url stringclasses 1
value | commit stringclasses 1
value | file_path stringlengths 21 79 | full_name stringlengths 3 121 | start listlengths 2 2 | end listlengths 2 2 | traced_tactics listlengths 1 128 |
|---|---|---|---|---|---|---|
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/RingTheory/IntegralRestrict.lean | Algebra.intTrace_eq_trace | [
216,
1
] | [
223,
81
] | [
{
"tactic": "ext x",
"annotated_tactic": [
"ext x",
[]
],
"state_before": "A : Type u_1\nK : Type u_2\nL : Type u_3\nB : Type u_4\ninst✝³⁰ : CommRing A\ninst✝²⁹ : CommRing B\ninst✝²⁸ : Algebra A B\ninst✝²⁷ : Field K\ninst✝²⁶ : Field L\ninst✝²⁵ : Algebra A K\ninst✝²⁴ : IsFractionRing A K\... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/NumberTheory/ModularForms/EisensteinSeries/Basic.lean | EisensteinSeries.vecMul_SL2_mem_gammaSet | [
61,
1
] | [
68,
7
] | [
{
"tactic": "refine ⟨?_, hv.2.vecMulSL γ⟩",
"annotated_tactic": [
"refine ⟨?_, hv.2.<a>vecMulSL</a> γ⟩",
[
{
"full_name": "IsCoprime.vecMulSL",
"def_path": "Mathlib/LinearAlgebra/Matrix/SpecialLinearGroup.lean",
"def_pos": [
464,
7
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Data/Matrix/Block.lean | Matrix.toBlocks₂₂_diagonal | [
310,
1
] | [
315,
61
] | [
{
"tactic": "unfold toBlocks₂₂",
"annotated_tactic": [
"unfold <a>toBlocks₂₂</a>",
[
{
"full_name": "Matrix.toBlocks₂₂",
"def_path": "Mathlib/Data/Matrix/Block.lean",
"def_pos": [
93,
5
],
"def_end_pos": [
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/AlgebraicTopology/DoldKan/EquivalencePseudoabelian.lean | CategoryTheory.Idempotents.DoldKan.hη | [
110,
1
] | [
116,
55
] | [
{
"tactic": "ext K : 3",
"annotated_tactic": [
"ext K : 3",
[]
],
"state_before": "C : Type u_1\ninst✝³ : Category.{u_2, u_1} C\ninst✝² : Preadditive C\ninst✝¹ : IsIdempotentComplete C\ninst✝ : HasFiniteCoproducts C\n⊢ Compatibility.τ₀ = Compatibility.τ₁ isoN₁ isoΓ₀ N₁Γ₀",
"state_aft... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/RingTheory/IntegralRestrict.lean | Algebra.algebraMap_intTrace_fractionRing | [
203,
1
] | [
212,
34
] | [
{
"tactic": "haveI : IsIntegralClosure B A (FractionRing B) :=\n IsIntegralClosure.of_isIntegrallyClosed _ _ _",
"annotated_tactic": [
"haveI : <a>IsIntegralClosure</a> B A (<a>FractionRing</a> B) :=\n <a>IsIntegralClosure.of_isIntegrallyClosed</a> _ _ _",
[
{
"full_name": ... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Analysis/Normed/Group/AddTorsor.lean | edist_vsub_vsub_le | [
197,
1
] | [
201,
26
] | [
{
"tactic": "simp only [edist_nndist]",
"annotated_tactic": [
"simp only [<a>edist_nndist</a>]",
[
{
"full_name": "edist_nndist",
"def_path": "Mathlib/Topology/MetricSpace/Pseudo/Defs.lean",
"def_pos": [
306,
9
],
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Data/Nat/Defs.lean | Nat.mul_add_mod' | [
1329,
1
] | [
1329,
98
] | [
{
"tactic": "rw [Nat.mul_comm, Nat.mul_add_mod]",
"annotated_tactic": [
"rw [<a>Nat.mul_comm</a>, <a>Nat.mul_add_mod</a>]",
[
{
"full_name": "Nat.mul_comm",
"def_path": ".lake/packages/lean4/src/lean/Init/Data/Nat/Basic.lean",
"def_pos": [
217,
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Topology/Bases.lean | TopologicalSpace.isTopologicalBasis_of_subbasis | [
108,
1
] | [
119,
70
] | [
{
"tactic": "subst t",
"annotated_tactic": [
"subst t",
[]
],
"state_before": "α : Type u\nβ : Type u_1\nt : TopologicalSpace α\nB : Set (Set α)\ns✝ : Set α\ns : Set (Set α)\nhs : t = generateFrom s\n⊢ IsTopologicalBasis ((fun f => ⋂₀ f) '' {f | f.Finite ∧ f ⊆ s})",
"state_after": "α... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/MeasureTheory/OuterMeasure/OfFunction.lean | MeasureTheory.OuterMeasure.restrict_biInf | [
472,
1
] | [
476,
26
] | [
{
"tactic": "haveI := hI.to_subtype",
"annotated_tactic": [
"haveI := hI.to_subtype",
[]
],
"state_before": "α : Type u_1\nι : Type u_2\nI : Set ι\nhI : I.Nonempty\ns : Set α\nm : ι → OuterMeasure α\n⊢ (restrict s) (⨅ i ∈ I, m i) = ⨅ i ∈ I, (restrict s) (m i)",
"state_after": "α : Ty... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Data/Finset/Basic.lean | Finset.disjoint_insert_right | [
1341,
1
] | [
1342,
76
] | [
{
"tactic": "rw [disjoint_insert_left, _root_.disjoint_comm]",
"annotated_tactic": [
"rw [<a>disjoint_insert_left</a>, <a>_root_.disjoint_comm</a>]",
[
{
"full_name": "Finset.disjoint_insert_left",
"def_path": "Mathlib/Data/Finset/Basic.lean",
"def_pos": [
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/RingTheory/Noetherian.lean | isNoetherian_of_fg_of_noetherian | [
576,
1
] | [
608,
53
] | [
{
"tactic": "let ⟨s, hs⟩ := hN",
"annotated_tactic": [
"let ⟨s, hs⟩ := hN",
[]
],
"state_before": "R : Type u_1\nM : Type u_2\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nN : Submodule R M\nI : IsNoetherianRing R\nhN : N.FG\n⊢ IsNoetherian R ↥N",
"state_after": "R :... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Data/Ordmap/Ordset.lean | Ordnode.dual_rotateL | [
336,
1
] | [
339,
54
] | [
{
"tactic": "cases r <;> simp [rotateL, rotateR, dual_node']",
"annotated_tactic": [
"cases r <;> simp [<a>rotateL</a>, <a>rotateR</a>, <a>dual_node'</a>]",
[
{
"full_name": "Ordnode.rotateL",
"def_path": "Mathlib/Data/Ordmap/Ordset.lean",
