chars int64 40 24k | content_type stringclasses 9
values | id stringlengths 13 64 | source stringclasses 5
values | subset stringclasses 31
values | text stringlengths 40 24k |
|---|---|---|---|---|---|
10,665 | lean_file_chunk | 68b2974a3223ab7d71e05c7431592061dea0415e2f31c15feab17320f58f4780 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Jiazhen Xia. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jiazhen Xia
-/
import LeanPool.WhiteheadTheorem.Auxiliary
import LeanPool.WhiteheadTheorem.Shapes.Disk
/-!
# LeanPool.WhiteheadTheorem.Shapes.Jar
Imported Lean Pool material for `LeanP... |
9,313 | lean_file_chunk | fc3770603d6d775c0419296042815a344599555164d72f1240744c4cd06d209d | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Jiazhen Xia. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jiazhen Xia
-/
import LeanPool.WhiteheadTheorem.Defs
import LeanPool.WhiteheadTheorem.Exponential
import LeanPool.WhiteheadTheorem.Shapes.Maps
import LeanPool.WhiteheadTheorem.Shapes.Pus... |
6,741 | lean_file_chunk | eb13ef9c1f56c4148a5f9ed1ebab4edf7d5df1fbf6b7b220ecc53c311544b158 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Jiazhen Xia. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jiazhen Xia
-/
import Mathlib.Topology.UnitInterval
import Mathlib.Topology.CompactOpen
import Mathlib.Topology.Category.TopCat.Basic
/-!
# LeanPool.WhiteheadTheorem.Shapes.Maps
Import... |
11,692 | lean_file_chunk | a025c1a7889f27364cec35fba9a696e1082944a915f611f454ecb880ac1c323e | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Jiazhen Xia. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jiazhen Xia
-/
import Mathlib.Topology.Homeomorph.Lemmas
import Mathlib.Topology.Category.TopCat.Limits.Basic
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square
/-!
# LeanPool.... |
1,395 | lean_file_chunk | 908daa406d22a412a2b54171f70270a6275331577d125119d97ed82ef1a40374 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Jiazhen Xia. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jiazhen Xia
-/
import Mathlib.Topology.UnitInterval
/-!
# LeanPool.WhiteheadTheorem.Shapes.UnitInterval
Imported Lean Pool material for `LeanPool.WhiteheadTheorem.Shapes.UnitInterval`.... |
1,950 | lean_file_chunk | 5395262558921759fb8b6f200b482d7c2340541a13f0df8259db30345b05fd2f | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Jiazhen Xia. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jiazhen Xia
-/
import LeanPool.WhiteheadTheorem.Auxiliary
import LeanPool.WhiteheadTheorem.Basic
import LeanPool.WhiteheadTheorem.Compressible.CWComplex
import LeanPool.WhiteheadTheorem.... |
6,082 | lean_file_chunk | 9d00b9d1057b98a5091f26ec884bed0fca2a08731b11c9a8ee31948754c14a74 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Vincent Trélat. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Vincent Trélat
-/
import Mathlib.SetTheory.ZFC.Basic
/-!
# LeanPool.ZFLean.Basic
Imported Lean Pool material for `LeanPool.ZFLean.Basic`.
-/
noncomputable section
namespace ZFSet
... |
13,293 | lean_file_chunk | 5d7bd1086efbd3491a8a9c39a42dfcb6f1744b2b2d85f63093c71aa0d25e3ee1 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Vincent Trélat. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Vincent Trélat
-/
import LeanPool.ZFLean.Basic
/-!
# Boolean algebra on `ZFSet`
This file defines the boolean algebra on `ZFSet` and the type of booleans `ZFBool`.
It defines the fo... |
2,868 | lean_file_chunk | 4e4ffd78a238e3d903b51ed922a5600882c511dd4aa9ca638eb6701f6a6fe30c | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Vincent Trélat. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Vincent Trélat
-/
import LeanPool.ZFLean.Functions
/-!
# LeanPool.ZFLean.Embeddings
Imported Lean Pool material for `LeanPool.ZFLean.Embeddings`.
-/
namespace ZFSet
/-- Imported ZF... |
23,973 | lean_file_chunk | 9b3a4d08d9072cc5dc5818fa7a63e2e6380503973ff2eb4b72fe97f24a33da9f | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Vincent Trélat. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Vincent Trélat
-/
import LeanPool.ZFLean.Rationals
import LeanPool.ZFLean.Booleans
import LeanPool.ZFLean.Tactics
/-!
