟩ : ℤ√d) = ⟨_, _⟩ := rfl\n _ = ⟨x * z + d * y * w, -(x * w + y * z)⟩ := by simp [add_comm]","source_end":30547,"source_start":30397,"syntax_kind":"Lean.calc"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"user_name":"d"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 246 | 22 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1c0c8fb4a42fe769e1d1bcd973d75da7919a1101dc6f21bc59036dd3fb3745ec | fb8d2a01a2c47ef0f55a53448ff7a33515568941b8f92342002465a34e9a3e99 | a68d4594ff751bb9635fc9b61eee7480dd8a18e4945b16bae898eb0d5a1f8c51 | e693f6c87291f8cecb76bd5c963b0c1c3c4473826393bde751a0f1252318fe68 |
cat-searcher/leandojo-benchmark-4-random | test | 2,788 | Zsqrtd.nonneg_mul | Mathlib/NumberTheory/Zsqrtd/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Zsqrtd.nonnegg_pos_neg</a>.2 (sqLe_mul.left (<a>Zsqrtd.nonnegg_neg_pos</a>.1 ha) (<a>Zsqrtd.nonnegg_neg_pos</a>.1 hb)) | d : ℕ
a b : ℤ√↑d
ha✝ : a.Nonneg
hb✝ : b.Nonneg
x y z w : ℕ
ha : { re := -↑x, im := ↑y }.Nonneg
hb : { re := -↑z, im := ↑w }.Nonneg
⊢ { re := ↑x * ↑z + ↑d * ↑y * ↑w, im := -(↑x * ↑w + ↑y * ↑z) }.Nonneg | ((:c Zsqrtd.Nonneg) (:fv _uniq.225509) ((:c Zsqrtd.mk) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)) ((:c HAdd.hAdd) (:c Int) (:c Int) (:c Int) ((:c instHAdd) (:c Int) (:c Int.instAdd)) ((:c HMul.hMul) (:c Int) (:c Int) (:c Int) ((:c instHMul) (:c Int) (:c Int.instMul)) ((:c Nat.cast) (:c Int) (:c ins... | [{"name":"d","sexp":"(:c Nat)"},{"name":"a","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"b","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"ha✝","sexp":"((:c Zsqrtd.Nonneg) (:fv _uniq.225509) (:fv _uniq.225625))"},{"nam... | (:app (:c Zsqrtd.Nonneg) (:arg :implicit 0) (:arg :explicit 1 (:app (:c Zsqrtd.mk) (:arg :implicit 0) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:c Int)) (:arg :implicit-type 2 (:c Int)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Int)) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"name":"d","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"name":"a","sexp":"(:app (:c Zsqrtd) (:arg :explicit 0 (:app (:c Na... | {"children":[{"source":"exact","sourceEnd":30569,"sourceStart":30564,"tag":"atom"},{"children":[{"children":[{"name":"Zsqrtd.nonnegg_pos_neg","semanticRole":"global","source":"nonnegg_pos_neg","sourceEnd":30585,"sourceStart":30570,"tag":"identifier"},{"source":".","sourceEnd":30586,"sourceStart":30585,"tag":"atom"},{"c... | [] | [{"source":"nonnegg_pos_neg.2 (sqLe_mul.left (nonnegg_neg_pos.1 ha) (nonnegg_neg_pos.1 hb))","source_end":30649,"source_start":30570,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"user_name":"d"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 246 | 30 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6e2da087aad140542d8f0332e2885343cc2d93541ddd74bb31b92634b35b22dd | e693f6c87291f8cecb76bd5c963b0c1c3c4473826393bde751a0f1252318fe68 | 5fc26521f738596d26d448d6d4dd65878b106518bee252c93223c352bffe5f32 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,789 | Zsqrtd.nonneg_mul | Mathlib/NumberTheory/Zsqrtd/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>add_comm</a>] | d : ℕ
a b : ℤ√↑d
ha✝ : a.Nonneg
hb✝ : b.Nonneg
x y z w : ℕ
ha : { re := -↑x, im := ↑y }.Nonneg
hb : { re := -↑z, im := ↑w }.Nonneg
⊢ {
re :=
{ re := -↑x, im := ↑y }.re * { re := -↑z, im := ↑w }.re +
↑d * { re := -↑x, im := ↑y }.im * { re := -↑z, im := ↑w }.im,
im :=
{ re := -↑x, im... | ((:c Eq) ((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509))) ((:c Zsqrtd.mk) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)) ((:c HAdd.hAdd) (:c Int) (:c Int) (:c Int) ((:c instHAdd) (:c Int) (:c Int.instAdd)) ((:c HMul.hMul) (:c Int) (:c Int) (:c Int) ((:c instHMul) (:c Int) (... | [{"name":"d","sexp":"(:c Nat)"},{"name":"a","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"b","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"ha✝","sexp":"((:c Zsqrtd.Nonneg) (:fv _uniq.225509) (:fv _uniq.225625))"},{"nam... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Zsqrtd) (:arg :explicit 0 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c Int)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c Int))))) (:arg :explicit 2 (:fv FV0)))))) (:arg :explicit 1 (:app (:c Zsqrtd.mk) (:arg :implicit 0) (:arg :explicit 1 (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"name":"d","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"name":"a","sexp":"(:app (:c Zsqrtd) (:arg :explicit 0 (:app (:c Na... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":30536,"sourceStart":30532,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"add_comm","source_end":30546,"source_start":30538,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"user_name":"d"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 246 | 26 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4e1111b44602896612042fee9860cd3346351ec74f01abedf3917c2000551653 | 9f85891302f8a0b30f71e5ae83271ce39f22c7eb906107006883c656e6e5b7b6 | bc870a142d0cdbd299ec13e0ddf10d517e7096385012adfe0901573d7c58da93 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,790 | Zsqrtd.nonneg_mul | Mathlib/NumberTheory/Zsqrtd/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [calc (⟨-x, y⟩ * ⟨z, -w⟩ : ℤ√d) = ⟨_, _⟩ := <a>rfl</a> _ = ⟨-(x * z + d * y * w), x * w + y * z⟩ := by simp [<a>add_comm</a>] ] | d : ℕ
a b : ℤ√↑d
ha✝ : a.Nonneg
hb✝ : b.Nonneg
x y z w : ℕ
ha : { re := -↑x, im := ↑y }.Nonneg
hb : { re := ↑z, im := -↑w }.Nonneg
⊢ ({ re := -↑x, im := ↑y } * { re := ↑z, im := -↑w }).Nonneg | d : ℕ
a b : ℤ√↑d
ha✝ : a.Nonneg
hb✝ : b.Nonneg
x y z w : ℕ
ha : { re := -↑x, im := ↑y }.Nonneg
hb : { re := ↑z, im := -↑w }.Nonneg
⊢ { re := -(↑x * ↑z + ↑d * ↑y * ↑w), im := ↑x * ↑w + ↑y * ↑z }.Nonneg | ((:c Zsqrtd.Nonneg) (:fv _uniq.225509) ((:c HMul.hMul) ((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509))) ((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509))) ((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509))) ((:c instHMul) ((:c Zsqrtd) ((:... | [{"name":"d","sexp":"(:c Nat)"},{"name":"a","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"b","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"ha✝","sexp":"((:c Zsqrtd.Nonneg) (:fv _uniq.225509) (:fv _uniq.225625))"},{"nam... | (:app (:c Zsqrtd.Nonneg) (:arg :implicit 0) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (:c Zsqrtd) (:arg :explicit 0 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c Int)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c Int))))) (:arg :explicit 2 (:fv FV0)))))) (:arg :imp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"name":"d","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"name":"a","sexp":"(:app (:c Zsqrtd) (:arg :explicit 0 (:app (:c Na... | {"children":[{"source":"rw","sourceEnd":30747,"sourceStart":30745,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":30749,"sourceStart":30748,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"c... | [] | [{"source":"calc\n (⟨-x, y⟩ * ⟨z, -w⟩ : ℤ√d) = ⟨_, _⟩ := rfl\n _ = ⟨-(x * z + d * y * w), x * w + y * z⟩ := by simp [add_comm]","source_end":30899,"source_start":30749,"syntax_kind":"Lean.calc"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"user_name":"d"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 246 | 35 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | db8b5fdc3a98b08e45f22eb81cb749b39b74614eb6dd867481b82b0bc4a436bc | 8bb6ae29ee84afdaa0fc9e87cc75be6a7be88223bd7c035730f5b587c721385b | d57305716888826d5925036724af3b13fcef86d8234417d046587b7000eac59d | d23651007482c04734168ee4d9d440c4739b84fe6888dd9c990cd3e804757cac |
cat-searcher/leandojo-benchmark-4-random | test | 2,791 | Zsqrtd.nonneg_mul | Mathlib/NumberTheory/Zsqrtd/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Zsqrtd.nonnegg_neg_pos</a>.2 (sqLe_mul.right.left (<a>Zsqrtd.nonnegg_neg_pos</a>.1 ha) (<a>Zsqrtd.nonnegg_pos_neg</a>.1 hb)) | d : ℕ
a b : ℤ√↑d
ha✝ : a.Nonneg
hb✝ : b.Nonneg
x y z w : ℕ
ha : { re := -↑x, im := ↑y }.Nonneg
hb : { re := ↑z, im := -↑w }.Nonneg
⊢ { re := -(↑x * ↑z + ↑d * ↑y * ↑w), im := ↑x * ↑w + ↑y * ↑z }.Nonneg | ((:c Zsqrtd.Nonneg) (:fv _uniq.225509) ((:c Zsqrtd.mk) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)) ((:c Neg.neg) (:c Int) (:c Int.instNegInt) ((:c HAdd.hAdd) (:c Int) (:c Int) (:c Int) ((:c instHAdd) (:c Int) (:c Int.instAdd)) ((:c HMul.hMul) (:c Int) (:c Int) (:c Int) ((:c instHMul) (:c Int) (:c In... | [{"name":"d","sexp":"(:c Nat)"},{"name":"a","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"b","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"ha✝","sexp":"((:c Zsqrtd.Nonneg) (:fv _uniq.225509) (:fv _uniq.225625))"},{"nam... | (:app (:c Zsqrtd.Nonneg) (:arg :implicit 0) (:arg :explicit 1 (:app (:c Zsqrtd.mk) (:arg :implicit 0) (:arg :explicit 1 (:app (:c Neg.neg) (:arg :implicit-type 0 (:c Int)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:c Int))))) (:arg :explicit 2 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Int)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"name":"d","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"name":"a","sexp":"(:app (:c Zsqrtd) (:arg :explicit 0 (:app (:c Na... | {"children":[{"source":"exact","sourceEnd":30921,"sourceStart":30916,"tag":"atom"},{"children":[{"children":[{"name":"Zsqrtd.nonnegg_neg_pos","semanticRole":"global","source":"nonnegg_neg_pos","sourceEnd":30937,"sourceStart":30922,"tag":"identifier"},{"source":".","sourceEnd":30938,"sourceStart":30937,"tag":"atom"},{"c... | [] | [{"source":"nonnegg_neg_pos.2 (sqLe_mul.right.left (nonnegg_neg_pos.1 ha) (nonnegg_pos_neg.1 hb))","source_end":31007,"source_start":30922,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"user_name":"d"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 246 | 43 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8d1a7f5ae93666f6d8bc0b43a90d73994293a8813e382b85ca4be5b10339938b | d23651007482c04734168ee4d9d440c4739b84fe6888dd9c990cd3e804757cac | 12d5bd6876fd4d7082bb852943e6827aeaeedafa7c3579afa7d2a3de5a6f1883 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,792 | Zsqrtd.nonneg_mul | Mathlib/NumberTheory/Zsqrtd/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>add_comm</a>] | d : ℕ
a b : ℤ√↑d
ha✝ : a.Nonneg
hb✝ : b.Nonneg
x y z w : ℕ
ha : { re := -↑x, im := ↑y }.Nonneg
hb : { re := ↑z, im := -↑w }.Nonneg
⊢ {
re :=
{ re := -↑x, im := ↑y }.re * { re := ↑z, im := -↑w }.re +
↑d * { re := -↑x, im := ↑y }.im * { re := ↑z, im := -↑w }.im,
im :=
{ re := -↑x, im... | ((:c Eq) ((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509))) ((:c Zsqrtd.mk) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)) ((:c HAdd.hAdd) (:c Int) (:c Int) (:c Int) ((:c instHAdd) (:c Int) (:c Int.instAdd)) ((:c HMul.hMul) (:c Int) (:c Int) (:c Int) ((:c instHMul) (:c Int) (... | [{"name":"d","sexp":"(:c Nat)"},{"name":"a","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"b","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"ha✝","sexp":"((:c Zsqrtd.Nonneg) (:fv _uniq.225509) (:fv _uniq.225625))"},{"nam... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Zsqrtd) (:arg :explicit 0 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c Int)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c Int))))) (:arg :explicit 2 (:fv FV0)))))) (:arg :explicit 1 (:app (:c Zsqrtd.mk) (:arg :implicit 0) (:arg :explicit 1 (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"name":"d","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"name":"a","sexp":"(:app (:c Zsqrtd) (:arg :explicit 0 (:app (:c Na... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":30888,"sourceStart":30884,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"add_comm","source_end":30898,"source_start":30890,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"user_name":"d"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 246 | 39 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8c09cbc0779264c7421bf8fce2ac687fa604b0c3a6f06fc62174a2087281e60f | 48a587d364b1d3be0510e1e7fedbd33be46ced9b274dfd44c6e56ec61591e9f1 | bc870a142d0cdbd299ec13e0ddf10d517e7096385012adfe0901573d7c58da93 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,793 | Zsqrtd.nonneg_mul | Mathlib/NumberTheory/Zsqrtd/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [calc (⟨x, -y⟩ * ⟨-z, w⟩ : ℤ√d) = ⟨_, _⟩ := <a>rfl</a> _ = ⟨-(x * z + d * y * w), x * w + y * z⟩ := by simp [<a>add_comm</a>] ] | d : ℕ
a b : ℤ√↑d
ha✝ : a.Nonneg
hb✝ : b.Nonneg
x y z w : ℕ
ha : { re := ↑x, im := -↑y }.Nonneg
hb : { re := -↑z, im := ↑w }.Nonneg
⊢ ({ re := ↑x, im := -↑y } * { re := -↑z, im := ↑w }).Nonneg | d : ℕ
a b : ℤ√↑d
ha✝ : a.Nonneg
hb✝ : b.Nonneg
x y z w : ℕ
ha : { re := ↑x, im := -↑y }.Nonneg
hb : { re := -↑z, im := ↑w }.Nonneg
⊢ { re := -(↑x * ↑z + ↑d * ↑y * ↑w), im := ↑x * ↑w + ↑y * ↑z }.Nonneg | ((:c Zsqrtd.Nonneg) (:fv _uniq.225509) ((:c HMul.hMul) ((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509))) ((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509))) ((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509))) ((:c instHMul) ((:c Zsqrtd) ((:... | [{"name":"d","sexp":"(:c Nat)"},{"name":"a","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"b","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"ha✝","sexp":"((:c Zsqrtd.Nonneg) (:fv _uniq.225509) (:fv _uniq.225625))"},{"nam... | (:app (:c Zsqrtd.Nonneg) (:arg :implicit 0) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (:c Zsqrtd) (:arg :explicit 0 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c Int)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c Int))))) (:arg :explicit 2 (:fv FV0)))))) (:arg :imp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"name":"d","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"name":"a","sexp":"(:app (:c Zsqrtd) (:arg :explicit 0 (:app (:c Na... | {"children":[{"source":"rw","sourceEnd":31105,"sourceStart":31103,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":31107,"sourceStart":31106,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"c... | [] | [{"source":"calc\n (⟨x, -y⟩ * ⟨-z, w⟩ : ℤ√d) = ⟨_, _⟩ := rfl\n _ = ⟨-(x * z + d * y * w), x * w + y * z⟩ := by simp [add_comm]","source_end":31257,"source_start":31107,"syntax_kind":"Lean.calc"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"user_name":"d"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 246 | 48 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 57d4313a151d6c8f928016ce67fe678a25f29fb9ff5fa60cce0e72af3cd1e645 | c3321c16648a636c651fd3cfe6f91c65e924a0e3a12fede2c9cfc295d0bb7389 | 22cd1618f18d647f78fcb06735a1bfc2454bee058f8f90f3384d4736c31f0070 | 053aea0f1313d1fb591a75e62ec2c13487b52c20bdca875b417b98f0bff35ae8 |
cat-searcher/leandojo-benchmark-4-random | test | 2,794 | Zsqrtd.nonneg_mul | Mathlib/NumberTheory/Zsqrtd/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Zsqrtd.nonnegg_neg_pos</a>.2 (sqLe_mul.right.right.left (<a>Zsqrtd.nonnegg_pos_neg</a>.1 ha) (<a>Zsqrtd.nonnegg_neg_pos</a>.1 hb)) | d : ℕ
a b : ℤ√↑d
ha✝ : a.Nonneg
hb✝ : b.Nonneg
x y z w : ℕ
ha : { re := ↑x, im := -↑y }.Nonneg
hb : { re := -↑z, im := ↑w }.Nonneg
⊢ { re := -(↑x * ↑z + ↑d * ↑y * ↑w), im := ↑x * ↑w + ↑y * ↑z }.Nonneg | ((:c Zsqrtd.Nonneg) (:fv _uniq.225509) ((:c Zsqrtd.mk) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)) ((:c Neg.neg) (:c Int) (:c Int.instNegInt) ((:c HAdd.hAdd) (:c Int) (:c Int) (:c Int) ((:c instHAdd) (:c Int) (:c Int.instAdd)) ((:c HMul.hMul) (:c Int) (:c Int) (:c Int) ((:c instHMul) (:c Int) (:c In... | [{"name":"d","sexp":"(:c Nat)"},{"name":"a","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"b","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"ha✝","sexp":"((:c Zsqrtd.Nonneg) (:fv _uniq.225509) (:fv _uniq.225625))"},{"nam... | (:app (:c Zsqrtd.Nonneg) (:arg :implicit 0) (:arg :explicit 1 (:app (:c Zsqrtd.mk) (:arg :implicit 0) (:arg :explicit 1 (:app (:c Neg.neg) (:arg :implicit-type 0 (:c Int)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:c Int))))) (:arg :explicit 2 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Int)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"name":"d","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"name":"a","sexp":"(:app (:c Zsqrtd) (:arg :explicit 0 (:app (:c Na... | {"children":[{"source":"exact","sourceEnd":31279,"sourceStart":31274,"tag":"atom"},{"children":[{"children":[{"name":"Zsqrtd.nonnegg_neg_pos","semanticRole":"global","source":"nonnegg_neg_pos","sourceEnd":31303,"sourceStart":31288,"tag":"identifier"},{"source":".","sourceEnd":31304,"sourceStart":31303,"tag":"atom"},{"c... | [] | [{"source":"nonnegg_neg_pos.2 (sqLe_mul.right.right.left (nonnegg_pos_neg.1 ha) (nonnegg_neg_pos.1 hb))","source_end":31379,"source_start":31288,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"user_name":"d"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 246 | 56 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9c60666f622221c47a978229a43ce971027a05d2223d45aa3fd6e8ea4244334e | 053aea0f1313d1fb591a75e62ec2c13487b52c20bdca875b417b98f0bff35ae8 | 0d8076a3e72a1ff7dd8d8737c27127f688cd0a5337a72c8870040707053ac881 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,795 | Zsqrtd.nonneg_mul | Mathlib/NumberTheory/Zsqrtd/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>add_comm</a>] | d : ℕ
a b : ℤ√↑d
ha✝ : a.Nonneg
hb✝ : b.Nonneg
x y z w : ℕ
ha : { re := ↑x, im := -↑y }.Nonneg
hb : { re := -↑z, im := ↑w }.Nonneg
⊢ {
re :=
{ re := ↑x, im := -↑y }.re * { re := -↑z, im := ↑w }.re +
↑d * { re := ↑x, im := -↑y }.im * { re := -↑z, im := ↑w }.im,
im :=
{ re := ↑x, im ... | ((:c Eq) ((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509))) ((:c Zsqrtd.mk) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)) ((:c HAdd.hAdd) (:c Int) (:c Int) (:c Int) ((:c instHAdd) (:c Int) (:c Int.instAdd)) ((:c HMul.hMul) (:c Int) (:c Int) (:c Int) ((:c instHMul) (:c Int) (... | [{"name":"d","sexp":"(:c Nat)"},{"name":"a","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"b","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"ha✝","sexp":"((:c Zsqrtd.Nonneg) (:fv _uniq.225509) (:fv _uniq.225625))"},{"nam... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Zsqrtd) (:arg :explicit 0 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c Int)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c Int))))) (:arg :explicit 2 (:fv FV0)))))) (:arg :explicit 1 (:app (:c Zsqrtd.mk) (:arg :implicit 0) (:arg :explicit 1 (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"name":"d","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"name":"a","sexp":"(:app (:c Zsqrtd) (:arg :explicit 0 (:app (:c Na... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":31246,"sourceStart":31242,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"add_comm","source_end":31256,"source_start":31248,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"user_name":"d"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 246 | 52 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e73d9dbb26362751cb9b06c5c93faa22acf7cf13875db2a482864b9b1f286518 | b76e312fb0a76d447acf53d5b0e45c734b0e8b510059d7de749adb06718eb6c0 | bc870a142d0cdbd299ec13e0ddf10d517e7096385012adfe0901573d7c58da93 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,796 | Zsqrtd.nonneg_mul | Mathlib/NumberTheory/Zsqrtd/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [calc (⟨x, -y⟩ * ⟨z, -w⟩ : ℤ√d) = ⟨_, _⟩ := <a>rfl</a> _ = ⟨x * z + d * y * w, -(x * w + y * z)⟩ := by simp [<a>add_comm</a>] ] | d : ℕ
a b : ℤ√↑d
ha✝ : a.Nonneg
hb✝ : b.Nonneg
x y z w : ℕ
ha : { re := ↑x, im := -↑y }.Nonneg
hb : { re := ↑z, im := -↑w }.Nonneg
⊢ ({ re := ↑x, im := -↑y } * { re := ↑z, im := -↑w }).Nonneg | d : ℕ
a b : ℤ√↑d
ha✝ : a.Nonneg
hb✝ : b.Nonneg
x y z w : ℕ
ha : { re := ↑x, im := -↑y }.Nonneg
hb : { re := ↑z, im := -↑w }.Nonneg
⊢ { re := ↑x * ↑z + ↑d * ↑y * ↑w, im := -(↑x * ↑w + ↑y * ↑z) }.Nonneg | ((:c Zsqrtd.Nonneg) (:fv _uniq.225509) ((:c HMul.hMul) ((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509))) ((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509))) ((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509))) ((:c instHMul) ((:c Zsqrtd) ((:... | [{"name":"d","sexp":"(:c Nat)"},{"name":"a","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"b","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"ha✝","sexp":"((:c Zsqrtd.Nonneg) (:fv _uniq.225509) (:fv _uniq.225625))"},{"nam... | (:app (:c Zsqrtd.Nonneg) (:arg :implicit 0) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (:c Zsqrtd) (:arg :explicit 0 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c Int)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c Int))))) (:arg :explicit 2 (:fv FV0)))))) (:arg :imp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"name":"d","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"name":"a","sexp":"(:app (:c Zsqrtd) (:arg :explicit 0 (:app (:c Na... | {"children":[{"source":"rw","sourceEnd":31477,"sourceStart":31475,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":31479,"sourceStart":31478,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"c... | [] | [{"source":"calc\n (⟨x, -y⟩ * ⟨z, -w⟩ : ℤ√d) = ⟨_, _⟩ := rfl\n _ = ⟨x * z + d * y * w, -(x * w + y * z)⟩ := by simp [add_comm]","source_end":31629,"source_start":31479,"syntax_kind":"Lean.calc"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"user_name":"d"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 246 | 61 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 583abf2735ac124a536733133aabfbdce018c924c5c81a3010639a50183271bb | 2eb756cbc5da2974d15b1770a46ba8cd9241c6a25da236f711989cc0ffc16da7 | a2ff04593198ebee1283aacd45471523d1ccc5c12e0a5201168b8d13bc9d591a | f6c478d43764734685c501ae7f65b5e0ab99397ff810bba9be5196cb50181ef4 |
cat-searcher/leandojo-benchmark-4-random | test | 2,797 | Zsqrtd.nonneg_mul | Mathlib/NumberTheory/Zsqrtd/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Zsqrtd.nonnegg_pos_neg</a>.2 (sqLe_mul.right.right.right (<a>Zsqrtd.nonnegg_pos_neg</a>.1 ha) (<a>Zsqrtd.nonnegg_pos_neg</a>.1 hb)) | d : ℕ
a b : ℤ√↑d
ha✝ : a.Nonneg
hb✝ : b.Nonneg
x y z w : ℕ
ha : { re := ↑x, im := -↑y }.Nonneg
hb : { re := ↑z, im := -↑w }.Nonneg
⊢ { re := ↑x * ↑z + ↑d * ↑y * ↑w, im := -(↑x * ↑w + ↑y * ↑z) }.Nonneg | ((:c Zsqrtd.Nonneg) (:fv _uniq.225509) ((:c Zsqrtd.mk) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)) ((:c HAdd.hAdd) (:c Int) (:c Int) (:c Int) ((:c instHAdd) (:c Int) (:c Int.instAdd)) ((:c HMul.hMul) (:c Int) (:c Int) (:c Int) ((:c instHMul) (:c Int) (:c Int.instMul)) ((:c Nat.cast) (:c Int) (:c ins... | [{"name":"d","sexp":"(:c Nat)"},{"name":"a","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"b","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"ha✝","sexp":"((:c Zsqrtd.Nonneg) (:fv _uniq.225509) (:fv _uniq.225625))"},{"nam... | (:app (:c Zsqrtd.Nonneg) (:arg :implicit 0) (:arg :explicit 1 (:app (:c Zsqrtd.mk) (:arg :implicit 0) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:c Int)) (:arg :implicit-type 2 (:c Int)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Int)) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"name":"d","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"name":"a","sexp":"(:app (:c Zsqrtd) (:arg :explicit 0 (:app (:c Na... | {"children":[{"source":"exact","sourceEnd":31651,"sourceStart":31646,"tag":"atom"},{"children":[{"children":[{"name":"Zsqrtd.nonnegg_pos_neg","semanticRole":"global","source":"nonnegg_pos_neg","sourceEnd":31675,"sourceStart":31660,"tag":"identifier"},{"source":".","sourceEnd":31676,"sourceStart":31675,"tag":"atom"},{"c... | [] | [{"source":"nonnegg_pos_neg.2\n (sqLe_mul.right.right.right (nonnegg_pos_neg.1 ha) (nonnegg_pos_neg.1 hb))","source_end":31762,"source_start":31660,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"user_name":"d"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 246 | 69 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 65911864940737861c0762c7e7c57ef2b4ae94f3957bc8b6af7674855c095a46 | f6c478d43764734685c501ae7f65b5e0ab99397ff810bba9be5196cb50181ef4 | 9de6fb94b463cbec72211ed99ef7ed294a5eab01d49665ec1c6ea9b7d56f3712 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,798 | Zsqrtd.nonneg_mul | Mathlib/NumberTheory/Zsqrtd/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>add_comm</a>] | d : ℕ
a b : ℤ√↑d
ha✝ : a.Nonneg
hb✝ : b.Nonneg
x y z w : ℕ
ha : { re := ↑x, im := -↑y }.Nonneg
hb : { re := ↑z, im := -↑w }.Nonneg
⊢ {
re :=
{ re := ↑x, im := -↑y }.re * { re := ↑z, im := -↑w }.re +