"def_pos": [
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.ofLe_eq_comap_incl | [
626,
1
] | [
629,
6
] | [
{
"tactic": "ext",
"annotated_tactic": [
"ext",
[]
],
"state_before": "R : Type u\nL : Type v\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\nL₂ : Type w\ninst✝¹ : LieRing L₂\ninst✝ : LieAlgebra R L₂\nf : L →ₗ⁅R⁆ L₂\nK K' : LieSubalgebra R L\nK₂ : LieSubalgebra R L₂\nh... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/MeasureTheory/Measure/Haar/OfBasis.lean | parallelepiped_single | [
153,
1
] | [
181,
35
] | [
{
"tactic": "ext x",
"annotated_tactic": [
"ext x",
[]
],
"state_before": "ι : Type u_1\nι' : Type u_2\nE : Type u_3\nF : Type u_4\ninst✝⁶ : Fintype ι\ninst✝⁵ : Fintype ι'\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module ℝ E\ninst✝² : AddCommGroup F\ninst✝¹ : Module ℝ F\ninst✝ : DecidableEq ι\n... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Data/Ordmap/Ordset.lean | Ordnode.dual_node3L | [
316,
1
] | [
318,
46
] | [
{
"tactic": "simp [node3L, node3R, dual_node', add_comm]",
"annotated_tactic": [
"simp [<a>node3L</a>, <a>node3R</a>, <a>dual_node'</a>, <a>add_comm</a>]",
[
{
"full_name": "Ordnode.node3L",
"def_path": "Mathlib/Data/Ordmap/Ordset.lean",
"def_pos": [
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/LinearAlgebra/Trace.lean | LinearMap.trace_eq_contract_of_basis' | [
155,
1
] | [
157,
76
] | [
{
"tactic": "simp [LinearEquiv.eq_comp_toLinearMap_symm, trace_eq_contract_of_basis b]",
"annotated_tactic": [
"simp [<a>LinearEquiv.eq_comp_toLinearMap_symm</a>, <a>trace_eq_contract_of_basis</a> b]",
[
{
"full_name": "LinearEquiv.eq_comp_toLinearMap_symm",
"def_path... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Algebra/Module/Basic.lean | map_ratCast_smul | [
64,
1
] | [
69,
56
] | [
{
"tactic": "rw [Rat.cast_def, Rat.cast_def, div_eq_mul_inv, div_eq_mul_inv, mul_smul, mul_smul,\n map_intCast_smul f R S, map_inv_natCast_smul f R S]",
"annotated_tactic": [
"rw [<a>Rat.cast_def</a>, <a>Rat.cast_def</a>, <a>div_eq_mul_inv</a>, <a>div_eq_mul_inv</a>, <a>mul_smul</a>, <a>mul_smul</a>,... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Topology/Order/DenselyOrdered.lean | tendsto_Ioo_atBot | [
378,
1
] | [
380,
62
] | [
{
"tactic": "rw [← comap_coe_Ioo_nhdsWithin_Ioi, tendsto_comap_iff]",
"annotated_tactic": [
"rw [← <a>comap_coe_Ioo_nhdsWithin_Ioi</a>, <a>tendsto_comap_iff</a>]",
[
{
"full_name": "comap_coe_Ioo_nhdsWithin_Ioi",
"def_path": "Mathlib/Topology/Order/DenselyOrdered.lean... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Algebra/Lie/OfAssociative.lean | LieModule.toEnd_lie | [
256,
1
] | [
258,
7
] | [
{
"tactic": "simp",
"annotated_tactic": [
"simp",
[]
],
"state_before": "R : Type u\nL : Type v\nM : Type w\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : LieRingModule L M\ninst✝ : LieModule R L M\nx y : L\nz : M... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Data/Set/Lattice.lean | Set.iUnion_univ_pi | [
1999,
1
] | [
2002,
26
] | [
{
"tactic": "ext",
"annotated_tactic": [
"ext",
[]
],
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nι✝ : Sort u_4\nι' : Sort u_5\nι₂ : Sort u_6\nκ : ι✝ → Sort u_7\nκ₁ : ι✝ → Sort u_8\nκ₂ : ι✝ → Sort u_9\nκ' : ι' → Sort u_10\nπ : α → Type u_11\nι : α → Type u_12\nt : (a : α) ... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Algebra/Algebra/Spectrum.lean | spectrum.units_smul_resolvent_self | [
187,
1
] | [
190,
42
] | [
{
"tactic": "simpa only [Units.smul_def, Algebra.id.smul_eq_mul, Units.inv_mul] using\n @units_smul_resolvent _ _ _ _ _ r r a",
"annotated_tactic": [
"simpa only [<a>Units.smul_def</a>, <a>Algebra.id.smul_eq_mul</a>, <a>Units.inv_mul</a>] using\n @<a>units_smul_resolvent</a> _ _ _ _ _ r r a",
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Data/Int/ModEq.lean | Int.gcd_a_modEq | [
274,
1
] | [
276,
54
] | [
{
"tactic": "rw [← add_zero ((a : ℤ) * _), Nat.gcd_eq_gcd_ab]",
"annotated_tactic": [
"rw [← <a>add_zero</a> ((a : ℤ) * _), <a>Nat.gcd_eq_gcd_ab</a>]",
[
{
"full_name": "add_zero",
"def_path": "Mathlib/Algebra/Group/Defs.lean",
"def_pos": [
482,
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Data/Set/Function.lean | Function.Semiconj.bijOn_range | [
1870,
1
] | [
1873,
63
] | [
{
"tactic": "rw [← image_univ]",
"annotated_tactic": [
"rw [← <a>image_univ</a>]",
[
{
"full_name": "Set.image_univ",
"def_path": "Mathlib/Data/Set/Image.lean",
"def_pos": [
701,
9
],
"def_end_pos": [
7... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Data/Matroid/Constructions.lean | Matroid.emptyOn_dual_eq | [
61,
9
] | [
62,
34
] | [
{
"tactic": "rw [← ground_eq_empty_iff]",
"annotated_tactic": [
"rw [← <a>ground_eq_empty_iff</a>]",
[
{
"full_name": "Matroid.ground_eq_empty_iff",
"def_path": "Mathlib/Data/Matroid/Constructions.lean",
"def_pos": [
57,
9
]... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/GroupTheory/Finiteness.lean | Subgroup.fg_iff | [
237,
1
] | [
240,
44
] | [
{
"tactic": "simp [hS]",
"annotated_tactic": [
"simp [hS]",
[]
],