# LeanPool.ZFLean.Functions
Imported Lean Pool material for `Le... |
23,950 | lean_file_chunk | bf51fef801d5f719bcd29ed83b11fcc53b22101afd07bf5dca57cef1f8863ace | lean_source_file | lean_pool_source_file_chunks | Function.Surjective @ᶻf := by
rintro ⟨y, yB⟩
obtain ⟨x, -, pair⟩ := surj y yB
have x_dom : x ∈ f.Dom := mem_dom (is_func_is_pfunc hf) pair
exists ⟨x, x_dom⟩
exact fapply.of_pair (is_func_is_pfunc hf) pair
theorem _root_.ZFSet.IsInjective.apply_surj_pfun {f A B : ZFSet}
(hf : IsPFunc f A B) (surj : f.IsSurj... |
23,968 | lean_file_chunk | e6808a79ee298e3f50e0e1926c9eab21a87448ddc57bf56025ea7c8c6c7c21c5 | lean_source_file | lean_pool_source_file_chunks | · rw [ZFSet.sUnion_pair, ZFSet.ZFBool.mem_𝔹_iff]
right
ext1 x
constructor
· intro hx
rcases ZFSet.mem_union.mp hx with hx | hx
· nomatch (ZFSet.notMem_empty x) hx
· exact hx
· intro hx
exact mem_union.mpr <| Or.inr hx
theorem sInter_sep_subset_of_𝔹_mem_𝔹 {D : ZFSet} {P : ... |
17,609 | lean_file_chunk | d432c415f66b9925ab103ea2de6ba82a4bbc4d2e76ca96d376ebb819d4b7983e | lean_source_file | lean_pool_source_file_chunks | · exact SetLike.coe_mem 0
· simp_rw [mem_funs, IsFunc, prod_empty_left, subset_refl, notMem_empty,
existsUnique_false, imp_self, implies_true, and_self]
· and_intros
· intro _ _ _ h
nomatch notMem_empty _ h
· intro _ h
nomatch notMem_empty _ h
| insert S x ih x_not_mem_S =>... |
23,988 | lean_file_chunk | 5326fd82423abd89dfc6c1d59bbd27f53eb1a40a64d07b10465093856eacfa43 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Vincent Trélat. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Vincent Trélat
-/
import LeanPool.ZFLean.Naturals
import Mathlib.Algebra.Order.Ring.Defs
import Mathlib.Algebra.Order.Group.Defs
import Mathlib.SetTheory.Cardinal.SchroederBernstein
/-... |
22,356 | lean_file_chunk | cba1a8007ceb411defe3fa9564768f63e1dc2185fa110c8416e12eea6519f84b | lean_source_file | lean_pool_source_file_chunks | induction n using Quotient.ind
induction m using Quotient.ind
rename_i n m
obtain ⟨a, b⟩ := n
obtain ⟨c, d⟩ := m
simp_rw [mk_eq] at h ⊢
rw [one_eq, add_eq, ZFNat.add_zero] at h
change a + d < b + (c + 1) at h
suffices a + d ≤ b + c by
rcases this with h | h
· left; exact h
· right; exact sou... |
23,978 | lean_file_chunk | f5f955d621b370b254a5b8c4df69b76984cd718b3034344cf0a0981bace1c395 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Vincent Trélat. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Vincent Trélat
-/
import LeanPool.ZFLean.Functions
/-!
# LeanPool.ZFLean.Isomorphisms
Imported Lean Pool material for `LeanPool.ZFLean.Isomorphisms`.
-/
namespace ZFSet
/-- Imported ... |
6,849 | lean_file_chunk | cdc26561405ca25cc6cf1d11701f98e205b9e8b1e18d2182ba15cac3952a1d91 | lean_source_file | lean_pool_source_file_chunks | use A.sep fun z ↦ z.pair zftrue ∈ fX, ?_
· intro y hy
unfold f at hy
rw [lambda_spec] at hy
exact hy.2.2
· beta_reduce
rw [lambda_spec]
refine ⟨fX_mem, ?_, rfl⟩
rw [mem_powerset]
exact sep_subset_self
open Classical in
/-- Imported ZFLean declaration.... |
9,113 | lean_file_chunk | 2d6a8e831154e1c36063f442dc5e6621651f35f2c665ab7f7ec32b064c4e12a8 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Vincent Trélat. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Vincent Trélat
-/
import LeanPool.ZFLean.Isomorphisms
/-!
# LeanPool.ZFLean.IsomorphismsFunsToPowRel
Imported Lean Pool material for `LeanPool.ZFLean.IsomorphismsFunsToPowRel`.
-/
... |
14,306 | lean_file_chunk | 27569d6f8aa45160557a826c00e5491c3034bd1496f5917602d74f53fe1984c4 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Vincent Trélat. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Vincent Trélat
-/
import LeanPool.ZFLean.Isomorphisms
/-!
# LeanPool.ZFLean.IsomorphismsZFNatIso
Imported Lean Pool material for `LeanPool.ZFLean.IsomorphismsZFNatIso`.
-/
namespac... |
23,985 | lean_file_chunk | fec56485eabcb71140dbf0e640d1a9f42960a7a9aa4946e56646bf52931b263c | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Vincent Trélat. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Vincent Trélat
-/
import LeanPool.ZFLean.Basic
import Mathlib.Algebra.Ring.Defs
import Mathlib.Tactic.Ring
/-! # ZFC Natural numbers
This file defines the natural numbers in ZF set ... |
23,946 | lean_file_chunk | c5a95e80da93b2f699268e710dc478c4ff761d30913e971096102250710710b9 | lean_source_file | lean_pool_source_file_chunks | | zero => rw [add_zero, addInst_eq, ZFNat.add, rec_zero]
| succ n ih => rw [← succ_add, add_succ, ih]
@[simp]
lemma add_assoc (n m k : ZFNat) : n + (m + k) = n + m + k := by
induction n with
| zero => rw [zero_add, zero_add]
| succ _ ih => rw [add_succ, add_succ, add_succ, ih]
lemma add_left_comm (n m k : ZFN... |
2,726 | lean_file_chunk | 23ef2c5def943a7c443b1ee3b11101e2ba994c7f3e1513512e5a56515f221a36 | lean_source_file | lean_pool_source_file_chunks | theorem _root_.ZFSet.Nat.is_inductive : inductiveSet Nat where
left := ZFNat.zero_in_Nat
right := fun _ _ => ZFNat.succ_mem_Nat' ‹_›
namespace ZFNat
theorem _root_.ZFSet.ZFNat.ofNat_inj {n m : ℕ} : (n : ZFNat) = (m : ZFNat) ↔ n = m where
mp := by
intro h
induction n generalizing m with
| zero =>
... |
16,932 | lean_file_chunk | b2b14bf69941ca00b70b8d77fdd9c61c9c383dfdca4ed45686a1e1a36a074370 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Vincent Trélat. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Vincent Trélat
-/
import LeanPool.ZFLean.Integers
/-! # ZFC Rational Numbers
This file defines the rational numbers in ZFC, based on the integers and using the `ZFInt` type.
-/
na... |
17,765 | lean_file_chunk | a633e62c7cb0da21a223fab6ca87e8f0639ea0e7ede6f12f6602606a29b38d81 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Vincent Trélat. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Vincent Trélat
-/
import LeanPool.ZFLean.Basic
import LeanPool.ZFLean.Booleans
import LeanPool.ZFLean.Integers
import LeanPool.ZFLean.Functions
/-!