↑d * { re := ↑x, im := -↑y }.im * { re := ↑z, im := -↑w }.im,
im :=
{ re := ↑x, im ... | ((:c Eq) ((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509))) ((:c Zsqrtd.mk) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)) ((:c HAdd.hAdd) (:c Int) (:c Int) (:c Int) ((:c instHAdd) (:c Int) (:c Int.instAdd)) ((:c HMul.hMul) (:c Int) (:c Int) (:c Int) ((:c instHMul) (:c Int) (... | [{"name":"d","sexp":"(:c Nat)"},{"name":"a","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"b","sexp":"((:c Zsqrtd) ((:c Nat.cast) (:c Int) (:c instNatCastInt) (:fv _uniq.225509)))"},{"name":"ha✝","sexp":"((:c Zsqrtd.Nonneg) (:fv _uniq.225509) (:fv _uniq.225625))"},{"nam... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Zsqrtd) (:arg :explicit 0 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c Int)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c Int))))) (:arg :explicit 2 (:fv FV0)))))) (:arg :explicit 1 (:app (:c Zsqrtd.mk) (:arg :implicit 0) (:arg :explicit 1 (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"name":"d","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"name":"a","sexp":"(:app (:c Zsqrtd) (:arg :explicit 0 (:app (:c Na... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":31618,"sourceStart":31614,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"add_comm","source_end":31628,"source_start":31620,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225509","is_instance":false,"is_let":false,"user_name":"d"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.225625","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":implicit","context_index":3,"internal_name":"_... | 246 | 65 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7b64b61172d609fb0487d772bc96684271d8719c69ca820902973ec071b292b2 | acbcd85720c25ff644dc20ca5232c1b75e4f8d071c527b72873b239054f47ae0 | bc870a142d0cdbd299ec13e0ddf10d517e7096385012adfe0901573d7c58da93 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,799 | equicontinuousAt_iff_range | Mathlib/Topology/UniformSpace/Equicontinuity.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>EquicontinuousAt</a>, <a>Set.forall_subtype_range_iff</a>] | ι : Type u_1
κ : Type u_2
X : Type u_3
X' : Type u_4
Y : Type u_5
Z : Type u_6
α : Type u_7
α' : Type u_8
β : Type u_9
β' : Type u_10
γ : Type u_11
𝓕 : Type u_12
tX : TopologicalSpace X
tY : TopologicalSpace Y
tZ : TopologicalSpace Z
uα : UniformSpace α
uβ : UniformSpace β
uγ : UniformSpace γ
F : ι → X → α
x₀ : X
⊢ Eq... | ((:c Iff) ((:c EquicontinuousAt) (:fv _uniq.68418) (:fv _uniq.68424) (:fv _uniq.68436) (:fv _uniq.68454) (:fv _uniq.68463) (:fv _uniq.68673) (:fv _uniq.68674)) ((:c EquicontinuousAt) ((:c Subtype) (:forall _ (:fv _uniq.68424) (:fv _uniq.68436)) (:lambda x (:forall _ (:fv _uniq.68424) (:fv _uniq.68436)) ((:c Membership.... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"κ","sexp":"(:sort (+ u_2 1))"},{"name":"X","sexp":"(:sort (+ u_3 1))"},{"name":"X'","sexp":"(:sort (+ u_4 1))"},{"name":"Y","sexp":"(:sort (+ u_5 1))"},{"name":"Z","sexp":"(:sort (+ u_6 1))"},{"name":"α","sexp":"(:sort (+ u_7 1))"},{"name":"α'","sexp":"(:sort (+ u_8 1))... | (:app (:c Iff) (:arg :explicit 0 (:app (:c EquicontinuousAt) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :implicit-type 2 (:fv FV6)) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instance-of (:app (:c UniformSpace) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68418","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68421","is_instance":false,"is_let":false,"name":"κ","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":24424,"sourceStart":24420,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":24429,"sourceStart":24425,"tag":"atom"}],"kind"... | [] | [{"source":"EquicontinuousAt","source_end":24447,"source_start":24431,"syntax_kind":"ident"},{"source":"forall_subtype_range_iff","source_end":24473,"source_start":24449,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.68418","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.68421","is_instance":false,"is_let":false,"user_name":"κ"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 98 | 2 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d879e9a95eed0e5f8abcd74b128a3fbec07d133f8dde5bf101ecadccb39ebcab | 2a020b26508dbaabb6a3afd752dbe0c328e7a37ee67d2f401308bfc07837ddf3 | ec620505f67d1a07cb8aacecb24ecf5c8be78579fab8657a0a1175cf77b54cb1 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,800 | Finsupp.iInf_ker_lapply_le_bot | Mathlib/LinearAlgebra/Finsupp.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>SetLike.le_def</a>, <a>Submodule.mem_iInf</a>, <a>LinearMap.mem_ker</a>, <a>Submodule.mem_bot</a>, <a>Finsupp.lapply_apply</a>] | α : Type u_1
M : Type u_2
N : Type u_3
P : Type u_4
R : Type u_5
S : Type u_6
inst✝⁷ : Semiring R
inst✝⁶ : Semiring S
inst✝⁵ : AddCommMonoid M
inst✝⁴ : Module R M
inst✝³ : AddCommMonoid N
inst✝² : Module R N
inst✝¹ : AddCommMonoid P
inst✝ : Module R P
⊢ ⨅ a, ker (lapply a) ≤ ⊥ | α : Type u_1
M : Type u_2
N : Type u_3
P : Type u_4
R : Type u_5
S : Type u_6
inst✝⁷ : Semiring R
inst✝⁶ : Semiring S
inst✝⁵ : AddCommMonoid M
inst✝⁴ : Module R M
inst✝³ : AddCommMonoid N
inst✝² : Module R N
inst✝¹ : AddCommMonoid P
inst✝ : Module R P
⊢ ∀ ⦃x : α →₀ M⦄, (∀ (i : α), x i = 0) → x = 0 | ((:c LE.le) ((:c Submodule) (:fv _uniq.90454) ((:c Finsupp) (:fv _uniq.90442) (:fv _uniq.90445) ((:c AddMonoid.toZero) (:fv _uniq.90445) ((:c AddCommMonoid.toAddMonoid) (:fv _uniq.90445) (:fv _uniq.90466)))) (:fv _uniq.90460) ((:c Finsupp.instAddCommMonoid) (:fv _uniq.90442) (:fv _uniq.90445) (:fv _uniq.90466)) ((:c Fi... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"N","sexp":"(:sort (+ u_3 1))"},{"name":"P","sexp":"(:sort (+ u_4 1))"},{"name":"R","sexp":"(:sort (+ u_5 1))"},{"name":"S","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁷","sexp":"((:c Semiring) (:fv _uniq.90454))"},{"name":"inst✝⁶","... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV4)) (:arg :explicit 1 (:app (:c Finsupp) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Zero) (:arg :explicit 0 (:fv FV1))))))) (:arg :instance 2 (:instance-of (:app (:c Semiring) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.90442","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.90445","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp","sourceEnd":10428,"sourceStart":10424,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":10433,"sourceStart":10429,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":104... | [] | [{"source":"SetLike.le_def","source_end":10449,"source_start":10435,"syntax_kind":"ident"},{"source":"mem_iInf","source_end":10459,"source_start":10451,"syntax_kind":"ident"},{"source":"mem_ker","source_end":10468,"source_start":10461,"syntax_kind":"ident"},{"source":"mem_bot","source_end":10477,"source_start":10470,"s... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.90442","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.90445","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 74 | 4 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 663bf94e7c3e24b52ffd7259df6375dd01a62ab7e21ada07910dcd5a9d4c2ecb | 268c8785564f01490a4c6b94fd3a1e9914fbabc82fa5e8ea3b371f4f88819c83 | 5d54165b0a466639681fa398daed13c0948f1c7d14691cb2b8375cad7047b25c | 42ff405de4c6657a47a87e911b7ef609841697a457986a8ce75c449a250e6739 |
cat-searcher/leandojo-benchmark-4-random | test | 2,801 | Finsupp.iInf_ker_lapply_le_bot | Mathlib/LinearAlgebra/Finsupp.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact fun a h => <a>Finsupp.ext</a> h | α : Type u_1
M : Type u_2
N : Type u_3
P : Type u_4
R : Type u_5
S : Type u_6
inst✝⁷ : Semiring R
inst✝⁶ : Semiring S
inst✝⁵ : AddCommMonoid M
inst✝⁴ : Module R M
inst✝³ : AddCommMonoid N
inst✝² : Module R N
inst✝¹ : AddCommMonoid P
inst✝ : Module R P
⊢ ∀ ⦃x : α →₀ M⦄, (∀ (i : α), x i = 0) → x = 0 | (:forall x ((:c Finsupp) (:fv _uniq.90442) (:fv _uniq.90445) ((:c AddMonoid.toZero) (:fv _uniq.90445) ((:c AddCommMonoid.toAddMonoid) (:fv _uniq.90445) (:fv _uniq.90466)))) (:forall _ (:forall i (:fv _uniq.90442) ((:c Eq) (:fv _uniq.90445) ((:c DFunLike.coe) ((:c Finsupp) (:fv _uniq.90442) (:fv _uniq.90445) ((:c AddMon... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"N","sexp":"(:sort (+ u_3 1))"},{"name":"P","sexp":"(:sort (+ u_4 1))"},{"name":"R","sexp":"(:sort (+ u_5 1))"},{"name":"S","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁷","sexp":"((:c Semiring) (:fv _uniq.90454))"},{"name":"inst✝⁶","... | (:forall x :strict-implicit (:app (:c Finsupp) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Zero) (:arg :explicit 0 (:fv FV1)))))) (:forall _ :explicit (:forall i :explicit (:fv FV0) (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c DFunLi... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.90442","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.90445","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":10500,"sourceStart":10495,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":10504,"sourceStart":10501,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"a","sourceEnd":10506,"sourceStart":10505,"tag":"identifier"},{"semanticRole":"scoped_loca... | [] | [{"source":"fun a h => Finsupp.ext h","source_end":10525,"source_start":10501,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.90442","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.90445","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 74 | 5 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 393be092aee1b48fd8b795d158d5159dd198214e1e0a074c05e29029af869b53 | 42ff405de4c6657a47a87e911b7ef609841697a457986a8ce75c449a250e6739 | ffa62372dbabaa0dbdd412b8e3f51b4ec2457f1bd324d6b5ccf54cb5f363da0d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,802 | Path.truncate_self | Mathlib/Topology/Connected/PathConnected.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>min_self</a>] | X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
x y z : X
ι : Type u_3
γ✝ : Path x y
a b : X
γ : Path a b
t : ℝ
⊢ γ.extend (min t t) = γ.extend t | ((:c Eq) (:fv _uniq.316677) ((:c Path.extend) (:fv _uniq.316677) (:fv _uniq.316683) (:fv _uniq.316744) (:fv _uniq.316746) (:fv _uniq.316793) ((:c Min.min) (:c Real) ((:c LinearOrderedRing.toMin) (:c Real) (:c Real.instLinearOrderedRing)) (:fv _uniq.316795) (:fv _uniq.316795))) ((:c Path.extend) (:fv _uniq.316677) (:fv ... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.316677))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.316680))"},{"name":"x","sexp":"(:fv _uniq.316677)"},{"name":"y","sexp":"(:fv _uniq.316677)"},{"name":"z","sexp"... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Path.extend) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit 2) (:arg :implicit 3) (:arg :explicit 4 (:fv FV11)) (:arg :explicit 5 (:app (:c Min.min) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.316677","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.316680","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":26483,"sourceStart":26481,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":26485,"sourceStart":26484,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"min_self","source_end":26493,"source_start":26485,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.316677","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.316680","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 164 | 2 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d6fc3cd1442c1472f793a94c7dce1342d4ebb13b0a4e936d0300829f815b9567 | 12b08d5f7526dc69312ba8b9c5117f1e746b6df26fc74433243fd9df5af981cb | fac3af16e01c802825757dec27720ddd109be1c9c49feb32ebaeb7ca4a5acec8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,803 | Path.truncate_self | Mathlib/Topology/Connected/PathConnected.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext x | X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
x y z : X
ι : Type u_3
γ✝ : Path x y
a b : X
γ : Path a b
t : ℝ
⊢ γ.truncate t t = (refl (γ.extend t)).cast ⋯ ⋯ | case a.h
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
x✝ y z : X
ι : Type u_3
γ✝ : Path x✝ y
a b : X
γ : Path a b
t : ℝ
x : ↑I
⊢ (γ.truncate t t) x = ((refl (γ.extend t)).cast ⋯ ⋯) x | ((:c Eq) ((:c Path) (:fv _uniq.316677) (:fv _uniq.316683) ((:c Path.extend) (:fv _uniq.316677) (:fv _uniq.316683) (:fv _uniq.316974) (:fv _uniq.316975) (:fv _uniq.316976) ((:c Min.min) (:c Real) ((:c LinearOrderedRing.toMin) (:c Real) (:c Real.instLinearOrderedRing)) (:fv _uniq.316977) (:fv _uniq.316977))) ((:c Path.ex... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.316677))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.316680))"},{"name":"x","sexp":"(:fv _uniq.316677)"},{"name":"y","sexp":"(:fv _uniq.316677)"},{"name":"z","sexp"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Path) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c Path.extend) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.316677","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.316680","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"ext","sourceEnd":26511,"sourceStart":26508,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":26513,"sourceStart":26512,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"x","sourceEnd":26513,"sourceStart":26512,"tag... | [{"role":"fresh_name","source":"x","source_end":26513,"source_start":26512,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.316677","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.316680","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 164 | 11 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1fcb1f0d287c6924318c0ab027b7dcc6e5b619cced0a6c9c3b834fa2b2456582 | 3ce41c258e3bcc8408c2b256540d282926cc0e0a0dfe1651e55fb76f923718be | ee522618587c4a8062e9541e92fad69d5c6e7dbdf5366e9d82c63ebe3c1e08c5 | 305ecf303a3c7fb660c80bcc1853d7caa652d6e9ee615e573d5430932ccd936c |
cat-searcher/leandojo-benchmark-4-random | test | 2,804 | Path.truncate_self | Mathlib/Topology/Connected/PathConnected.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Path.cast_coe</a>] | case a.h
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
x✝ y z : X
ι : Type u_3
γ✝ : Path x✝ y
a b : X
γ : Path a b
t : ℝ
x : ↑I
⊢ (γ.truncate t t) x = ((refl (γ.extend t)).cast ⋯ ⋯) x | case a.h
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
x✝ y z : X
ι : Type u_3
γ✝ : Path x✝ y
a b : X
γ : Path a b
t : ℝ
x : ↑I
⊢ (γ.truncate t t) x = (refl (γ.extend t)) x | ((:c Eq) (:fv _uniq.316677) ((:c DFunLike.coe) ((:c Path) (:fv _uniq.316677) (:fv _uniq.316683) ((:c Path.extend) (:fv _uniq.316677) (:fv _uniq.316683) (:fv _uniq.316974) (:fv _uniq.316975) (:fv _uniq.316976) ((:c Min.min) (:c Real) ((:c LinearOrderedRing.toMin) (:c Real) (:c Real.instLinearOrderedRing)) (:fv _uniq.316... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.316677))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.316680))"},{"name":"x✝","sexp":"(:fv _uniq.316677)"},{"name":"y","sexp":"(:fv _uniq.316677)"},{"name":"z","sexp... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Path) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c Path.extend) (:arg :implicit-type 0 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.316677","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.316680","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rw","sourceEnd":26518,"sourceStart":26516,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":26520,"sourceStart":26519,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Path.cast_coe","... | [] | [{"source":"cast_coe","source_end":26528,"source_start":26520,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.316677","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.316680","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 164 | 12 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fb3ac69ac888081217ec54909ab85701a55f3feaf357e0651a283d67f4aaafa4 | 305ecf303a3c7fb660c80bcc1853d7caa652d6e9ee615e573d5430932ccd936c | ba2ebf0c1a47345be0010f491d822d8b344a96422f4e9624d2f6d29272eaed6a | 29d752cade1433b4e0e8184bd5471e50e49c74607de2e67f3bc8bf3a1bf3f071 |
cat-searcher/leandojo-benchmark-4-random | test | 2,805 | Path.truncate_self | Mathlib/Topology/Connected/PathConnected.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Path.truncate</a>, <a>DFunLike.coe</a>, <a>Path.refl</a>, <a>min_def</a>, <a>max_def</a>] | case a.h
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
x✝ y z : X
ι : Type u_3
γ✝ : Path x✝ y
a b : X
γ : Path a b
t : ℝ
x : ↑I
⊢ (γ.truncate t t) x = (refl (γ.extend t)) x | case a.h
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
x✝ y z : X
ι : Type u_3
γ✝ : Path x✝ y
a b : X
γ : Path a b
t : ℝ
x : ↑I
⊢ γ.extend (if (if ↑x ≤ t then t else ↑x) ≤ t then if ↑x ≤ t then t else ↑x else t) = γ.extend t | ((:c Eq) (:fv _uniq.316677) ((:c DFunLike.coe) ((:c Path) (:fv _uniq.316677) (:fv _uniq.316683) ((:c Path.extend) (:fv _uniq.316677) (:fv _uniq.316683) (:fv _uniq.316974) (:fv _uniq.316975) (:fv _uniq.316976) ((:c Min.min) (:c Real) ((:c LinearOrderedRing.toMin) (:c Real) (:c Real.instLinearOrderedRing)) (:fv _uniq.316... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.316677))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.316680))"},{"name":"x✝","sexp":"(:fv _uniq.316677)"},{"name":"y","sexp":"(:fv _uniq.316677)"},{"name":"z","sexp... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Path) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c Path.extend) (:arg :implicit-type 0 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.316677","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.316680","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"simp","sourceEnd":26536,"sourceStart":26532,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":26541,"sourceStart":26537,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":265... | [] | [{"source":"truncate","source_end":26551,"source_start":26543,"syntax_kind":"ident"},{"source":"DFunLike.coe","source_end":26565,"source_start":26553,"syntax_kind":"ident"},{"source":"refl","source_end":26571,"source_start":26567,"syntax_kind":"ident"},{"source":"min_def","source_end":26580,"source_start":26573,"syntax... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.316677","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.316680","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 164 | 15 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4fe388881d84031feb6cb1c7f852d101cba29f93fed45028e17451212f44e649 | 29d752cade1433b4e0e8184bd5471e50e49c74607de2e67f3bc8bf3a1bf3f071 | a355a1b9047f5edd38db4c9d72efe8a9809734e67baf0d1776f74bcdd79c6446 | a2ba2acdfb7e3bd234b330d33dbc39c4b4f5801dcd91d92ca884ba1a6f8cc64a |
cat-searcher/leandojo-benchmark-4-random | test | 2,806 | Path.truncate_self | Mathlib/Topology/Connected/PathConnected.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | split_ifs with h₁ h₂ <;> congr | case a.h
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
x✝ y z : X
ι : Type u_3
γ✝ : Path x✝ y
a b : X
γ : Path a b
t : ℝ
x : ↑I
⊢ γ.extend (if (if ↑x ≤ t then t else ↑x) ≤ t then if ↑x ≤ t then t else ↑x else t) = γ.extend t | ((:c Eq) (:fv _uniq.316677) ((:c Path.extend) (:fv _uniq.316677) (:fv _uniq.316683) (:fv _uniq.316974) (:fv _uniq.316975) (:fv _uniq.316976) ((:c ite) (:c Real) ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c LinearOrder.toPartialOrder) (:c Real) (:c Real.linearOrder))))... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.316677))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.316680))"},{"name":"x✝","sexp":"(:fv _uniq.316677)"},{"name":"y","sexp":"(:fv _uniq.316677)"},{"name":"z","sexp... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Path.extend) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit 2) (:arg :implicit 3) (:arg :explicit 4 (:fv FV12)) (:arg :explicit 5 (:app (:c ite) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.316677","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.316680","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"source":"split_ifs","sourceEnd":26602,"sourceStart":26593,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"with","sourceEnd":26607,"sourceStart":26603,"tag":"atom"},{"children":[{"children":[{"source":"h₁","sourceEnd":26612,"sourceStart":26608,"tag... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.316677","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.316680","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 164 | 16 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e5bc31ef369c1396cc3fe9d87bc26eb9d3379af2d028890aad48a360f6e7b7a3 | a2ba2acdfb7e3bd234b330d33dbc39c4b4f5801dcd91d92ca884ba1a6f8cc64a | 32efbbf20a7093f53a8c64af7efed2391dbd1ddeeaa82eaf6753f2880346448b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,807 | WeierstrassCurve.Jacobian.map_addX | Mathlib/AlgebraicGeometry/EllipticCurve/Jacobian.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>WeierstrassCurve.Jacobian.addX</a>] | R : Type u
inst✝² : CommRing R
W' : Jacobian R
F : Type v
inst✝¹ : Field F
W : Jacobian F
S : Type u_1
inst✝ : CommRing S
f : R →+* S
P Q : Fin 3 → R
⊢ addX (map W' f) (⇑f ∘ P) (⇑f ∘ Q) = f (W'.addX P Q) | ((:c Eq) (:fv _uniq.1093351) ((:c WeierstrassCurve.Jacobian.addX) (:fv _uniq.1093351) (:fv _uniq.1093354) ((:c WeierstrassCurve.map) (:fv _uniq.1093334) (:fv _uniq.1093337) (:fv _uniq.1093340) (:fv _uniq.1093351) (:fv _uniq.1093354) (:fv _uniq.1093746)) ((:c Function.comp) ((:c Fin) ((:c OfNat.ofNat) (:c Nat) (:lit 3) ... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝²","sexp":"((:c CommRing) (:fv _uniq.1093334))"},{"name":"W'","sexp":"((:c WeierstrassCurve.Jacobian) (:fv _uniq.1093334))"},{"name":"F","sexp":"(:sort (+ v 1))"},{"name":"inst✝¹","sexp":"((:c Field) (:fv _uniq.1093342))"},{"name":"W","sexp":"((:c WeierstrassCurve.Ja... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV6)) (:arg :explicit 1 (:app (:c WeierstrassCurve.Jacobian.addX) (:arg :implicit-type 0 (:fv FV6)) (:arg :instance 1 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV6))))) (:arg :explicit 2 (:app (:c WeierstrassCurve.map) (:arg :implicit-type 0 (:fv FV0)) (:arg :ins... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1093334","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1093337","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CommRing) (:arg :ex... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":78456,"sourceStart":78452,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"addX","source_end":78462,"source_start":78458,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1093334","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1093337","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"in... | 302 | 2 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2f47c243402ac67f00d9b8407a9784cd79b97a9d0a6a7271032c2ad775b1634c | 87a83a83bb124e4a55995235326904af250691088b99b11f1c35e544f840732a | b17c374ddf944666b16397f381055393d28e5d54f5c979d828291400023ecdad | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,808 | Set.ncard_le_one_iff | Mathlib/Data/Set/Card.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.ncard_le_one</a> hs] | α : Type u_1
β : Type u_2
s t : Set α
f : α → β
hs : autoParam s.Finite _auto✝
⊢ s.ncard ≤ 1 ↔ ∀ {a b : α}, a ∈ s → b ∈ s → a = b | α : Type u_1
β : Type u_2
s t : Set α
f : α → β
hs : autoParam s.Finite _auto✝
⊢ (∀ a ∈ s, ∀ b ∈ s, a = b) ↔ ∀ {a b : α}, a ∈ s → b ∈ s → a = b | ((:c Iff) ((:c LE.le) (:c Nat) (:c instLENat) ((:c Set.ncard) (:fv _uniq.221725) (:fv _uniq.221731)) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) (:forall a (:fv _uniq.221725) (:forall b (:fv _uniq.221725) (:forall _ ((:c Membership.mem) (:fv _uniq.221725) ((:c Set) (:fv _uniq.221725)) ((:c Set.in... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.221725))"},{"name":"t","sexp":"((:c Set) (:fv _uniq.221725))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.221725) (:fv _uniq.221728))"},{"name":"hs","sexp":"((:c autoParam) ((:c Set.Finite) (:fv _uni... | (:app (:c Iff) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c Set.ncard) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)))) (:arg :explicit 3 (:app (:c OfNat.ofNat) (:arg :implicit... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.221725","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.221728","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":51936,"sourceStart":51934,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":51938,"sourceStart":51937,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Set... | [] | [{"source":"ncard_le_one hs","source_end":51953,"source_start":51938,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.221725","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.221728","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 266 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b2a9014283165efb789dc23fa679d903985c71a7a5d6ea8f070799a7b49d03cc | c526c98180c69929954f460ef479d1a1bdcd44470e02187faa9b3b7cf5840624 | d640f75674a59bcfcd48c26363e163687b8cb1bf04939dbe42dfebcba30c1c3c | 1661aa230da3bced4eb426b68be21a2c4c245f553ee9398ee00f3dd9747e0923 |