"state_before": "M : Type u_1\nN : Type u_2\ninst✝³ : Monoid M\ninst✝² : AddMonoid N\nG : Type u_3\nH : Type u_4\ninst✝¹ : Group G\ninst✝ : AddGroup H\nP : Subgroup G\nx✝ : ∃ S, closure S = P ∧ S.Finite\nS : Set G\nhS : cl... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/RingTheory/FractionalIdeal/Basic.lean | IsFractional.sup | [
452,
1
] | [
462,
42
] | [
{
"tactic": "rcases mem_sup.mp hb with ⟨bI, hbI, bJ, hbJ, rfl⟩",
"annotated_tactic": [
"rcases mem_sup.mp hb with ⟨bI, hbI, bJ, hbJ, rfl⟩",
[]
],
"state_before": "R : Type u_1\ninst✝² : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝¹ : CommRing P\ninst✝ : Algebra R P\nloc : IsLocalizat... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/LinearAlgebra/TensorProduct/Vanishing.lean | TensorProduct.forall_vanishesTrivially_iff_forall_rTensor_injective | [
230,
1
] | [
238,
81
] | [
{
"tactic": "constructor",
"annotated_tactic": [
"constructor",
[]
],
"state_before": "R : Type u\ninst✝⁵ : CommRing R\nM : Type u\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\nN : Type u\ninst✝² : AddCommGroup N\ninst✝¹ : Module R N\nι : Type u\ninst✝ : Fintype ι\nm : ι → M\nn : ι → N\... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Algebra/BigOperators/Group/Finset.lean | Finset.prod_powerset_cons | [
515,
1
] | [
524,
69
] | [
{
"tactic": "classical\nsimp_rw [cons_eq_insert]\nrw [prod_powerset_insert ha, prod_attach _ fun t ↦ f (insert a t)]",
"annotated_tactic": [
"classical\n simp_rw [<a>cons_eq_insert</a>]\n rw [<a>prod_powerset_insert</a> ha, <a>prod_attach</a> _ fun t ↦ f (<a>insert</a> a t)]",
[
{
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Probability/Kernel/MeasureCompProd.lean | MeasureTheory.Measure.compProd_add_left | [
82,
1
] | [
85,
73
] | [
{
"tactic": "rw [Measure.compProd, kernel.const_add, kernel.compProd_add_left]",
"annotated_tactic": [
"rw [<a>Measure.compProd</a>, <a>kernel.const_add</a>, <a>kernel.compProd_add_left</a>]",
[
{
"full_name": "MeasureTheory.Measure.compProd",
"def_path": "Mathlib/Pro... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Algebra/DirectSum/Basic.lean | DirectSum.toAddMonoid.unique | [
217,
1
] | [
221,
25
] | [
{
"tactic": "congr",
"annotated_tactic": [
"congr",
[]
],
"state_before": "ι : Type v\ndec_ι : DecidableEq ι\nβ : ι → Type w\ninst✝¹ : (i : ι) → AddCommMonoid (β i)\nγ : Type u₁\ninst✝ : AddCommMonoid γ\nφ : (i : ι) → β i →+ γ\nψ : (⨁ (i : ι), β i) →+ γ\nf : ⨁ (i : ι), β i\n⊢ ψ f = (toAd... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Data/Fintype/Card.lean | Fintype.card_eq_zero_iff | [
537,
1
] | [
538,
52
] | [
{
"tactic": "rw [card, Finset.card_eq_zero, univ_eq_empty_iff]",
"annotated_tactic": [
"rw [<a>card</a>, <a>Finset.card_eq_zero</a>, <a>univ_eq_empty_iff</a>]",
[
{
"full_name": "Fintype.card",
"def_path": "Mathlib/Data/Fintype/Card.lean",
"def_pos": [
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | mem_vectorSpan_pair | [
1294,
1
] | [
1296,
53
] | [
{
"tactic": "rw [vectorSpan_pair, Submodule.mem_span_singleton]",
"annotated_tactic": [
"rw [<a>vectorSpan_pair</a>, <a>Submodule.mem_span_singleton</a>]",
[
{
"full_name": "vectorSpan_pair",
"def_path": "Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean",
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Topology/Algebra/InfiniteSum/Order.lean | one_lt_tprod | [
220,
1
] | [
223,
51
] | [
{
"tactic": "rw [← tprod_one]",
"annotated_tactic": [
"rw [← <a>tprod_one</a>]",
[
{
"full_name": "tprod_one",
"def_path": "Mathlib/Topology/Algebra/InfiniteSum/Basic.lean",
"def_pos": [
416,
9
],
"def_end_pos": [
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/AlgebraicGeometry/Morphisms/QuasiSeparated.lean | AlgebraicGeometry.IsAffineOpen.isQuasiSeparated | [
272,
1
] | [
275,
77
] | [
{
"tactic": "rw [isQuasiSeparated_iff_quasiSeparatedSpace]",
"annotated_tactic": [
"rw [<a>isQuasiSeparated_iff_quasiSeparatedSpace</a>]",
[
{
"full_name": "isQuasiSeparated_iff_quasiSeparatedSpace",
"def_path": "Mathlib/Topology/QuasiSeparated.lean",
"def_p... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/RepresentationTheory/Character.lean | FdRep.average_char_eq_finrank_invariants | [
106,
1
] | [
109,
57
] | [
{
"tactic": "erw [← (isProj_averageMap V.ρ).trace]",
"annotated_tactic": [
"erw [← (<a>isProj_averageMap</a> V.ρ).<a>trace</a>]",
[
{
"full_name": "Representation.isProj_averageMap",
"def_path": "Mathlib/RepresentationTheory/Invariants.lean",
"def_pos": [
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Order/SymmDiff.lean | symmDiff_hnot_self | [
357,
1
] | [
357,
87
] | [
{
"tactic": "rw [symmDiff_comm, hnot_symmDiff_self]",
"annotated_tactic": [
"rw [<a>symmDiff_comm</a>, <a>hnot_symmDiff_self</a>]",
[
{
"full_name": "symmDiff_comm",
"def_path": "Mathlib/Order/SymmDiff.lean",
"def_pos": [
113,
9
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Algebra/Order/Ring/Basic.lean | le_self_pow | [
100,
1
] | [
101,
76
] | [
{
"tactic": "simpa only [pow_one] using pow_le_pow_right ha <| Nat.pos_iff_ne_zero.2 h",
"annotated_tactic": [
"simpa only [<a>pow_one</a>] using <a>pow_le_pow_right</a> ha <| <a>Nat.pos_iff_ne_zero</a>.2 h",
[
{
"full_name": "pow_one",
"def_path": "Mathlib/Algebra/Gr... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Data/Seq/Computation.lean | Computation.results_bind | [