# LeanPool.ZFLean.Sum
Imported Le... |
1,122 | lean_file_chunk | e83435bac14dd3d69c7bfae072d9910d01b536cf2133e38d6d3812dbefd3cbc3 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Vincent Trélat. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Vincent Trélat
-/
import Mathlib.CategoryTheory.Category.Basic
/-!
# LeanPool.ZFLean.Tactics
Imported Lean Pool material for `LeanPool.ZFLean.Tactics`.
-/
/-- Imported ZFLean declar... |
906 | lean_file_chunk | 76477981c36943a4b4756cdba1d802297cc5779ddbcae0af86fa3cdb0bea19cf | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Vincent Trélat. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Vincent Trélat
-/
import LeanPool.ZFLean.Basic
import LeanPool.ZFLean.Booleans
import LeanPool.ZFLean.Naturals
import LeanPool.ZFLean.Integers
import LeanPool.ZFLean.Rationals
import ... |
23,989 | lean_file_chunk | dedaa13a7652d12d2a4d3ab938ab01d2a7cd58fa0abcad82c06e8c0a95069510 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Junqi Liu, Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junqi Liu, Jujian Zhang
-/
import Mathlib.Data.Int.Star
import Mathlib.Analysis.Complex.ExponentialBounds
import Mathlib.NumberTheory.LSeries.HurwitzZetaValues
import Mathlib... |
23,981 | lean_file_chunk | 1c458017a3304a56fe9f8a3b0ff9cd93cd0464045ba01f384f004136148773ae | lean_source_file | lean_pool_source_file_chunks | apply ContinuousOn.mul continuousOn_fst continuousOn_snd
· apply ContinuousOn.pow
apply ContinuousOn.sub continuousOn_const continuousOn_snd
· apply ContinuousOn.pow
apply ContinuousOn.sub continuousOn_const
apply ContinuousOn.mul _ continuousOn_const
apply ContinuousOn.s... |
7,293 | lean_file_chunk | 43bb8951ab7800e7ee0a72703a52283a97827a8ba4a615a5bd698146c1551333 | lean_source_file | lean_pool_source_file_chunks | · exact Summable_of_zeta_two'
linarith
apply Finset.sum_le_sum
intro i _
rw [div_le_div_iff₀, one_mul, one_mul]
· apply pow_le_pow_right₀ <;> linarith
· positivity
· positivity
· intro m
simp only [one_div, pow_succ]
positivity
· positivity
theorem JJ_upper (n : ... |
9,356 | lean_file_chunk | 642fc54d8b2a4d75eb611e4f23577b77e608f8d4bc9a254a090c8309fb5ef1c8 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Junqi Liu, Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junqi Liu, Jujian Zhang
-/
import Mathlib.Analysis.RCLike.Basic
import Mathlib.Algebra.Order.Star.Real
/-!
# LeanPool.Zeta3Irrational.Bound
-/
namespace LeanPool.Zeta3Irrat... |
22,891 | lean_file_chunk | 3a970b6dd0c7c7e8ba3a1a35fe5c5104c24bb6003035605a416f6c54106d707c | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Junqi Liu, Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junqi Liu, Jujian Zhang
-/
import Mathlib.Algebra.Lie.OfAssociative
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Algebra.Order.Star.Real
import Mathlib.Analysis.Comp... |
11,977 | lean_file_chunk | ded6e0f0f8d963af907c21a4ea982e2851eed9c5ca7ddc1f70e78bf85b30e171 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Junqi Liu, Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junqi Liu, Jujian Zhang
-/
import Mathlib.Algebra.GCDMonoid.Finset
import Mathlib.Algebra.GCDMonoid.Nat
import Mathlib.Analysis.SpecialFunctions.Log.Base
import Mathlib.Data.... |
5,975 | lean_file_chunk | 0b9d169fbc14855236ecf5cbdbff00506bb6a780ef707ddd739865f34457f486 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Junqi Liu, Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junqi Liu, Jujian Zhang
-/
import LeanPool.Zeta3Irrational.Integral
/-!
# LeanPool.Zeta3Irrational.Equality
-/
namespace LeanPool.Zeta3Irrational
open scoped Nat
open BigO... |
23,976 | lean_file_chunk | 4a23402ed4861e3220f2dc3f96cf5c400166162d05c852958564418c5b30da8a | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Junqi Liu, Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junqi Liu, Jujian Zhang
-/
import Mathlib.Analysis.Normed.Field.Instances
import Mathlib.Analysis.PSeries
import Mathlib.Analysis.SpecialFunctions.Integrals.Basic
import Math... |
23,924 | lean_file_chunk | 4b9e2381ac520056478e70ded204ee4beae31267dc3376484fe2581addc12488 | lean_source_file | lean_pool_source_file_chunks | ENNReal.ofReal (1 / (k + s + 1) ^ 2) := by
rw [← MeasureTheory.lintegral_mul_const]
· apply MeasureTheory.setLIntegral_congr_fun (by measurability)
rintro y ⟨hy1, hy2⟩
change ENNReal.ofReal (y ^ (k + r) / (↑k + ↑s + 1) ^ 2) =
ENNReal.ofReal (y ^ (k + r)) * ENNReal.ofReal (1 / (↑k +... |
1,067 | lean_file_chunk | 9df82a712d03bd1e1afc2c129fb43a21a2cd753d106156b200c2564c14fc1719 | lean_source_file | lean_pool_source_file_chunks | simp only [range_one, one_div, sum_singleton, CharP.cast_eq_zero, ne_eq,
OfNat.ofNat_ne_zero, not_false_eq_true, zero_pow, inv_zero, zero_div, zero_add]
rw [Nat_Ico_succ_right]
· linarith
· simp only [gt_iff_lt, not_lt] at h1
have h2 : s > r := by
by_contra!; apply h; linarith
rw [... |
23,957 | lean_file_chunk | c80b00156997734eb87f8dc1db2b73aed911221054b696487afbe2d16d9472f5 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Junqi Liu, Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junqi Liu, Jujian Zhang
-/
import Mathlib.Algebra.Lie.OfAssociative
import Mathlib.Algebra.Polynomial.Derivative
import Mathlib.Algebra.Polynomial.Eval.SMul
import Mathlib.An... |
3,762 | lean_file_chunk | 504dd5209cb1e0c195fd9c73fa5932c1c2b999a100f943b4e2fe5af705844319 | lean_source_file | lean_pool_source_file_chunks | apply ContinuousOn.mul continuousOn_const
· apply ContinuousOn.mul
· simp_rw [Polynomial.iterate_derivative_X_pow_eq_smul]
simp only [eval_smul, eval_pow, eval_X, smul_eq_mul]
apply ContinuousOn.mul continuousOn_const (ContinuousOn.pow continuousOn_id _)
· rw [show (1 - X : ℝ[X... |
7,962 | lean_file_chunk | 0289441d8bbaa21d48cc4dbe3671e744ec60e2a4b08b7d978c1bf5aa2e3e1296 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Junqi Liu, Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junqi Liu, Jujian Zhang
-/
import LeanPool.Zeta3Irrational.Integral
import LeanPool.Zeta3Irrational.D
/-!