cat-searcher/leandojo-benchmark-4-random | test | 2,809 | Set.ncard_le_one_iff | Mathlib/Data/Set/Card.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | tauto | α : Type u_1
β : Type u_2
s t : Set α
f : α → β
hs : autoParam s.Finite _auto✝
⊢ (∀ a ∈ s, ∀ b ∈ s, a = b) ↔ ∀ {a b : α}, a ∈ s → b ∈ s → a = b | ((:c Iff) (:forall a (:fv _uniq.221725) (:forall _ ((:c Membership.mem) (:fv _uniq.221725) ((:c Set) (:fv _uniq.221725)) ((:c Set.instMembership) (:fv _uniq.221725)) 0 (:fv _uniq.221731)) (:forall b (:fv _uniq.221725) (:forall _ ((:c Membership.mem) (:fv _uniq.221725) ((:c Set) (:fv _uniq.221725)) ((:c Set.instMembersh... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.221725))"},{"name":"t","sexp":"((:c Set) (:fv _uniq.221725))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.221725) (:fv _uniq.221728))"},{"name":"hs","sexp":"((:c autoParam) ((:c Set.Finite) (:fv _uni... | (:app (:c Iff) (:arg :explicit 0 (:forall a :explicit (:fv FV0) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.221725","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.221728","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"tauto","sourceEnd":51962,"sourceStart":51957,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.Tauto.tauto","source":"tauto","sourceEnd":51962,"sourceStart":51957,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.221725","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.221728","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 266 | 7 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | da0920cec4450c9034d36f058e23a960ffb9494ac4b89a77ba28280e147f9d7d | 1661aa230da3bced4eb426b68be21a2c4c245f553ee9398ee00f3dd9747e0923 | 78175d0e14580017b7abde3d46f7acc510808867e2ea0a22535e39b5dff68317 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,810 | NNReal.tendsto_rpow_atTop | Mathlib/Analysis/SpecialFunctions/Pow/Asymptotics.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Filter.tendsto_atTop_atTop</a>] | y : ℝ
hy : 0 < y
⊢ Tendsto (fun x => x ^ y) atTop atTop | y : ℝ
hy : 0 < y
⊢ ∀ (b : ℝ≥0), ∃ i, ∀ (a : ℝ≥0), i ≤ a → b ≤ a ^ y | ((:c Filter.Tendsto) (:c NNReal) (:c NNReal) (:lambda x (:c NNReal) ((:c HPow.hPow) (:c NNReal) (:c Real) (:c NNReal) ((:c instHPow) (:c NNReal) (:c Real) (:c NNReal.instPowReal)) 0 (:fv _uniq.30979))) ((:c Filter.atTop) (:c NNReal) ((:c PartialOrder.toPreorder) (:c NNReal) ((:c StrictOrderedSemiring.toPartialOrder) (:... | [{"name":"y","sexp":"(:c Real)"},{"name":"hy","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.30979))"}] | (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:c NNReal)) (:arg :implicit-type 1 (:c NNReal)) (:arg :explicit 2 (:lambda x :explicit (:c NNReal) (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c NNReal)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c NNReal)) (:arg :instance 3 (:instance-of (:app (:c HP... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30979","is_instance":false,"is_let":false,"name":"y","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.30980","is_instance":false,"is_let":false,"name":"hy","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c Real... | {"children":[{"source":"rw","sourceEnd":7374,"sourceStart":7372,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7376,"sourceStart":7375,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Filter.tendsto_atTop... | [] | [{"source":"Filter.tendsto_atTop_atTop","source_end":7402,"source_start":7376,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30979","is_instance":false,"is_let":false,"user_name":"y"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.30980","is_instance":false,"is_let":false,"user_name":"hy"}] | 30 | 4 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0898d000615938192cedbabad10c95f511e3ad3286f91d7cf6353ebab1a3bfdd | c5ec624003ab08bbcbbde268ca798ad96dc23246d7dcd419f9f8034acef7c1cc | 9410adbb065fcb20ef10a082137779e21303c1f6c929d98013e1a0fb66d45a29 | d5256cd36dac053bf4addccfde34064a37d7203e86492e735f8ce270798ec047 |
cat-searcher/leandojo-benchmark-4-random | test | 2,811 | NNReal.tendsto_rpow_atTop | Mathlib/Analysis/SpecialFunctions/Pow/Asymptotics.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro b | y : ℝ
hy : 0 < y
⊢ ∀ (b : ℝ≥0), ∃ i, ∀ (a : ℝ≥0), i ≤ a → b ≤ a ^ y | y : ℝ
hy : 0 < y
b : ℝ≥0
⊢ ∃ i, ∀ (a : ℝ≥0), i ≤ a → b ≤ a ^ y | (:forall b (:c NNReal) ((:c Exists) (:c NNReal) (:lambda i (:c NNReal) (:forall a (:c NNReal) (:forall _ ((:c LE.le) (:c NNReal) ((:c Preorder.toLE) (:c NNReal) ((:c PartialOrder.toPreorder) (:c NNReal) ((:c SemilatticeSup.toPartialOrder) (:c NNReal) (:c instNNRealSemilatticeSup)))) 1 0) ((:c LE.le) (:c NNReal) ((:c Pr... | [{"name":"y","sexp":"(:c Real)"},{"name":"hy","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.30979))"}] | (:forall b :explicit (:c NNReal) (:app (:c Exists) (:arg :implicit-type 0 (:c NNReal)) (:arg :explicit 1 (:lambda i :explicit (:c NNReal) (:forall a :explicit (:c NNReal) (:forall _ :explicit (:app (:c LE.le) (:arg :implicit-type 0 (:c NNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c NNReal)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30979","is_instance":false,"is_let":false,"name":"y","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.30980","is_instance":false,"is_let":false,"name":"hy","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c Real... | {"children":[{"source":"intro","sourceEnd":7411,"sourceStart":7406,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"b","sourceEnd":7413,"sourceStart":7412,"tag":"identifier"}],"kind":"null","source":"b","sourceEnd":7413,"sourceStart":7412,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source":"int... | [{"role":"fresh_name","source":"b","source_end":7413,"source_start":7412,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30979","is_instance":false,"is_let":false,"user_name":"y"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.30980","is_instance":false,"is_let":false,"user_name":"hy"}] | 30 | 7 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a181741d2aec7cea349c20ce92cdce2443f85327e41530282b1518b50d3bb04f | d5256cd36dac053bf4addccfde34064a37d7203e86492e735f8ce270798ec047 | 7cee481b254d1b3fddfe93f15ca5787a9de449e1e5342746e03fa42f17235698 | 0f67ebffb3545cd2bb6462d790cd91ea12f6c5724cbb552fd36f6891bfb535e2 |
cat-searcher/leandojo-benchmark-4-random | test | 2,812 | NNReal.tendsto_rpow_atTop | Mathlib/Analysis/SpecialFunctions/Pow/Asymptotics.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨c, hc⟩ := tendsto_atTop_atTop.mp (<a>tendsto_rpow_atTop</a> hy) b | y : ℝ
hy : 0 < y
b : ℝ≥0
⊢ ∃ i, ∀ (a : ℝ≥0), i ≤ a → b ≤ a ^ y | case intro
y : ℝ
hy : 0 < y
b : ℝ≥0
c : ℝ
hc : ∀ (a : ℝ), c ≤ a → ↑b ≤ a ^ y
⊢ ∃ i, ∀ (a : ℝ≥0), i ≤ a → b ≤ a ^ y | ((:c Exists) (:c NNReal) (:lambda i (:c NNReal) (:forall a (:c NNReal) (:forall _ ((:c LE.le) (:c NNReal) ((:c Preorder.toLE) (:c NNReal) ((:c PartialOrder.toPreorder) (:c NNReal) ((:c SemilatticeSup.toPartialOrder) (:c NNReal) (:c instNNRealSemilatticeSup)))) 1 0) ((:c LE.le) (:c NNReal) ((:c Preorder.toLE) (:c NNReal... | [{"name":"y","sexp":"(:c Real)"},{"name":"hy","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.30979))"},{"name":"b","sexp":"(:c NNReal)"}] | (:app (:c Exists) (:arg :implicit-type 0 (:c NNReal)) (:arg :explicit 1 (:lambda i :explicit (:c NNReal) (:forall a :explicit (:c NNReal) (:forall _ :explicit (:app (:c LE.le) (:arg :implicit-type 0 (:c NNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c NNReal))))) (:arg :explicit 2 1) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30979","is_instance":false,"is_let":false,"name":"y","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.30980","is_instance":false,"is_let":false,"name":"hy","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c Real... | {"children":[{"source":"obtain","sourceEnd":7422,"sourceStart":7416,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":7426,"sourceStart":7423,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"c","sourceEnd":7... | [] | [{"source":"tendsto_atTop_atTop.mp (tendsto_rpow_atTop hy) b","source_end":7486,"source_start":7438,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨c, hc⟩","source_end":7434,"source_start":7423,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30979","is_instance":false,"is_let":false,"user_name":"y"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.30980","is_instance":false,"is_let":false,"user_name":"hy"},{"binder_role":":explicit","context_index":2,"internal_name":"_u... | 30 | 8 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2c9553d15f5e0cff4ccaad289962e08c4384f8a5521fcb260b5d89c5e53c7ba3 | 0f67ebffb3545cd2bb6462d790cd91ea12f6c5724cbb552fd36f6891bfb535e2 | b3729d907a70821b18f6aebd532e946197a8879715651fdeedd78e3e882ec41c | ea2c67c73b6f1b526c7e6f098ac3482e4b49aa7bb75c1eb03701e2a8f14fbb19 |
cat-searcher/leandojo-benchmark-4-random | test | 2,813 | NNReal.tendsto_rpow_atTop | Mathlib/Analysis/SpecialFunctions/Pow/Asymptotics.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | use c.toNNReal | case intro
y : ℝ
hy : 0 < y
b : ℝ≥0
c : ℝ
hc : ∀ (a : ℝ), c ≤ a → ↑b ≤ a ^ y
⊢ ∃ i, ∀ (a : ℝ≥0), i ≤ a → b ≤ a ^ y | case h
y : ℝ
hy : 0 < y
b : ℝ≥0
c : ℝ
hc : ∀ (a : ℝ), c ≤ a → ↑b ≤ a ^ y
⊢ ∀ (a : ℝ≥0), c.toNNReal ≤ a → b ≤ a ^ y | ((:c Exists) (:c NNReal) (:lambda i (:c NNReal) (:forall a (:c NNReal) (:forall _ ((:c LE.le) (:c NNReal) ((:c Preorder.toLE) (:c NNReal) ((:c PartialOrder.toPreorder) (:c NNReal) ((:c SemilatticeSup.toPartialOrder) (:c NNReal) (:c instNNRealSemilatticeSup)))) 1 0) ((:c LE.le) (:c NNReal) ((:c Preorder.toLE) (:c NNReal... | [{"name":"y","sexp":"(:c Real)"},{"name":"hy","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.30979))"},{"name":"b","sexp":"(:c NNReal)"},{"name":"c","sexp":"(:c Real)"},{"name":"hc","sexp":"(:forall a (:c Real) (:forall _... | (:app (:c Exists) (:arg :implicit-type 0 (:c NNReal)) (:arg :explicit 1 (:lambda i :explicit (:c NNReal) (:forall a :explicit (:c NNReal) (:forall _ :explicit (:app (:c LE.le) (:arg :implicit-type 0 (:c NNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c NNReal))))) (:arg :explicit 2 1) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30979","is_instance":false,"is_let":false,"name":"y","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.30980","is_instance":false,"is_let":false,"name":"hy","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c Real... | {"children":[{"source":"use","sourceEnd":7492,"sourceStart":7489,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"name":"Real.toNNReal","semanticRole":"global","source":"c.toNNReal","sourceEnd":7503,"sourceStart":7493,"tag":"iden... | [] | [{"source":"c.toNNReal","source_end":7503,"source_start":7493,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30979","is_instance":false,"is_let":false,"user_name":"y"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.30980","is_instance":false,"is_let":false,"user_name":"hy"},{"binder_role":":explicit","context_index":2,"internal_name":"_u... | 30 | 9 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | faea44bf7bb9b2a5b117e6c387f3802a2aaec28cdb9fe647c7eca0db9ed50170 | ea2c67c73b6f1b526c7e6f098ac3482e4b49aa7bb75c1eb03701e2a8f14fbb19 | 09ac43089cda8e26ac0f09916f9f2e6986bf1bd136a0149a9581b177b3183efc | 2332f5a35ba066af8e56712230ec3abd4d03dc86a31231329d9ff3de3edaf7a4 |
cat-searcher/leandojo-benchmark-4-random | test | 2,814 | NNReal.tendsto_rpow_atTop | Mathlib/Analysis/SpecialFunctions/Pow/Asymptotics.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro a ha | case h
y : ℝ
hy : 0 < y
b : ℝ≥0
c : ℝ
hc : ∀ (a : ℝ), c ≤ a → ↑b ≤ a ^ y
⊢ ∀ (a : ℝ≥0), c.toNNReal ≤ a → b ≤ a ^ y | case h
y : ℝ
hy : 0 < y
b : ℝ≥0
c : ℝ
hc : ∀ (a : ℝ), c ≤ a → ↑b ≤ a ^ y
a : ℝ≥0
ha : c.toNNReal ≤ a
⊢ b ≤ a ^ y | (:forall a (:c NNReal) (:forall _ ((:c LE.le) (:c NNReal) ((:c Preorder.toLE) (:c NNReal) ((:c PartialOrder.toPreorder) (:c NNReal) ((:c SemilatticeSup.toPartialOrder) (:c NNReal) (:c instNNRealSemilatticeSup)))) ((:c Real.toNNReal) (:fv _uniq.31729)) 0) ((:c LE.le) (:c NNReal) ((:c Preorder.toLE) (:c NNReal) ((:c Part... | [{"name":"y","sexp":"(:c Real)"},{"name":"hy","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.30979))"},{"name":"b","sexp":"(:c NNReal)"},{"name":"c","sexp":"(:c Real)"},{"name":"hc","sexp":"(:forall a (:c Real) (:forall _... | (:forall a :explicit (:c NNReal) (:forall _ :explicit (:app (:c LE.le) (:arg :implicit-type 0 (:c NNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c NNReal))))) (:arg :explicit 2 (:app (:c Real.toNNReal) (:arg :explicit 0 (:fv FV3)))) (:arg :explicit 3 0)) (:app (:c LE.le) (:arg :implicit-type... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30979","is_instance":false,"is_let":false,"name":"y","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.30980","is_instance":false,"is_let":false,"name":"hy","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c Real... | {"children":[{"source":"intro","sourceEnd":7511,"sourceStart":7506,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"a","sourceEnd":7513,"sourceStart":7512,"tag":"identifier"},{"semanticRole":"scoped_local","source":"ha","sourceEnd":7516,"sourceStart":7514,"tag":"identifier"}],"kind":"null","source":"... | [{"role":"fresh_name","source":"a","source_end":7513,"source_start":7512,"syntax_kind":"ident"},{"role":"fresh_name","source":"ha","source_end":7516,"source_start":7514,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30979","is_instance":false,"is_let":false,"user_name":"y"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.30980","is_instance":false,"is_let":false,"user_name":"hy"},{"binder_role":":explicit","context_index":2,"internal_name":"_u... | 30 | 10 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 077387f1eb3502af461895bbba8bea02ed2bdaae39d1a2e36a9150641814c593 | 2332f5a35ba066af8e56712230ec3abd4d03dc86a31231329d9ff3de3edaf7a4 | d3051573cbe4fa4120dd9aa61cc5eac53633ef1f904bfd012ae1cf7a0c5ddf4c | bfb5da4b46bced7b5db4f8561d37616803d6afa5f4da8df95ed8ff0eec9e4956 |
cat-searcher/leandojo-benchmark-4-random | test | 2,815 | NNReal.tendsto_rpow_atTop | Mathlib/Analysis/SpecialFunctions/Pow/Asymptotics.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact mod_cast hc a (Real.toNNReal_le_iff_le_coe.mp ha) | case h
y : ℝ
hy : 0 < y
b : ℝ≥0
c : ℝ
hc : ∀ (a : ℝ), c ≤ a → ↑b ≤ a ^ y
a : ℝ≥0
ha : c.toNNReal ≤ a
⊢ b ≤ a ^ y | ((:c LE.le) (:c NNReal) ((:c Preorder.toLE) (:c NNReal) ((:c PartialOrder.toPreorder) (:c NNReal) ((:c StrictOrderedSemiring.toPartialOrder) (:c NNReal) (:c instNNRealStrictOrderedSemiring)))) (:fv _uniq.31388) ((:c HPow.hPow) (:c NNReal) (:c Real) (:c NNReal) ((:c instHPow) (:c NNReal) (:c Real) (:c NNReal.instPowReal... | [{"name":"y","sexp":"(:c Real)"},{"name":"hy","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.30979))"},{"name":"b","sexp":"(:c NNReal)"},{"name":"c","sexp":"(:c Real)"},{"name":"hc","sexp":"(:forall a (:c Real) (:forall _... | (:app (:c LE.le) (:arg :implicit-type 0 (:c NNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c NNReal))))) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c NNReal)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c NNReal)) (:arg :instan... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30979","is_instance":false,"is_let":false,"name":"y","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.30980","is_instance":false,"is_let":false,"name":"hy","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c Real... | {"children":[{"source":"exact","sourceEnd":7524,"sourceStart":7519,"tag":"atom"},{"children":[{"source":"mod_cast","sourceEnd":7533,"sourceStart":7525,"tag":"atom"},{"children":[{"contextIndex":4,"semanticRole":"local","source":"hc","sourceEnd":7536,"sourceStart":7534,"tag":"identifier"},{"children":[{"contextIndex":5,... | [] | [{"source":"mod_cast hc a (Real.toNNReal_le_iff_le_coe.mp ha)","source_end":7574,"source_start":7525,"syntax_kind":"Lean.modCast"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30979","is_instance":false,"is_let":false,"user_name":"y"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.30980","is_instance":false,"is_let":false,"user_name":"hy"},{"binder_role":":explicit","context_index":2,"internal_name":"_u... | 30 | 11 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8447315291cb7b8f2974a4cd15840fcd2512038644d34a2d163a8fe725f788c8 | bfb5da4b46bced7b5db4f8561d37616803d6afa5f4da8df95ed8ff0eec9e4956 | d9157e1a8c712c695efa4b0a52169c568f4d7ccd738118dec2260e6c98c5194b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,816 | pcontinuous_iff' | Mathlib/Topology/Partial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | constructor | X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
⊢ PContinuous f ↔ ∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y) | case mp
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
⊢ PContinuous f → ∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y)
case mpr
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
⊢ (∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (�... | ((:c Iff) ((:c PContinuous) (:fv _uniq.1126) (:fv _uniq.1129) (:fv _uniq.1132) (:fv _uniq.1135) (:fv _uniq.1245)) (:forall x (:fv _uniq.1126) (:forall y (:fv _uniq.1129) (:forall h ((:c Membership.mem) (:fv _uniq.1129) ((:c Part) (:fv _uniq.1129)) ((:c Part.instMembership) (:fv _uniq.1129)) 0 ((:fv _uniq.1245) 1)) ((:c... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.1126))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.1129))"},{"name":"f","sexp":"((:c PFun) (:fv _uniq.1126) (:fv _uniq.1129))"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c PContinuous) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"source":"constructor","sourceEnd":2076,"sourceStart":2065,"tag":"atom"}],"kind":"Lean.Parser.Tactic.constructor","source":"constructor","sourceEnd":2076,"sourceStart":2065,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 19 | 4 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2cfd62ba252164001b0f16ae6ee29b95906121caeb48985ae7af6c2a355d4f30 | 3c2b3b073a9705fd399e1f88e44f651bb8cc8481a1942b0571dcd65077f4c52e | e3c1703abf8a6b3df04dd30e184fe02bb6724f46830b544562ff083169371068 | 457a6d04f337b114f67da9935813265a81cba01ab0328cc583ae002bc5452a8d |
cat-searcher/leandojo-benchmark-4-random | test | 2,817 | pcontinuous_iff' | Mathlib/Topology/Partial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro hf s os | case mpr
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
⊢ (∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y)) → PContinuous f | case mpr
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
hf : ∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y)
s : Set Y
os : IsOpen s
⊢ IsOpen (f.preimage s) | (:forall _ (:forall x (:fv _uniq.1126) (:forall y (:fv _uniq.1129) (:forall h ((:c Membership.mem) (:fv _uniq.1129) ((:c Part) (:fv _uniq.1129)) ((:c Part.instMembership) (:fv _uniq.1129)) 0 ((:fv _uniq.1245) 1)) ((:c Filter.PTendsto') (:fv _uniq.1126) (:fv _uniq.1129) (:fv _uniq.1245) ((:c nhds) (:fv _uniq.1126) (:fv ... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.1126))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.1129))"},{"name":"f","sexp":"((:c PFun) (:fv _uniq.1126) (:fv _uniq.1129))"}] | (:forall _ :explicit (:forall x :implicit (:fv FV0) (:forall y :implicit (:fv FV1) (:forall h :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Part) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"source":"intro","sourceEnd":2272,"sourceStart":2267,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"hf","sourceEnd":2275,"sourceStart":2273,"tag":"identifier"},{"semanticRole":"scoped_local","source":"s","sourceEnd":2277,"sourceStart":2276,"tag":"identifier"},{"semanticRole":"scoped_l... | [{"role":"fresh_name","source":"hf","source_end":2275,"source_start":2273,"syntax_kind":"ident"},{"role":"fresh_name","source":"s","source_end":2277,"source_start":2276,"syntax_kind":"ident"},{"role":"fresh_name","source":"os","source_end":2280,"source_start":2278,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 19 | 13 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3f3e142a33154686ba16af604bf24fdf79262a5997954ac94cf9528164c7e337 | 1237b3997db0889d2b68b9eef28b5c0461384409e7eba5ed275074a63a60fb43 | bea9620a0f50074c76510c8af82c921014e9db24a038b1f679b724eadcb3b59a | 47a49898612f441c2326460d39103d697692bd9ea67b52ecd240f2871813dfc5 |
cat-searcher/leandojo-benchmark-4-random | test | 2,818 | pcontinuous_iff' | Mathlib/Topology/Partial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>isOpen_iff_nhds</a>] | case mpr
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
hf : ∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y)
s : Set Y
os : IsOpen s
⊢ IsOpen (f.preimage s) | case mpr
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
hf : ∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y)
s : Set Y
os : IsOpen s
⊢ ∀ x ∈ f.preimage s, 𝓝 x ≤ 𝓟 (f.preimage s) | ((:c IsOpen) (:fv _uniq.1126) (:fv _uniq.1132) ((:c PFun.preimage) (:fv _uniq.1126) (:fv _uniq.1129) (:fv _uniq.1245) (:fv _uniq.1724))) | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.1126))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.1129))"},{"name":"f","sexp":"((:c PFun) (:fv _uniq.1126) (:fv _uniq.1129))"},{"name":"hf","sexp":"(:forall x (:fv... | (:app (:c IsOpen) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c PFun.preimage) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:fv FV5)) (:arg :explicit 3 (:fv FV7))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"source":"rw","sourceEnd":2285,"sourceStart":2283,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2287,"sourceStart":2286,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"isOpen_iff_nhds","se... | [] | [{"source":"isOpen_iff_nhds","source_end":2302,"source_start":2287,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 19 | 14 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 34d498074265e645cfb07740373203fab181482b9271129cfa8843d884211bf5 | 47a49898612f441c2326460d39103d697692bd9ea67b52ecd240f2871813dfc5 | f2ac4516f4ad516a2c0a163fe66dd7d5972fe5b0abcbcea116e1e63697440de4 | 04ba4fb115a7548a45665b651c835b3a49d05da965beb699784c7c085fd88695 |
cat-searcher/leandojo-benchmark-4-random | test | 2,819 | pcontinuous_iff' | Mathlib/Topology/Partial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro x ⟨y, ys, fxy⟩ t | case mpr
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
hf : ∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y)
s : Set Y
os : IsOpen s
⊢ ∀ x ∈ f.preimage s, 𝓝 x ≤ 𝓟 (f.preimage s) | case mpr.intro.intro
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
hf : ∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y)
s : Set Y
os : IsOpen s
x : X
y : Y
ys : y ∈ s
fxy : y ∈ f x
t : Set X
⊢ t ∈ 𝓟 (f.preimage s) → t ∈ 𝓝 x | (:forall x (:fv _uniq.1126) (:forall _ ((:c Membership.mem) (:fv _uniq.1126) ((:c Set) (:fv _uniq.1126)) ((:c Set.instMembership) (:fv _uniq.1126)) 0 ((:c PFun.preimage) (:fv _uniq.1126) (:fv _uniq.1129) (:fv _uniq.1245) (:fv _uniq.1724))) ((:c LE.le) ((:c Filter) (:fv _uniq.1126)) ((:c Preorder.toLE) ((:c Filter) (:fv... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.1126))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.1129))"},{"name":"f","sexp":"((:c PFun) (:fv _uniq.1126) (:fv _uniq.1129))"},{"name":"hf","sexp":"(:forall x (:fv... | (:forall x :explicit (:fv FV0) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"source":"rintro","sourceEnd":2312,"sourceStart":2306,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":2314,"sourceStart":2313,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"x","sourceEnd":2314,"sourceStart":2313,"tag":"... | [{"role":"fresh_name","source":"x","source_end":2314,"source_start":2313,"syntax_kind":"ident"},{"role":"fresh_name","source":"y","source_end":2319,"source_start":2318,"syntax_kind":"ident"},{"role":"fresh_name","source":"ys","source_end":2323,"source_start":2321,"syntax_kind":"ident"},{"role":"fresh_name","source":"fx... | [{"source":"⟨y, ys, fxy⟩","source_end":2331,"source_start":2315,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 19 | 17 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d632cf4b1f26c54691c6dc9695f5a007981ee50deddac361be7689718a6e4476 | 04ba4fb115a7548a45665b651c835b3a49d05da965beb699784c7c085fd88695 | 420404eae67403259cb986530af8ec1fb98c6bb356876de2a0e05f2b8ed7bc7f | f5573850751084a69ea3a94b43676804df027f72282cf28f4353a59e944eb5af |
