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 |
|---|---|---|---|---|---|
340 | lean_file_chunk | 2786ba7b96965598181c4dfa81b50f19590c5cdc8ec080db8e3e99f0b4c9af93 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä
-/
import LeanPool.VirasoroProject.ToMathlib.Topology.Algebra.Module.LinearMap.Defs
/-!
# Linear Map Support
Import-only index for linear-map support modules used by the ... |
351 | lean_file_chunk | 5ccbcf3eb1937c3c23c15d436e700285b58fdeb8aacbab33e677412335c4bc6f | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä
-/
import LeanPool.VirasoroProject.ToMathlib.Topology.Algebra.Module.LinearMap
/-!
# Topological Module Support
Import-only index for topological module support modules u... |
560 | lean_file_chunk | eb5a894502ebb47c9725ebc0d9c13634e773f01cd08be03a215d9c2d5e67ad16 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä
-/
import LeanPool.VirasoroProject.ToMathlib.Topology.Algebra.BigOperators
import LeanPool.VirasoroProject.ToMathlib.Topology.Algebra.ConstMulAction
import LeanPool.Virasor... |
525 | lean_file_chunk | 588eda028a34a680835064e8e7210e7f7c22e25496788b10f494df26be6bb9d8 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä
-/
import Mathlib.Topology.Order
/-!
# LeanPool.VirasoroProject.ToMathlib.Topology.Order
-/
section
open Filter
open scoped Topology
lemma DiscreteTopology.tendsto_nhds_... |
371 | lean_file_chunk | 3db06ea8b28136ddcdd42a087b4d38626958b5bd7671de51744874ab5483c113 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä
-/
import LeanPool.VirasoroProject.ToMathlib.Topology.Algebra
import LeanPool.VirasoroProject.ToMathlib.Topology.Order
/-!
# Topology Support
Import-only index for topolo... |
464 | lean_file_chunk | 07b8a82c351a25cfa22a470e3832a9446835d54331333349f1166d21321c1871 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä
-/
import LeanPool.VirasoroProject.ToMathlib.Algebra
import LeanPool.VirasoroProject.ToMathlib.LinearAlgebra
import LeanPool.VirasoroProject.ToMathlib.Topology
/-!
# Viras... |
11,468 | lean_file_chunk | fbb353a78a00cefaf10accd9c018d165943e850123c7b52acd4565a7a11c4058 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä
-/
import Mathlib.Algebra.Lie.OfAssociative
import Mathlib.GroupTheory.GroupAction.Ring
import Mathlib.Order.CompletePartialOrder
/-!
# Verma modules over algebras
This fi... |
8,449 | lean_file_chunk | 909528540e25487833ff543526d53ed01104ffd753afcd28cb876759501ab324 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä
-/
import LeanPool.VirasoroProject.IsCentralExtension
import LeanPool.VirasoroProject.ToMathlib.Algebra.Lie.Abelian
import LeanPool.VirasoroProject.VirasoroCocycle
/-!
# Th... |
6,026 | lean_file_chunk | fce7f4effecf29b7d682cdff40cb39dd8d0e0e5c73fb9c90e9ab88ef8b742a67 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä
-/
import Mathlib.Algebra.Azumaya.Basic
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Analysis.Normed.Ring.Lemmas
import Mathlib.Data.Int.Star
import Mathlib.GroupTh... |
13,910 | lean_file_chunk | d569ef04a08cbadfc712581693514d60a44bac8aeb5553070f24e883586c0743 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä
-/
import LeanPool.VirasoroProject.IndexTri
import LeanPool.VirasoroProject.LieVerma
import LeanPool.VirasoroProject.VirasoroAlgebra
/-!
# Verma modules for the Virasoro al... |
5,503 | lean_file_chunk | 2301e0768918f071253517a0687e515a8708afb9a1d6da994bd2aebb5f25d735 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä
-/
import Mathlib.Algebra.Lie.OfAssociative
import Mathlib.LinearAlgebra.Basis.Bilinear
import LeanPool.VirasoroProject.CyclicTripleSum
import LeanPool.VirasoroProject.ToMat... |
9,932 | lean_file_chunk | e292f266c8bedebccd507abd9a61d70312550de3a46aad72e412f6c7a8088a0b | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä
-/
import LeanPool.VirasoroProject.VirasoroCocycle
/-!
# The 2-cohomology of the Witt algebra is generated by the Virasoro cocycle
In this file it is proven that the 2-coh... |
1,427 | lean_file_chunk | 3163bb4ff2483fa969642afb7b1c6022be312a046b10692899dc9971d277c81a | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä
-/
import LeanPool.VirasoroProject.CentralExtension
import LeanPool.VirasoroProject.CyclicTripleSum
import LeanPool.VirasoroProject.FockSpace
import LeanPool.VirasoroProjec... |
840 | lean_file_chunk | 2258d0a4a1a1a9c19fb5029009d22341fcb77f6f1b6cb7be1ce2745e02587b38 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Joseph K. Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph K. Miller
-/
import Mathlib.Analysis.InnerProductSpace.PiL2
/-! # Ambient geometry for the optimal-transport / Vlasov development
Throughout, `d : ℕ` is the spatial dimensio... |
254 | lean_file_chunk | 17aeefb28cc04f5b9bfdfdca5378cc2c46e9e67795f78905b1e2fa1f5603e6bc | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Joseph K. Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph K. Miller
-/
import LeanPool.Vlasov.Base.Geometry
/-! # Ambient geometry: the physical and phase spaces. -/ |
23,920 | lean_file_chunk | ce20cbcdbf8cd5c8d91fb841700f1315767e1eb5f5fcb5ed4a1fbaa60a2aade0 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Joseph K. Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph K. Miller
-/
import Mathlib.Analysis.Calculus.ContDiff.Basic
import Mathlib.Analysis.Calculus.Deriv.Add
import Mathlib.Analysis.Calculus.Deriv.Basic
import Mathlib.Analysis.Ca... |
23,986 | lean_file_chunk | 6f21fe27e90ee9895715b33564c7ec826dbba68f94bda12c680f5f60bc5e3244 | lean_source_file | lean_pool_source_file_chunks | (-(1 / (N : ℝ)) • ∑ j : Fin N, if j ≠ i then gradW (X t i - X t j) else (0 : PhysSpace d))
(gradVφ (X t i, V t i))
= -(1 / (N : ℝ)) *
(@inner ℝ (PhysSpace d) _ (∑ j : Fin N, gradW (X t i - X t j)) (gradVφ (X t i, V t i))
- @inner ℝ (PhysSpace d) _ (gradW 0) (gradVφ (X t i, V t i))) :=... |
23,991 | lean_file_chunk | a4e71f0f5bfaf50e02eb4699bc0f07e5c484ddb88cf8d20dde38e099ae54dd03 | lean_source_file | lean_pool_source_file_chunks | /-! ## §11 Theorem (Dobrushin, 1979) (`tex: thm:dobrushin`) -/
-- The Wasserstein-1 distance (`wasserstein1`), `wassersteinCost`, and
-- `wassersteinBar` OT core live in `LeanPool/Vlasov/OT/Wasserstein.lean`.