# LeanPool.Zeta3Irrational.LinearForm
-/
namespace LeanPool.Zeta3I... |
1,049 | lean_file_chunk | 380978f49cbd1005c557d7704e68debd5eb64e7eed602fe89eb51c62275b6ffc | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Junqi Liu, Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junqi Liu, Jujian Zhang
-/
import LeanPool.Zeta3Irrational.Basic
import LeanPool.Zeta3Irrational.Bound
import LeanPool.Zeta3Irrational.Chebyshev
import LeanPool.Zeta3Irration... |
23,974 | lean_file_chunk | ebefcc5705f77374700dd76e1eea33fcd67579ad7733f2e88dacfa69a3b42340 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Evan Chen, Kenny Lau, Ken Ono, Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Evan Chen, Kenny Lau, Ken Ono, Jujian Zhang
-/
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Algebra.Ring.... |
23,966 | lean_file_chunk | 061552a18b0f2e9876188c18942cde5fbfbedeba259d2134908d8f8f54454f90 | lean_source_file | lean_pool_source_file_chunks | rw [hsum1, hsum2] at hkey
omega
/-- **Maximal removed non-top row.** From a removal `r` with `∑ r = q` whose top-row
value is `≤ q-1`, there is a maximal row `j < d` that loses a stone, with no removed
rows strictly between `j` and `d`. -/
theorem row_select_j (q d : ℕ) (hq : 2 ≤ q) (r : Fin (d + 1) → ℕ)
(hrsum ... |
23,972 | lean_file_chunk | 1b27b446a4b633b1fbb2b84ef79e34979af0234b2cf5610b109f7f3b72ae683c | lean_source_file | lean_pool_source_file_chunks | -- Chain from i to j using strong induction on the gap.
have chain : ∀ n : ℕ, ∀ e : ℕ, e + n ≤ d → 0 < n →
gWeight q d (e + n) < gWeight q d e := by
intro n
induction n with
| zero => omega
| succ m ih =>
intro e hle hpos
rcases Nat.eq_zero_or_pos m with hm | hm
· subst hm
... |
23,945 | lean_file_chunk | ab384363e8ce2f09e184428b9d72a99310510c64f7a881b809465b198b2cbd86 | lean_source_file | lean_pool_source_file_chunks | Finset.sum_insert (by simp [hITJT]), Finset.sum_singleton,
Finset.sum_insert (by simp [hIJ, hIIT, hIJT]),
Finset.sum_insert (by simp [hITJ.symm, hJJT]),
Finset.sum_insert (by simp [hITJT]), Finset.sum_singleton]
rw [hdigI n, hdigJ n, hdigIT n, hdigJT n]
by_cases hni : n = m - i... |
18,447 | lean_file_chunk | fd4e497d9fb972417489b5dcad37e56989d0b20eaacc0954150b9524bf10742a | lean_source_file | lean_pool_source_file_chunks | _ ≤ q ^ (k + 1) := Nat.pow_le_pow_left hq2 _
-- digits vanish above N
have hzero : ∀ (x : ℕ), x ≤ k → ∀ n, N ≤ n → digit q x n = 0 := by
intro x hx n hn
have hxq : x < q ^ n := by
calc x ≤ k := hx
_ < q ^ N := hkN
_ ≤ q ^ n := Nat.pow_le_pow_right (by omega) hn
unfold digit
rw ... |
23,938 | lean_file_chunk | 3d6ee435c9938f7b60af7767c02b312aa9a26971a26366f0f4488c73818dd9b7 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Evan Chen, Kenny Lau, Ken Ono, Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Evan Chen, Kenny Lau, Ken Ono, Jujian Zhang
-/
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.AlgebraicTopo... |
23,983 | lean_file_chunk | a771299d45ffe5e3ce0d909fe52b54dd804f6b8840a0633a118dce313e06aa9c | lean_source_file | lean_pool_source_file_chunks | + ∑ r ∈ Finset.range (d - 1), (d - 1 - r) * blockSum q k1 L (r + 2) := by
unfold Phi
obtain ⟨e, rfl⟩ : ∃ e, d = e + 1 := ⟨d - 1, by omega⟩
rw [Finset.sum_range_succ']
simp only [Nat.add_sub_cancel, Nat.sub_zero]
rw [Nat.add_comm]
simp_all
-- Recurrence for `slotList`: appending the slots at position `Lx`.