776,
1
] | [
789,
32
] | [
{
"tactic": "have := h1.mem",
"annotated_tactic": [
"have := h1.mem",
[]
],
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : Computation α\nf : α → Computation β\na : α\nb : β\nm n : ℕ\nh1 : s.Results a m\nh2 : (f a).Results b n\n⊢ (s.bind f).Results b (n + m)",
"state_after"... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | .lake/packages/batteries/Batteries/Data/String/Lemmas.lean | Substring.Valid.foldr | [
1038,
1
] | [
1039,
74
] | [
{
"tactic": "simp [h.foldr, h.toString]",
"annotated_tactic": [
"simp [h.foldr, h.toString]",
[]
],
"state_before": "α : Type u_1\nf : Char → α → α\ninit : α\nx✝ : Substring\nh✝ : x✝.Valid\nw✝² w✝¹ w✝ : List Char\nh : ValidFor w✝² w✝¹ w✝ x✝\n⊢ Substring.foldr f init x✝ = List.foldr f ini... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Analysis/Calculus/ContDiff/Defs.lean | contDiff_succ_iff_hasFDerivAt | [
1533,
1
] | [
1537,
91
] | [
{
"tactic": "simp only [← contDiffOn_univ, ← hasFDerivWithinAt_univ,\n contDiffOn_succ_iff_hasFDerivWithin uniqueDiffOn_univ, Set.mem_univ, forall_true_left]",
"annotated_tactic": [
"simp only [← <a>contDiffOn_univ</a>, ← <a>hasFDerivWithinAt_univ</a>,\n <a>contDiffOn_succ_iff_hasFDerivWithin</a> ... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Data/Complex/ExponentialBounds.lean | Real.exp_neg_one_gt_d9 | [
44,
1
] | [
48,
13
] | [
{
"tactic": "rw [exp_neg, lt_inv _ (exp_pos _)]",
"annotated_tactic": [
"rw [<a>exp_neg</a>, <a>lt_inv</a> _ (<a>exp_pos</a> _)]",
[
{
"full_name": "Real.exp_neg",
"def_path": "Mathlib/Data/Complex/Exponential.lean",
"def_pos": [
862,
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Analysis/InnerProductSpace/Adjoint.lean | LinearMap.adjoint_inner_left | [
381,
1
] | [
385,
53
] | [
{
"tactic": "haveI := FiniteDimensional.complete 𝕜 E",
"annotated_tactic": [
"haveI := <a>FiniteDimensional.complete</a> 𝕜 E",
[
{
"full_name": "FiniteDimensional.complete",
"def_path": "Mathlib/Topology/Algebra/Module/FiniteDimension.lean",
"def_pos": [
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/CategoryTheory/Abelian/Homology.lean | homology'.π'_map | [
207,
1
] | [
235,
9
] | [
{
"tactic": "simp [h, β.w.symm]",
"annotated_tactic": [
"simp [h, β.w.symm]",
[]
],
"state_before": "A : Type u\ninst✝¹ : Category.{v, u} A\ninst✝ : Abelian A\nX Y Z : A\nf : X ⟶ Y\ng : Y ⟶ Z\nw : f ≫ g = 0\nX' Y' Z' : A\nf' : X' ⟶ Y'\ng' : Y' ⟶ Z'\nw' : f' ≫ g' = 0\nα : Arrow.mk f ⟶ Arr... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Data/List/Rotate.lean | List.IsRotated.refl | [
433,
1
] | [
434,
15
] | [
{
"tactic": "simp",
"annotated_tactic": [
"simp",
[]
],
"state_before": "α : Type u\nl✝ l' l : List α\n⊢ l.rotate 0 = l",
"state_after": "no goals"
}
] |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Order/Interval/Finset/Basic.lean | Finset.Ioc_eq_empty_iff | [
88,
1
] | [
89,
53
] | [
{
"tactic": "rw [← coe_eq_empty, coe_Ioc, Set.Ioc_eq_empty_iff]",
"annotated_tactic": [
"rw [← <a>coe_eq_empty</a>, <a>coe_Ioc</a>, <a>Set.Ioc_eq_empty_iff</a>]",
[
{
"full_name": "Finset.coe_eq_empty",
"def_path": "Mathlib/Data/Finset/Basic.lean",
"def_pos"... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.sum_cramer_apply | [
160,
1
] | [
170,
29
] | [
{
"tactic": "rw [sum_cramer, cramer_apply, cramer_apply]",
"annotated_tactic": [
"rw [<a>sum_cramer</a>, <a>cramer_apply</a>, <a>cramer_apply</a>]",
[
{
"full_name": "Matrix.sum_cramer",
"def_path": "Mathlib/LinearAlgebra/Matrix/Adjugate.lean",
"def_pos": [
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Algebra/Polynomial/FieldDivision.lean | Polynomial.rootSet_prod | [
494,
1
] | [
499,
47
] | [
{
"tactic": "classical\nsimp only [rootSet, aroots, ← Finset.mem_coe]\nrw [Polynomial.map_prod, roots_prod, Finset.bind_toFinset, s.val_toFinset, Finset.coe_biUnion]\nrwa [← Polynomial.map_prod, Ne, map_eq_zero]",
"annotated_tactic": [
"classical\n simp only [<a>rootSet</a>, <a>aroots</a>, ← <a>Finse... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Analysis/Normed/Field/Basic.lean | Real.toNNReal_mul_nnnorm | [
1065,
1
] | [
1068,
19
] | [
{
"tactic": "ext",
"annotated_tactic": [
"ext",
[]
],
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nι : Type u_4\nx y : ℝ\nhx : 0 ≤ x\n⊢ x.toNNReal * ‖y‖₊ = ‖x * y‖₊",
"state_after": "case a\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nι : Type u_4\nx y : ℝ\nhx : 0 ≤ x\n⊢ ... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/CategoryTheory/Adjunction/Basic.lean | CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_right_symm | [
334,
1
] | [
336,
33
] | [
{
"tactic": "rw [Equiv.symm_apply_eq]",
"annotated_tactic": [
"rw [<a>Equiv.symm_apply_eq</a>]",
[
{
"full_name": "Equiv.symm_apply_eq",
"def_path": "Mathlib/Logic/Equiv/Defs.lean",
"def_pos": [
342,
9
],
"def_end_... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Data/NNRat/Lemmas.lean | Rat.toNNRat_inv | [
47,
1
] | [
51,
32
] | [
{
"tactic": "obtain hq | hq := le_total q 0",
"annotated_tactic": [
"obtain hq | hq := <a>le_total</a> q 0",
[
{
"full_name": "le_total",
"def_path": "Mathlib/Init/Order/Defs.lean",
"def_pos": [
297,
9
],