-- `HasFiniteFirstMoment` (PhaseSpace-specific) stays here.
/-- Completeness of `(𝒫_1(PhysSpace d), W₁)` for... |
18,284 | lean_file_chunk | 4e323b107f87d5bf99dd1a9bd3eee3f2ad0763bce673e3811c62fe52b146f0ec | lean_source_file | lean_pool_source_file_chunks | (hφ_lip : LipschitzWith 1 φ) :
ContinuousOn (fun t => ∫ z, φ z ∂(f t)) (Set.Icc 0 T) := by
-- Step 1: Destructure IsLagrangianVlasovSolution
obtain ⟨_, charX, charV, hflow, hpush, hflow_meas⟩ := hf_lag
obtain ⟨hflow_init, hflow_x, hflow_v⟩ := hflow
-- Step 2: Rewrite ∫ φ d(f t) = ∫ (φ ∘ (charX t, charV t)) ... |
6,473 | lean_file_chunk | 4f539f8189e9c708c715533232e8cd1070a7ea2948f2ec1aed05990ac0176177 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Winston Yin, Joseph K. Miller
-/
import Mathlib.Analysis.ODE.PicardLindelof
/-!
# Picard-Lindelöf with explicit confinement conjunct (vendored from Mathlib)
This fi... |
281 | lean_file_chunk | da151d63ca1483e3ce4e6c3133d1d4466f63418781f71f174a1c3d8850242fe8 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Joseph K. Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph K. Miller
-/
import LeanPool.Vlasov.ForMathlib.PicardLindelof
/-! # Vendored Picard-Lindelof with an explicit confinement conjunct. -/ |
23,951 | lean_file_chunk | 2a1e179e531f84cd8086f3c709fc20ffdef63bfdb8b7147a866685e0e0675058 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Joseph K. Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph K. Miller
-/
import Mathlib.Algebra.Order.Field.GeomSum
import Mathlib.Analysis.Calculus.ParametricIntegral
import Mathlib.MeasureTheory.Integral.Prod
import LeanPool.Vlasov.B... |
23,995 | lean_file_chunk | 3606bbd528bb30ef2a28f40ddc55b14bfb0d2e4f0116cea0c0897177a3554c67 | lean_source_file | lean_pool_source_file_chunks | -- AEStronglyMeasurability of `uncurry g` over the product measure
have hg_aesm : AEStronglyMeasurable (Function.uncurry g)
((MeasureTheory.volume.restrict (Set.uIoc (0 : ℝ) t)).prod π) := by
have h1 : AEStronglyMeasurable (fun p : ℝ × Ω => L * ‖w p.1 p.2‖)
((MeasureTheory.volume.restrict (Set.uIoc ... |
23,944 | lean_file_chunk | 14780cf046fad92324477c22006284e53fdad1961536666d2f7d64c733bf26c9 | lean_source_file | lean_pool_source_file_chunks | ∀ t ∈ Set.Icc 0 T, ∀ z : PhaseSpace d,
‖(charX t z, charV t z)‖ ≤
gronwallBound ‖z‖ (1 + (L : ℝ)) (‖gradW 0‖ + (L : ℝ) * m t) t := by
intro t ht z
set K : ℝ := 1 + (L : ℝ) with hK_def
-- m t ≥ 0 (moment of a probability measure is nonneg, bounded by m t).
have hmt_nn : 0 ≤ m t :=
le_trans (int... |
23,944 | lean_file_chunk | ec52196b407fd958c2bb8f6ddeceef8c45a16c7098688253aafd993a3a68292e | lean_source_file | lean_pool_source_file_chunks | (fun x : PhysSpace d => convolveFunctionMeasure gradW (ρ t) x) :=
convolveFunctionMeasure_lipschitz_in_x gradW L hL (ρ t) (h_int t)
-- Negate (`Neg.neg` is 1-Lipschitz): `x ↦ -(∇W ∗ ρ_t)(x)` is still `L`-Lipschitz.