cat-searcher/leandojo-benchmark-4-random | test | 2,820 | pcontinuous_iff' | Mathlib/Topology/Partial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Filter.mem_principal</a>] | case mpr.intro.intro
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
hf : ∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y)
s : Set Y
os : IsOpen s
x : X
y : Y
ys : y ∈ s
fxy : y ∈ f x
t : Set X
⊢ t ∈ 𝓟 (f.preimage s) → t ∈ 𝓝 x | case mpr.intro.intro
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
hf : ∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y)
s : Set Y
os : IsOpen s
x : X
y : Y
ys : y ∈ s
fxy : y ∈ f x
t : Set X
⊢ f.preimage s ⊆ t → t ∈ 𝓝 x | (:forall _ ((:c Membership.mem) ((:c Set) (:fv _uniq.1126)) ((:c Filter) (:fv _uniq.1126)) ((:c instMembershipSetFilter) (:fv _uniq.1126)) (:fv _uniq.1791) ((:c Filter.principal) (:fv _uniq.1126) ((:c PFun.preimage) (:fv _uniq.1126) (:fv _uniq.1129) (:fv _uniq.1245) (:fv _uniq.1724)))) ((:c Membership.mem) ((:c Set) (:... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.1126))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.1129))"},{"name":"f","sexp":"((:c PFun) (:fv _uniq.1126) (:fv _uniq.1129))"},{"name":"hf","sexp":"(:forall x (:fv... | (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c Filter) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"source":"rw","sourceEnd":2338,"sourceStart":2336,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2340,"sourceStart":2339,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Filter.mem_principal... | [] | [{"source":"mem_principal","source_end":2353,"source_start":2340,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 19 | 18 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 63bef97cdad95b6c931f8247fc557d158a9c2b7f8a2dfbc6f8ab574d839893dd | f5573850751084a69ea3a94b43676804df027f72282cf28f4353a59e944eb5af | efe1d6c833a146c7d7afed716173729907df57735d30cbe6131098308229ee55 | 6c046b76ec05ab31da388aa68920c7279e88ce9170538d6ab8378d0b37b590d2 |
cat-searcher/leandojo-benchmark-4-random | test | 2,821 | pcontinuous_iff' | Mathlib/Topology/Partial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro (h : f.preimage s ⊆ t) | case mpr.intro.intro
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
hf : ∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y)
s : Set Y
os : IsOpen s
x : X
y : Y
ys : y ∈ s
fxy : y ∈ f x
t : Set X
⊢ f.preimage s ⊆ t → t ∈ 𝓝 x | case mpr.intro.intro
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
hf : ∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y)
s : Set Y
os : IsOpen s
x : X
y : Y
ys : y ∈ s
fxy : y ∈ f x
t : Set X
h : f.preimage s ⊆ t
⊢ t ∈ 𝓝 x | (:forall _ ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.1126)) ((:c Set.instHasSubset) (:fv _uniq.1126)) ((:c PFun.preimage) (:fv _uniq.1126) (:fv _uniq.1129) (:fv _uniq.1245) (:fv _uniq.1724)) (:fv _uniq.1791)) ((:c Membership.mem) ((:c Set) (:fv _uniq.1126)) ((:c Filter) (:fv _uniq.1126)) ((:c instMembershipSetFilter)... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.1126))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.1129))"},{"name":"f","sexp":"((:c PFun) (:fv _uniq.1126) (:fv _uniq.1129))"},{"name":"hf","sexp":"(:forall x (:fv... | (:forall _ :explicit (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:app (:c PFun.preimage) (:arg :implicit-type 0 (:fv FV0)) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"source":"intro","sourceEnd":2362,"sourceStart":2357,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":2364,"sourceStart":2363,"tag":"atom"},{"semanticRole":"scoped_local","source":"h","sourceEnd":2365,"sourceStart":2364,"tag":"identifier"},{"source":":","sourceEnd":2367,"sourceStart":2366... | [{"role":"fresh_name","source":"h","source_end":2365,"source_start":2364,"syntax_kind":"ident"}] | [{"source":"f.preimage s ⊆ t","source_end":2386,"source_start":2368,"syntax_kind":"«term_⊆_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 19 | 21 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 91b77a77f50134805138f7599baa8b635b491b87c4b7b6b81399286126241d86 | 6c046b76ec05ab31da388aa68920c7279e88ce9170538d6ab8378d0b37b590d2 | 4e8db90fb64afe107db2007ffa575c7bb5ca1752144eefa8ae5f92bd0626946c | 69675ea26c28863fb33f3711c4b692f9cb32c25863d606d6ce4122bf805d0453 |
cat-searcher/leandojo-benchmark-4-random | test | 2,822 | pcontinuous_iff' | Mathlib/Topology/Partial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>Filter.mem_of_superset</a> _ h | case mpr.intro.intro
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
hf : ∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y)
s : Set Y
os : IsOpen s
x : X
y : Y
ys : y ∈ s
fxy : y ∈ f x
t : Set X
h : f.preimage s ⊆ t
⊢ t ∈ 𝓝 x | X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
hf : ∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y)
s : Set Y
os : IsOpen s
x : X
y : Y
ys : y ∈ s
fxy : y ∈ f x
t : Set X
h : f.preimage s ⊆ t
⊢ f.preimage s ∈ 𝓝 x | ((:c Membership.mem) ((:c Set) (:fv _uniq.1126)) ((:c Filter) (:fv _uniq.1126)) ((:c instMembershipSetFilter) (:fv _uniq.1126)) (:fv _uniq.1791) ((:c nhds) (:fv _uniq.1126) (:fv _uniq.1132) (:fv _uniq.1749))) | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.1126))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.1129))"},{"name":"f","sexp":"((:c PFun) (:fv _uniq.1126) (:fv _uniq.1129))"},{"name":"hf","sexp":"(:forall x (:fv... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c Filter) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Filter)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"source":"apply","sourceEnd":2417,"sourceStart":2412,"tag":"atom"},{"children":[{"name":"Filter.mem_of_superset","semanticRole":"global","source":"mem_of_superset","sourceEnd":2433,"sourceStart":2418,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":2435,"sourceStart":2434,"tag":"ato... | [] | [{"source":"mem_of_superset _ h","source_end":2437,"source_start":2418,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 19 | 23 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 688e85c3ec2d17d48dbda63a545d1c0192a1dfd40602eec6217c663578cc7bd8 | 69675ea26c28863fb33f3711c4b692f9cb32c25863d606d6ce4122bf805d0453 | b106ef8eac0f3a6afda54f6e45a460b2b6aab8681d3940ef4b32401bb93a13ff | 7e4a49dabaa7aed1baa401287f21395595fa3dfa3fe1c1779fd827c2a658ef47 |
cat-searcher/leandojo-benchmark-4-random | test | 2,823 | pcontinuous_iff' | Mathlib/Topology/Partial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h' : ∀ s ∈ 𝓝 y, f.preimage s ∈ 𝓝 x := by intro s hs have : <a>Filter.PTendsto'</a> f (𝓝 x) (𝓝 y) := hf fxy rw [<a>Filter.ptendsto'_def</a>] at this exact this s hs | X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
hf : ∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y)
s : Set Y
os : IsOpen s
x : X
y : Y
ys : y ∈ s
fxy : y ∈ f x
t : Set X
h : f.preimage s ⊆ t
⊢ f.preimage s ∈ 𝓝 x | X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
hf : ∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y)
s : Set Y
os : IsOpen s
x : X
y : Y
ys : y ∈ s
fxy : y ∈ f x
t : Set X
h : f.preimage s ⊆ t
h' : ∀ s ∈ 𝓝 y, f.preimage s ∈ 𝓝 x
⊢ f.preimage s ∈ 𝓝 x | ((:c Membership.mem) ((:c Set) (:fv _uniq.1126)) ((:c Filter) (:fv _uniq.1126)) ((:c instMembershipSetFilter) (:fv _uniq.1126)) ((:c PFun.preimage) (:fv _uniq.1126) (:fv _uniq.1129) (:fv _uniq.1245) (:fv _uniq.1724)) ((:c nhds) (:fv _uniq.1126) (:fv _uniq.1132) (:fv _uniq.1749))) | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.1126))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.1129))"},{"name":"f","sexp":"((:c PFun) (:fv _uniq.1126) (:fv _uniq.1129))"},{"name":"hf","sexp":"(:forall x (:fv... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c Filter) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Filter)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"source":"have","sourceEnd":2444,"sourceStart":2440,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h'","sourceEnd":2447,"sourceStart":2445,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h'","sourceEnd":2447,"sourceStart":2445,"tag":"node"},{"... | [] | [{"source":"∀ s ∈ 𝓝 y, f.preimage s ∈ 𝓝 x","source_end":2491,"source_start":2450,"syntax_kind":"Lean.«term∀__,_»"},{"source":"PTendsto' f (𝓝 x) (𝓝 y)","source_end":2553,"source_start":2524,"syntax_kind":"Lean.Parser.Term.app"},{"source":"hf fxy","source_end":2563,"source_start":2557,"syntax_kind":"Lean.Parser.Term.... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 19 | 24 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5d29e4a56ddd8fd5da5089ed4f5be9f12a70bd4c92991ec2e8c0797da1237026 | 7e4a49dabaa7aed1baa401287f21395595fa3dfa3fe1c1779fd827c2a658ef47 | 2a3c732032a56d3f0ce8090770ddedfbfa3c5b300e452ad2d5890cd02236b95a | de9eebc41063047721400f835aff725d0c6cc49ca9f4bcd173ed84273558c451 |
cat-searcher/leandojo-benchmark-4-random | test | 2,824 | pcontinuous_iff' | Mathlib/Topology/Partial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply h' | X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
hf : ∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y)
s : Set Y
os : IsOpen s
x : X
y : Y
ys : y ∈ s
fxy : y ∈ f x
t : Set X
h : f.preimage s ⊆ t
h' : ∀ s ∈ 𝓝 y, f.preimage s ∈ 𝓝 x
⊢ f.preimage s ∈ 𝓝 x | case a
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
hf : ∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y)
s : Set Y
os : IsOpen s
x : X
y : Y
ys : y ∈ s
fxy : y ∈ f x
t : Set X
h : f.preimage s ⊆ t
h' : ∀ s ∈ 𝓝 y, f.preimage s ∈ 𝓝 x
⊢ s ∈ 𝓝 y | ((:c Membership.mem) ((:c Set) (:fv _uniq.1126)) ((:c Filter) (:fv _uniq.1126)) ((:c instMembershipSetFilter) (:fv _uniq.1126)) ((:c PFun.preimage) (:fv _uniq.1126) (:fv _uniq.1129) (:fv _uniq.1245) (:fv _uniq.1724)) ((:c nhds) (:fv _uniq.1126) (:fv _uniq.1132) (:fv _uniq.1749))) | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.1126))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.1129))"},{"name":"f","sexp":"((:c PFun) (:fv _uniq.1126) (:fv _uniq.1129))"},{"name":"hf","sexp":"(:forall x (:fv... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c Filter) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Filter)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"source":"apply","sourceEnd":2653,"sourceStart":2648,"tag":"atom"},{"contextIndex":15,"semanticRole":"local","source":"h'","sourceEnd":2656,"sourceStart":2654,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply h'","sourceEnd":2656,"sourceStart":2648,"tag":"node"} | [] | [{"source":"h'","source_end":2656,"source_start":2654,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 19 | 33 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9350a6d27f66f701faa340e45700de2f84689c12964da8b4ed05bbd013c7ea81 | de9eebc41063047721400f835aff725d0c6cc49ca9f4bcd173ed84273558c451 | 681ca4aa4ee833cc73b9c8e4c772614f4f9d92cb6ea1058c114ea9bc0b77c221 | eb174f62716e459f14116a2d3c6b92d76572245c330cd6be9730aab5fb743ad4 |
cat-searcher/leandojo-benchmark-4-random | test | 2,825 | pcontinuous_iff' | Mathlib/Topology/Partial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>mem_nhds_iff</a>] | case a
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
hf : ∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y)
s : Set Y
os : IsOpen s
x : X
y : Y
ys : y ∈ s
fxy : y ∈ f x
t : Set X
h : f.preimage s ⊆ t
h' : ∀ s ∈ 𝓝 y, f.preimage s ∈ 𝓝 x
⊢ s ∈ 𝓝 y | case a
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
hf : ∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y)
s : Set Y
os : IsOpen s
x : X
y : Y
ys : y ∈ s
fxy : y ∈ f x
t : Set X
h : f.preimage s ⊆ t
h' : ∀ s ∈ 𝓝 y, f.preimage s ∈ 𝓝 x
⊢ ∃ t ⊆ s, IsOpen t ∧ y ∈ t | ((:c Membership.mem) ((:c Set) (:fv _uniq.1129)) ((:c Filter) (:fv _uniq.1129)) ((:c instMembershipSetFilter) (:fv _uniq.1129)) (:fv _uniq.1724) ((:c nhds) (:fv _uniq.1129) (:fv _uniq.1135) (:fv _uniq.1769))) | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.1126))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.1129))"},{"name":"f","sexp":"((:c PFun) (:fv _uniq.1126) (:fv _uniq.1129))"},{"name":"hf","sexp":"(:forall x (:fv... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :implicit-type 1 (:app (:c Filter) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c Filter)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"source":"rw","sourceEnd":2661,"sourceStart":2659,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2663,"sourceStart":2662,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"mem_nhds_iff","seman... | [] | [{"source":"mem_nhds_iff","source_end":2675,"source_start":2663,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 19 | 34 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6dff1a189596eba09af611b831da4618e2c8b761d1688f4635c1d4821734485d | eb174f62716e459f14116a2d3c6b92d76572245c330cd6be9730aab5fb743ad4 | 8e093a95c62088a2af0a4296b85d6708318fae8ca1c760dbe940c994f87eb8e3 | a47e5b0e6673340b7740d7acee8db6ab80dce8b7fadda114136eaac668a6013d |
cat-searcher/leandojo-benchmark-4-random | test | 2,826 | pcontinuous_iff' | Mathlib/Topology/Partial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨s, <a>Set.Subset.refl</a> _, os, ys⟩ | case a
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
hf : ∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y)
s : Set Y
os : IsOpen s
x : X
y : Y
ys : y ∈ s
fxy : y ∈ f x
t : Set X
h : f.preimage s ⊆ t
h' : ∀ s ∈ 𝓝 y, f.preimage s ∈ 𝓝 x
⊢ ∃ t ⊆ s, IsOpen t ∧ y ∈ t | ((:c Exists) ((:c Set) (:fv _uniq.1129)) (:lambda t ((:c Set) (:fv _uniq.1129)) ((:c And) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.1129)) ((:c Set.instHasSubset) (:fv _uniq.1129)) 0 (:fv _uniq.1724)) ((:c And) ((:c IsOpen) (:fv _uniq.1129) (:fv _uniq.1135) 0) ((:c Membership.mem) (:fv _uniq.1129) ((:c Set) (:fv _uni... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.1126))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.1129))"},{"name":"f","sexp":"((:c PFun) (:fv _uniq.1126) (:fv _uniq.1129))"},{"name":"hf","sexp":"(:forall x (:fv... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:lambda t :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV1))) (:app (:c And) (:arg :explicit 0 (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 1 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"source":"exact","sourceEnd":2684,"sourceStart":2679,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":2688,"sourceStart":2685,"tag":"atom"},{"children":[{"contextIndex":7,"semanticRole":"local","source":"s","sourceEnd":2689,"sourceStart":2688,"tag":"identifier"},{"source":",","sourceEnd":2690,"sourceS... | [] | [{"source":"⟨s, Set.Subset.refl _, os, ys⟩","source_end":2719,"source_start":2685,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 19 | 37 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0a6386ff329d8d7e38c118ed72b530c0a8240a3359d6c70efa68f8ee7a8e4922 | a47e5b0e6673340b7740d7acee8db6ab80dce8b7fadda114136eaac668a6013d | 415361af549aea798af1e3fad5b4fa7a8ade9e477521e56ccd5d304b396f7955 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,827 | pcontinuous_iff' | Mathlib/Topology/Partial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro h x y h' | case mp
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
⊢ PContinuous f → ∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y) | case mp
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
h : PContinuous f
x : X
y : Y
h' : y ∈ f x
⊢ PTendsto' f (𝓝 x) (𝓝 y) | (:forall _ ((:c PContinuous) (:fv _uniq.1126) (:fv _uniq.1129) (:fv _uniq.1132) (:fv _uniq.1135) (:fv _uniq.1245)) (:forall x (:fv _uniq.1126) (:forall y (:fv _uniq.1129) (:forall h ((:c Membership.mem) (:fv _uniq.1129) ((:c Part) (:fv _uniq.1129)) ((:c Part.instMembership) (:fv _uniq.1129)) 0 ((:fv _uniq.1245) 1)) ((:... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.1126))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.1129))"},{"name":"f","sexp":"((:c PFun) (:fv _uniq.1126) (:fv _uniq.1129))"}] | (:forall _ :explicit (:app (:c PContinuous) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 4 (:fv F... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"source":"intro","sourceEnd":2087,"sourceStart":2082,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":2089,"sourceStart":2088,"tag":"identifier"},{"semanticRole":"scoped_local","source":"x","sourceEnd":2091,"sourceStart":2090,"tag":"identifier"},{"semanticRole":"scoped_lo... | [{"role":"fresh_name","source":"h","source_end":2089,"source_start":2088,"syntax_kind":"ident"},{"role":"fresh_name","source":"x","source_end":2091,"source_start":2090,"syntax_kind":"ident"},{"role":"fresh_name","source":"y","source_end":2093,"source_start":2092,"syntax_kind":"ident"},{"role":"fresh_name","source":"h'"... | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 19 | 9 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f64118676ab5668291bf713335434451ff2ecbfa4a4392cfe9ebd1707bcb51d6 | 33ba64dbd94838acd4d6d29481cacbbad2d0d91af48612521ed79f1eaff1cbd4 | 6a5da843d1fecaf0245ed946c4248a3551be4a7467a756b4a3234def2f0ae38c | b6971efa36b65870ee5adc5bcf3d302b9b361507efe2f954f8805858f596aced |
cat-searcher/leandojo-benchmark-4-random | test | 2,828 | pcontinuous_iff' | Mathlib/Topology/Partial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Filter.ptendsto'_def</a>, <a>mem_nhds_iff</a>] | case mp
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
h : PContinuous f
x : X
y : Y
h' : y ∈ f x
⊢ PTendsto' f (𝓝 x) (𝓝 y) | case mp
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
h : PContinuous f
x : X
y : Y
h' : y ∈ f x
⊢ ∀ (s : Set Y), (∃ t ⊆ s, IsOpen t ∧ y ∈ t) → ∃ t ⊆ f.preimage s, IsOpen t ∧ x ∈ t | ((:c Filter.PTendsto') (:fv _uniq.1126) (:fv _uniq.1129) (:fv _uniq.1245) ((:c nhds) (:fv _uniq.1126) (:fv _uniq.1132) (:fv _uniq.1263)) ((:c nhds) (:fv _uniq.1129) (:fv _uniq.1135) (:fv _uniq.1266))) | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.1126))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.1129))"},{"name":"f","sexp":"((:c PFun) (:fv _uniq.1126) (:fv _uniq.1129))"},{"name":"h","sexp":"((:c PContinuous... | (:app (:c Filter.PTendsto') (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:fv FV5)) (:arg :explicit 3 (:app (:c nhds) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV7)))) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"source":"simp","sourceEnd":2105,"sourceStart":2101,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":2110,"sourceStart":2106,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":2110,"s... | [] | [{"source":"ptendsto'_def","source_end":2125,"source_start":2112,"syntax_kind":"ident"},{"source":"mem_nhds_iff","source_end":2139,"source_start":2127,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 19 | 10 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e7aa4c5633c7f8c10914cefc1c090ac7720acfa47d69f7e932e1ee2e6795a95b | b6971efa36b65870ee5adc5bcf3d302b9b361507efe2f954f8805858f596aced | 40512390495c400ae26b687f7d54119a033ec8ea0ed1794725242126f94a0fe2 | 83675307c55c4cd451a56275d77694a76748ceda9880184b3083cc23ff255ce1 |
cat-searcher/leandojo-benchmark-4-random | test | 2,829 | pcontinuous_iff' | Mathlib/Topology/Partial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro s ⟨t, tsubs, opent, yt⟩ | case mp
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
h : PContinuous f
x : X
y : Y
h' : y ∈ f x
⊢ ∀ (s : Set Y), (∃ t ⊆ s, IsOpen t ∧ y ∈ t) → ∃ t ⊆ f.preimage s, IsOpen t ∧ x ∈ t | case mp.intro.intro.intro
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
h : PContinuous f
x : X
y : Y
h' : y ∈ f x
s t : Set Y
tsubs : t ⊆ s
opent : IsOpen t
yt : y ∈ t
⊢ ∃ t ⊆ f.preimage s, IsOpen t ∧ x ∈ t | (:forall s ((:c Set) (:fv _uniq.1129)) (:forall _ ((:c Exists) ((:c Set) (:fv _uniq.1129)) (:lambda t ((:c Set) (:fv _uniq.1129)) ((:c And) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.1129)) ((:c Set.instHasSubset) (:fv _uniq.1129)) 0 1) ((:c And) ((:c IsOpen) (:fv _uniq.1129) (:fv _uniq.1135) 0) ((:c Membership.mem) (... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.1126))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.1129))"},{"name":"f","sexp":"((:c PFun) (:fv _uniq.1126) (:fv _uniq.1129))"},{"name":"h","sexp":"((:c PContinuous... | (:forall s :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV1))) (:forall _ :explicit (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:lambda t :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV1))) (:app (:c And) (:arg :explicit 0 (:app (:c HasSubset.Subset) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"source":"rintro","sourceEnd":2151,"sourceStart":2145,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"s","sourceEnd":2153,"sourceStart":2152,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"s","sourceEnd":2153,"sourceStart":2152,"tag":"... | [{"role":"fresh_name","source":"s","source_end":2153,"source_start":2152,"syntax_kind":"ident"},{"role":"fresh_name","source":"t","source_end":2158,"source_start":2157,"syntax_kind":"ident"},{"role":"fresh_name","source":"tsubs","source_end":2165,"source_start":2160,"syntax_kind":"ident"},{"role":"fresh_name","source":... | [{"source":"⟨t, tsubs, opent, yt⟩","source_end":2179,"source_start":2154,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 19 | 11 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c808bcdaf8e4e429546a38977e81c066a54644bfed0a8ad97c7b7185140db11b | 83675307c55c4cd451a56275d77694a76748ceda9880184b3083cc23ff255ce1 | fd361904eaf4308549b95a72ccd5d53f1b8f616346f01d10ab6cdb8d581d6782 | a5ce9c7bffda2d85f3052f0c8fff03132ae3b85740ef4096f1c43775cb6d0926 |
cat-searcher/leandojo-benchmark-4-random | test | 2,830 | pcontinuous_iff' | Mathlib/Topology/Partial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨f.preimage t, <a>PFun.preimage_mono</a> _ tsubs, h _ opent, ⟨y, yt, h'⟩⟩ | case mp.intro.intro.intro
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
h : PContinuous f
x : X
y : Y
h' : y ∈ f x
s t : Set Y
tsubs : t ⊆ s
opent : IsOpen t
yt : y ∈ t
⊢ ∃ t ⊆ f.preimage s, IsOpen t ∧ x ∈ t | ((:c Exists) ((:c Set) (:fv _uniq.1126)) (:lambda t ((:c Set) (:fv _uniq.1126)) ((:c And) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.1126)) ((:c Set.instHasSubset) (:fv _uniq.1126)) 0 ((:c PFun.preimage) (:fv _uniq.1126) (:fv _uniq.1129) (:fv _uniq.1245) (:fv _uniq.1562))) ((:c And) ((:c IsOpen) (:fv _uniq.1126) (:fv ... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.1126))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.1129))"},{"name":"f","sexp":"((:c PFun) (:fv _uniq.1126) (:fv _uniq.1129))"},{"name":"h","sexp":"((:c PContinuous... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda t :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c And) (:arg :explicit 0 (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"source":"exact","sourceEnd":2189,"sourceStart":2184,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":2193,"sourceStart":2190,"tag":"atom"},{"children":[{"children":[{"source":"f.preimage","sourceEnd":2203,"sourceStart":2193,"tag":"identifier"},{"children":[{"contextIndex":11,"semanticRole":"local","s... | [] | [{"source":"⟨f.preimage t, PFun.preimage_mono _ tsubs, h _ opent, ⟨y, yt, h'⟩⟩","source_end":2264,"source_start":2190,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 19 | 12 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 34b4e42d8b6dc5f39d76c10277364ffc31a158a799059d5048233893ec7750c9 | a5ce9c7bffda2d85f3052f0c8fff03132ae3b85740ef4096f1c43775cb6d0926 | 978e6cf5847977843e5fd30fd4c13d9e12a8020fd0e4a75854dd2ed63f8d92c5 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,831 | pcontinuous_iff' | Mathlib/Topology/Partial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro s hs | X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