... |
23,978 | lean_file_chunk | 56756ffb00791e325b3bd4d5751a44fdf376c5bc489f421fba038f8ce24f0b1f | lean_source_file | lean_pool_source_file_chunks | theorem window_len {α : Type*} (L : List α) (a n : ℕ) (h : a + n ≤ L.length) :
((L.drop a).take n).length = n := by
rw [List.length_take, List.length_drop]
omega
theorem pow_sum_modEq (q : ℕ) (hq : 2 ≤ q) (w : List ℕ)
(hpow : ∀ x ∈ w, ∃ e, x = q ^ e) :
w.sum ≡ w.length [MOD (q - 1)] := by
induction w... |
23,982 | lean_file_chunk | da48666ffc81a409748cbf2c4ba76c37ec5fcd84a95130dc406a702898c6d158 | lean_source_file | lean_pool_source_file_chunks | calc d * k + d * β = d * (k + β) := by ring
_ = d * s1 := by rw [hL1]
_ = (d - 1 + 1) * s1 := by rw [hd1]
_ = (d - 1) * s1 + s1 := by ring
omega
/-- Hard direction of the composition identity:
`s_{d-1}(s_1(k)) + s_1(k) ≤ s_d(k)`. Assembled from the slot formula on `s_d`
and `s_{d-1}` plus the `lay... |
1,287 | lean_file_chunk | 5304a79e405b4af129fd2669778c7e51848f13d29f760fb8f80a5be468a67404 | lean_source_file | lean_pool_source_file_chunks | apply Nat.mul_le_mul_left; omega
omega
have : (d - 1) * (q - 1) ≤ (q - 1) * ((d - 1) * ((k + u) + 1) + 1) := by
rw [Nat.mul_comm]
apply Nat.mul_le_mul_left; exact hge
omega
have hcore : Phi q (k - 1) d (slotLen q d k)
< d * u + Phi q ((k - 1) + u) (d - 1) (slotLen q (d - 1) (s1 + j)) :... |
13,786 | lean_file_chunk | 3350a29a03fd03e051692f6247f498db152392aeea5a890f9f6cb0081646c707 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Evan Chen, Kenny Lau, Ken Ono, Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Evan Chen, Kenny Lau, Ken Ono, Jujian Zhang
-/
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Analysis.Normed.Ring.Lemmas
import Mathlib.Data.Int.S... |
23,991 | lean_file_chunk | 99d119d3c2a2751ef99bc9a8dc03d72989372c97a392194c036e1dfc269e8f00 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Evan Chen, Kenny Lau, Ken Ono, Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Evan Chen, Kenny Lau, Ken Ono, Jujian Zhang
-/
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Analysis.Normed.Ring.Lemmas
import Mathlib.Data.Int.S... |
23,959 | lean_file_chunk | 9eb53903d3d384bd15442736eaa3fe8f4ec338d78ffc6f794e4d3860c25e9a39 | lean_source_file | lean_pool_source_file_chunks | (CarryFree p [kk, ∑ i, m i] ∧ CarryFree p (List.ofFn m)) ↔
CarryFree p (kk :: List.ofFn m) := by
have hsum : (List.ofFn m).sum = ∑ i, m i := by rw [List.sum_ofFn]
unfold CarryFree
simp only [List.map_cons, List.map_nil, List.sum_cons, List.sum_nil, add_zero]
constructor
· rintro ⟨h1, h2⟩ e
have hc :... |
8,658 | lean_file_chunk | 54698e1e35af8b4075b51a1fdc0cc3454a87000adcfa6424fee4b538f59d811f | lean_source_file | lean_pool_source_file_chunks | Finset.single_le_sum (f := fun j : Fin d => ((j : ℕ)+1) * m j)
(fun j _ => Nat.zero_le _) (Finset.mem_univ i)
have hset : {m : Fin d → ℕ | ((d * k : ℕ) + weight d m : ℤ) = n} = ↑FS := by
ext m
rw [Finset.mem_coe, hFS, Finset.mem_filter, Fintype.mem_piFinset]
simp only [Set.mem_ofPred_eq, Finset.... |
624 | lean_file_chunk | c3611ea252d6a0582be98fde3061c2a308fda98ccb56e8a27ad1213f28273530 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Evan Chen, Kenny Lau, Ken Ono, Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Evan Chen, Kenny Lau, Ken Ono, Jujian Zhang
-/
import LeanPool.ZetaH123.H1
import LeanPool.ZetaH123.H2
import LeanPool.ZetaH123.H3
import LeanPool.ZetaH12... |
23,972 | lean_file_chunk | ce7e26e3e3edf3144350a372552ebc78f69d25605f5cf5e9d948d0c65673774f | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Christopher Boone. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Boone
-/
import LeanPool.ZhangYeungInequality.Delta
import LeanPool.ZhangYeungInequality.Prelude
import LeanPool.ZhangYeungInequality.PFR.ForMathlib.ConditionalIndepend... |
791 | lean_file_chunk | 5719562577128049c30b1b05d668395e305dca611aa61cf0ce6aa1930b91b1a0 | lean_source_file | lean_pool_source_file_chunks | (hSecond : IdentDistrib (fun ω' => (X₁ ω', Y₁ ω', Z' ω', U' ω'))
(fun ω => (X ω, Y ω, Z ω, U ω)) ν μ)
(hCond : CondIndepFun (fun ω' => (X' ω', Y' ω'))
(fun ω' => (X₁ ω', Y₁ ω'))
(fun ω' => (Z' ω', U' ω')) ν) :
I[Z : U; μ] - 2 * I[Z ... |
9,970 | lean_file_chunk | afbcb6433ec3e1f59c5221730f0dc013cb1177052cb9c72d9a7b4cfee4fedaff | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Christopher Boone. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Boone
-/
import LeanPool.ZhangYeungInequality.Prelude
/-!
# The Zhang-Yeung delta quantity
The Zhang-Yeung delta
`Δ(Z, U | X, Y) := I(Z; U) - I(Z; U | X) - I(Z; U ... |
8,144 | lean_file_chunk | 2ca07b989ff6b946a192cb75509778e5b179d6f1a0559428cc7be0cb6db26050 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Christopher Boone. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Boone
-/
import LeanPool.ZhangYeungInequality.Prelude
/-!