have h_neg_conv : LipschitzWith L
(fun x : PhysSpace d => -convolveFunctionMeasure gradW (ρ... |
23,948 | lean_file_chunk | 50a8cce5905b3ea77b5a62fb7558af66a5c0098a6c2ccd129f725d8f5475267e | lean_source_file | lean_pool_source_file_chunks | (-(convolveFunctionMeasure gradW (ρ t) (β t).1))
(Set.Icc t_start (t_start + δ)) t)
(h_β_in_ball : ∀ s ∈ Set.Icc t_start (t_start + δ),
(β s).1 ∈ Metric.closedBall w.1 (3 * (a : ℝ) / 2))
(hbound : ∀ t ∈ Set.Icc t_start (t_start + 1),
∀ x ∈ Metric.closedBall w.1 (3 * (a : ℝ) / 2),
... |
23,981 | lean_file_chunk | a49fd955fe19fa727ea360e38d2b21a24e6375b44d5456d3761b1670cb3d6d05 | lean_source_file | lean_pool_source_file_chunks | (hV_max_def : V_max = ‖z₀.2‖₊ + a / 2 + M * Real.toNNReal T)
(hR : 2 * (a : ℝ) + (‖z₀.2‖ + (a : ℝ) / 2) * T + (M : ℝ) * T ^ 2 ≤ R)
(hbound : ∀ t ∈ Set.Icc (0 : ℝ) T,
∀ x ∈ Metric.closedBall z₀.1 (R : ℝ),
‖convolveFunctionMeasure gradW (ρ t) x‖ ≤ M)
(δ' : ℝ) (hδ'_pos : 0 < δ')
... |
23,993 | lean_file_chunk | cd1ee91c9886d987dc94c9789524874ef781b98735b0113017393cd375e1cd97 | lean_source_file | lean_pool_source_file_chunks | have h_a_nn : (0 : ℝ) ≤ (a : ℝ) / 2 := by linarith [ha_real]
have h_step : (L_pl : ℝ) * (2 * δ) ≤ (L_pl : ℝ) *
(2 * ((a : ℝ) / 2 / (2 * ((L_pl : ℝ) + 1)))) := by
apply mul_le_mul_of_nonneg_left _ h_Lpl_nn
linarith [hδ_le_ratio]
have h_simp : (L_pl : ℝ) *
(2 * ((a : ℝ) / 2... |
23,925 | lean_file_chunk | 0df2328b862c5367813faecf8394ee7d2491de5e024f31276a45737c189d3775 | lean_source_file | lean_pool_source_file_chunks | {d : ℕ}
(charX charV : ℝ → PhaseSpace d → PhysSpace d)
(f₀ : Measure (PhaseSpace d))
(φ : PhaseSpace d → ℝ) (hφ_cont : Continuous φ)
(h_flow_meas : ∀ s, AEMeasurable
(fun z : PhaseSpace d => (charX s z, charV s z)) f₀)
(t : ℝ) :
∀ᶠ s' in nhds t, AEStronglyMeasurable
(fun z => φ (char... |
23,978 | lean_file_chunk | 2127107b9738a974094243aa597a1e854e001072211bdb93a587c87ec0119dcb | lean_source_file | lean_pool_source_file_chunks | apply mul_le_mul (hM_φ _) h_vel_bnd (norm_nonneg _) hM_φ_nn
_ ≤ M_φ * (K * C_T + ε₀) * (‖z‖ + 1) := by
have hz1 : 1 ≤ ‖z‖ + 1 := by linarith [norm_nonneg z]
nlinarith [mul_nonneg hM_φ_nn hε₀_nn,
mul_nonneg (mul_nonneg hM_φ_nn hε₀_nn)
(by li... |
23,964 | lean_file_chunk | 205cf50887ddd1ef75cdd77a048b0435784bbc713c43e5c25a84d48e70099cb1 | lean_source_file | lean_pool_source_file_chunks | integrability of `‖·‖`, and W₁-continuity at every time in `[0, T]`.
The W₁-continuity field is phrased per-base-point `s ∈ [0, T]` as
`ContinuousWithinAt` of `t ↦ W₁(ρ s, ρ t).toReal` at `s` (which equals 0 at
`t = s`). This is strictly stronger than naive ContinuousOn on the diagonal
— it gives the dominator we nee... |
23,947 | lean_file_chunk | f1ee2aa222b9a083ce994568a087ec430be097723cc7fcf0e0cdf3f089d30c4d | lean_source_file | lean_pool_source_file_chunks | (-(convolveFunctionMeasure gradW (ρ t) (γ t).1)) t) ∧
(∀ t ∈ Set.Icc (0 : ℝ) T,
HasDerivWithinAt (fun s => (γ s).1) (γ t).2 (Set.Icc 0 T) t ∧
HasDerivWithinAt (fun s => (γ s).2)
(-(convolveFunctionMeasure gradW (ρ t) (γ t).1)) (Set.Icc 0 T) t) := by
intro z
exact exists_vlasov_tr... |
23,977 | lean_file_chunk | c713502e57985946dd1c5abb4d880fba443d3fad1f5e679f37265abf2219ecbb | lean_source_file | lean_pool_source_file_chunks | isProb := Phi_isProbabilityMeasure charX f₀ h_meas
hasMoment := fun t ht =>
Phi_hasMoment_le charX f₀ h_meas T hT C_T hC_T_nn h_growth h_f₀_int M_f₀ hM_f₀ t ht
yIntegrable := fun t ht =>
Phi_yIntegrable charX f₀ h_meas T hT C_T hC_T_nn h_growth h_f₀_int t ht
hW1Cont :=
Phi_hW1Cont charX f₀ h_meas h_in... |
23,958 | lean_file_chunk | a524f06d9cfed5efd9447448ead03b3bda5b54d9680985b0e0abcae9c7b7ae63 | lean_source_file | lean_pool_source_file_chunks | -- feeds the time-local Gronwall forcing).
have hm_M : ∀ t ∈ Set.Icc (0 : ℝ) T, ∫ y, ‖y‖ ∂(ρ.extend t) ≤ M t := by
intro t ht
have h_eq : ρ.extend t = ρ.ρ t := by
unfold VlasovMeasureCurve.extend clampToIcc
congr 1
rw [min_eq_left ht.2, max_eq_right ht.1]
rw [h_eq]; exact ρ.hasMoment t h... |
23,952 | lean_file_chunk | 540fc9e365c03ba179a52227a9d68b43ee2af67952a14b3cbe7498a1f06c2a40 | lean_source_file | lean_pool_source_file_chunks | have hφ_meas_νf : AEStronglyMeasurable φ (Measure.map f f₀) :=
hφ_cont.aestronglyMeasurable
have hφ_meas_νg : AEStronglyMeasurable φ (Measure.map g f₀) :=
hφ_cont.aestronglyMeasurable
have hφ_abs_bound : ∀ y : PhysSpace d, |φ y| ≤ |φ 0| + ‖y‖ := fun y => by
have h_lip := hφ.dist_le_mul y 0
rw [Real.... |
11,295 | lean_file_chunk | 914d0c1a914c86a458d5ece2ba376ea499220d248560ecdfd45fee3cda5988bb | lean_source_file | lean_pool_source_file_chunks | `wasserstein1 (x n t) (y t) ≤ wasserstein1 (x n t) (x m t) + wasserstein1 (x m t) (y t)`.