"def_end_... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mk_equiv_eq_arrow_of_lift_eq | [
1123,
1
] | [
1128,
62
] | [
{
"tactic": "obtain ⟨e⟩ := lift_mk_eq'.mp leq",
"annotated_tactic": [
"obtain ⟨e⟩ := lift_mk_eq'.mp leq",
[]
],
"state_before": "α β : Type u\nβ' : Type v\ninst✝ : Infinite α\nleq : lift.{v, u} #α = lift.{u, v} #β'\neq : #α = #β\n⊢ #(α ≃ β') = #(α → β')",
"state_after": "case intro\n... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/RingTheory/Coalgebra/Basic.lean | Prod.comul_comp_inl | [
129,
1
] | [
131,
12
] | [
{
"tactic": "ext",
"annotated_tactic": [
"ext",
[]
],
"state_before": "R : Type u\nA : Type v\nB : Type w\ninst✝⁶ : CommSemiring R\ninst✝⁵ : AddCommMonoid A\ninst✝⁴ : AddCommMonoid B\ninst✝³ : Module R A\ninst✝² : Module R B\ninst✝¹ : Coalgebra R A\ninst✝ : Coalgebra R B\n⊢ comul ∘ₗ inl ... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Topology/Connected/PathConnected.lean | Path.trans_pi_eq_pi_trans | [
581,
1
] | [
586,
20
] | [
{
"tactic": "ext t i",
"annotated_tactic": [
"ext t i",
[]
],
"state_before": "X : Type u_1\nY : Type u_2\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\nx y z : X\nι : Type u_3\nγ : Path x y\nχ : ι → Type u_4\ninst✝ : (i : ι) → TopologicalSpace (χ i)\nas bs cs : (i : ι) → χ i... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Data/QPF/Multivariate/Constructions/Cofix.lean | MvQPF.Cofix.abs_repr | [
432,
1
] | [
445,
6
] | [
{
"tactic": "let R := fun x y : Cofix F α => abs (repr y) = x",
"annotated_tactic": [
"let R := fun x y : <a>Cofix</a> F α => <a>abs</a> (<a>repr</a> y) = x",
[
{
"full_name": "MvQPF.Cofix",
"def_path": "Mathlib/Data/QPF/Multivariate/Constructions/Cofix.lean",
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Analysis/Calculus/Deriv/Basic.lean | norm_deriv_le_of_lip' | [
792,
1
] | [
795,
76
] | [
{
"tactic": "simpa [norm_deriv_eq_norm_fderiv] using norm_fderiv_le_of_lip' 𝕜 hC₀ hlip",
"annotated_tactic": [
"simpa [<a>norm_deriv_eq_norm_fderiv</a>] using <a>norm_fderiv_le_of_lip'</a> 𝕜 hC₀ hlip",
[
{
"full_name": "norm_deriv_eq_norm_fderiv",
"def_path": "Mathl... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Algebra/Order/Field/Basic.lean | lt_one_div | [
384,
1
] | [
384,
100
] | [
{
"tactic": "simpa using lt_inv ha hb",
"annotated_tactic": [
"simpa using <a>lt_inv</a> ha hb",
[
{
"full_name": "lt_inv",
"def_path": "Mathlib/Algebra/Order/Field/Basic.lean",
"def_pos": [
223,
9
],
"def_end_pos"... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Probability/Kernel/WithDensity.lean | ProbabilityTheory.kernel.withDensity_apply | [
60,
11
] | [
65,
6
] | [
{
"tactic": "classical\nrw [withDensity, dif_pos hf]\nrfl",
"annotated_tactic": [
"classical\n rw [<a>withDensity</a>, <a>dif_pos</a> hf]\n rfl",
[
{
"full_name": "ProbabilityTheory.kernel.withDensity",
"def_path": "Mathlib/Probability/Kernel/WithDensity.lean",
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.compQuasiMeasurePreserving_eq_mk | [
228,
1
] | [
231,
75
] | [
{
"tactic": "rw [← compQuasiMeasurePreserving_mk g.aestronglyMeasurable hf, mk_coeFn]",
"annotated_tactic": [
"rw [← <a>compQuasiMeasurePreserving_mk</a> g.aestronglyMeasurable hf, <a>mk_coeFn</a>]",
[
{
"full_name": "MeasureTheory.AEEqFun.compQuasiMeasurePreserving_mk",
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.Measure.outerMeasure_le_iff | [
148,
1
] | [
149,
68
] | [
{
"tactic": "simpa only [μ.trimmed] using OuterMeasure.le_trim_iff (m₂ := μ.1)",
"annotated_tactic": [
"simpa only [μ.trimmed] using <a>OuterMeasure.le_trim_iff</a> (m₂ := μ.1)",
[
{
"full_name": "MeasureTheory.OuterMeasure.le_trim_iff",
"def_path": "Mathlib/MeasureTh... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/CategoryTheory/Subobject/Limits.lean | CategoryTheory.Limits.kernelSubobjectMap_arrow | [
158,
1
] | [
160,
28
] | [
{
"tactic": "simp [kernelSubobjectMap]",
"annotated_tactic": [
"simp [<a>kernelSubobjectMap</a>]",
[
{
"full_name": "CategoryTheory.Limits.kernelSubobjectMap",
"def_path": "Mathlib/CategoryTheory/Subobject/Limits.lean",
"def_pos": [
151,
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | .lake/packages/batteries/Batteries/Data/RBMap/Lemmas.lean | Batteries.RBNode.Stream.foldl_eq_foldl_toList | [
209,
1
] | [
210,
75
] | [
{
"tactic": "induction t generalizing init <;> simp [*, RBNode.foldl_eq_foldl_toList]",
"annotated_tactic": [
"induction t generalizing init <;> simp [*, <a>RBNode.foldl_eq_foldl_toList</a>]",
[
{
"full_name": "Batteries.RBNode.foldl_eq_foldl_toList",
"def_path": ".la... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/CategoryTheory/Category/Cat.lean | CategoryTheory.Cat.associator_hom_app | [
132,
1
] | [
134,
6
] | [
{
"tactic": "simp",
"annotated_tactic": [
"simp",
[]
],
"state_before": "B C D E : Cat\nF : B ⟶ C\nG : C ⟶ D\nH : D ⟶ E\nX : ↑B\n⊢ ((F ≫ G) ≫ H).obj X = (F ≫ G ≫ H).obj X",
"state_after": "no goals"
}
] |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/MeasureTheory/Decomposition/SignedHahn.lean | MeasureTheory.SignedMeasure.exists_subset_restrict_nonpos | [
266,
1
] | [
328,
34
] | [
{
"tactic": "have hi₁ : MeasurableSet i := by_contradiction fun h => ne_of_lt hi <| s.not_measurable h",