hf : ∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y)
s : Set Y
os : IsOpen s
x : X
y : Y
ys : y ∈ s
fxy : y ∈ f x
t : Set X
h : f.preimage s ⊆ t
⊢ ∀ s ∈ 𝓝 y, f.preimage s ∈ 𝓝 x | X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
hf : ∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y)
s✝ : Set Y
os : IsOpen s✝
x : X
y : Y
ys : y ∈ s✝
fxy : y ∈ f x
t : Set X
h : f.preimage s✝ ⊆ t
s : Set Y
hs : s ∈ 𝓝 y
⊢ f.preimage s ∈ 𝓝 x | (:forall s ((:c Set) (:fv _uniq.1129)) (:forall _ ((:c Membership.mem) ((:c Set) (:fv _uniq.1129)) ((:c Filter) (:fv _uniq.1129)) ((:c instMembershipSetFilter) (:fv _uniq.1129)) 0 ((:c nhds) (:fv _uniq.1129) (:fv _uniq.1135) (:fv _uniq.1769))) ((:c Membership.mem) ((:c Set) (:fv _uniq.1126)) ((:c Filter) (:fv _uniq.112... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.1126))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.1129))"},{"name":"f","sexp":"((:c PFun) (:fv _uniq.1126) (:fv _uniq.1129))"},{"name":"hf","sexp":"(:forall x (:fv... | (:forall s :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV1))) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :implicit-type 1 (:app (:c Filter) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"source":"intro","sourceEnd":2507,"sourceStart":2502,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"s","sourceEnd":2509,"sourceStart":2508,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hs","sourceEnd":2512,"sourceStart":2510,"tag":"identifier"}],"kind":"null","source":"... | [{"role":"fresh_name","source":"s","source_end":2509,"source_start":2508,"syntax_kind":"ident"},{"role":"fresh_name","source":"hs","source_end":2512,"source_start":2510,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 19 | 26 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 163c30c7ccdfc823aa244b2efd2a1c02e827d246553728dd28f008aec24c53f1 | dc9c674cb923ef2871c0e4a50c04642e9c92f5eed7af70ed98edbf4fcf171ba4 | 7efa99c53f9cbe8bb490675f144d09b2569a79e2d9902d691b34e36ba60dcc9b | edb26322723b46f091857bb207c1abf6972ad780121f1b165b9a7d38e839e716 |
cat-searcher/leandojo-benchmark-4-random | test | 2,832 | pcontinuous_iff' | Mathlib/Topology/Partial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : <a>Filter.PTendsto'</a> f (𝓝 x) (𝓝 y) := hf fxy | X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
hf : ∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y)
s✝ : Set Y
os : IsOpen s✝
x : X
y : Y
ys : y ∈ s✝
fxy : y ∈ f x
t : Set X
h : f.preimage s✝ ⊆ t
s : Set Y
hs : s ∈ 𝓝 y
⊢ f.preimage s ∈ 𝓝 x | X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
hf : ∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y)
s✝ : Set Y
os : IsOpen s✝
x : X
y : Y
ys : y ∈ s✝
fxy : y ∈ f x
t : Set X
h : f.preimage s✝ ⊆ t
s : Set Y
hs : s ∈ 𝓝 y
this : PTendsto' f (𝓝 x) (𝓝 y)
⊢ f.preimage s ... | ((:c Membership.mem) ((:c Set) (:fv _uniq.1126)) ((:c Filter) (:fv _uniq.1126)) ((:c instMembershipSetFilter) (:fv _uniq.1126)) ((:c PFun.preimage) (:fv _uniq.1126) (:fv _uniq.1129) (:fv _uniq.1245) (:fv _uniq.2024)) ((:c nhds) (:fv _uniq.1126) (:fv _uniq.1132) (:fv _uniq.1749))) | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.1126))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.1129))"},{"name":"f","sexp":"((:c PFun) (:fv _uniq.1126) (:fv _uniq.1129))"},{"name":"hf","sexp":"(:forall x (:fv... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c Filter) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Filter)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"source":"have","sourceEnd":2521,"sourceStart":2517,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":2522,"sourceStart":2522,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":2522,"sourceStart":2522,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"PTendsto' f (𝓝 x) (𝓝 y)","source_end":2553,"source_start":2524,"syntax_kind":"Lean.Parser.Term.app"},{"source":"hf fxy","source_end":2563,"source_start":2557,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 19 | 27 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7efb5969157765a5849613ad648a20e20296f0436c08518213daa40bab0102ec | edb26322723b46f091857bb207c1abf6972ad780121f1b165b9a7d38e839e716 | 5313a80112256fc8c2646127d4c8076f2439540ee813c9ca78da72207c259823 | 9e3493d85422f3a8db2ab18cda8b78467d27179c40f879e6e3b718243b06299f |
cat-searcher/leandojo-benchmark-4-random | test | 2,833 | pcontinuous_iff' | Mathlib/Topology/Partial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Filter.ptendsto'_def</a>] at this | X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
hf : ∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y)
s✝ : Set Y
os : IsOpen s✝
x : X
y : Y
ys : y ∈ s✝
fxy : y ∈ f x
t : Set X
h : f.preimage s✝ ⊆ t
s : Set Y
hs : s ∈ 𝓝 y
this : PTendsto' f (𝓝 x) (𝓝 y)
⊢ f.preimage s ... | X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
hf : ∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y)
s✝ : Set Y
os : IsOpen s✝
x : X
y : Y
ys : y ∈ s✝
fxy : y ∈ f x
t : Set X
h : f.preimage s✝ ⊆ t
s : Set Y
hs : s ∈ 𝓝 y
this : ∀ s ∈ 𝓝 y, f.preimage s ∈ 𝓝 x
⊢ f.preim... | ((:c Membership.mem) ((:c Set) (:fv _uniq.1126)) ((:c Filter) (:fv _uniq.1126)) ((:c instMembershipSetFilter) (:fv _uniq.1126)) ((:c PFun.preimage) (:fv _uniq.1126) (:fv _uniq.1129) (:fv _uniq.1245) (:fv _uniq.2024)) ((:c nhds) (:fv _uniq.1126) (:fv _uniq.1132) (:fv _uniq.1749))) | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.1126))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.1129))"},{"name":"f","sexp":"((:c PFun) (:fv _uniq.1126) (:fv _uniq.1129))"},{"name":"hf","sexp":"(:forall x (:fv... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c Filter) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Filter)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"source":"rw","sourceEnd":2570,"sourceStart":2568,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2572,"sourceStart":2571,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Filter.ptendsto'_def... | [] | [{"source":"ptendsto'_def","source_end":2585,"source_start":2572,"syntax_kind":"ident"},{"source":"this","source_end":2594,"source_start":2590,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 19 | 28 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1cd7746a25b20635018eae2f701a65d256d5ece145fdc6643a18471e65d42a04 | 9e3493d85422f3a8db2ab18cda8b78467d27179c40f879e6e3b718243b06299f | a4fce440d79ae65ffc5f74e6405bbd1b59f874c0443d48acc3c7dd1ad9b482e6 | 2462d68ead2fe8f7c56b9be66b51dba01af390de33ebc089ef3025cb6e8d6a42 |
cat-searcher/leandojo-benchmark-4-random | test | 2,834 | pcontinuous_iff' | Mathlib/Topology/Partial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact this s hs | X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
f : X →. Y
hf : ∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y)
s✝ : Set Y
os : IsOpen s✝
x : X
y : Y
ys : y ∈ s✝
fxy : y ∈ f x
t : Set X
h : f.preimage s✝ ⊆ t
s : Set Y
hs : s ∈ 𝓝 y
this : ∀ s ∈ 𝓝 y, f.preimage s ∈ 𝓝 x
⊢ f.preim... | ((:c Membership.mem) ((:c Set) (:fv _uniq.1126)) ((:c Filter) (:fv _uniq.1126)) ((:c instMembershipSetFilter) (:fv _uniq.1126)) ((:c PFun.preimage) (:fv _uniq.1126) (:fv _uniq.1129) (:fv _uniq.1245) (:fv _uniq.2024)) ((:c nhds) (:fv _uniq.1126) (:fv _uniq.1132) (:fv _uniq.1749))) | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.1126))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.1129))"},{"name":"f","sexp":"((:c PFun) (:fv _uniq.1126) (:fv _uniq.1129))"},{"name":"hf","sexp":"(:forall x (:fv... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c Filter) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Filter)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"source":"exact","sourceEnd":2604,"sourceStart":2599,"tag":"atom"},{"children":[{"contextIndex":17,"semanticRole":"local","source":"this","sourceEnd":2609,"sourceStart":2605,"tag":"identifier"},{"children":[{"contextIndex":15,"semanticRole":"local","source":"s","sourceEnd":2611,"sourceStart":2610,"tag":"i... | [] | [{"source":"this s hs","source_end":2614,"source_start":2605,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1126","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1129","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 19 | 31 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 42b08dccb352c9ced10b9b4d9deee7e530e604838abaa37623828ce0d1c8c6fd | 2462d68ead2fe8f7c56b9be66b51dba01af390de33ebc089ef3025cb6e8d6a42 | dd683d0065d82c6f16c9b5c0c844aee6330e127cb59bc4d839eeb011088b213e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,835 | Matrix.det_nonsing_inv_mul_det | Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Matrix.det_mul</a>, A.nonsing_inv_mul h, <a>Matrix.det_one</a>] | l : Type u_1
m : Type u
n : Type u'
α : Type v
inst✝² : Fintype n
inst✝¹ : DecidableEq n
inst✝ : CommRing α
A B : Matrix n n α
h : IsUnit A.det
⊢ A⁻¹.det * A.det = 1 | ((:c Eq) (:fv _uniq.174150) ((:c HMul.hMul) (:fv _uniq.174150) (:fv _uniq.174150) (:fv _uniq.174150) ((:c instHMul) (:fv _uniq.174150) ((:c NonUnitalNonAssocRing.toMul) (:fv _uniq.174150) ((:c NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing) (:fv _uniq.174150) ((:c NonUnitalCommRing.toNonUnitalNonAssocCommRing) (:fv ... | [{"name":"l","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:sort (+ u 1))"},{"name":"n","sexp":"(:sort (+ u' 1))"},{"name":"α","sexp":"(:sort (+ v 1))"},{"name":"inst✝²","sexp":"((:c Fintype) (:fv _uniq.174148))"},{"name":"inst✝¹","sexp":"((:c DecidableEq) (:fv _uniq.174148))"},{"name":"inst✝","sexp":"((:c CommRing)... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:fv FV3)) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.174144","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.174146","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":20488,"sourceStart":20486,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":20490,"sourceStart":20489,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"... | [] | [{"source":"det_mul","source_end":20501,"source_start":20494,"syntax_kind":"ident"},{"source":"A.nonsing_inv_mul h","source_end":20522,"source_start":20503,"syntax_kind":"Lean.Parser.Term.app"},{"source":"det_one","source_end":20531,"source_start":20524,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.174144","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.174146","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 146 | 2 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ce6a722c2dbdd20bf795b0159016af44e1f107abe107ee84ce2b3bd1ae698fac | cd1676257eb972ee05e6586cec6765d2d7d9913ffcc58fdd5a872ecefa7052c3 | 0855caeb6bcbcfca487835b0846db5a5c9812b851152790a449e190111d1a641 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,836 | Filter.Tendsto.uniformContinuous_of_uniformEquicontinuous | Mathlib/Topology/UniformSpace/Equicontinuity.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>uniformContinuousOn_univ</a>, ← <a>uniformEquicontinuousOn_univ</a>, <a>tendsto_pi_nhds</a>] at * | ι : Type u_1
κ : Type u_2
X : Type u_3
X' : Type u_4
Y : Type u_5
Z : Type u_6
α : Type u_7
α' : Type u_8
β : Type u_9
β' : Type u_10
γ : Type u_11
𝓕 : Type u_12
tX : TopologicalSpace X
tY : TopologicalSpace Y
tZ : TopologicalSpace Z
uα : UniformSpace α
uβ : UniformSpace β
uγ : UniformSpace γ
l : Filter ι
inst✝ : l.Ne... | ι : Type u_1
κ : Type u_2
X : Type u_3
X' : Type u_4
Y : Type u_5
Z : Type u_6
α : Type u_7
α' : Type u_8
β : Type u_9
β' : Type u_10
γ : Type u_11
𝓕 : Type u_12
tX : TopologicalSpace X
tY : TopologicalSpace Y
tZ : TopologicalSpace Z
uα : UniformSpace α
uβ : UniformSpace β
uγ : UniformSpace γ
l : Filter ι
inst✝ : l.Ne... | ((:c UniformContinuous) (:fv _uniq.125266) (:fv _uniq.125260) (:fv _uniq.125290) (:fv _uniq.125287) (:fv _uniq.125517)) | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"κ","sexp":"(:sort (+ u_2 1))"},{"name":"X","sexp":"(:sort (+ u_3 1))"},{"name":"X'","sexp":"(:sort (+ u_4 1))"},{"name":"Y","sexp":"(:sort (+ u_5 1))"},{"name":"Z","sexp":"(:sort (+ u_6 1))"},{"name":"α","sexp":"(:sort (+ u_7 1))"},{"name":"α'","sexp":"(:sort (+ u_8 1))... | (:app (:c UniformContinuous) (:arg :implicit-type 0 (:fv FV8)) (:arg :implicit-type 1 (:fv FV6)) (:arg :instance 2 (:instance-of (:app (:c UniformSpace) (:arg :explicit 0 (:fv FV8))))) (:arg :instance 3 (:instance-of (:app (:c UniformSpace) (:arg :explicit 0 (:fv FV6))))) (:arg :explicit 4 (:fv FV22))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125242","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.125245","is_instance":false,"is_let":false,"name":"κ","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":58653,"sourceStart":58651,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":58655,"sourceStart":58654,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":58658,"sourceSt... | [] | [{"source":"uniformContinuousOn_univ","source_end":58683,"source_start":58659,"syntax_kind":"ident"},{"source":"uniformEquicontinuousOn_univ","source_end":58717,"source_start":58689,"syntax_kind":"ident"},{"source":"tendsto_pi_nhds","source_end":58734,"source_start":58719,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125242","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.125245","is_instance":false,"is_let":false,"user_name":"κ"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 182 | 4 | exact | true | 1 | 24 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9ea33af50c8f4ea549b706033f65d4c085fe432e156f5ec5ad4713066e05ae04 | 77f8d509070d93855d60e63a91cf45b5604a30f71d878723f30a299f67aa8fd4 | d9b4bc60ecfc974cfb4ea156b9e3538509d9697b08745a860a4c9ea5942990f6 | 94e215818fde2e325af6be15ac28dc08e488f49940e3bf142fd03bbfeebfd38a |
cat-searcher/leandojo-benchmark-4-random | test | 2,837 | Filter.Tendsto.uniformContinuous_of_uniformEquicontinuous | Mathlib/Topology/UniformSpace/Equicontinuity.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Filter.Tendsto.uniformContinuousOn_of_uniformEquicontinuousOn</a> (fun x _ ↦ h₁ x) h₂ | ι : Type u_1
κ : Type u_2
X : Type u_3
X' : Type u_4
Y : Type u_5
Z : Type u_6
α : Type u_7
α' : Type u_8
β : Type u_9
β' : Type u_10
γ : Type u_11
𝓕 : Type u_12
tX : TopologicalSpace X
tY : TopologicalSpace Y
tZ : TopologicalSpace Z
uα : UniformSpace α
uβ : UniformSpace β
uγ : UniformSpace γ
l : Filter ι
inst✝ : l.Ne... | ((:c UniformContinuousOn) (:fv _uniq.125266) (:fv _uniq.125260) (:fv _uniq.125290) (:fv _uniq.125287) (:fv _uniq.125517) ((:c Set.univ) (:fv _uniq.125266))) | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"κ","sexp":"(:sort (+ u_2 1))"},{"name":"X","sexp":"(:sort (+ u_3 1))"},{"name":"X'","sexp":"(:sort (+ u_4 1))"},{"name":"Y","sexp":"(:sort (+ u_5 1))"},{"name":"Z","sexp":"(:sort (+ u_6 1))"},{"name":"α","sexp":"(:sort (+ u_7 1))"},{"name":"α'","sexp":"(:sort (+ u_8 1))... | (:app (:c UniformContinuousOn) (:arg :implicit-type 0 (:fv FV8)) (:arg :implicit-type 1 (:fv FV6)) (:arg :instance 2 (:instance-of (:app (:c UniformSpace) (:arg :explicit 0 (:fv FV8))))) (:arg :instance 3 (:instance-of (:app (:c UniformSpace) (:arg :explicit 0 (:fv FV6))))) (:arg :explicit 4 (:fv FV22)) (:arg :explicit... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125242","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.125245","is_instance":false,"is_let":false,"name":"κ","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":58748,"sourceStart":58743,"tag":"atom"},{"children":[{"name":"Filter.Tendsto.uniformContinuousOn_of_uniformEquicontinuousOn","semanticRole":"global","source":"uniformContinuousOn_of_uniformEquicontinuousOn","sourceEnd":58795,"sourceStart":58749,"tag":"identifier"},{"children":... | [] | [{"source":"uniformContinuousOn_of_uniformEquicontinuousOn (fun x _ ↦ h₁ x) h₂","source_end":58821,"source_start":58749,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.125242","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.125245","is_instance":false,"is_let":false,"user_name":"κ"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 182 | 9 | exact | true | 1 | 24 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2eb3ef90a27af3ddcf943a16bbd30920d8003211eb490b0b6ee5588147dca79c | 94e215818fde2e325af6be15ac28dc08e488f49940e3bf142fd03bbfeebfd38a | d318f96433519068fcc769ad6217d4c31a1fe4573a8a9119e5cf840a5b8aa731 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,838 | List.range_eq_range' | .lake/packages/batteries/Batteries/Data/List/Lemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Nat.zero_add</a>] | n : Nat
⊢ range' 0 (0 + n) = range' 0 n | ((:c Eq) ((:c List) (:c Nat)) ((:c List.range') ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))) (:fv _uniq.181038)) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ... | [{"name":"n","sexp":"(:c Nat)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:c Nat)))) (:arg :explicit 1 (:app (:c List.range') (:arg :explicit 0 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.181038","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"}] | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":58505,"sourceStart":58503,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":58507,"sourceStart":58506,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"Nat.zero_add","source_end":58519,"source_start":58507,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.181038","is_instance":false,"is_let":false,"user_name":"n"}] | 343 | 2 | exact | true | 1 | 1 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6990bbe5566435f294b72e69614003787580c245083cc8b4b86a6c182c00942b | 30953c547cdfbd437ac64d999278d3bff165e81a2b4a663d9c384b76d42ba510 | 327c266eb4ef6c19085249c1f1ac847909a7195dbd2835b422e88e03e8bc35ac | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,839 | List.mem_mem_ranges_iff_lt_natSum | Mathlib/Data/List/Range.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>List.mem_range</a>, ← <a>List.ranges_join'</a>, <a>List.mem_join</a>] | α : Type u
l : List ℕ
n : ℕ
⊢ (∃ s ∈ l.ranges, n ∈ s) ↔ n < Nat.sum l | ((:c Iff) ((:c Exists) ((:c List) (:c Nat)) (:lambda s ((:c List) (:c Nat)) ((:c And) ((:c Membership.mem) ((:c List) (:c Nat)) ((:c List) ((:c List) (:c Nat))) ((:c List.instMembership) ((:c List) (:c Nat))) 0 ((:c List.ranges) (:fv _uniq.13703))) ((:c Membership.mem) (:c Nat) ((:c List) (:c Nat)) ((:c List.instMember... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"l","sexp":"((:c List) (:c Nat))"},{"name":"n","sexp":"(:c Nat)"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Exists) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:c Nat)))) (:arg :explicit 1 (:lambda s :explicit (:app (:c List) (:arg :explicit 0 (:c Nat))) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.13653","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.13703","is_instance":false,"is_let":false,"name":"l","sexp":"(:app (:c List) (:arg :explicit 0 (:c Nat)))"}... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":10622,"sourceStart":10620,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10624,"sourceStart":10623,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"... | [] | [{"source":"mem_range","source_end":10637,"source_start":10628,"syntax_kind":"ident"},{"source":"ranges_join'","source_end":10655,"source_start":10643,"syntax_kind":"ident"},{"source":"mem_join","source_end":10665,"source_start":10657,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.13653","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.13703","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 101 | 2 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9ebd283f8c40aae23a0dfecc5af74d00af615f209accd7e58b258a6d29b48cc8 | 37c4e6df0678c7452faaea0278756de6af3eb4b51afbcf4b9c6f80713dbfe4fa | e4e45d964c5eb5e294b200b62ed79ed955676c0c8f47c4d984e7003b423ed089 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,840 | Ordinal.fp_family_unbounded | Mathlib/SetTheory/Ordinal/FixedPoint.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← hi, <a>Function.mem_fixedPoints_iff</a>] | ι : Type u
f : ι → Ordinal.{max u v} → Ordinal.{max u v}
H : ∀ (i : ι), IsNormal (f i)
a : Ordinal.{max u v}
s : Set Ordinal.{max u v}
x✝ : s ∈ Set.range fun i => fixedPoints (f i)
i : ι
hi : (fun i => fixedPoints (f i)) i = s
⊢ nfpFamily f a ∈ s | ι : Type u
f : ι → Ordinal.{max u v} → Ordinal.{max u v}
H : ∀ (i : ι), IsNormal (f i)
a : Ordinal.{max u v}
s : Set Ordinal.{max u v}
x✝ : s ∈ Set.range fun i => fixedPoints (f i)
i : ι
hi : (fun i => fixedPoints (f i)) i = s
⊢ f i (nfpFamily f a) = nfpFamily f a | ((:c Membership.mem) (:c Ordinal) ((:c Set) (:c Ordinal)) ((:c Set.instMembership) (:c Ordinal)) ((:c Ordinal.nfpFamily) (:fv _uniq.4577) (:fv _uniq.4583) (:fv _uniq.4747)) (:fv _uniq.4777)) | [{"name":"ι","sexp":"(:sort (+ u 1))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.4577) (:forall _ (:c Ordinal) (:c Ordinal)))"},{"name":"H","sexp":"(:forall i (:fv _uniq.4577) ((:c Ordinal.IsNormal) ((:fv _uniq.4583) 0)))"},{"name":"a","sexp":"(:c Ordinal)"},{"name":"s","sexp":"((:c Set) (:c Ordinal))"},{"name":"x✝","s... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Ordinal)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:c Ordinal)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c Ordinal)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:c Ordinal))))))) (:arg :explicit 3 (:app (:c O... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4577","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.4583","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:fv FV0) (:forall _ :expli... | {"children":[{"source":"rw","sourceEnd":6272,"sourceStart":6270,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6274,"sourceStart":6273,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":6277,"sourceStart":... | [] | [{"source":"hi","source_end":6280,"source_start":6278,"syntax_kind":"ident"},{"source":"mem_fixedPoints_iff","source_end":6301,"source_start":6282,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4577","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.4583","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq... | 39 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 51e48588ebde5534c46fb5cadc5c939ad9b218e67d22d91cac1d6658ddd04572 | c5439657fb303b6eb94279acfdc70ca96d840f794d492c88c740727b5571b9cd | f4710d480e3ee95e5e90c4975f87c5f07e6cb91da58de370a97704d0c0f850fe | a6c03841ab91c502339720b75d9b5d8183b86b721ba4a6a73dc438f4b3d0c40d |
cat-searcher/leandojo-benchmark-4-random | test | 2,841 | Ordinal.fp_family_unbounded | Mathlib/SetTheory/Ordinal/FixedPoint.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Ordinal.nfpFamily_fp</a>.{u, v} (H i) a | ι : Type u
f : ι → Ordinal.{max u v} → Ordinal.{max u v}
H : ∀ (i : ι), IsNormal (f i)
a : Ordinal.{max u v}
s : Set Ordinal.{max u v}
x✝ : s ∈ Set.range fun i => fixedPoints (f i)
i : ι
hi : (fun i => fixedPoints (f i)) i = s
⊢ f i (nfpFamily f a) = nfpFamily f a | ((:c Eq) (:c Ordinal) ((:fv _uniq.4583) (:fv _uniq.4811) ((:c Ordinal.nfpFamily) (:fv _uniq.4577) (:fv _uniq.4583) (:fv _uniq.4747))) ((:c Ordinal.nfpFamily) (:fv _uniq.4577) (:fv _uniq.4583) (:fv _uniq.4747))) | [{"name":"ι","sexp":"(:sort (+ u 1))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.4577) (:forall _ (:c Ordinal) (:c Ordinal)))"},{"name":"H","sexp":"(:forall i (:fv _uniq.4577) ((:c Ordinal.IsNormal) ((:fv _uniq.4583) 0)))"},{"name":"a","sexp":"(:c Ordinal)"},{"name":"s","sexp":"((:c Set) (:c Ordinal))"},{"name":"x✝","s... | (:app (:c Eq) (:arg :implicit-type 0 (:c Ordinal)) (:arg :explicit 1 (:app (:fv FV1) (:arg :explicit 0 (:fv FV7)) (:arg :explicit 1 (:app (:c Ordinal.nfpFamily) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV4)))))) (:arg :explicit 2 (:app (:c Ordinal.nfpFamily) (:arg :implicit-... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4577","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.4583","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:fv FV0) (:forall _ :expli... | {"children":[{"source":"exact","sourceEnd":6312,"sourceStart":6307,"tag":"atom"},{"children":[{"children":[{"name":"Ordinal.nfpFamily_fp","semanticRole":"global","source":"nfpFamily_fp","sourceEnd":6325,"sourceStart":6313,"tag":"identifier"},{"source":".{","sourceEnd":6327,"sourceStart":6325,"tag":"atom"},{"children":[... | [] | [{"source":"nfpFamily_fp.{u, v} (H i) a","source_end":6340,"source_start":6313,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4577","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.4583","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq... | 39 | 8 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 91b25dbb06263e0d59646f046b6ea543a3892738a50e7a58a67e99a3b1a1b4b0 | a6c03841ab91c502339720b75d9b5d8183b86b721ba4a6a73dc438f4b3d0c40d | 8d2bdec4e940a6052657983671e217edefef9957d61076603b8a26db4d5a67d2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,842 | Field.primitive_element_inf_aux_of_finite_intermediateField | Mathlib/FieldTheory/PrimitiveElement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let f : F → <a>IntermediateField</a> F E := fun x ↦ F⟮α + x • β⟯ | F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