The first term `≤ supW1On (x n) (x m) < ε` by Cauchy; the second `→ 0` by
pointwise tendsto. Apply `ENNReal.le_of_forall_pos_le_add` for the limit
passage. -/
lemma picard_iterate_limit_uniform_tendsto {d : ℕ}
(S : Set ℝ) (x ... |
23,999 | lean_file_chunk | 01a728ed8aaab20997d3ef658dc1c2e6fa94caaef01c0e66b06cb4656ba74984 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Joseph K. Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph K. Miller
-/
import Mathlib.Analysis.Convex.Cone.InnerDual
import Mathlib.MeasureTheory.Measure.LevyProkhorovMetric
import Mathlib.Probability.Kernel.Composition.MeasureComp
i... |
23,940 | lean_file_chunk | 0e296d2d1a91472d6e157d67b4a04b0b2d67c828b4d5721f1bd23eaae4fd361d | lean_source_file | lean_pool_source_file_chunks | (as : ℕ → α) (x₀ : α) (N : ℕ) :
∃ T : α → α,
Measurable T ∧
(Set.range T).Finite ∧
(∀ n < N, ∀ x ∈ As n, T x = as n) ∧
(∀ x ∈ (⋃ n ∈ Finset.range N, As n)ᶜ, T x = x₀) := by
classical
-- measurability of the recursive step map, for any list of indices
have hmeas : ∀ l : List ℕ,
Me... |
23,975 | lean_file_chunk | 89b024d39462128a2dfbd99dbe1a280cf9026ccd9dce3247e43edd70340f485a | lean_source_file | lean_pool_source_file_chunks | · change (c : ℝ) * (∑ j, P i j) = ∑ j, (c : ℝ) * P i j
rw [Finset.mul_sum]
· change (c : ℝ) * (∑ i, P i j) = ∑ i, (c : ℝ) * P i j
rw [Finset.mul_sum]
· change (c : ℝ) * ((∑ i, ∑ j, Cost i j * P i j) + s)
= (∑ i, ∑ j, Cost i j * ((c : ℝ) * P i j)) + (c : ℝ) * s
... |
22,726 | lean_file_chunk | ded8bbd2a05eebe2e84234536b413c055fb22316e8e06675cce79f0a4dbfde82 | lean_source_file | lean_pool_source_file_chunks | have hg_ge_u : ∀ a' ∈ Set.range T, u a' ≤ g a' := by
intro a' ha'
have h : u a' - c a' a' ≤ g a' := Finset.le_sup' (fun a => u a - c a' a) (hmemA a' ha')
rwa [hc_self, sub_zero] at h
-- g b ≤ −v b on range S (from u a − c a b ≤ −v b)
have hg_le_negv : ∀ b ∈ Set.range S, g b ≤ -v b := by
intro b hb
... |
23,946 | lean_file_chunk | 5e69beab85d29a66514dc48abf69387cf654efd34c049caddf3f9c9796219009 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Joseph K. Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph K. Miller
-/
import Mathlib.MeasureTheory.Integral.Bochner.Basic
import Mathlib.MeasureTheory.Integral.DominatedConvergence
import Mathlib.MeasureTheory.Measure.HasOuterApprox... |
19,156 | lean_file_chunk | d631546e87e37cdea455e1cccde3b79b9f29e60d249736e82a1c7ca2aacc9335 | lean_source_file | lean_pool_source_file_chunks | ⟨wassersteinCost_self _ μ, wassersteinCost_comm _ μ ν,
wassersteinCost_triangle _ μ ν τ, wassersteinCost_dual_lower_bound _ μ ν f hf⟩
/-! ### `wassersteinBar` — the truncated (cutoff) Wasserstein-1 distance Wbar
`Wbar := wassersteinCost (min(dist, 1))` (Dobrushin 1979 §5). The bounded
cost makes the dual test cla... |
23,943 | lean_file_chunk | 2efdcde9a9466b5cd4295b6908c3af650f6942e817bd56e37b2bbdbee04506fa | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Joseph K. Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph K. Miller
-/
import Mathlib.Analysis.Calculus.BumpFunction.Convolution
import Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension
import Mathlib.Analysis.Calculus.InverseFu... |
23,969 | lean_file_chunk | da1be5e6f6656aa2755c8e450c446b45e1cd784fdef19cd9d777a1a3b6d31ce1 | lean_source_file | lean_pool_source_file_chunks | ContDiffBump.convolution_tendsto_right_of_continuous hrout_tendsto hg_cont x
-- Uniform bound `‖gn n x‖ ≤ C` (averaging keeps the sup bound).
have hgn_bound : ∀ n, ∀ x, ‖gn n x‖ ≤ C := by
intro n x
rw [hgn]
simp only
rw [convolution_lsmul]
calc ‖∫ t, (φ n).normed volume t • gf (x - t) ∂volume‖
... |
23,989 | lean_file_chunk | 4862af2fbaf3b86a9c1fa5193b4d7666370decc663f290c08cafae6b225b5054 | lean_source_file | lean_pool_source_file_chunks | have ht0 : (0 : ℝ) ≤ t := ht.1
have htT : t ≤ T := ht.2
have hmaj : ∀ n, ∀ s ∈ Set.Icc (0 : ℝ) T,
‖picardIter 𝒜 x₀ n s‖ ≤ (K * T) ^ n / n.factorial * ‖x₀‖ := by
intro n s hs
refine le_trans ((hcb n).2 s hs) ?_
have hKs : 0 ≤ K * s := mul_nonneg hK hs.1
have hle : K * s ≤ K * T := mul_le_mul_o... |
23,986 | lean_file_chunk | f7e591dd65fa525c86768cabe503e79775f97d6ceb163146983855b6ab27a14d | lean_source_file | lean_pool_source_file_chunks | obtain ⟨KA, hKA⟩ :=
(isCompact_Icc (a := (0 : ℝ)) (b := T)).exists_bound_of_continuousOn hA
have hK'0 : (0 : ℝ) ≤ max KA 0 := le_max_right _ _
have hbound : ∀ t ∈ Set.Icc (0 : ℝ) T, ‖ContinuousLinearMap.compL ℝ F F F (A t)‖ ≤ max KA 0 := by
intro t ht
have h1 : ‖ContinuousLinearMap.compL ℝ F F F (A t)‖ ... |
23,957 | lean_file_chunk | db39b3e100a1ffc80bc5e04667f49467b6f0178c9f75205bcc2bb18b6d01bff4 | lean_source_file | lean_pool_source_file_chunks | = uh t - mh t from rfl, ← dist_eq_norm]
calc dist (uh t) (mh t)
≤ gronwallBound 0 Kr εf t := hlim
_ = εf * Cgron := hgb_val
_ = η * G * ‖h‖ := by rw [hεf, hG]; ring
_ ≤ c * ‖h‖ := mul_le_mul_of_nonneg_right hηG (norm_nonneg h)
end CharFlowDeriv
omit [NeZero d] in
/-- **C3 #3 — the variational equa... |
23,993 | lean_file_chunk | 65838a024608dfd8a24888fd6d47ba7236e2b2e555ea718cd33dee34bf359b79 | lean_source_file | lean_pool_source_file_chunks | exists_global_c1_inverse_of_antilipschitz hderiv hM_cont hanti hlip
refine ⟨Ψ, e, ?_, hLeft, hRight, hΨlip.continuous, hΨderiv⟩
intro z; rw [he_coe z]; exact hderiv z
section Step3Joint
open Filter Topology Asymptotics
/-- **Step 3 gating lemma (generic) — joint `C¹` from continuous partial derivatives** on a
`ℝ ... |
23,968 | lean_file_chunk | ae719d8e0c37ea52fe046e2b9169aa6dd6cf4a97bf39abfa0e1cc41707f6c96b | lean_source_file | lean_pool_source_file_chunks | set Mfun : ℝ × PhaseSpace d → (PhaseSpace d →L[ℝ] PhaseSpace d) :=
fun p => fundamentalMatrix (A p.2) p.1 with hMfun_def
-- z-partial at base via D1c — needs `A` TRANSPARENT (its coefficient is `vlasovFieldJacobian`).