"annotated_tactic": [
"have hi₁ : <a>MeasurableSet</a> i := <a>by_contradiction</a> fun h => <a>ne_of_lt</a> hi <| s.not_measurable h",
[
{
"full_name": "MeasurableSet",
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Data/List/Sigma.lean | List.keys_kreplace | [
368,
1
] | [
372,
69
] | [
{
"tactic": "rintro ⟨a₁, b₂⟩ ⟨a₂, b₂⟩",
"annotated_tactic": [
"rintro ⟨a₁, b₂⟩ ⟨a₂, b₂⟩",
[]
],
"state_before": "α : Type u\nβ : α → Type v\nl l₁ l₂ : List (Sigma β)\ninst✝ : DecidableEq α\na : α\nb : β a\n⊢ ∀ (a_1 b_1 : Sigma β), (b_1 ∈ if a = a_1.fst then some ⟨a, b⟩ else none) → a_1.f... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Topology/StoneCech.lean | ultrafilter_extend_extends | [
197,
1
] | [
200,
77
] | [
{
"tactic": "letI : TopologicalSpace α := ⊥",
"annotated_tactic": [
"letI : <a>TopologicalSpace</a> α := ⊥",
[
{
"full_name": "TopologicalSpace",
"def_path": "Mathlib/Topology/Defs/Basic.lean",
"def_pos": [
63,
7
],
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/GroupTheory/PushoutI.lean | Monoid.PushoutI.induction_on | [
167,
1
] | [
184,
47
] | [
{
"tactic": "delta PushoutI PushoutI.of PushoutI.base at *",
"annotated_tactic": [
"delta <a>PushoutI</a> <a>PushoutI.of</a> <a>PushoutI.base</a> at *",
[
{
"full_name": "Monoid.PushoutI",
"def_path": "Mathlib/GroupTheory/PushoutI.lean",
"def_pos": [
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Topology/ProperMap.lean | isProperMap_of_comp_of_t2 | [
157,
1
] | [
165,
16
] | [
{
"tactic": "rw [isProperMap_iff_ultrafilter_of_t2]",
"annotated_tactic": [
"rw [<a>isProperMap_iff_ultrafilter_of_t2</a>]",
[
{
"full_name": "isProperMap_iff_ultrafilter_of_t2",
"def_path": "Mathlib/Topology/ProperMap.lean",
"def_pos": [
117,
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Data/Nat/Digits.lean | Nat.ofDigits_mod_eq_head! | [
666,
1
] | [
667,
49
] | [
{
"tactic": "induction l <;> simp [Nat.ofDigits, Int.ModEq]",
"annotated_tactic": [
"induction l <;> simp [<a>Nat.ofDigits</a>, <a>Int.ModEq</a>]",
[
{
"full_name": "Nat.ofDigits",
"def_path": "Mathlib/Data/Nat/Digits.lean",
"def_pos": [
162,
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Algebra/Tropical/BigOperators.lean | untrop_sum_eq_sInf_image | [
126,
1
] | [
130,
68
] | [
{
"tactic": "rcases s.eq_empty_or_nonempty with (rfl | h)",
"annotated_tactic": [
"rcases s.eq_empty_or_nonempty with (rfl | h)",
[]
],
"state_before": "R : Type u_1\nS : Type u_2\ninst✝ : ConditionallyCompleteLinearOrder R\ns : Finset S\nf : S → Tropical (WithTop R)\n⊢ untrop (∑ i ∈ s, ... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.bsup_not_succ_of_ne_bsup | [
1518,
1
] | [
1522,
45
] | [
{
"tactic": "rw [← sup_eq_bsup] at *",
"annotated_tactic": [
"rw [← <a>sup_eq_bsup</a>] at *",
[
{
"full_name": "Ordinal.sup_eq_bsup",
"def_path": "Mathlib/SetTheory/Ordinal/Arithmetic.lean",
"def_pos": [
1439,
9
],
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Topology/Basic.lean | Set.Finite.interior_sInter | [
325,
1
] | [
327,
46
] | [
{
"tactic": "rw [sInter_eq_biInter, hS.interior_biInter]",
"annotated_tactic": [
"rw [<a>sInter_eq_biInter</a>, hS.interior_biInter]",
[
{
"full_name": "Set.sInter_eq_biInter",
"def_path": "Mathlib/Data/Set/Lattice.lean",
"def_pos": [
1308,
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Topology/Homotopy/HSpaces.lean | Path.delayReflRight_one | [
246,
1
] | [
248,
41
] | [
{
"tactic": "ext t",
"annotated_tactic": [
"ext t",
[]
],
"state_before": "X : Type u\ninst✝ : TopologicalSpace X\nx y : X\nγ : Path x y\n⊢ delayReflRight 1 γ = γ",
"state_after": "case a.h\nX : Type u\ninst✝ : TopologicalSpace X\nx y : X\nγ : Path x y\nt : ↑I\n⊢ (delayReflRight 1 γ)... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/NumberTheory/KummerDedekind.lean | KummerDedekind.normalizedFactors_ideal_map_eq_normalizedFactors_min_poly_mk_map | [
286,
1
] | [
327,
81
] | [
{
"tactic": "ext J",
"annotated_tactic": [
"ext J",
[]
],
"state_before": "R : Type u_1\nS : Type u_2\ninst✝⁶ : CommRing R\ninst✝⁵ : CommRing S\ninst✝⁴ : Algebra R S\nx : S\nI : Ideal R\ninst✝³ : IsDomain R\ninst✝² : IsIntegrallyClosed R\ninst✝¹ : IsDedekindDomain S\ninst✝ : NoZeroSMulDi... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Algebra/GradedMonoid.lean | SetLike.coe_list_dProd | [
726,
1
] | [
734,
41
] | [
{
"tactic": "match l with\n| [] =>\n rw [List.dProd_nil, coe_gOne, List.map_nil, List.prod_nil]\n| head::tail =>\n rw [List.dProd_cons, coe_gMul, List.map_cons, List.prod_cons,\n SetLike.coe_list_dProd _ _ _ tail]",
"annotated_tactic": [
"match l with\n | [] =>\n rw [<a>List.dProd_nil</a>, <a... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Algebra/CubicDiscriminant.lean | Cubic.ne_zero | [
178,
9
] | [
181,
29
] | [
{
"tactic": "contrapose! h0",
"annotated_tactic": [
"contrapose! h0",
[]
],
"state_before": "R : Type u_1\nS : Type u_2\nF : Type u_3\nK : Type u_4\nP Q : Cubic R\na b c d a' b' c' d' : R\ninst✝ : Semiring R\nh0 : P.a ≠ 0 ∨ P.b ≠ 0 ∨ P.c ≠ 0 ∨ P.d ≠ 0\n⊢ P.toPoly ≠ 0",
"state_after":... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Topology/UniformSpace/Equicontinuity.lean | Filter.Tendsto.continuousWithinAt_of_equicontinuousWithinAt | [