# Entropy-region infrastructure for Theorem 4
This module packages the generic `Fin n` set-function surface ... |
15,548 | lean_file_chunk | 7239adcc36694488939a399cfacfc4f84c3592d350c02da19c8b6794bba85b0e | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 PFR contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: PFR contributors
-/
module
public import Mathlib.Tactic.Finiteness
public import LeanPool.ZhangYeungInequality.PFR.Mathlib.Probability.IdentDistrib
public import LeanPool.ZhangYeun... |
23,945 | lean_file_chunk | 9d0d870aebebc028723790f2ec4d078adfb64d871b5ec705cb7a09e5a4efdb8b | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 PFR contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: PFR contributors
-/
module
public import LeanPool.ZhangYeungInequality.PFR.ForMathlib.ConditionalIndependence
public import LeanPool.ZhangYeungInequality.PFR.ForMathlib.Entropy.Ker... |
23,952 | lean_file_chunk | a77742d9a3a7882817bb473816f244c27a7b5d9a823b3cd30a676af05338e4db | lean_source_file | lean_pool_source_file_chunks | [MeasurableSingletonClass U] (μ : Measure Ω) [IsFiniteMeasure μ] (hX : Measurable X)
(hY : Measurable Y) (f : T → S → U) (hf : ∀ t, Injective (f t)) [FiniteRange Y] :
H[(fun ω ↦ f (Y ω) (X ω)) | Y; μ] = H[X | Y; μ] := by
rw [condEntropy_eq_sum _ _ _ hY, condEntropy_eq_sum _ _ _ hY]
have : ∀ y, H[fun ω ↦ f (... |
9,617 | lean_file_chunk | 6cb4da00abef0210217806c8c0fd7cee3cb14596ed853d6f1cd9c3957bde82d8 | lean_source_file | lean_pool_source_file_chunks | (μ : Measure Ω) [IsZeroOrProbabilityMeasure μ]
[FiniteRange X] [FiniteRange Y] [FiniteRange Z]
{f : S → S'} (hf : Function.Injective f)
{g : T → T'} (hg : Function.Injective g)
{h : U → U'} (hh : Function.Injective h)
: I[f ∘ X : g ∘ Y | h ∘ Z; μ] = I[X : Y | Z; μ] := calc
_ = I[f ∘ X : g ∘ Y | ... |
19,416 | lean_file_chunk | 03f4b8930085deacb975bae4ed73406612b9628873843146bbbf002b0d401c90 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 PFR contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: PFR contributors
-/
module
public import Mathlib.MeasureTheory.Integral.Prod
public import LeanPool.ZhangYeungInequality.PFR.ForMathlib.Entropy.Measure
public import LeanPool.Zhang... |
17,978 | lean_file_chunk | 481e5826fd577bda54a3fd83c2048883919f076a8e6924efe1b471776129ab99 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 PFR contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: PFR contributors
-/
module
public import LeanPool.ZhangYeungInequality.PFR.Mathlib.Probability.Kernel.Composition.Comp
public import LeanPool.ZhangYeungInequality.PFR.ForMathlib.En... |
23,944 | lean_file_chunk | c0c2254c4803d07dac31392daebbe1e310221c30c77eb3e76afa9a996e28cdde | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 PFR contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: PFR contributors
-/
module
public import Mathlib.Analysis.SpecialFunctions.Log.NegMulLog
public import Mathlib.MeasureTheory.Integral.Bochner.Basic
public import LeanPool.ZhangYeun... |
10,889 | lean_file_chunk | 493d94083182bc29c4ea56921a658e2cac29f8a68b4a7799eb245f6b7dea611c | lean_source_file | lean_pool_source_file_chunks | simpa using Prod.swap_injective.preimage_image {(s, t)}
@[simp]
lemma _root_.ProbabilityTheory.measureMutualInfo_prod
{μ : Measure S} {ν : Measure T} [FiniteSupport μ] [FiniteSupport ν]
[IsProbabilityMeasure μ] [IsProbabilityMeasure ν] :
Im[μ.prod ν] = 0 := by
rw [measureMutualInfo_def, measureEntropy_pr... |
1,730 | lean_file_chunk | 389c018f072eaf098d57383ef9de85de9b011e7d246851b35bd90143ba2b0662 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 PFR contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: PFR contributors
-/
module
public import Mathlib.Probability.ConditionalProbability
public import LeanPool.ZhangYeungInequality.PFR.ForMathlib.FiniteRange.Defs
/-!
# LeanPool.Zhan... |
7,612 | lean_file_chunk | e7f213144e6b91029ca0977753dfa44fe1e981cbbd97fd74c9fec13430c4b130 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 PFR contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: PFR contributors
-/
module
public import Mathlib.MeasureTheory.Measure.Map
/-!
# LeanPool.ZhangYeungInequality.PFR.ForMathlib.FiniteRange.Defs
Imported Lean Pool material for `Le... |
758 | lean_file_chunk | 64f43044cd1d94dc1132d3eda36a9befc615718c8e93966f1375c11082f3b624 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 PFR contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: PFR contributors
-/
module
public import Mathlib.Util.Notation3
public import Mathlib.Tactic.Basic
/-!
# LeanPool.ZhangYeungInequality.PFR.ForMathlib.Pair
Imported Lean Pool mate... |
15,678 | lean_file_chunk | 33f948fdd2a616a78db4572ef0a6a56474abc3a1373fa7e4df735748a58ccb40 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 PFR contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: PFR contributors
-/
module
public import Mathlib.MeasureTheory.Measure.Real
public import Mathlib.Probability.IdentDistrib
public import LeanPool.ZhangYeungInequality.PFR.ForMathli... |
6,266 | lean_file_chunk | 35314645e67b546446f379f891853b1c482ff26b63913c7a6e6ca88212ffc361 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 PFR contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: PFR contributors
-/
module
public import Mathlib.Algebra.BigOperators.Field
public import Mathlib.Analysis.Convex.Jensen
public import Mathlib.Analysis.SpecialFunctions.Log.NegMulL... |
598 | lean_file_chunk | 2488263937d7035fa5a4d758d37f66e29935ee56ba640fffb2b23ed284be7e5a | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 PFR contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: PFR contributors
-/
module
public import Mathlib.Data.Set.Basic
/-!