have hDz_all : ∀ s₀ ∈ Set.Ioo (0 : ℝ) T, ∀ z₀ : PhaseSpace d,
HasFDerivAt (fun z => (cha... |
23,982 | lean_file_chunk | b3d12e48691213574501c605178abfe782af4456201975b8b7115bab51c75239 | lean_source_file | lean_pool_source_file_chunks | Measure.volume_eq_prod _ _]
infer_instance
have hg_uc : UniformContinuous g := hg_cs.uniformContinuous_of_continuous hg_cont
rw [Metric.uniformContinuous_iff] at hg_uc
rw [Metric.tendstoUniformly_iff]
intro ε hε
obtain ⟨δ, hδ, hδ_prop⟩ := hg_uc (ε / 2) (by positivity)
have hev : ∀ᶠ n in atTop, (φ n).rOu... |
23,984 | lean_file_chunk | 5eb7e9d4fe04a0dbf7f6832b89dc542cbd9544a1781239c323b2c34a4ba240e2 | lean_source_file | lean_pool_source_file_chunks | simpa using h
-- pointwise convergence (0th order): ∫ χ_n d(f σ) → ∫ χ d(f σ)
have hfg : ∀ σ ∈ Set.Ioo (0 : ℝ) T, Tendsto (fun n => ∫ z, χn n z ∂(f σ)) atTop
(𝓝 (∫ z, χ z ∂(f σ))) := by
intro σ hσ
have : IsProbabilityMeasure (f σ) := (hf_mom σ (Set.Ioo_subset_Icc_self hσ)).1
exact integral_tendst... |
23,992 | lean_file_chunk | a4218ba800815531d1a8cb0a959f32492118e9879f8f9062fa3adb1a12a5aaee | lean_source_file | lean_pool_source_file_chunks | (hf_weak : IsVlasovSolutionOn gradW f T)
(hf_mom : ∀ t ∈ Set.Icc (0 : ℝ) T, HasFiniteFirstMoment (f t))
(hf_narrow : ∀ (g : PhaseSpace d → ℝ), Continuous g → HasCompactSupport g →
ContinuousOn (fun s => ∫ z, g z ∂(f s)) (Set.Icc 0 T))
-- B2 enrichment: threaded through to `weakEvolution_test_C1c_On` (... |
23,973 | lean_file_chunk | 68600951f9186a9ca761930527659e895ff4e8655c49087640c486fdd2228584 | lean_source_file | lean_pool_source_file_chunks | exact hp2
_ = δ := by ring
· -- s₀ > 0: locally G' = g (Ψ (min · t) ·)
have heq : (fun p : ℝ × PhaseSpace d => G' p.1 p.2) =ᶠ[𝓝 (s₀, z₀)]
(fun p => g (Ψ (min p.1 t) p.2)) := by
have hmem : {p : ℝ × PhaseSpace d | 0 < p.1} ∈ 𝓝 (s₀, z₀) :=
(isOpen_lt continuous_const cont... |
14,140 | lean_file_chunk | 1860c8bb40d24d94d27f4afedf28399fce20a3134372087e0abea3bb3b27b9a5 | lean_source_file | lean_pool_source_file_chunks | omit [NeZero d] in
/-- **C3 #8 — the weak solution equals its frozen-field pushforward on the window.**
`f t = (Φ_t)_# (f 0)` on `[0,T]`. Skeleton: `measure_eq_of_forall_Cc_integral_eq` (#9) reduces
this to per-`C_c^∞`-test integral equality, and `integral_map` turns the pushforward side into
`∫ φ∘Φ_t d(f 0)` — leavi... |
23,997 | lean_file_chunk | 25e996baca95485292cf1d67849f0cbce10875d1164eddabc3f8c3988d042780 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Joseph K. Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph K. Miller
-/
import LeanPool.Vlasov.OT.CharacteristicFlow
/-!
# Well-posedness ladder for the Vlasov equation + Dobrushin stability
This file builds on the characteristic-fl... |
23,963 | lean_file_chunk | cfde31fafd0e051c26c1a10a0fa59bd737257297b9124f546e3f470b70a301f7 | lean_source_file | lean_pool_source_file_chunks | hCI_ν.1 hCI_l.1 hCI_ν.2.1 hCI_l.2.1
hCI_ν.2.2.2.1 hCI_l.2.2.2.1 hCI_ν.2.2.2.2.1 hCI_l.2.2.2.2.1
hCI_ν.2.2.2.2.2 hCI_l.2.2.2.2.2 t ht
have h_mono : gronwallBound 0 ((max 1 L : NNReal) : ℝ) ((L:ℝ) * D) t
≤ gronwallBound 0 ((max 1 L : NNReal) : ℝ) ((L:ℝ) * D) T :=
gronwallBound_mono (le_refl 0) (mul_no... |
23,962 | lean_file_chunk | 437b951be46e5620d53c4887daab9223670798dcf70f5bc45ac570bbab39af21 | lean_source_file | lean_pool_source_file_chunks | Measure.isProbabilityMeasure_map measurable_fst.aemeasurable
have hμ₀_int : Integrable (fun y : PhysSpace d => ‖y‖) (spatialMarginal f₀) := by
unfold spatialMarginal
rw [integrable_map_measure
(Continuous.aestronglyMeasurable continuous_norm) measurable_fst.aemeasurable]
-- Need: Integrable (‖·‖ ∘ P... |
23,969 | lean_file_chunk | b24aa61fbed5171904ac61a36f7aa1ea46ecdedc529e3d0b05ca3859d9a97753 | lean_source_file | lean_pool_source_file_chunks | 4. Apply `picard_iterate_isCauchy_of_contraction` to get the ENNReal-form
Cauchy condition on the `supW1On` pseudodistance.