942,
1
] | [
951,
28
] | [
{
"tactic": "intro U hU",
"annotated_tactic": [
"intro U hU",
[]
],
"state_before": "ι : Type u_1\nκ : Type u_2\nX : Type u_3\nX' : Type u_4\nY : Type u_5\nZ : Type u_6\nα : Type u_7\nα' : Type u_8\nβ : Type u_9\nβ' : Type u_10\nγ : Type u_11\n𝓕 : Type u_12\ntX : TopologicalSpace X\ntY ... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/SetTheory/Ordinal/Basic.lean | Cardinal.ord_one | [
1425,
1
] | [
1425,
56
] | [
{
"tactic": "simpa using ord_nat 1",
"annotated_tactic": [
"simpa using <a>ord_nat</a> 1",
[
{
"full_name": "Cardinal.ord_nat",
"def_path": "Mathlib/SetTheory/Ordinal/Basic.lean",
"def_pos": [
1416,
9
],
"def_end_p... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Geometry/RingedSpace/OpenImmersion.lean | AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullbackConeOfLeftLift_fst | [
423,
1
] | [
439,
23
] | [
{
"tactic": "refine PresheafedSpace.Hom.ext _ _ ?_ <| NatTrans.ext _ _ <| funext fun x => ?_",
"annotated_tactic": [
"refine <a>PresheafedSpace.Hom.ext</a> _ _ ?_ <| <a>NatTrans.ext</a> _ _ <| <a>funext</a> fun x => ?_",
[
{
"full_name": "AlgebraicGeometry.PresheafedSpace.Hom.e... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/MeasureTheory/MeasurableSpace/Basic.lean | MeasurableSet.tProd | [
1075,
1
] | [
1079,
25
] | [
{
"tactic": "induction' l with i l ih",
"annotated_tactic": [
"induction' l with i l ih",
[]
],
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\nδ' : Type u_5\nι : Sort uι\ns✝ t u : Set α\nπ : δ → Type u_6\ninst✝ : (x : δ) → MeasurableSpace (π x)\nl : List δ\ns : ... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_singleton | [
1682,
1
] | [
1684,
84
] | [
{
"tactic": "simp only [restrict_singleton, lintegral_smul_measure, lintegral_dirac, mul_comm]",
"annotated_tactic": [
"simp only [<a>restrict_singleton</a>, <a>lintegral_smul_measure</a>, <a>lintegral_dirac</a>, <a>mul_comm</a>]",
[
{
"full_name": "MeasureTheory.Measure.restri... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.isSymm_iff_eq_flip | [
244,
1
] | [
250,
6
] | [
{
"tactic": "constructor <;> intro h",
"annotated_tactic": [
"constructor <;> intro h",
[]
],
"state_before": "R : Type u_1\nR₁ : Type u_2\nR₂ : Type u_3\nR₃ : Type u_4\nM : Type u_5\nM₁ : Type u_6\nM₂ : Type u_7\nM₃ : Type u_8\nMₗ₁ : Type u_9\nMₗ₁' : Type u_10\nMₗ₂ : Type u_11\nMₗ₂' : T... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Data/Nat/Bits.lean | Nat.shiftLeft'_sub | [
270,
1
] | [
275,
32
] | [
{
"tactic": "rw [succ_sub_succ_eq_sub, shiftLeft', Nat.add_comm, shiftRight_add]",
"annotated_tactic": [
"rw [<a>succ_sub_succ_eq_sub</a>, <a>shiftLeft'</a>, <a>Nat.add_comm</a>, <a>shiftRight_add</a>]",
[
{
"full_name": "Nat.succ_sub_succ_eq_sub",
"def_path": ".lake/... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/CategoryTheory/Sites/OneHypercover.lean | CategoryTheory.PreOneHypercover.sieve₁_eq_pullback_sieve₁' | [
94,
1
] | [
103,
47
] | [
{
"tactic": "ext Z g",
"annotated_tactic": [
"ext Z g",
[]
],
"state_before": "C : Type u\ninst✝² : Category.{v, u} C\nA : Type u_1\ninst✝¹ : Category.{?u.6702, u_1} A\nS : C\nE : PreOneHypercover S\ni₁ i₂ : E.I₀\ninst✝ : HasPullback (E.f i₁) (E.f i₂)\nW : C\np₁ : W ⟶ E.X i₁\np₂ : W ⟶ E.... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/RingTheory/IntegralRestrict.lean | Algebra.intTrace_eq_of_isLocalization | [
230,
1
] | [
270,
76
] | [
{
"tactic": "by_cases hM : 0 ∈ M",
"annotated_tactic": [
"by_cases hM : 0 ∈ M",
[]
],
"state_before": "A : Type u_1\nK : Type u_2\nL : Type u_3\nB : Type u_4\ninst✝³⁵ : CommRing A\ninst✝³⁴ : CommRing B\ninst✝³³ : Algebra A B\ninst✝³² : Field K\ninst✝³¹ : Field L\ninst✝³⁰ : Algebra A K\ni... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Algebra/Order/Group/Defs.lean | mul_inv_lt_iff_le_mul' | [
553,
1
] | [
554,
41
] | [
{
"tactic": "rw [← inv_mul_lt_iff_lt_mul, mul_comm]",
"annotated_tactic": [
"rw [← <a>inv_mul_lt_iff_lt_mul</a>, <a>mul_comm</a>]",
[
{
"full_name": "inv_mul_lt_iff_lt_mul",
"def_path": "Mathlib/Algebra/Order/Group/Defs.lean",
"def_pos": [
178,
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Data/Part.lean | Part.ofOption_dom | [
337,
1
] | [
339,
40
] | [
{
"tactic": "simp [ofOption, none]",
"annotated_tactic": [
"simp [<a>ofOption</a>, <a>none</a>]",
[
{
"full_name": "Part.ofOption",
"def_path": "Mathlib/Data/Part.lean",
"def_pos": [
325,
5
],
"def_end_pos": [
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Analysis/InnerProductSpace/Adjoint.lean | ContinuousLinearMap.norm_map_iff_adjoint_comp_self | [
521,
1
] | [
523,
85
] | [
{
"tactic": "rw [LinearMap.norm_map_iff_inner_map_map u, u.inner_map_map_iff_adjoint_comp_self]",
"annotated_tactic": [
"rw [<a>LinearMap.norm_map_iff_inner_map_map</a> u, u.inner_map_map_iff_adjoint_comp_self]",
[
{
"full_name": "LinearMap.norm_map_iff_inner_map_map",
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Topology/UniformSpace/Basic.lean | Filter.HasBasis.lebesgue_number_lemma | [
1833,
11
] | [
1838,
89
] | [
{
"tactic": "refine (hbasis.exists_iff ?_).1 (lebesgue_number_lemma hK hopen hcover)",
"annotated_tactic": [