⊢ ∃ γ, F⟮α, β⟯ = F⟮γ⟯ | F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
⊢ ∃ γ, F⟮α, β⟯ = F⟮γ⟯ | ((:c Exists) (:fv _uniq.37059) (:lambda γ (:fv _uniq.37059) ((:c Eq) ((:c IntermediateField) (:fv _uniq.37050) (:fv _uniq.37059) (:fv _uniq.37053) (:fv _uniq.37062) (:fv _uniq.37247)) ((:c IntermediateField.adjoin) (:fv _uniq.37050) (:fv _uniq.37053) (:fv _uniq.37059) (:fv _uniq.37062) (:fv _uniq.37247) ((:c Insert.ins... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.37050))"},{"name":"inst✝³","sexp":"((:c Infinite) (:fv _uniq.37050))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.37059))"},{"name":"ϕ","sexp":"((:c RingHom) (:fv _uniq.37050) (:fv _uniq... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda γ :explicit (:fv FV3) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c IntermediateField) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :instance 2 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV0))))) (:arg :instanc... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"let","sourceEnd":8275,"sourceStart":8272,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"f","sourceEnd":8277,"sourceStart":8276,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":":","sourceEnd":8279,"so... | [] | [{"source":"F → IntermediateField F E","source_end":8307,"source_start":8280,"syntax_kind":"Lean.Parser.Term.arrow"},{"source":"fun x ↦ F⟮α + x • β⟯","source_end":8341,"source_start":8311,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":instance-implicit","context_index":... | 23 | 4 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 60deed1b3c1eeda4bbc9e9db3aea14e8932b06a865b66c0e3ada72a7c3868025 | 4717ecfbcfd28804364ad30b5137d30f56f862159d1ece13c800b3b7f171f05f | e321415a4c4a238caec2fda09e45d1583f042038723a16ccbe5977b23012b3b3 | 433945bafef3f4dfe4120980f162c4e2acd2e3e434598db191ad387f1cc554b2 |
cat-searcher/leandojo-benchmark-4-random | test | 2,843 | Field.primitive_element_inf_aux_of_finite_intermediateField | Mathlib/FieldTheory/PrimitiveElement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨x, y, hneq, heq⟩ := <a>Finite.exists_ne_map_eq_of_infinite</a> f | F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
⊢ ∃ γ, F⟮α, β⟯ = F⟮γ⟯ | case intro.intro.intro
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : x ≠ y
heq : f x = f y
⊢ ∃ γ, F⟮α, β⟯ = F⟮γ⟯ | ((:c Exists) (:fv _uniq.37059) (:lambda γ (:fv _uniq.37059) ((:c Eq) ((:c IntermediateField) (:fv _uniq.37050) (:fv _uniq.37059) (:fv _uniq.37053) (:fv _uniq.37062) (:fv _uniq.37247)) ((:c IntermediateField.adjoin) (:fv _uniq.37050) (:fv _uniq.37053) (:fv _uniq.37059) (:fv _uniq.37062) (:fv _uniq.37247) ((:c Insert.ins... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.37050))"},{"name":"inst✝³","sexp":"((:c Infinite) (:fv _uniq.37050))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.37059))"},{"name":"ϕ","sexp":"((:c RingHom) (:fv _uniq.37050) (:fv _uniq... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda γ :explicit (:fv FV3) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c IntermediateField) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :instance 2 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV0))))) (:arg :instanc... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"obtain","sourceEnd":8350,"sourceStart":8344,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":8354,"sourceStart":8351,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":8... | [] | [{"source":"Finite.exists_ne_map_eq_of_infinite f","source_end":8413,"source_start":8376,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨x, y, hneq, heq⟩","source_end":8372,"source_start":8351,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":instance-implicit","context_index":... | 23 | 5 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1e31214bde0afc9836e0ea8dc7322d3baaa6970d90f1032cc87fe86eb3f729af | 433945bafef3f4dfe4120980f162c4e2acd2e3e434598db191ad387f1cc554b2 | d0dfa08f4db25e04be0353e0796192384dcec465a65cddd0ef1ed70f43aa7f78 | acf8f2246a75de6873a9fd9e51575379b295145561e372f87e2bee5cabcae9ef |
cat-searcher/leandojo-benchmark-4-random | test | 2,844 | Field.primitive_element_inf_aux_of_finite_intermediateField | Mathlib/FieldTheory/PrimitiveElement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | use α + x • β | case intro.intro.intro
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : x ≠ y
heq : f x = f y
⊢ ∃ γ, F⟮α, β⟯ = F⟮γ⟯ | case h
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : x ≠ y
heq : f x = f y
⊢ F⟮α, β⟯ = F⟮α + x • β⟯ | ((:c Exists) (:fv _uniq.37059) (:lambda γ (:fv _uniq.37059) ((:c Eq) ((:c IntermediateField) (:fv _uniq.37050) (:fv _uniq.37059) (:fv _uniq.37053) (:fv _uniq.37062) (:fv _uniq.37247)) ((:c IntermediateField.adjoin) (:fv _uniq.37050) (:fv _uniq.37053) (:fv _uniq.37059) (:fv _uniq.37062) (:fv _uniq.37247) ((:c Insert.ins... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.37050))"},{"name":"inst✝³","sexp":"((:c Infinite) (:fv _uniq.37050))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.37059))"},{"name":"ϕ","sexp":"((:c RingHom) (:fv _uniq.37050) (:fv _uniq... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda γ :explicit (:fv FV3) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c IntermediateField) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :instance 2 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV0))))) (:arg :instanc... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"use","sourceEnd":8419,"sourceStart":8416,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"children":[{"contextIndex":6,"semanticRole":"local","source":"α","sourceEnd":8422,"sourceStart":8420,"tag":"identif... | [] | [{"source":"α + x • β","source_end":8433,"source_start":8420,"syntax_kind":"«term_+_»"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":instance-implicit","context_index":... | 23 | 6 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 263eeaf598d6730a22dfe15374c19862c84ec73fb79e8f12697d605ebd4543bd | acf8f2246a75de6873a9fd9e51575379b295145561e372f87e2bee5cabcae9ef | d531605b50c845d31ce45b2843b206927259f4115bb8997959b893c04ab5c7c2 | 58b2d527e98df07e18e7a24724d085f2ab19ce55db3b4f0e87260a1c077a7aac |
cat-searcher/leandojo-benchmark-4-random | test | 2,845 | Field.primitive_element_inf_aux_of_finite_intermediateField | Mathlib/FieldTheory/PrimitiveElement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>le_antisymm</a> | case h
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : x ≠ y
heq : f x = f y
⊢ F⟮α, β⟯ = F⟮α + x • β⟯ | case h.a
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : x ≠ y
heq : f x = f y
⊢ F⟮α, β⟯ ≤ F⟮α + x • β⟯
case h.a
F : Type u_1
inst✝⁴ : Fie... | ((:c Eq) ((:c IntermediateField) (:fv _uniq.37050) (:fv _uniq.37059) (:fv _uniq.37053) (:fv _uniq.37062) (:fv _uniq.37247)) ((:c IntermediateField.adjoin) (:fv _uniq.37050) (:fv _uniq.37053) (:fv _uniq.37059) (:fv _uniq.37062) (:fv _uniq.37247) ((:c Insert.insert) (:fv _uniq.37059) ((:c Set) (:fv _uniq.37059)) ((:c Set... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.37050))"},{"name":"inst✝³","sexp":"((:c Infinite) (:fv _uniq.37050))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.37059))"},{"name":"ϕ","sexp":"((:c RingHom) (:fv _uniq.37050) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c IntermediateField) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :instance 2 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV3))))) (:arg :instance 4 (:instance-of (:... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"apply","sourceEnd":8441,"sourceStart":8436,"tag":"atom"},{"name":"le_antisymm","semanticRole":"global","source":"le_antisymm","sourceEnd":8453,"sourceStart":8442,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply le_antisymm","sourceEnd":8453,"sourceStart":8436,"tag":"node"} | [] | [{"source":"le_antisymm","source_end":8453,"source_start":8442,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":instance-implicit","context_index":... | 23 | 7 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a6e5a458629fb2af81ab88aaf6c0a1f46522b745c0023376343f73a8a78be17f | 58b2d527e98df07e18e7a24724d085f2ab19ce55db3b4f0e87260a1c077a7aac | 0abfddcb77ef175f592e63086534058d51fe8d6b63ac2fff9f69f045bc0962dc | 69b6e4f552561bdcc1c752fbaa5ffe8448e3cc2b4d62089d3a06e677182e99af |
cat-searcher/leandojo-benchmark-4-random | test | 2,846 | Field.primitive_element_inf_aux_of_finite_intermediateField | Mathlib/FieldTheory/PrimitiveElement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>IntermediateField.adjoin_le_iff</a>] | case h.a
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : x ≠ y
heq : f x = f y
⊢ F⟮α, β⟯ ≤ F⟮α + x • β⟯ | case h.a
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : x ≠ y
heq : f x = f y
⊢ {α, β} ≤ ↑F⟮α + x • β⟯ | ((:c LE.le) ((:c IntermediateField) (:fv _uniq.37050) (:fv _uniq.37059) (:fv _uniq.37053) (:fv _uniq.37062) (:fv _uniq.37247)) ((:c Preorder.toLE) ((:c IntermediateField) (:fv _uniq.37050) (:fv _uniq.37059) (:fv _uniq.37053) (:fv _uniq.37062) (:fv _uniq.37247)) ((:c PartialOrder.toPreorder) ((:c IntermediateField) (:fv... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.37050))"},{"name":"inst✝³","sexp":"((:c Infinite) (:fv _uniq.37050))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.37059))"},{"name":"ϕ","sexp":"((:c RingHom) (:fv _uniq.37050) (:fv _uniq... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c IntermediateField) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :instance 2 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV3))))) (:arg :instance 4 (:instance-of... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"rw","sourceEnd":8461,"sourceStart":8459,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8463,"sourceStart":8462,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"IntermediateField.ad... | [] | [{"source":"adjoin_le_iff","source_end":8476,"source_start":8463,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":instance-implicit","context_index":... | 23 | 12 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ad13255e51566868b0fbb50a25c67c3157f3aee89cb2effb49386bd90d4c784e | 5ef5eaf4fb2385ce3f66bbb1b2295bef0fea94df06ca439dbdc776f6841ee65c | e7037aa618476618101285eea174033aa91c82dbfb7570920064899940e8a68d | f2d5d065428c8155a7ef06bff924f23786d68020d8e8be7ab4801a9a1e7a1518 |
cat-searcher/leandojo-benchmark-4-random | test | 2,847 | Field.primitive_element_inf_aux_of_finite_intermediateField | Mathlib/FieldTheory/PrimitiveElement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have αxβ_in_K : α + x • β ∈ F⟮α + x • β⟯ := <a>IntermediateField.mem_adjoin_simple_self</a> F _ | case h.a
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : x ≠ y
heq : f x = f y
⊢ {α, β} ≤ ↑F⟮α + x • β⟯ | case h.a
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : x ≠ y
heq : f x = f y
αxβ_in_K : α + x • β ∈ F⟮α + x • β⟯
⊢ {α, β} ≤ ↑F⟮α + x • β... | ((:c LE.le) ((:c Set) (:fv _uniq.37059)) ((:c Set.instLE) (:fv _uniq.37059)) ((:c Insert.insert) (:fv _uniq.37059) ((:c Set) (:fv _uniq.37059)) ((:c Set.instInsert) (:fv _uniq.37059)) (:fv _uniq.37178) ((:c Singleton.singleton) (:fv _uniq.37059) ((:c Set) (:fv _uniq.37059)) ((:c Set.instSingletonSet) (:fv _uniq.37059))... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.37050))"},{"name":"inst✝³","sexp":"((:c Infinite) (:fv _uniq.37050))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.37059))"},{"name":"ϕ","sexp":"((:c RingHom) (:fv _uniq.37050) (:fv _uniq... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV3)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV3))))))) (:arg :explicit 2 (:app (:c Insert.insert) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c Set) (:arg ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"have","sourceEnd":8486,"sourceStart":8482,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"αxβ_in_K","sourceEnd":8497,"sourceStart":8487,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"αxβ_in_K","sourceEnd":8497,"sourceStart":8487,"tag... | [] | [{"source":"α + x • β ∈ F⟮α + x • β⟯","source_end":8538,"source_start":8500,"syntax_kind":"«term_∈_»"},{"source":"mem_adjoin_simple_self F _","source_end":8568,"source_start":8542,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":instance-implicit","context_index":... | 23 | 15 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 72c8aa1eddde8cca1440842b3e534ea9d470eb140a1d11af775695c19d3ba1cb | f2d5d065428c8155a7ef06bff924f23786d68020d8e8be7ab4801a9a1e7a1518 | 2d7db15b06a1a0124713452455b238a905994c16521d272b74213c37ff853e18 | b4826f4879f5b0eedbf36f1ed73a71f18ae848ece9dddf8d3ae91ce93abff58a |
cat-searcher/leandojo-benchmark-4-random | test | 2,848 | Field.primitive_element_inf_aux_of_finite_intermediateField | Mathlib/FieldTheory/PrimitiveElement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have αyβ_in_K : α + y • β ∈ F⟮α + y • β⟯ := <a>IntermediateField.mem_adjoin_simple_self</a> F _ | case h.a
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : x ≠ y
heq : f x = f y
αxβ_in_K : α + x • β ∈ F⟮α + x • β⟯
⊢ {α, β} ≤ ↑F⟮α + x • β... | case h.a
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : x ≠ y
heq : f x = f y
αxβ_in_K : α + x • β ∈ F⟮α + x • β⟯
αyβ_in_K : α + y • β ∈ ... | ((:c LE.le) ((:c Set) (:fv _uniq.37059)) ((:c Set.instLE) (:fv _uniq.37059)) ((:c Insert.insert) (:fv _uniq.37059) ((:c Set) (:fv _uniq.37059)) ((:c Set.instInsert) (:fv _uniq.37059)) (:fv _uniq.37178) ((:c Singleton.singleton) (:fv _uniq.37059) ((:c Set) (:fv _uniq.37059)) ((:c Set.instSingletonSet) (:fv _uniq.37059))... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.37050))"},{"name":"inst✝³","sexp":"((:c Infinite) (:fv _uniq.37050))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.37059))"},{"name":"ϕ","sexp":"((:c RingHom) (:fv _uniq.37050) (:fv _uniq... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV3)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV3))))))) (:arg :explicit 2 (:app (:c Insert.insert) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c Set) (:arg ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"have","sourceEnd":8577,"sourceStart":8573,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"αyβ_in_K","sourceEnd":8588,"sourceStart":8578,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"αyβ_in_K","sourceEnd":8588,"sourceStart":8578,"tag... | [] | [{"source":"α + y • β ∈ F⟮α + y • β⟯","source_end":8629,"source_start":8591,"syntax_kind":"«term_∈_»"},{"source":"mem_adjoin_simple_self F _","source_end":8659,"source_start":8633,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":instance-implicit","context_index":... | 23 | 16 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cfdfd6788eb65d57f3c32941d3b364e77c3bb4f77eed0e30f1b8e1de3dc55bc9 | b4826f4879f5b0eedbf36f1ed73a71f18ae848ece9dddf8d3ae91ce93abff58a | f73ef1926994626bb47d092d2fbe9b5c41950b9b36f35f6720c0d4b2a3c66c24 | 54b6d28643e9b8a15fcc9521c8db2a7228d4a5eb6d9413c96c2fa83b56c7de81 |
cat-searcher/leandojo-benchmark-4-random | test | 2,849 | Field.primitive_element_inf_aux_of_finite_intermediateField | Mathlib/FieldTheory/PrimitiveElement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp [f] at * | case h.a
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : x ≠ y
heq : f x = f y
αxβ_in_K : α + x • β ∈ F⟮α + x • β⟯
αyβ_in_K : α + y • β ∈ ... | case h.a
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : ¬x = y
heq : F⟮α + x • β⟯ = F⟮α + y • β⟯
αxβ_in_K : α + x • β ∈ F⟮α + x • β⟯
αyβ_... | ((:c LE.le) ((:c Set) (:fv _uniq.37059)) ((:c Set.instLE) (:fv _uniq.37059)) ((:c Insert.insert) (:fv _uniq.37059) ((:c Set) (:fv _uniq.37059)) ((:c Set.instInsert) (:fv _uniq.37059)) (:fv _uniq.37178) ((:c Singleton.singleton) (:fv _uniq.37059) ((:c Set) (:fv _uniq.37059)) ((:c Set.instSingletonSet) (:fv _uniq.37059))... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.37050))"},{"name":"inst✝³","sexp":"((:c Infinite) (:fv _uniq.37050))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.37059))"},{"name":"ϕ","sexp":"((:c RingHom) (:fv _uniq.37050) (:fv _uniq... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV3)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV3))))))) (:arg :explicit 2 (:app (:c Insert.insert) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c Set) (:arg ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"dsimp","sourceEnd":8669,"sourceStart":8664,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8671,"sourceStart":8670,"tag":"atom... | [] | [{"source":"f","source_end":8672,"source_start":8671,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":instance-implicit","context_index":... | 23 | 17 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 30b274e4a54f70398dad23d86778f55522acc1146b35d145c8e8a5732d1a6e01 | 54b6d28643e9b8a15fcc9521c8db2a7228d4a5eb6d9413c96c2fa83b56c7de81 | e8c6d5b68258a2403e1f8fc27ecad756fd53d54d8f1ff4acff1385b0874ec2f0 | 181ffc2c5ba50f7da671a40665f20398508df6201121bb643a80198775018a14 |
cat-searcher/leandojo-benchmark-4-random | test | 2,850 | Field.primitive_element_inf_aux_of_finite_intermediateField | Mathlib/FieldTheory/PrimitiveElement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [← heq] at αyβ_in_K | case h.a
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : ¬x = y
heq : F⟮α + x • β⟯ = F⟮α + y • β⟯
αxβ_in_K : α + x • β ∈ F⟮α + x • β⟯
αyβ_... | case h.a
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : ¬x = y
heq : F⟮α + x • β⟯ = F⟮α + y • β⟯
αxβ_in_K : α + x • β ∈ F⟮α + x • β⟯
αyβ_... | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.37059)) ((:c Set.instHasSubset) (:fv _uniq.37059)) ((:c Insert.insert) (:fv _uniq.37059) ((:c Set) (:fv _uniq.37059)) ((:c Set.instInsert) (:fv _uniq.37059)) (:fv _uniq.37178) ((:c Singleton.singleton) (:fv _uniq.37059) ((:c Set) (:fv _uniq.37059)) ((:c Set.instSingletonSet) ... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.37050))"},{"name":"inst✝³","sexp":"((:c Infinite) (:fv _uniq.37050))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.37059))"},{"name":"ϕ","sexp":"((:c RingHom) (:fv _uniq.37050) (:fv _uniq... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV3)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV3))))))) (:arg :explicit 2 (:app (:c Insert.insert) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:a... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"simp","sourceEnd":8687,"sourceStart":8683,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":8692,"sourceStart":8688,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":8692,"s... | [] | [{"source":"heq","source_end":8701,"source_start":8698,"syntax_kind":"ident"},{"source":"αyβ_in_K","source_end":8716,"source_start":8706,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":instance-implicit","context_index":... | 23 | 18 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d4c4eb191806708248654e4d3e1fb1f6a248e40a29994ff1d14f607c244c6a46 | 181ffc2c5ba50f7da671a40665f20398508df6201121bb643a80198775018a14 | 13d9d04aaf5317adc9fd8aa12405b08e016d797bb5bb144a4f96e13df1812c0c | 53ed17e86a8938aec394ee2797fa596828828dc1444f8cc1fa57175f36acce0b |
cat-searcher/leandojo-benchmark-4-random | test | 2,851 | Field.primitive_element_inf_aux_of_finite_intermediateField | Mathlib/FieldTheory/PrimitiveElement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have β_in_K := <a>sub_mem</a> αxβ_in_K αyβ_in_K | case h.a
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : ¬x = y
heq : F⟮α + x • β⟯ = F⟮α + y • β⟯
αxβ_in_K : α + x • β ∈ F⟮α + x • β⟯
αyβ_... | case h.a
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : ¬x = y
heq : F⟮α + x • β⟯ = F⟮α + y • β⟯
αxβ_in_K : α + x • β ∈ F⟮α + x • β⟯
αyβ_... | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.37059)) ((:c Set.instHasSubset) (:fv _uniq.37059)) ((:c Insert.insert) (:fv _uniq.37059) ((:c Set) (:fv _uniq.37059)) ((:c Set.instInsert) (:fv _uniq.37059)) (:fv _uniq.37178) ((:c Singleton.singleton) (:fv _uniq.37059) ((:c Set) (:fv _uniq.37059)) ((:c Set.instSingletonSet) ... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.37050))"},{"name":"inst✝³","sexp":"((:c Infinite) (:fv _uniq.37050))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.37059))"},{"name":"ϕ","sexp":"((:c RingHom) (:fv _uniq.37050) (:fv _uniq... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV3)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV3))))))) (:arg :explicit 2 (:app (:c Insert.insert) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:a... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"have","sourceEnd":8725,"sourceStart":8721,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"β_in_K","sourceEnd":8733,"sourceStart":8726,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"β_in_K","sourceEnd":8733,"sourceStart":8726,"tag":"n... | [] | [{"source":"sub_mem αxβ_in_K αyβ_in_K","source_end":8766,"source_start":8737,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":instance-implicit","context_index":... | 23 | 19 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dadf41fe2d074f9b5a65b8a9181f2f96c8d709707796cf9d0d20a3577a420be9 | 53ed17e86a8938aec394ee2797fa596828828dc1444f8cc1fa57175f36acce0b | 5932242094bdd233dad8b45af2873299c6bf8f5cfeb85b91ac5c974d19228b31 | dec07a9a79f9bc0f03eb121977934bc10755990056efc346c5b0296c74f47609 |
cat-searcher/leandojo-benchmark-4-random | test | 2,852 | Field.primitive_element_inf_aux_of_finite_intermediateField | Mathlib/FieldTheory/PrimitiveElement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [show (α + x • β) - (α + y • β) = (x - y) • β by rw [<a>sub_smul</a>]; abel1] at β_in_K | case h.a
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : ¬x = y
heq : F⟮α + x • β⟯ = F⟮α + y • β⟯
αxβ_in_K : α + x • β ∈ F⟮α + x • β⟯
αyβ_... | case h.a
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : ¬x = y
heq : F⟮α + x • β⟯ = F⟮α + y • β⟯
αxβ_in_K : α + x • β ∈ F⟮α + x • β⟯
αyβ_... | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.37059)) ((:c Set.instHasSubset) (:fv _uniq.37059)) ((:c Insert.insert) (:fv _uniq.37059) ((:c Set) (:fv _uniq.37059)) ((:c Set.instInsert) (:fv _uniq.37059)) (:fv _uniq.37178) ((:c Singleton.singleton) (:fv _uniq.37059) ((:c Set) (:fv _uniq.37059)) ((:c Set.instSingletonSet) ... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.37050))"},{"name":"inst✝³","sexp":"((:c Infinite) (:fv _uniq.37050))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.37059))"},{"name":"ϕ","sexp":"((:c RingHom) (:fv _uniq.37050) (:fv _uniq... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV3)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV3))))))) (:arg :explicit 2 (:app (:c Insert.insert) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:a... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"rw","sourceEnd":8773,"sourceStart":8771,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8775,"sourceStart":8774,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"show"... | [] | [{"source":"β_in_K","source_end":8866,"source_start":8859,"syntax_kind":"ident"},{"source":"show (α + x • β) - (α + y • β) = (x - y) • β by rw [sub_smul]; abel1","source_end":8854,"source_start":8775,"syntax_kind":"Lean.Parser.Term.show"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":instance-implicit","context_index":... | 23 | 20 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c6abf1545261c7607a141d6dd00911e2fd46805e56e67ee972e7b95712a85cff | dec07a9a79f9bc0f03eb121977934bc10755990056efc346c5b0296c74f47609 | 7516bff2954e3d1cd4a201226a64526b05f531ff56b01ad8dc0d8a700a5208aa | 4625ffa00cc9cdd84c3ee11704fa5e80fe26634e82525728b4eee64a39342f2c |