5. Apply `picard_iterate_exists_limit` to extract the
limit `ρ_lim : VlasovMeasureCurve d T M` plus pointwise W₁-tendsto.
6. Self-consistency `Φ(ρ_lim) = ρ_lim`: triangle through `ρ_n` usi... |
23,974 | lean_file_chunk | 1884be2342d7e1fe6c66b8d1366d1634e7b5bd5a6abc088e5c3bf907921b3187 | lean_source_file | lean_pool_source_file_chunks | congrArg spatialMarginal hfnext
rw [← hfnext_spat] at hV_big
constructor
· exact hX_big.congr_of_eventuallyEq_of_mem hX_ev ht
· exact hV_big.congr_of_eventuallyEq_of_mem hV_ev ht
· -- T < t: use hg_boundary + chain rule
push Not at ht_le
simp only [if_neg (not_le.mpr ht_le)]
have h... |
23,999 | lean_file_chunk | e0e02bef6c1b42aff051d10f9dd4b52bd1c992317ae27ec7b0fcd788e456ee0b | lean_source_file | lean_pool_source_file_chunks | `‖(gradW ⋆ ρ) x‖ ≤ ‖gradW 0‖ + L·‖x‖ + L·M` for a probability measure `ρ`
with `∫ ‖y‖ ∂ρ ≤ M`. -/
private lemma vlasovGlue_conv_force_bound
{d : ℕ} [NeZero d]
(gradW : PhysSpace d → PhysSpace d)
(L : NNReal) (hL : LipschitzWith L gradW)
(ρ : Measure (PhysSpace d)) [IsProbabilityMeasure ρ]
(M : ℝ) (h... |
23,950 | lean_file_chunk | 3c8b901e2ce34792ce7d842d18a65fd563c1cd39f8b77b342af698a68e50dc3b | lean_source_file | lean_pool_source_file_chunks | congrArg spatialMarginal h_fnext_T
have h_aemeas_f₀_T : AEMeasurable
(fun z : PhaseSpace d => (charX_prev T z, charV_prev T z)) f₀ :=
h_prev_init ▸ h_prev_aemeas T hT_Icc
have h_meq : f_next T
= Measure.map
(fun z : PhaseSpace d => (charX_prev T z, charV_prev T z)) f₀ := by
... |
23,961 | lean_file_chunk | 49392f4ba1c6efa73a29df2e37b0c36c24edac4dbc57d059ba091409c90dc893 | lean_source_file | lean_pool_source_file_chunks | have h_ev : (fun s => if s ≤ T then charX_prev s z
else charX_g (s - T) (charX_prev T z, charV_prev T z)) =ᶠ[nhds t]
(fun s => charX_prev s z) := by
apply Filter.Eventually.mono (eventually_lt_nhds ht_lt)
intro s hs; simp [le_of_lt hs]
exact ((h_prev_flowX t ⟨ht.1, ht_lt⟩ z).co... |
23,938 | lean_file_chunk | 7c7e829b5b8a41dd7730f014d0fd5b4507786c113c1746af85d9f42e9b7306be | lean_source_file | lean_pool_source_file_chunks | · apply Filter.Eventually.mono h_nhd_R
intro s hs
have hsT_Icc : s - T ∈ Set.Icc (0 : ℝ) T_0 :=
⟨by linarith [hs.1], by linarith [hs.2]⟩
have h_g_at_sT : AEMeasurable
(fun z : PhaseSpace d => (charX_g (s - T) z, charV_g (s - T) z))
(Measure.map (fun z : PhaseSpace d =>
... |
23,977 | lean_file_chunk | 48272b94b037e05a9ad87caf2cbde93838080a88099ea962b7302ebfb95531c6 | lean_source_file | lean_pool_source_file_chunks | vlasovGlue_seam_contRight gradW L hL f₀ hf₀_int hT_pos hT_0_pos
f_prev h_prev_init h_prev_mom hM_prev charX_prev charV_prev
h_prev_push h_prev_aemeas h_prev_boundary h_prev_ic
g charX_g charV_g hg_init hg_mom hg_mom_unif hg_push_ex
hg_aemeas_ex hg_... |
23,977 | lean_file_chunk | 59e5c0ee1de26eac125ecdc3afac06ca04797714808950b447186e67d3529396 | lean_source_file | lean_pool_source_file_chunks | (μ : ℝ → Measure (PhaseSpace d)) (ν : Measure (PhaseSpace d))
(hpush : ∀ t ∈ Set.Icc (0 : ℝ) T,
μ t = Measure.map (fun z => (charX t z, charV t z)) ν)
(haem : ∀ s ∈ Set.Icc (0 : ℝ) T,
AEMeasurable (fun z : PhaseSpace d => (charX s z, charV s z)) ν) :
∀ s ∈ Set.Icc (0 : ℝ) T, ∀ x : PhysSpace d,
... |
23,936 | lean_file_chunk | 33fb0245522fa3f1a5a97489798a45cbadbab41e099266e6d770fe0a27d2d24b | lean_source_file | lean_pool_source_file_chunks | - convolveFunctionMeasure gradW (spatialMarginal (f s)) x) := by
rw [hb_f_s, hb_g_s]
simp only [vlasovVectorField, Prod.mk_sub_mk, sub_self, hx_def]
refine Prod.ext rfl ?_
change -(convolveFunctionMeasure gradW (spatialMarginal (f s)) (X_g s ω).1)
- -(convolveFunctionMeasure gradW (spatialMarg... |
23,985 | lean_file_chunk | cf09bddab721ab8e22f774cbe4a8bc09f5e4d0ca6165962acc606f7cbb2a4ef2 | lean_source_file | lean_pool_source_file_chunks | have hcg : Continuous (fun s => b_g s (X_g s ω)) := by
have h := dobrushinFlow_field_continuous gradW L hL T K clampT hclampT_mem
charX_g charV_g g (g 0) K_g b_g
(fun s z => (charX_g (clampT s) z, charV_g (clampT s) z)) hb_g_def rfl
(fun z => (hcontIcc_g z).comp_continuous hclampT_cont (fu... |
23,937 | lean_file_chunk | 6dab016ab2875cec1e02ef5101e5b5375585f7360ddb82803381fa5d2ab56abc | lean_source_file | lean_pool_source_file_chunks | -- Step 4. Define the universal-in-forward-time solution.