"refine (hbasis.exists_iff ?_).1 (<a>lebesgue_number_lemma</a> hK hopen hcover)",
[
{
"full_name": "lebesgue_number_lemma",
"def_path": "Mathlib/Topology/Unifo... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Data/NNReal/Basic.lean | Real.nnabs_of_nonneg | [
1200,
1
] | [
1202,
52
] | [
{
"tactic": "ext",
"annotated_tactic": [
"ext",
[]
],
"state_before": "x : ℝ\nh : 0 ≤ x\n⊢ nnabs x = x.toNNReal",
"state_after": "case a\nx : ℝ\nh : 0 ≤ x\n⊢ ↑(nnabs x) = ↑x.toNNReal"
},
{
"tactic": "rw [coe_toNNReal x h, coe_nnabs, abs_of_nonneg h]",
"annotated_tactic": ... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/CategoryTheory/CommSq.lean | CategoryTheory.CommSq.HasLift.iff_op | [
246,
1
] | [
248,
84
] | [
{
"tactic": "rw [iff, iff]",
"annotated_tactic": [
"rw [<a>iff</a>, <a>iff</a>]",
[
{
"full_name": "CategoryTheory.CommSq.HasLift.iff",
"def_path": "Mathlib/CategoryTheory/CommSq.lean",
"def_pos": [
241,
9
],
"def_... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Probability/Kernel/Disintegration/Density.lean | ProbabilityTheory.kernel.densityProcess_antitone_kernel_right | [
342,
1
] | [
359,
45
] | [
{
"tactic": "unfold densityProcess",
"annotated_tactic": [
"unfold <a>densityProcess</a>",
[
{
"full_name": "ProbabilityTheory.kernel.densityProcess",
"def_path": "Mathlib/Probability/Kernel/Disintegration/Density.lean",
"def_pos": [
93,
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/LinearAlgebra/AffineSpace/Slope.lean | lineMap_slope_lineMap_slope_lineMap | [
132,
1
] | [
138,
20
] | [
{
"tactic": "obtain rfl | hab : a = b ∨ a ≠ b := Classical.em _",
"annotated_tactic": [
"obtain rfl | hab : a = b ∨ a ≠ b := <a>Classical.em</a> _",
[
{
"full_name": "Classical.em",
"def_path": ".lake/packages/lean4/src/lean/Init/Classical.lean",
"def_pos": ... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Algebra/Homology/ShortComplex/Preadditive.lean | CategoryTheory.ShortComplex.opcyclesMap'_sub | [
241,
1
] | [
245,
65
] | [
{
"tactic": "simp only [sub_eq_add_neg, opcyclesMap'_add, opcyclesMap'_neg]",
"annotated_tactic": [
"simp only [<a>sub_eq_add_neg</a>, <a>opcyclesMap'_add</a>, <a>opcyclesMap'_neg</a>]",
[
{
"full_name": "sub_eq_add_neg",
"def_path": "Mathlib/Algebra/Group/Defs.lean",... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Data/Ordmap/Ordset.lean | Ordnode.insertWith.valid_aux | [
1507,
1
] | [
1534,
33
] | [
{
"tactic": "rw [insertWith, cmpLE]",
"annotated_tactic": [
"rw [<a>insertWith</a>, <a>cmpLE</a>]",
[
{
"full_name": "Ordnode.insertWith",
"def_path": "Mathlib/Data/Ordmap/Ordnode.lean",
"def_pos": [
964,
5
],
"def... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Order/WellFounded.lean | WellFounded.self_le_of_strictMono | [
173,
1
] | [
176,
37
] | [
{
"tactic": "by_contra! h₁",
"annotated_tactic": [
"by_contra! h₁",
[]
],
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nr r' : α → α → Prop\ninst✝¹ : LinearOrder β\nh : WellFounded fun x x_1 => x < x_1\ninst✝ : PartialOrder γ\nf : β → β\nhf : StrictMono f\n⊢ ∀ (n : β), n ≤ f... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/RingTheory/FractionalIdeal/Operations.lean | FractionalIdeal.map_div | [
524,
1
] | [
530,
29
] | [
{
"tactic": "by_cases H : J = 0",
"annotated_tactic": [
"by_cases H : J = 0",
[]
],
"state_before": "R : Type u_1\ninst✝⁹ : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝⁸ : CommRing P\ninst✝⁷ : Algebra R P\nloc : IsLocalization S P\nR₁ : Type u_3\ninst✝⁶ : CommRing R₁\nK : Type u_4\ni... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/MeasureTheory/Constructions/BorelSpace/Real.lean | Real.borel_eq_generateFrom_Ioi_rat | [
56,
1
] | [
66,
64
] | [
{
"tactic": "rw [borel_eq_generateFrom_Ioi]",
"annotated_tactic": [
"rw [<a>borel_eq_generateFrom_Ioi</a>]",
[
{
"full_name": "borel_eq_generateFrom_Ioi",
"def_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/Order.lean",
"def_pos": [
77,
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Order/Heyting/Basic.lean | sdiff_le_sdiff_of_sup_le_sup_left | [
670,
1
] | [
672,
31
] | [
{
"tactic": "rw [← sup_sdiff_left_self, ← @sup_sdiff_left_self _ _ _ b]",
"annotated_tactic": [
"rw [← <a>sup_sdiff_left_self</a>, ← @<a>sup_sdiff_left_self</a> _ _ _ b]",
[
{
"full_name": "sup_sdiff_left_self",
"def_path": "Mathlib/Order/Heyting/Basic.lean",
... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/Data/Nat/PartENat.lean | PartENat.get_le_get | [
318,
1
] | [
321,
48
] | [
{
"tactic": "conv =>\n lhs\n rw [← coe_le_coe, natCast_get, natCast_get]",
"annotated_tactic": [
"conv =>\n lhs\n rw [← <a>coe_le_coe</a>, <a>natCast_get</a>, <a>natCast_get</a>]",
[
{
"full_name": "PartENat.coe_le_coe",
"def_path": "Mathlib/Data/Nat/PartENat.... |
https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.cycleType_of_card_le_mem_cycleType_add_two | [
310,
1
] | [
318,
62
] | [
{
"tactic": "obtain ⟨c, g', rfl, hd, hc, rfl⟩ := mem_cycleType_iff.1 hng",
"annotated_tactic": [
"obtain ⟨c, g', rfl, hd, hc, rfl⟩ := <a>mem_cycleType_iff</a>.1 hng",
[
{
"full_name": "Equiv.Perm.mem_cycleType_iff",
"def_path": "Mathlib/GroupTheory/Perm/Cycle/Type.lea... |
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