cat-searcher/leandojo-benchmark-4-random | test | 2,853 | Field.primitive_element_inf_aux_of_finite_intermediateField | Mathlib/FieldTheory/PrimitiveElement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | replace β_in_K := <a>IntermediateField.smul_mem</a> _ β_in_K (x := (x - y)⁻¹) | case h.a
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : ¬x = y
heq : F⟮α + x • β⟯ = F⟮α + y • β⟯
αxβ_in_K : α + x • β ∈ F⟮α + x • β⟯
αyβ_... | case h.a
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : ¬x = y
heq : F⟮α + x • β⟯ = F⟮α + y • β⟯
αxβ_in_K : α + x • β ∈ F⟮α + x • β⟯
αyβ_... | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.37059)) ((:c Set.instHasSubset) (:fv _uniq.37059)) ((:c Insert.insert) (:fv _uniq.37059) ((:c Set) (:fv _uniq.37059)) ((:c Set.instInsert) (:fv _uniq.37059)) (:fv _uniq.37178) ((:c Singleton.singleton) (:fv _uniq.37059) ((:c Set) (:fv _uniq.37059)) ((:c Set.instSingletonSet) ... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.37050))"},{"name":"inst✝³","sexp":"((:c Infinite) (:fv _uniq.37050))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.37059))"},{"name":"ϕ","sexp":"((:c RingHom) (:fv _uniq.37050) (:fv _uniq... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV3)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV3))))))) (:arg :explicit 2 (:app (:c Insert.insert) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:a... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"replace","sourceEnd":8878,"sourceStart":8871,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"β_in_K","sourceEnd":8886,"sourceStart":8879,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"β_in_K","sourceEnd":8886,"sourceStart":8879,"tag"... | [] | [{"source":"smul_mem _ β_in_K (x := (x - y)⁻¹)","source_end":8928,"source_start":8890,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":instance-implicit","context_index":... | 23 | 30 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2b8d810828cbeadd751100911062803f189f543423f1734e6afc1c126870ab7b | 4625ffa00cc9cdd84c3ee11704fa5e80fe26634e82525728b4eee64a39342f2c | ce6828fece6946d49173fcd875765a0ada5a0a8a993bf3980eebb9eef30f5232 | fffc17c9075d65ce4507e9ffae561373834dd4c095caf3d681e84c6867b5c4eb |
cat-searcher/leandojo-benchmark-4-random | test | 2,854 | Field.primitive_element_inf_aux_of_finite_intermediateField | Mathlib/FieldTheory/PrimitiveElement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>smul_smul</a>, <a>inv_mul_eq_div</a>, <a>div_self</a> (<a>sub_ne_zero</a>.2 hneq), <a>one_smul</a>] at β_in_K | case h.a
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : ¬x = y
heq : F⟮α + x • β⟯ = F⟮α + y • β⟯
αxβ_in_K : α + x • β ∈ F⟮α + x • β⟯
αyβ_... | case h.a
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : ¬x = y
heq : F⟮α + x • β⟯ = F⟮α + y • β⟯
αxβ_in_K : α + x • β ∈ F⟮α + x • β⟯
αyβ_... | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.37059)) ((:c Set.instHasSubset) (:fv _uniq.37059)) ((:c Insert.insert) (:fv _uniq.37059) ((:c Set) (:fv _uniq.37059)) ((:c Set.instInsert) (:fv _uniq.37059)) (:fv _uniq.37178) ((:c Singleton.singleton) (:fv _uniq.37059) ((:c Set) (:fv _uniq.37059)) ((:c Set.instSingletonSet) ... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.37050))"},{"name":"inst✝³","sexp":"((:c Infinite) (:fv _uniq.37050))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.37059))"},{"name":"ϕ","sexp":"((:c RingHom) (:fv _uniq.37050) (:fv _uniq... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV3)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV3))))))) (:arg :explicit 2 (:app (:c Insert.insert) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:a... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"rw","sourceEnd":8935,"sourceStart":8933,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8937,"sourceStart":8936,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"smul_smul","semantic... | [] | [{"source":"smul_smul","source_end":8946,"source_start":8937,"syntax_kind":"ident"},{"source":"β_in_K","source_end":9015,"source_start":9008,"syntax_kind":"ident"},{"source":"inv_mul_eq_div","source_end":8962,"source_start":8948,"syntax_kind":"ident"},{"source":"div_self (sub_ne_zero.2 hneq)","source_end":8993,"source_... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":instance-implicit","context_index":... | 23 | 31 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2c69a37a8963a79d044775a767d0bc37fb24b4ff4f1dd0e82d01e53a23989670 | fffc17c9075d65ce4507e9ffae561373834dd4c095caf3d681e84c6867b5c4eb | 4c2b107bd4a9e062c74e0d14af4f530fc20100d151a7e45c17d1686bc336529c | 9c7008e1ed153e6019f3a9ae6aaadfe1674e2a3834549fa2ce0674e4e4bd23db |
cat-searcher/leandojo-benchmark-4-random | test | 2,855 | Field.primitive_element_inf_aux_of_finite_intermediateField | Mathlib/FieldTheory/PrimitiveElement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have α_in_K : α ∈ F⟮α + x • β⟯ := by convert ← <a>sub_mem</a> αxβ_in_K (<a>IntermediateField.smul_mem</a> _ β_in_K) apply <a>add_sub_cancel_right</a> | case h.a
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : ¬x = y
heq : F⟮α + x • β⟯ = F⟮α + y • β⟯
αxβ_in_K : α + x • β ∈ F⟮α + x • β⟯
αyβ_... | case h.a
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : ¬x = y
heq : F⟮α + x • β⟯ = F⟮α + y • β⟯
αxβ_in_K : α + x • β ∈ F⟮α + x • β⟯
αyβ_... | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.37059)) ((:c Set.instHasSubset) (:fv _uniq.37059)) ((:c Insert.insert) (:fv _uniq.37059) ((:c Set) (:fv _uniq.37059)) ((:c Set.instInsert) (:fv _uniq.37059)) (:fv _uniq.37178) ((:c Singleton.singleton) (:fv _uniq.37059) ((:c Set) (:fv _uniq.37059)) ((:c Set.instSingletonSet) ... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.37050))"},{"name":"inst✝³","sexp":"((:c Infinite) (:fv _uniq.37050))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.37059))"},{"name":"ϕ","sexp":"((:c RingHom) (:fv _uniq.37050) (:fv _uniq... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV3)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV3))))))) (:arg :explicit 2 (:app (:c Insert.insert) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:a... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"have","sourceEnd":9024,"sourceStart":9020,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"α_in_K","sourceEnd":9032,"sourceStart":9025,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"α_in_K","sourceEnd":9032,"sourceStart":9025,"tag":"n... | [] | [{"source":"α ∈ F⟮α + x • β⟯","source_end":9062,"source_start":9035,"syntax_kind":"«term_∈_»"},{"source":"sub_mem αxβ_in_K (smul_mem _ β_in_K)","source_end":9126,"source_start":9087,"syntax_kind":"Lean.Parser.Term.app"},{"source":"add_sub_cancel_right","source_end":9159,"source_start":9139,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":instance-implicit","context_index":... | 23 | 37 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 61c7fc8ecf0efb821d635f944617ba344ddc83e4380bc15c355c1490a45ccac4 | 9c7008e1ed153e6019f3a9ae6aaadfe1674e2a3834549fa2ce0674e4e4bd23db | cb6eb84ecf91801f4a5ecb9bcb9bbde7ead285ec3b91d1a62519f9c877e620d7 | 3117f32e5d698ebaf0446746f5f359663047e3a801b0e02c5398355ce3fb050b |
cat-searcher/leandojo-benchmark-4-random | test | 2,856 | Field.primitive_element_inf_aux_of_finite_intermediateField | Mathlib/FieldTheory/PrimitiveElement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro x (rfl | rfl) <;> assumption | case h.a
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : ¬x = y
heq : F⟮α + x • β⟯ = F⟮α + y • β⟯
αxβ_in_K : α + x • β ∈ F⟮α + x • β⟯
αyβ_... | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.37059)) ((:c Set.instHasSubset) (:fv _uniq.37059)) ((:c Insert.insert) (:fv _uniq.37059) ((:c Set) (:fv _uniq.37059)) ((:c Set.instInsert) (:fv _uniq.37059)) (:fv _uniq.37178) ((:c Singleton.singleton) (:fv _uniq.37059) ((:c Set) (:fv _uniq.37059)) ((:c Set.instSingletonSet) ... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.37050))"},{"name":"inst✝³","sexp":"((:c Infinite) (:fv _uniq.37050))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.37059))"},{"name":"ϕ","sexp":"((:c RingHom) (:fv _uniq.37050) (:fv _uniq... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV3)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV3))))))) (:arg :explicit 2 (:app (:c Insert.insert) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:a... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"children":[{"source":"rintro","sourceEnd":9170,"sourceStart":9164,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":9172,"sourceStart":9171,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"x","sourceEnd":9172,"sourceStart"... | [] | [{"source":"(rfl | rfl)","source_end":9184,"source_start":9173,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.paren"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":instance-implicit","context_index":... | 23 | 41 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3e1b50baf3bc9a4a8fc9a91361e9767a83253095aa63bd65da7913f91426d0f4 | 3117f32e5d698ebaf0446746f5f359663047e3a801b0e02c5398355ce3fb050b | 6d1b7513487f4f26f9717bd35206cf3dc962abd967c1ccfdad001470a77086dd | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,857 | Field.primitive_element_inf_aux_of_finite_intermediateField | Mathlib/FieldTheory/PrimitiveElement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>sub_smul</a>] | F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : ¬x = y
heq : F⟮α + x • β⟯ = F⟮α + y • β⟯
αxβ_in_K : α + x • β ∈ F⟮α + x • β⟯
αyβ_in_K : α ... | F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : ¬x = y
heq : F⟮α + x • β⟯ = F⟮α + y • β⟯
αxβ_in_K : α + x • β ∈ F⟮α + x • β⟯
αyβ_in_K : α ... | ((:c Eq) (:fv _uniq.37059) ((:c HSub.hSub) (:fv _uniq.37059) (:fv _uniq.37059) (:fv _uniq.37059) ((:c instHSub) (:fv _uniq.37059) ((:c Ring.toSub) (:fv _uniq.37059) ((:c DivisionRing.toRing) (:fv _uniq.37059) ((:c Field.toDivisionRing) (:fv _uniq.37059) (:fv _uniq.37062))))) ((:c HAdd.hAdd) (:fv _uniq.37059) (:fv _uniq... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.37050))"},{"name":"inst✝³","sexp":"((:c Infinite) (:fv _uniq.37050))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.37059))"},{"name":"ϕ","sexp":"((:c RingHom) (:fv _uniq.37050) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c HSub.hSub) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:fv FV3)) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c HSub) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"rw","sourceEnd":8836,"sourceStart":8834,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8838,"sourceStart":8837,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"sub_smul","semanticR... | [] | [{"source":"sub_smul","source_end":8846,"source_start":8838,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":instance-implicit","context_index":... | 23 | 24 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8583bee06ceaafd720685b45b94cbef19e9dabbd548564419b85bfbb119e754f | 74c79fd3f382a75d9e6672fdec58af47a64f1442062bfa915ae7828ddfbf0a89 | 07da632efdae953505806c963398c87f4dfe84f6e94df3d1ed8adb58e6ca4efd | 0e4950a0efc8bd44b4d1246564f6282e3c51ead902860fd9915ac0f0014f86d6 |
cat-searcher/leandojo-benchmark-4-random | test | 2,858 | Field.primitive_element_inf_aux_of_finite_intermediateField | Mathlib/FieldTheory/PrimitiveElement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | abel1 | F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : ¬x = y
heq : F⟮α + x • β⟯ = F⟮α + y • β⟯
αxβ_in_K : α + x • β ∈ F⟮α + x • β⟯
αyβ_in_K : α ... | ((:c Eq) (:fv _uniq.37059) ((:c HSub.hSub) (:fv _uniq.37059) (:fv _uniq.37059) (:fv _uniq.37059) ((:c instHSub) (:fv _uniq.37059) ((:c Ring.toSub) (:fv _uniq.37059) ((:c DivisionRing.toRing) (:fv _uniq.37059) ((:c Field.toDivisionRing) (:fv _uniq.37059) (:fv _uniq.37062))))) ((:c HAdd.hAdd) (:fv _uniq.37059) (:fv _uniq... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.37050))"},{"name":"inst✝³","sexp":"((:c Infinite) (:fv _uniq.37050))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.37059))"},{"name":"ϕ","sexp":"((:c RingHom) (:fv _uniq.37050) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c HSub.hSub) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:fv FV3)) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c HSub) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"abel1","sourceEnd":8854,"sourceStart":8849,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.Abel.abel1","source":"abel1","sourceEnd":8854,"sourceStart":8849,"tag":"node"} | [] | [] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":instance-implicit","context_index":... | 23 | 28 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 313995a5824f28e7d6cdf880b0f333e8cf81b88360aa22e1698a51faaf96bec4 | 0e4950a0efc8bd44b4d1246564f6282e3c51ead902860fd9915ac0f0014f86d6 | ecb0a99c4a7d3b9bed6e9f4b1dbf6f9438175410c4cfc6a5dbd28166e8d49e0c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,859 | Field.primitive_element_inf_aux_of_finite_intermediateField | Mathlib/FieldTheory/PrimitiveElement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert ← <a>sub_mem</a> αxβ_in_K (<a>IntermediateField.smul_mem</a> _ β_in_K) | F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : ¬x = y
heq : F⟮α + x • β⟯ = F⟮α + y • β⟯
αxβ_in_K : α + x • β ∈ F⟮α + x • β⟯
αyβ_in_K : α ... | case h.e'_4
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : ¬x = y
heq : F⟮α + x • β⟯ = F⟮α + y • β⟯
αxβ_in_K : α + x • β ∈ F⟮α + x • β⟯
α... | ((:c Membership.mem) (:fv _uniq.37059) ((:c IntermediateField) (:fv _uniq.37050) (:fv _uniq.37059) (:fv _uniq.37053) (:fv _uniq.37062) (:fv _uniq.37247)) ((:c SetLike.instMembership) ((:c IntermediateField) (:fv _uniq.37050) (:fv _uniq.37059) (:fv _uniq.37053) (:fv _uniq.37062) (:fv _uniq.37247)) (:fv _uniq.37059) ((:c... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.37050))"},{"name":"inst✝³","sexp":"((:c Infinite) (:fv _uniq.37050))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.37059))"},{"name":"ϕ","sexp":"((:c RingHom) (:fv _uniq.37050) (:fv _uniq... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c IntermediateField) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :instance 2 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Field) (:arg :explicit 0 (:... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"convert","sourceEnd":9082,"sourceStart":9075,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"←","sourceEnd":9086,"sourceStart":9083,"tag":"atom"}],"kind":"null","source":"←","sourceEnd":9086,"sourceStart":9083,"tag":"node"},{"children":[{"name":"sub_m... | [] | [{"source":"sub_mem αxβ_in_K (smul_mem _ β_in_K)","source_end":9126,"source_start":9087,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":instance-implicit","context_index":... | 23 | 39 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 848a0980c8880bd9778aecc3120ef81ff162602353b033b9a90b7d40cb11e403 | 7e4881907a0e39122002f40b4b451fab444428d22c740e0a4bd66c96e5181c67 | 7e087480d04fbcf0643add90a23da4e311c5efd5a5e7d80e50fa0d2bb8474654 | a2dda142888fb1bfa5457fee79e8424302517b40c3ab7d2c39ae326afe1d95fb |
cat-searcher/leandojo-benchmark-4-random | test | 2,861 | Field.primitive_element_inf_aux_of_finite_intermediateField | Mathlib/FieldTheory/PrimitiveElement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>IntermediateField.adjoin_simple_le_iff</a>] | case h.a
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : x ≠ y
heq : f x = f y
⊢ F⟮α + x • β⟯ ≤ F⟮α, β⟯ | case h.a
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : x ≠ y
heq : f x = f y
⊢ α + x • β ∈ F⟮α, β⟯ | ((:c LE.le) ((:c IntermediateField) (:fv _uniq.37050) (:fv _uniq.37059) (:fv _uniq.37053) (:fv _uniq.37062) (:fv _uniq.37247)) ((:c Preorder.toLE) ((:c IntermediateField) (:fv _uniq.37050) (:fv _uniq.37059) (:fv _uniq.37053) (:fv _uniq.37062) (:fv _uniq.37247)) ((:c PartialOrder.toPreorder) ((:c IntermediateField) (:fv... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.37050))"},{"name":"inst✝³","sexp":"((:c Infinite) (:fv _uniq.37050))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.37059))"},{"name":"ϕ","sexp":"((:c RingHom) (:fv _uniq.37050) (:fv _uniq... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c IntermediateField) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :instance 2 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV3))))) (:arg :instance 4 (:instance-of... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"rw","sourceEnd":9207,"sourceStart":9205,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":9209,"sourceStart":9208,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"IntermediateField.ad... | [] | [{"source":"adjoin_simple_le_iff","source_end":9229,"source_start":9209,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":instance-implicit","context_index":... | 23 | 50 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3ac7a2817e4e8fafea6bf5985ed8e9fad450e748220cb119aa03366e4b77d969 | 8c283890d9e8545eb35714acd6e3ef17d6762c7925a1889f5e5615568f846c46 | 56d86b93b64db687daf93146d1a6873fdafea0ccd195c47f512be63778634a5c | 1724721156d189cf737ec95bcb0e99a06a3ee19ca5e6855fb70f3bf6f7ee6ed8 |
cat-searcher/leandojo-benchmark-4-random | test | 2,862 | Field.primitive_element_inf_aux_of_finite_intermediateField | Mathlib/FieldTheory/PrimitiveElement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have α_in_Fαβ : α ∈ F⟮α, β⟯ := <a>IntermediateField.subset_adjoin</a> F {α, β} (<a>Set.mem_insert</a> α {β}) | case h.a
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : x ≠ y
heq : f x = f y
⊢ α + x • β ∈ F⟮α, β⟯ | case h.a
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : x ≠ y
heq : f x = f y
α_in_Fαβ : α ∈ F⟮α, β⟯
⊢ α + x • β ∈ F⟮α, β⟯ | ((:c Membership.mem) (:fv _uniq.37059) ((:c IntermediateField) (:fv _uniq.37050) (:fv _uniq.37059) (:fv _uniq.37053) (:fv _uniq.37062) (:fv _uniq.37247)) ((:c SetLike.instMembership) ((:c IntermediateField) (:fv _uniq.37050) (:fv _uniq.37059) (:fv _uniq.37053) (:fv _uniq.37062) (:fv _uniq.37247)) (:fv _uniq.37059) ((:c... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.37050))"},{"name":"inst✝³","sexp":"((:c Infinite) (:fv _uniq.37050))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.37059))"},{"name":"ϕ","sexp":"((:c RingHom) (:fv _uniq.37050) (:fv _uniq... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c IntermediateField) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :instance 2 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Field) (:arg :explicit 0 (:... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"have","sourceEnd":9239,"sourceStart":9235,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"α_in_Fαβ","sourceEnd":9251,"sourceStart":9240,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"α_in_Fαβ","sourceEnd":9251,"sourceStart":9240,"tag... | [] | [{"source":"α ∈ F⟮α, β⟯","source_end":9274,"source_start":9254,"syntax_kind":"«term_∈_»"},{"source":"subset_adjoin F {α, β} (Set.mem_insert α {β})","source_end":9327,"source_start":9278,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":instance-implicit","context_index":... | 23 | 53 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d318b30fafd02dc135d4c119cbdc2479e80e09173c5c10a540517078f2f22e18 | 1724721156d189cf737ec95bcb0e99a06a3ee19ca5e6855fb70f3bf6f7ee6ed8 | 4875d35825a0c2270e344011ddca579583d4ec337b96c827c90b0da2f45046d8 | 69d29cb2d3ee613268def44b6c37d4855c6c04cfecef7f6f5a1266c595dc299a |
cat-searcher/leandojo-benchmark-4-random | test | 2,863 | Field.primitive_element_inf_aux_of_finite_intermediateField | Mathlib/FieldTheory/PrimitiveElement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have β_in_Fαβ : β ∈ F⟮α, β⟯ := <a>IntermediateField.subset_adjoin</a> F {α, β} (<a>Set.mem_insert_of_mem</a> α <a>rfl</a>) | case h.a
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : x ≠ y
heq : f x = f y
α_in_Fαβ : α ∈ F⟮α, β⟯
⊢ α + x • β ∈ F⟮α, β⟯ | case h.a
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : x ≠ y
heq : f x = f y
α_in_Fαβ : α ∈ F⟮α, β⟯
β_in_Fαβ : β ∈ F⟮α, β⟯
⊢ α + x • β ∈... | ((:c Membership.mem) (:fv _uniq.37059) ((:c IntermediateField) (:fv _uniq.37050) (:fv _uniq.37059) (:fv _uniq.37053) (:fv _uniq.37062) (:fv _uniq.37247)) ((:c SetLike.instMembership) ((:c IntermediateField) (:fv _uniq.37050) (:fv _uniq.37059) (:fv _uniq.37053) (:fv _uniq.37062) (:fv _uniq.37247)) (:fv _uniq.37059) ((:c... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.37050))"},{"name":"inst✝³","sexp":"((:c Infinite) (:fv _uniq.37050))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.37059))"},{"name":"ϕ","sexp":"((:c RingHom) (:fv _uniq.37050) (:fv _uniq... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c IntermediateField) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :instance 2 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Field) (:arg :explicit 0 (:... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"have","sourceEnd":9336,"sourceStart":9332,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"β_in_Fαβ","sourceEnd":9348,"sourceStart":9337,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"β_in_Fαβ","sourceEnd":9348,"sourceStart":9337,"tag... | [] | [{"source":"β ∈ F⟮α, β⟯","source_end":9371,"source_start":9351,"syntax_kind":"«term_∈_»"},{"source":"subset_adjoin F {α, β} (Set.mem_insert_of_mem α rfl)","source_end":9430,"source_start":9375,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":instance-implicit","context_index":... | 23 | 54 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3e8c7b859e0796eb72b4748272db60d91d855a57c3c1cb24b3aac256681a217d | 69d29cb2d3ee613268def44b6c37d4855c6c04cfecef7f6f5a1266c595dc299a | 2995ee90fc2b9dde0f5c6a997cd1ddc53f48d97b76cd2b4a0a6861315bf695b8 | 236b54fecc5e2f0a1c8d6ceb78facf2899461a07bee4cd6e75024b48d90b7737 |
cat-searcher/leandojo-benchmark-4-random | test | 2,864 | Field.primitive_element_inf_aux_of_finite_intermediateField | Mathlib/FieldTheory/PrimitiveElement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact F⟮α, β⟯.<a>IntermediateField.add_mem</a> α_in_Fαβ (F⟮α, β⟯.<a>IntermediateField.smul_mem</a> β_in_Fαβ) | case h.a
F : Type u_1
inst✝⁴ : Field F
inst✝³ : Infinite F
E : Type u_2
inst✝² : Field E
ϕ : F →+* E
α β : E
inst✝¹ : Algebra F E
inst✝ : Finite (IntermediateField F E)
f : F → IntermediateField F E := fun x => F⟮α + x • β⟯
x y : F
hneq : x ≠ y
heq : f x = f y
α_in_Fαβ : α ∈ F⟮α, β⟯
β_in_Fαβ : β ∈ F⟮α, β⟯
⊢ α + x • β ∈... | ((:c Membership.mem) (:fv _uniq.37059) ((:c IntermediateField) (:fv _uniq.37050) (:fv _uniq.37059) (:fv _uniq.37053) (:fv _uniq.37062) (:fv _uniq.37247)) ((:c SetLike.instMembership) ((:c IntermediateField) (:fv _uniq.37050) (:fv _uniq.37059) (:fv _uniq.37053) (:fv _uniq.37062) (:fv _uniq.37247)) (:fv _uniq.37059) ((:c... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.37050))"},{"name":"inst✝³","sexp":"((:c Infinite) (:fv _uniq.37050))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c Field) (:fv _uniq.37059))"},{"name":"ϕ","sexp":"((:c RingHom) (:fv _uniq.37050) (:fv _uniq... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c IntermediateField) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :instance 2 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Field) (:arg :explicit 0 (:... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"exact","sourceEnd":9440,"sourceStart":9435,"tag":"atom"},{"children":[{"children":[{"children":[{"contextIndex":0,"semanticRole":"local","source":"F","sourceEnd":9442,"sourceStart":9441,"tag":"identifier"},{"source":"⟮","sourceEnd":9445,"sourceStart":9442,"tag":"atom"},{"children":[{"contextInde... | [] | [{"source":"F⟮α, β⟯.add_mem α_in_Fαβ (F⟮α, β⟯.smul_mem β_in_Fαβ)","source_end":9511,"source_start":9441,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.37050","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.37053","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":instance-implicit","context_index":... | 23 | 55 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0dc24831ace7d71c260ec25147f96db899f28d598e45044914010024e1ec324d | 236b54fecc5e2f0a1c8d6ceb78facf2899461a07bee4cd6e75024b48d90b7737 | 89b8b038d9a7f58c50a3da02feb1871b7d3fdf27dbb7ca3884d0d45260f2ed42 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,865 | antilipschitzWith_lineMap | Mathlib/Analysis/NormedSpace/AddTorsor.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>dist_lineMap_lineMap</a>, <a>NNReal.coe_inv</a>, ← <a>dist_nndist</a>, <a>mul_left_comm</a>, <a>inv_mul_cancel</a> (<a>dist_ne_zero</a>.2 h), <a>mul_one</a>] | α : Type u_1
V : Type u_2
P : Type u_3