-- For t ≥ 0: use sol ⌈t⌉₊ at t. For t < 0: f₀ (unconstrained by the
-- forward-only statement; the claims below only quantify over t ≥ 0).
let f : ℝ → Measure (PhaseSpace d) :=
fun t => if 0 ≤ t then sol (⌈t⌉₊) t else f₀
-- Step 5. Prove the four c... |
14,751 | lean_file_chunk | 6e3e8cd003683f612553de70c4e072e4add3686b1af4ee37a44d2a1887b14769 | lean_source_file | lean_pool_source_file_chunks | -- Rewrite via integral_map: ∫ g df_sol(t) = ∫ z, g(z.1+t•z.2, z.2) df₀.
have h_rw : ∀ t, ∫ z, g z ∂f_sol t = ∫ z, g (z.1 + t • z.2, z.2) ∂f₀ := by
intro t
simp only [f_sol, charX, charV]
rw [integral_map (by fun_prop) (by fun_prop)]
simp_rw [h_rw]
-- Apply continuous_of_domina... |
440 | lean_file_chunk | fce7bc4e27ebd794ce43771d50fc6676dd1d18d14cb1baacd7d2ecc81e830dfd | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Joseph K. Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph K. Miller
-/
import LeanPool.Vlasov.OT.CharacteristicFlow
import LeanPool.Vlasov.OT.Coupling
import LeanPool.Vlasov.OT.Wasserstein
import LeanPool.Vlasov.OT.WeakToLagrangian
... |
592 | lean_file_chunk | 3c4d458b5cb8dc781ad9b1ad8954db9a787ecb030fefcead838f38874499e607 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Joseph K. Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph K. Miller
-/
import LeanPool.Vlasov.Base
import LeanPool.Vlasov.ForMathlib
import LeanPool.Vlasov.OT
/-!
# Mean-field derivation and well-posedness of the Vlasov equation
S... |
5,617 | lean_file_chunk | 1f2cae1ba5c17817877507682bef1999319f496cbe290c36be01c37d8a962f21 | 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.Algebra.Order.Archimedean.Basic
import Mathlib.Data.Fintype.Lattice
import Mathlib.Order.ConditionallyCompleteLattice.Finset
import Mathlib.Topology.Homotop... |
2,231 | lean_file_chunk | b264f17601a84e4cd4840530faf708243862b26a229a56bf020700ec1bd8753c | 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.Compressible.CWComplex
import LeanPool.WhiteheadTheorem.Compressible.Defs
import LeanPool.White... |
7,775 | lean_file_chunk | 70631f956a29753b77df8e6f41b0dcbd2a4918fbd135dcdeeca629f914f9cdfd | 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.Shapes.Disk
import Mathlib.Topology.Category.TopCat.Limits.Basic
import Mathlib.CategoryTheory.Limits.Shapes.Products
import Mathlib.Categ... |
23,987 | lean_file_chunk | 100dd9b150f6ac745173883268529932ef571b3a7ca60e78b9be40477f68688c | 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 WhiteheadTheorem.Shapes.Cube
import LeanPool.WhiteheadTheorem.CWComplex.Basic
import LeanPool.WhiteheadTheorem.Auxiliary
import LeanPool.WhiteheadTheorem.Exponen... |
23,987 | lean_file_chunk | 0de0fddde613d3894c7644b26e78106e6534114f74edf788def2a70769e8a810 | lean_source_file | lean_pool_source_file_chunks | cubeBoundary.mapOfBotTopSides (IProd.cubeAttBotOrTop X α) (IProd.cubeAttSides X α)
(IProd.cubeAtt_compatible X α) =
(diskPair.homeoCubePairULift n).hom.right ≫ IProd.cubeAttBotOrTop X α t from by
congr 1]
-- Unfold cubeAttBotOrTop α t and use `hom.right ≫ inv.right = 𝟙 _`.
... |
272 | lean_file_chunk | c58fcb85cc86554c899689d5abd05f96c667d05356265447d4c9f897fe59c9d3 | lean_source_file | lean_pool_source_file_chunks | (Limits.Sigma.desc fun a ↦ isEmptyElim a)
(Limits.Sigma.map fun _ ↦ diskBoundaryIncl 0) }
| n + 1 =>
{ cells := (X.attachCells n).cells
attachMaps := IProd.attachMaps X
isoPushout := (IProd.pushoutSkSk X n).isoPushout }
end CWComplex |
12,460 | lean_file_chunk | 619437a808bbab47fb430ab068d9e531fffc7e8ae2f98d5890031a7c469bdba7 | 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.CWComplex.IProd.Def
import Mathlib.CategoryTheory.Adjunction.Limits
/-!
This file verifies that the pair `(X.IProd.sk 0, X.IProd)` is hom... |
18,178 | lean_file_chunk | e7313fe03311f06d785590b808162006e841b37e84830ccf91b9c3ed8d73c1e4 | 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.CWComplex.IProd.Iso
import LeanPool.WhiteheadTheorem.HEP.Cofibration
import LeanPool.WhiteheadTheorem.Compressible.Defs
/-!
This file pro... |
6,119 | lean_file_chunk | 4d40717d191e60a25abc5903af2a93e8036d8b701c92d3c304ca260ce146401b | 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.Exponential
import LeanPool.WhiteheadTheorem.Shapes.Maps
import Mathlib.Topology.Category.TopCat.Limits.Basic
import Mathlib.Topology.Homo... |
23,945 | lean_file_chunk | 63ebf9840caf15cca7ed2a10b7e652ec84efde86d11484ae94c0bd2d6dc7737b | 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.Compressible.Defs
import LeanPool.WhiteheadTheorem.Shapes.MappingCylinder
import LeanPool.WhiteheadTheorem.HomotopyGroup.ChangeBasePt
impo... |
6,688 | lean_file_chunk | 56500a85863838b9e071094a6f17256c90f0420fd7c6f144aa2925ef7189d89e | lean_source_file | lean_pool_source_file_chunks | let g : C(disk.{u} (n + 1), X) := ContinuousMap.const (𝔻 (n + 1)) a
have gr : Set.range g ⊆ A := Set.range_subset_iff.mpr fun _ ↦ a.property
apply homotopicRel_boundary_of_homotopicWith_isMapOfPairs X A
use g
/-- For `n ≥ 1`, if the relative homotopy group `π_rel (n + 1) X A a` is zero
(regardless of the basepo... |
7,337 | lean_file_chunk | d0c7cfb73c14492842eecce10ae58543d5869206a5c9d6865c2aee39a4aa7af0 | 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.Compressible.Disk
import LeanPool.WhiteheadTheorem.Compressible.CWComplex
/-!