# LeanPool.ZhangYeungInequality.PFR.Mathlib.Data.Set.Basic
Imported Lean Pool material for `LeanPool.ZhangYeun... |
934 | lean_file_chunk | 83e3651dbc56fb45cfb8bba0e43b6c4f34271eb5640891105a8e1c512180bc7b | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 PFR contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: PFR contributors
-/
module
public import Mathlib.Data.Set.Card
public import LeanPool.ZhangYeungInequality.PFR.Mathlib.Data.Set.Basic
public import LeanPool.ZhangYeungInequality.PF... |
727 | lean_file_chunk | bcd62de8417c8687212040c818620cee2bcbc5d7e8ef32084e976000be6d90d8 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 PFR contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: PFR contributors
-/
module
public import Mathlib.Data.Set.Insert
/-!
# LeanPool.ZhangYeungInequality.PFR.Mathlib.Data.Set.Insert
Imported Lean Pool material for `LeanPool.ZhangYe... |
1,527 | lean_file_chunk | d1b025fa1e0a8684ae0f1f52c62c903546659f4ed74d54b637a1d1d64c70f7dc | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 PFR contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: PFR contributors
-/
module
public import Mathlib.MeasureTheory.Constructions.Pi
/-!
# LeanPool.ZhangYeungInequality.PFR.Mathlib.MeasureTheory.Constructions.Pi
Imported Lean Pool ... |
904 | lean_file_chunk | f50b62d8c56604f0214fb1746a4f293c1707084c68d356bc7413a2e18a7e9b14 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 PFR contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: PFR contributors
-/
module
public import Mathlib.MeasureTheory.Integral.Lebesgue.Basic
/-!
# TODO
Rename `setLIntegral_congr` to `setLIntegral_congr_set`
-/
public section
open... |
1,565 | lean_file_chunk | 3e10c2fcc7ccef958e6149f860478803fab5246868b531aa28f046c412a4b932 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 PFR contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: PFR contributors
-/
module
public import Mathlib.MeasureTheory.Integral.Lebesgue.Countable
/-!
# LeanPool.ZhangYeungInequality.PFR.Mathlib.MeasureTheory.Integral.Lebesgue.Countabl... |
695 | lean_file_chunk | 71b4a48f442ca8f29b4d3e877dae9650d313910e0147bb676da9b89827d51de5 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 PFR contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: PFR contributors
-/
module
public import Mathlib.MeasureTheory.Measure.Dirac
/-!
# LeanPool.ZhangYeungInequality.PFR.Mathlib.MeasureTheory.Measure.Dirac
Imported Lean Pool materi... |
2,665 | lean_file_chunk | 2bb16f64c644d3473009ccb4b60a4029ae8890226666161fba9aeed133574af2 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 PFR contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: PFR contributors
-/
module
public import Mathlib.MeasureTheory.Measure.Prod
/-!
# LeanPool.ZhangYeungInequality.PFR.Mathlib.MeasureTheory.Measure.Prod
Imported Lean Pool material... |
2,239 | lean_file_chunk | 0c1c2cd15cc27480223f02e7704024d3ff41b2c1d5c3d241af2b78f69b66d2aa | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 PFR contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: PFR contributors
-/
module
public import Mathlib.MeasureTheory.Measure.Real
public import LeanPool.ZhangYeungInequality.PFR.Mathlib.MeasureTheory.Measure.Prod
/-!
# LeanPool.Zhang... |
1,322 | lean_file_chunk | fda3d35dc317fa3dd00ebc7d2b3f2397e1bdfe2f27e21d2b8b7cf9c7806451a5 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 PFR contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: PFR contributors
-/
module
public import Mathlib.Probability.ConditionalProbability
/-!
# LeanPool.ZhangYeungInequality.PFR.Mathlib.Probability.ConditionalProbability
Imported Le... |
20,897 | lean_file_chunk | e4e351c52a7b581c16b9b4866b4e2cb3b329317d438024f171795446cf4c01b5 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 PFR contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: PFR contributors
-/
module
public import Mathlib.Probability.IdentDistrib
public import LeanPool.ZhangYeungInequality.PFR.Mathlib.MeasureTheory.Constructions.Pi
public import LeanP... |
16,284 | lean_file_chunk | 101e9cc9b1cb5176d41fa2ca659342464bc34e3c44f230a0585a53e445f8c3df | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 PFR contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: PFR contributors
-/
module
public import Mathlib.MeasureTheory.Constructions.Pi
public import Mathlib.Probability.Independence.Basic
public import LeanPool.ZhangYeungInequality.PFR... |
6,285 | lean_file_chunk | 750a1ffd4f523e74afe0ccfc5dfae1aac80dfa57c052f72deaa6b86ae6162043 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 PFR contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: PFR contributors
-/
module
public import Mathlib.Data.Finset.Pairwise
public import Mathlib.Probability.Independence.Kernel.IndepFun
/-!
# LeanPool.ZhangYeungInequality.PFR.Mathli... |
8,485 | lean_file_chunk | 2acd6991840737b250805110c72a28b167770433594db7f37e6d9461fc5494c9 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 PFR contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: PFR contributors
-/
module
public import Mathlib.Probability.Kernel.Composition.Comp
public import LeanPool.ZhangYeungInequality.PFR.Mathlib.Probability.Kernel.Disintegration
/-!