W : Type u_4
Q : Type u_5
inst✝⁸ : SeminormedAddCommGroup V
inst✝⁷ : PseudoMetricSpace P
inst✝⁶ : NormedAddTorsor V P
inst✝⁵ : NormedAddCommGroup W
inst✝⁴ : MetricSpace Q
inst✝³ : NormedAddTorsor W Q
𝕜 : Type u_6
inst✝² : NormedField 𝕜
inst✝¹ : NormedSpace 𝕜 V
inst✝ : NormedSpa... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Dist.dist) (:fv _uniq.87462) ((:c PseudoMetricSpace.toDist) (:fv _uniq.87462) ((:c MetricSpace.toPseudoMetricSpace) (:fv _uniq.87462) ((:c NormedField.toMetricSpace) (:fv _uniq.87462) (:fv _uniq.87465)))) (:fv _uniq.89912) (:fv _uniq.89915)) ((:c HMul.hMul) (:c Real) (:c Real... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"W","sexp":"(:sort (+ u_4 1))"},{"name":"Q","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁸","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.87167))"},{"name":"inst✝⁷","sexp":"((:c PseudoMetricSp... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Dist.dist) (:arg :implicit-type 0 (:fv FV11)) (:arg :instance 1 (:instance-of (:app (:c Dist) (:arg :explicit 0 (:fv FV11))))) (:arg :explicit 2 (:fv FV19)) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.87164","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.87167","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":9970,"sourceStart":9968,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":9972,"sourceStart":9971,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"dist_lineMap_lineMap","source_end":9992,"source_start":9972,"syntax_kind":"ident"},{"source":"NNReal.coe_inv","source_end":10008,"source_start":9994,"syntax_kind":"ident"},{"source":"dist_nndist","source_end":10025,"source_start":10014,"syntax_kind":"ident"},{"source":"mul_left_comm","source_end":10040,"sou... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.87164","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.87167","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 76 | 2 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d51cd6ceac80e30a56c1ec56dccd3096f594f1b1b9f7b6a9ec7b624fe10277de | 558bffefaab5f698c5138bda125030c976dea3243f761daf7669074d97c73793 | bfcb4f947c67b2584f531f06839875000f9eb337299703796ccf11573e9ab9e5 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,866 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have := <a>zorn_subset</a> {s : <a>Set</a> α | <a>CompleteLattice.SetIndependent</a> s ∧ <a>Disjoint</a> b (<a>SupSet.sSup</a> s) ∧ ∀ a ∈ s, <a>IsAtom</a> a} fun c hc1 hc2 => ⟨⋃₀ c, ⟨<a>CompleteLattice.independent_sUnion_of_directed</a> hc2.directedOn fun s hs => (hc1 hs).1, ?_, fun a ⟨s, sc, as⟩ => (hc1 sc).2.2 a as⟩,... | ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
⊢ ∃ s, CompleteLattice.SetIndependent s ∧ IsCompl b (sSup s) ∧ ∀ ⦃a : α⦄, a ∈ s → IsAtom a | case refine_2
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
this :
∃ m ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a},
∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Dis... | ((:c Exists) ((:c Set) (:fv _uniq.84775)) (:lambda s ((:c Set) (:fv _uniq.84775)) ((:c And) ((:c CompleteLattice.SetIndependent) (:fv _uniq.84775) (:fv _uniq.84778) 0) ((:c And) ((:c IsCompl) (:fv _uniq.84775) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.84775) ((:c CompleteLattice.toCompleteSemilatticeInf) (... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:lambda s :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV1))) (:app (:c And) (:arg :explicit 0 (:app (:c CompleteLattice.SetIndependent) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"have","sourceEnd":27819,"sourceStart":27815,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":27820,"sourceStart":27820,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":27820,"sourceStart":27820,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"zorn_subset\n {s : Set α | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}\n fun c hc1 hc2 =>\n ⟨⋃₀ c,\n ⟨CompleteLattice.independent_sUnion_of_directed hc2.directedOn fun s hs => (hc1 hs).1, ?_,\n fun a ⟨s, sc, as⟩ => (hc1 sc).2.2 a as⟩,\n fun _... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e995896268ca08f8e3f4e70d234f3bcb82c92c822dc7a4b1379fa49db4a0498b | c28898519d17b75d8327956d87d5577832fc115d1563bf1783a5d42e81e9069a | 2deafa0d06a8016157b46d5698cceaf705fc71a278b1ea6c93393afc0cff76f5 | 2475d2025330c564c610a77c09f16d9e4bb84bc2163c70e006d0a80de6b4f22c |
cat-searcher/leandojo-benchmark-4-random | test | 2,868 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨s, ⟨s_ind, b_inf_Sup_s, s_atoms⟩, s_max⟩ := this | case refine_2
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
this :
∃ m ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a},
∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Dis... | case refine_2.intro.intro.intro.intro
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind ... | ((:c Exists) ((:c Set) (:fv _uniq.84775)) (:lambda s ((:c Set) (:fv _uniq.84775)) ((:c And) ((:c CompleteLattice.SetIndependent) (:fv _uniq.84775) (:fv _uniq.84778) 0) ((:c And) ((:c IsCompl) (:fv _uniq.84775) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.84775) ((:c CompleteLattice.toCompleteSemilatticeInf) (... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:lambda s :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV1))) (:app (:c And) (:arg :explicit 0 (:app (:c CompleteLattice.SetIndependent) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"obtain","sourceEnd":28409,"sourceStart":28403,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":28413,"sourceStart":28410,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"s","sourceEn... | [] | [{"source":"this","source_end":28467,"source_start":28463,"syntax_kind":"ident"},{"source":"⟨s, ⟨s_ind, b_inf_Sup_s, s_atoms⟩, s_max⟩","source_end":28459,"source_start":28410,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 29 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f0a9ef6d8965b458a5cd9f3f91abc7ca06cc71b8361c1e139ce4d021634caabb | 94d90f3a54f1233709a0600b060aa3049b5c2c0307e912b036f232eb9156905f | b55fdd798b64225320061735b75b8a083e3cf39b1f5879c6aebfc200f4e9e959 | 2a73b5fca027085c010cb2bf71e78218b46a5df2f3cd3e3a16f8f3e75f0b676e |
cat-searcher/leandojo-benchmark-4-random | test | 2,869 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨s, s_ind, ⟨b_inf_Sup_s, ?_⟩, s_atoms⟩ | case refine_2.intro.intro.intro.intro
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind ... | case refine_2.intro.intro.intro.intro
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind ... | ((:c Exists) ((:c Set) (:fv _uniq.84775)) (:lambda s ((:c Set) (:fv _uniq.84775)) ((:c And) ((:c CompleteLattice.SetIndependent) (:fv _uniq.84775) (:fv _uniq.84778) 0) ((:c And) ((:c IsCompl) (:fv _uniq.84775) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.84775) ((:c CompleteLattice.toCompleteSemilatticeInf) (... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:lambda s :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV1))) (:app (:c And) (:arg :explicit 0 (:app (:c CompleteLattice.SetIndependent) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"refine","sourceEnd":28476,"sourceStart":28470,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":28480,"sourceStart":28477,"tag":"atom"},{"children":[{"contextIndex":9,"semanticRole":"local","source":"s","sourceEnd":28481,"sourceStart":28480,"tag":"identifier"},{"source":",","sourceEnd":28482,... | [] | [{"source":"⟨s, s_ind, ⟨b_inf_Sup_s, ?_⟩, s_atoms⟩","source_end":28523,"source_start":28477,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 30 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f8b70be96e7e860f7f7f4774df75d3b3f4f7597309c1ec849ba9ab8af7df5200 | 2a73b5fca027085c010cb2bf71e78218b46a5df2f3cd3e3a16f8f3e75f0b676e | b406442eeea1112f1b731884e4ffa81bad3beb5d24e48cc4aa460e9b729f6e22 | bad8826e474c7323fc8fd2beeb7b602d46d1d6f29cd5e35e4ebfdfa0fbc695de |
cat-searcher/leandojo-benchmark-4-random | test | 2,870 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>codisjoint_iff_le_sup</a>, ← h, <a>sSup_le_iff</a>] | case refine_2.intro.intro.intro.intro
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind ... | case refine_2.intro.intro.intro.intro
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind ... | ((:c Codisjoint) (:fv _uniq.84775) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.84775) ((:c CompleteLattice.toCompleteSemilatticeInf) (:fv _uniq.84775) (:fv _uniq.84778))) ((:c BoundedOrder.toOrderTop) (:fv _uniq.84775) ((:c Preorder.toLE) (:fv _uniq.84775) ((:c PartialOrder.toPreorder) (:fv _uniq.84775) ((:c... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c Codisjoint) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c PartialOrder) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 2 (:instance-of (:app (:c OrderTop) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1)))))))) (:arg :explici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":28528,"sourceStart":28526,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":28530,"sourceStart":28529,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"codisjoint_iff_l... | [] | [{"source":"codisjoint_iff_le_sup","source_end":28551,"source_start":28530,"syntax_kind":"ident"},{"source":"h","source_end":28558,"source_start":28557,"syntax_kind":"ident"},{"source":"sSup_le_iff","source_end":28571,"source_start":28560,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 31 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1030ac00b1631867428818c342fbbe1df5f98526f40a88e72e86bed4ba174cc6 | bad8826e474c7323fc8fd2beeb7b602d46d1d6f29cd5e35e4ebfdfa0fbc695de | c405241a38734e7dd5fa76eb42c9b680c0eca3510e6d437ee73ac75d3ccc935e | ee3637db6e1c71ffa8c40f196db60ff573b1266d6ea545ffd62bdaf7aa592278 |
cat-searcher/leandojo-benchmark-4-random | test | 2,871 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro a ha | case refine_2.intro.intro.intro.intro
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind ... | case refine_2.intro.intro.intro.intro
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind ... | (:forall b (:fv _uniq.84775) (:forall _ ((:c Membership.mem) (:fv _uniq.84775) ((:c Set) (:fv _uniq.84775)) ((:c Set.instMembership) (:fv _uniq.84775)) 0 ((:c setOf) (:fv _uniq.84775) (:lambda a (:fv _uniq.84775) ((:c IsAtom) (:fv _uniq.84775) ((:c PartialOrder.toPreorder) (:fv _uniq.84775) ((:c CompleteSemilatticeInf.... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:forall b :explicit (:fv FV1) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"intro","sourceEnd":28580,"sourceStart":28575,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"a","sourceEnd":28582,"sourceStart":28581,"tag":"identifier"},{"semanticRole":"scoped_local","source":"ha","sourceEnd":28585,"sourceStart":28583,"tag":"identifier"}],"kind":"null","sou... | [{"role":"fresh_name","source":"a","source_end":28582,"source_start":28581,"syntax_kind":"ident"},{"role":"fresh_name","source":"ha","source_end":28585,"source_start":28583,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 36 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 262c5bd76008a6ff1dad3055d8596f6b91aef0f470d28972329aed922667cd58 | ee3637db6e1c71ffa8c40f196db60ff573b1266d6ea545ffd62bdaf7aa592278 | d3051573cbe4fa4120dd9aa61cc5eac53633ef1f904bfd012ae1cf7a0c5ddf4c | c106c07d74cc2652e1abd826c8c16bd4a9b4a0a1de68a0782212689c610904f6 |
cat-searcher/leandojo-benchmark-4-random | test | 2,872 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>inf_eq_left</a>] | case refine_2.intro.intro.intro.intro
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind ... | case refine_2.intro.intro.intro.intro
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind ... | ((:c LE.le) (:fv _uniq.84775) ((:c Preorder.toLE) (:fv _uniq.84775) ((:c PartialOrder.toPreorder) (:fv _uniq.84775) ((:c CompleteSemilatticeSup.toPartialOrder) (:fv _uniq.84775) ((:c CompleteLattice.toCompleteSemilatticeSup) (:fv _uniq.84775) (:fv _uniq.84778))))) (:fv _uniq.86944) ((:c Sup.sup) (:fv _uniq.84775) ((:c ... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:fv FV14)) (:arg :explicit 3 (:app (:c Sup.sup) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Sup) (:arg :explicit 0 (:fv FV1))))) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":28590,"sourceStart":28588,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":28592,"sourceStart":28591,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":28595,"sourceSt... | [] | [{"source":"inf_eq_left","source_end":28607,"source_start":28596,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 37 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3c3718c94fa21a11dd480d19fdc50c70d9daf8acf9c284d86204c988ff14466e | c106c07d74cc2652e1abd826c8c16bd4a9b4a0a1de68a0782212689c610904f6 | 1003e81edd81ef73dfbcebdacb0dd8e12ba48ac4bbfb4e6379fadea368416829 | 64245dbca01be19ab6c377b4568daa207393ae19282231af6b29027972cd9255 |
cat-searcher/leandojo-benchmark-4-random | test | 2,873 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine (ha.le_iff.mp <a>inf_le_left</a>).<a>Or.resolve_left</a> fun con => ha.1 ?_ | case refine_2.intro.intro.intro.intro
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind ... | case refine_2.intro.intro.intro.intro
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind ... | ((:c Eq) (:fv _uniq.84775) ((:c Inf.inf) (:fv _uniq.84775) ((:c SemilatticeInf.toInf) (:fv _uniq.84775) ((:c Lattice.toSemilatticeInf) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLattice) (:fv _uniq.84775) ((:c CompleteLattice.toConditionallyCompleteLattice) (:fv _uniq.84775) (:fv _uniq.84778))))) (:fv _uniq.... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Inf.inf) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Inf) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:fv FV14)) (:arg :explicit 3 (:app (:c Sup.sup) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"refine","sourceEnd":28617,"sourceStart":28611,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":28619,"sourceStart":28618,"tag":"atom"},{"children":[{"source":"ha.le_iff.mp","sourceEnd":28631,"sourceStart":28619,"tag":"identifier"},{"children":[{"name":"inf_le_left",... | [] | [{"source":"(ha.le_iff.mp inf_le_left).resolve_left fun con => ha.1 ?_","source_end":28676,"source_start":28618,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 40 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0ddfc51ee6e4aaf32ba7de84e78531b080c4fd3f3b4a1f64683a310446763779 | 64245dbca01be19ab6c377b4568daa207393ae19282231af6b29027972cd9255 | 4d791f74fa98bcbe2063eada6543f44a0ab1471108719fd7a26dfa0a52af38b6 | dc8dc6f92b176cae6a7e351dde4c72af18b2e0a9e55b0914c1df5266955c9bc3 |
cat-searcher/leandojo-benchmark-4-random | test | 2,874 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← con, <a>eq_comm</a>, <a>inf_eq_left</a>] | case refine_2.intro.intro.intro.intro
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind ... | case refine_2.intro.intro.intro.intro
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind ... | ((:c Eq) (:fv _uniq.84775) (:fv _uniq.86944) ((:c Bot.bot) (:fv _uniq.84775) ((:c OrderBot.toBot) (:fv _uniq.84775) ((:c Preorder.toLE) (:fv _uniq.84775) ((:c PartialOrder.toPreorder) (:fv _uniq.84775) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.84775) ((:c CompleteLattice.toCompleteSemilatticeInf) (:fv _uni... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV14)) (:arg :explicit 2 (:app (:c Bot.bot) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Bot) (:arg :explicit 0 (:fv FV1)))))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":28681,"sourceStart":28679,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":28683,"sourceStart":28682,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":28686,"sourceSt... | [] | [{"source":"con","source_end":28690,"source_start":28687,"syntax_kind":"ident"},{"source":"eq_comm","source_end":28699,"source_start":28692,"syntax_kind":"ident"},{"source":"inf_eq_left","source_end":28712,"source_start":28701,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 41 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f514a3e19db5a80bfac7f4494c94a11fda5d35f30f01a72f35ca498d84f88234 | dc8dc6f92b176cae6a7e351dde4c72af18b2e0a9e55b0914c1df5266955c9bc3 | 65c96ab1ef2974637c53edb22910e0248bfef2d47603054058d9ffa901e61c34 | 41d3c3320a3610a5ff80846c18079b3c7472f83ec15e35cafec6ca1ec8eb184b |
cat-searcher/leandojo-benchmark-4-random | test | 2,875 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine (<a>le_sSup</a> ?_).<a>LE.le.trans</a> <a>le_sup_right</a> | case refine_2.intro.intro.intro.intro
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind ... | case refine_2.intro.intro.intro.intro
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind ... | ((:c LE.le) (:fv _uniq.84775) ((:c Preorder.toLE) (:fv _uniq.84775) ((:c PartialOrder.toPreorder) (:fv _uniq.84775) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.84775) ((:c Lattice.toSemilatticeInf) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLattice) (:fv _uniq.84775) ((:c CompleteLattice.toConditionallyCo... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:fv FV14)) (:arg :explicit 3 (:app (:c Sup.sup) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Sup) (:arg :explicit 0 (:fv FV1))))) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"refine","sourceEnd":28722,"sourceStart":28716,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":28724,"sourceStart":28723,"tag":"atom"},{"children":[{"name":"le_sSup","semanticRole":"global","source":"le_sSup","sourceEnd":28731,"sourceStart":28724,"tag":"identifier"}... | [] | [{"source":"(le_sSup ?_).trans le_sup_right","source_end":28754,"source_start":28723,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 46 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9b9bb2c0bf60d0f494aecf20f2dbc5da2cf81e7d555dd3f18374f49554412213 | 41d3c3320a3610a5ff80846c18079b3c7472f83ec15e35cafec6ca1ec8eb184b | 7fd1b12ad2c5260028333377ef78d9b11902b6ad36b9f73f07be4274001b1019 | eda5e83eb7262c5ac4efff19cd873de6eafc8b567f0e2fec5969a5f224abb966 |
cat-searcher/leandojo-benchmark-4-random | test | 2,876 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>disjoint_iff</a>] at con | case refine_2.intro.intro.intro.intro
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind ... | case refine_2.intro.intro.intro.intro
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind ... | ((:c Membership.mem) (:fv _uniq.84775) ((:c Set) (:fv _uniq.84775)) ((:c Set.instMembership) (:fv _uniq.84775)) (:fv _uniq.86944) (:fv _uniq.86318)) | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 3 (:fv FV14)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":28759,"sourceStart":28757,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":28761,"sourceStart":28760,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":28764,"sourceSt... | [] | [{"source":"disjoint_iff","source_end":28777,"source_start":28765,"syntax_kind":"ident"},{"source":"con","source_end":28785,"source_start":28782,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 47 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6421c43d34746dd226e4e871542df02e6e26aa9ae1f1daaa65c3a78a255123b1 | eda5e83eb7262c5ac4efff19cd873de6eafc8b567f0e2fec5969a5f224abb966 | 9712d45c8cc905c788487d278b5ca4d701cbd16b2003efbd20f73c95ce6a6c69 | 7b365f3a8097f8bae5693c5a3e991a1c7859b59690bfb04d8190487620ff1c5d |
cat-searcher/leandojo-benchmark-4-random | test | 2,877 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have a_dis_Sup_s : <a>Disjoint</a> a (<a>SupSet.sSup</a> s) := con.mono_right <a>le_sup_right</a> | case refine_2.intro.intro.intro.intro
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind ... | case refine_2.intro.intro.intro.intro
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind ... | ((:c Membership.mem) (:fv _uniq.84775) ((:c Set) (:fv _uniq.84775)) ((:c Set.instMembership) (:fv _uniq.84775)) (:fv _uniq.86944) (:fv _uniq.86318)) | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 3 (:fv FV14)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"have","sourceEnd":28792,"sourceStart":28788,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"a_dis_Sup_s","sourceEnd":28804,"sourceStart":28793,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"a_dis_Sup_s","sourceEnd":28804,"sourceStart... | [] | [{"source":"Disjoint a (sSup s)","source_end":28826,"source_start":28807,"syntax_kind":"Lean.Parser.Term.app"},{"source":"con.mono_right le_sup_right\n -- Porting note: The two following `fun x hx => _` are no-op","source_end":28857,"source_start":28830,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 50 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 59396fa250ce78bb1e424895a6aa0623243ac543a64c29dc7a698c2aba16535e | 7b365f3a8097f8bae5693c5a3e991a1c7859b59690bfb04d8190487620ff1c5d | 09132967fabb1f13bfe37e76801ccb5ccd86159f87bbbec788fc1fdece13b2d5 | 301bc4c671c1d56b500387e0bd602dd52427afe4cf523633985cc0ca3ae060e1 |
cat-searcher/leandojo-benchmark-4-random | test | 2,878 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← s_max (s ∪ {a}) ⟨fun x hx => _, _, fun x hx => _⟩ <a>Set.subset_union_left</a>] | case refine_2.intro.intro.intro.intro
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind ... | case refine_2.intro.intro.intro.intro
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind ... | ((:c Membership.mem) (:fv _uniq.84775) ((:c Set) (:fv _uniq.84775)) ((:c Set.instMembership) (:fv _uniq.84775)) (:fv _uniq.86944) (:fv _uniq.86318)) | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 3 (:fv FV14)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":28925,"sourceStart":28923,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":28927,"sourceStart":28926,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":28930,"sourceSt... | [] | [{"source":"s_max (s ∪ {a}) ⟨fun x hx => _, _, fun x hx => _⟩ Set.subset_union_left","source_end":29008,"source_start":28931,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 51 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b1fabe4f85a7af1070ee0bfb51707476cbc552bbbbf1557472bd132af3ee28ac | 301bc4c671c1d56b500387e0bd602dd52427afe4cf523633985cc0ca3ae060e1 | cbf8d5c525a75fef672eba73edfdd8961d42cd8854dc7abda221215d3c2e35b1 | 461ce9f7172e5414fffa2f0adbd1af6633f721d209372fda7c68c8d31f28e48b |
cat-searcher/leandojo-benchmark-4-random | test | 2,879 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>sSup_sUnion</a>, ← <a>sSup_image</a>, <a>DirectedOn.disjoint_sSup_right</a>] | case refine_1
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
c : Set (Set α)
hc1 : c ⊆ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}
hc2 : IsChain (fun x x_1 => x ⊆ x_1) c
⊢ Di... | case refine_1
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
c : Set (Set α)
hc1 : c ⊆ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}
hc2 : IsChain (fun x x_1 => x ⊆ x_1) c
⊢ ∀ ... | ((:c Disjoint) (:fv _uniq.84775) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.84775) ((:c CompleteLattice.toCompleteSemilatticeInf) (:fv _uniq.84775) (:fv _uniq.84778))) ((:c BoundedOrder.toOrderBot) (:fv _uniq.84775) ((:c Preorder.toLE) (:fv _uniq.84775) ((:c PartialOrder.toPreorder) (:fv _uniq.84775) ((:c C... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c Disjoint) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c PartialOrder) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 2 (:instance-of (:app (:c OrderBot) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1)))))))) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":28194,"sourceStart":28192,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":28196,"sourceStart":28195,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"sSup_sUnion","se... | [] | [{"source":"sSup_sUnion","source_end":28207,"source_start":28196,"syntax_kind":"ident"},{"source":"sSup_image","source_end":28223,"source_start":28213,"syntax_kind":"ident"},{"source":"DirectedOn.disjoint_sSup_right","source_end":28255,"source_start":28225,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 10 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4733c4685430d0b090c57cf7654cb1f55b56bc4befbf63a5e9c1271c71e57207 | e2a4f9ed5c6fda289267f63a587f46a0c0ae331af9da5a340342753780506301 | a6e12320f952bac7e4a63849673093af00ee5a983e5c4630a3fd9ecc1e6b8b0e | d3050e0e63c0538ed990c7d84cd79d4c514d29a77cbfeb021a2496d3079951d7 |
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