... |
23,980 | lean_file_chunk | 6ba917a1a213762554fc1d3c9824045b10542bb6cab3409c104bc36e04c7a753 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 PFR contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: PFR contributors
-/
module
public import Mathlib.Probability.Independence.Basic
public import Mathlib.Probability.Kernel.Composition.Prod
public import Mathlib.Probability.Kernel.C... |
15,505 | lean_file_chunk | 10c45b8ecfcfd37dd455536a4916eaf6f69d23549ecaa1379974cb531bc6ac14 | lean_source_file | lean_pool_source_file_chunks | ∀ᵐ t ∂μ, ∃ A : Finset S, κ t Aᶜ = 0
lemma _root_.ProbabilityTheory.Kernel.FiniteKernelSupport.aefiniteKernelSupport
{κ : Kernel T S} (hκ : FiniteKernelSupport κ)
(μ : Measure T) :
AEFiniteKernelSupport κ μ :=
ae_of_all μ hκ
@[simp] lemma finiteKernelSupport_zero : FiniteKernelSupport (0 : Kernel T S) :=... |
3,438 | lean_file_chunk | 92aec67a26d85b849d7f719687acb483a514a8f9cd076b2d6fe0899b4bfa4cc8 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 PFR contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: PFR contributors
-/
module
public import Mathlib.Probability.UniformOn
public import LeanPool.ZhangYeungInequality.PFR.Mathlib.Data.Set.Card
/-!
# LeanPool.ZhangYeungInequality.PF... |
6,597 | lean_file_chunk | 03e58fd7f5aec500fbbf6affa102313b494e975922b5104976b057ca6cab96c8 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Christopher Boone. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Boone
-/
/- Import surface for PFR's Shannon entropy API. Brings entropy notation (H[X], I[X:Y],
I[X:Y|Z])
into scope for downstream modules, and hosts generic helpers ... |
10,203 | lean_file_chunk | 9ed85327225dbfbc4c51bdb51e8bf0e69d8c380958745efb9e5c95a124da8c3f | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Christopher Boone. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Boone
-/
import LeanPool.ZhangYeungInequality.CopyLemma
/-!
# LeanPool.ZhangYeungInequality.Test.CopyLemma
Imported Lean Pool material for `LeanPool.ZhangYeungInequal... |
3,504 | lean_file_chunk | acbe8325e5e2382b25309f3317f4e3cc127e58ba63603f433404602419bfe6f6 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Christopher Boone. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Boone
-/
import LeanPool.ZhangYeungInequality.Delta
/-!
# LeanPool.ZhangYeungInequality.Test.Delta
Imported Lean Pool material for `LeanPool.ZhangYeungInequality.Test... |
2,091 | lean_file_chunk | abf19b95c726751c933c42233f58a10ccd5d7031e5fafc50cf6fe5bf7066148e | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Christopher Boone. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Boone
-/
import LeanPool.ZhangYeungInequality.EntropyRegion
import LeanPool.ZhangYeungInequality.Theorem4
/-!
# LeanPool.ZhangYeungInequality.Test.EntropyRegion
Impor... |
3,713 | lean_file_chunk | c7e766fea4d540d4833f9dc65e89639deb7fd2ba8068ee8d04a513af1fd6cf8e | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Christopher Boone. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Boone
-/
import LeanPool.ZhangYeungInequality.Theorem2
/-!
# LeanPool.ZhangYeungInequality.Test.Theorem2
Imported Lean Pool material for `LeanPool.ZhangYeungInequalit... |
5,602 | lean_file_chunk | 1bb63a5297298e9d76f2eba79a28b30b9a2d8f003c66c37e0b712068df155bb1 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Christopher Boone. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Boone
-/
import LeanPool.ZhangYeungInequality.Theorem3
/-!
# LeanPool.ZhangYeungInequality.Test.Theorem3
Imported Lean Pool material for `LeanPool.ZhangYeungInequalit... |
7,975 | lean_file_chunk | 3bbb37db9d958500aed2fa568b025734584135533bc1741951940575f3a767ea | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Christopher Boone. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Boone
-/
import LeanPool.ZhangYeungInequality.Theorem4
/-!
# LeanPool.ZhangYeungInequality.Test.Theorem4
Imported Lean Pool material for `LeanPool.ZhangYeungInequalit... |
7,861 | lean_file_chunk | 8a4758f963271b3ebe6a05b001b7779a2da93d3a56869a4e410ddac7b553a07c | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Christopher Boone. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Boone
-/
import LeanPool.ZhangYeungInequality.Theorem5
/-!
# LeanPool.ZhangYeungInequality.Test.Theorem5
Imported Lean Pool material for `LeanPool.ZhangYeungInequalit... |
697 | lean_file_chunk | 0ae4a02223999caba76f42b5d3fb00821745d839be676398c804a07108e34c51 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Christopher Boone. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Boone
-/
/- Test import surface for the Zhang-Yeung formalization. -/
import LeanPool.ZhangYeungInequality.Test.CopyLemma
import LeanPool.ZhangYeungInequality.Test.Delt... |
23,987 | lean_file_chunk | 0f4b90b87c4b58e9fcf5c9d3f57c0276d2d6ae96ef008dfa40fbd425057b270f | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Christopher Boone. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Boone
-/
import LeanPool.ZhangYeungInequality.Delta
import LeanPool.ZhangYeungInequality.Prelude
import LeanPool.ZhangYeungInequality.PFR.Mathlib.Analysis.SpecialFuncti... |
23,913 | lean_file_chunk | 949137fe7b5d7a89fcc56ed899bb2040ce33f65e32af23b5882de37241ca3bb5 | lean_source_file | lean_pool_source_file_chunks | {α β : Type*} [MeasurableSpace α] [MeasurableSingletonClass α]
[MeasurableSpace β] [MeasurableSingletonClass β]
{Ω' : Type*} [MeasurableSpace Ω'] {f : Ω' → α} {g : Ω' → β}
(hf : Measurable f) (hg : Measurable g)
{μ : Measure Ω'} [IsFiniteMeasure μ]
(h_indep : IndepFun f g μ) (a : α) (b : β) :
(μ... |
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