This file proves that if `B` and `Y` are CW-complexes
and `... |
1,105 | lean_file_chunk | d6f407b0479df10a6f74f84ab1970141ee78369d7ae30026101516707401b0be | 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.HomotopyGroup.InducedMaps
/-!
# LeanPool.WhiteheadTheorem.Defs
Imported Lean Pool material for `LeanPool.WhiteheadTheorem.Defs`.
-/
op... |
7,596 | lean_file_chunk | 91860d50c0c067b7af46507e14b1216d0d4101c5662d89360b067813922618bc | 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.Limits.Products
/-!
# LeanPool.WhiteheadTheorem.Exponenti... |
19,706 | lean_file_chunk | b7dae0597031a1aa3ca4b4dfa874bbaec5e9c1c11ad87fe4c55eff22a8d5b667 | 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.Shapes.Jar
import LeanPool.WhiteheadTheorem.Shapes.Maps
import LeanPool.WhiteheadTheorem.CWComplex.Basic
import LeanPool.WhiteheadTheorem.... |
2,909 | lean_file_chunk | fc97963756a02dad4ba27a4cc14c41ee70052a66880f51af0afae17f5fcbe769 | 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.CWComplex.Basic
import LeanPool.WhiteheadTheorem.Shapes.DiskHomeoCube
import LeanPool.WhiteheadTheorem.HEP.Cofibration
/-!
In this file, ... |
19,155 | lean_file_chunk | efac5666e5e7cb2b39fdfb3c42a8f0e0c2280262f2065d05f55e1db2007730f7 | 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.HEP.Cofibration
import LeanPool.WhiteheadTheorem.HEP.Retract
import LeanPool.WhiteheadTheorem.Shapes.Cube
/-!
This file proves that the p... |
15,470 | lean_file_chunk | 522fb6bce486c6c351ee62164a0c3e68941c4925d2c387aa4c77d6afd4774045 | 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.HEP.Cube
import LeanPool.WhiteheadTheorem.Shapes.Cube
import LeanPool.WhiteheadTheorem.Shapes.UnitInterval
import Mathlib.Analysis.Convex.... |
23,994 | lean_file_chunk | db9e51846f22486976098deef8a44664e4d7762ca3fba509e24df15b4fe21ca3 | 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.RelHomotopyGroup.Defs
import LeanPool.WhiteheadTheorem.HEP.Cube
import LeanPool.WhiteheadTheorem.HEP... |
690 | lean_file_chunk | 3ba6715cc825ef9d62ce254b4d83852f35a9da35ad21e1dd875ca50f833dbc02 | lean_source_file | lean_pool_source_file_chunks | exact (Pointed.isIso_iff_bijective _).mpr ⟨inj_f, surj_f⟩
theorem isIso_inducedPointedHom'_of_isHomotopyEquiv
(n : ℕ) {X Y : TopCat.{u}} (x₀ : X) (f : X ⟶ Y)
(hf : IsHomotopyEquiv f.hom) : IsIso (inducedPointedHom' n x₀ f) := by
rw [inducedPointedHom'_eq_inducedPointedHom]
apply isIso_inducedPointedHom_of_... |
15,459 | lean_file_chunk | a3c38debb19ec7751c406c93019a56f24ba3fe6d056925c508497ef59d6609fd | 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.RelHomotopyGroup.Defs
import Mathlib.Algebra.Category.Grp.Basic
import Mathlib.CategoryTheory.Category.Pointed
import Mathlib.CategoryTheo... |
4,535 | lean_file_chunk | cd678becb087f7485867128e107978f7b6d00961c7def80ab53cf3ae48e80478 | 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.Logic.Function.Basic
import Mathlib.Data.Set.Basic
import Mathlib.Tactic.Common
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.NormNum
import Mathlib.... |
5,618 | lean_file_chunk | f73b46afd440083d834b30e361228f0081eb687d5b0f2991fdd5e40634e44bfb | 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.RelHomotopyGroup.Defs
import LeanPool.WhiteheadTheorem.HEP.Retract
/-!
# LeanPool.WhiteheadTheorem.RelHomotopyGroup.Compression
Imported... |
10,808 | lean_file_chunk | e2c87cfbf7201c151ab25664de6e41fc9872e5567c64325c817f3d44e1aa189a | 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.Shapes.Cube
import LeanPool.WhiteheadTheorem.RelHomotopyGroup.Algebra -- IsPointedMap
import Mathlib.Topology.Homotopy.HomotopyGroup
/-... |
21,890 | lean_file_chunk | 9ff6de9976af588cfac541abd9dcb473c0426d5643ebb3ca4e4785ac64c84db2 | 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.RelHomotopyGroup.Compression
/-!
# LeanPool.WhiteheadTheorem.RelHomotopyGroup.LongExactSeq
Imported Lean Pool material for `LeanPool.Whi... |
18,995 | lean_file_chunk | 3820eeb7ec42b3f88c358f9767def26469aed9eea43065f99190c64e67782d75 | 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.UnitInterval
import Mathlib.Topology.Homotopy.HomotopyGroup
/-!
# LeanPool.WhiteheadThe... |
7,045 | lean_file_chunk | bd583807498729f779b344c68d05987643d7f3339ed078bd6fc06105eeafa658 | 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.Shapes.Cube
import LeanPool.WhiteheadTheorem.Auxiliary
import LeanPool.WhiteheadTheorem.Shapes.UnitInterval
/-!
# LeanPool.WhiteheadTheor... |
1,794 | lean_file_chunk | 5bea0ebd071765266571014167fb75552ae58fb751ae263579a36bd52f403e63 | 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.Category.TopCat.Limits.Basic
import Mathlib.Analysis.InnerProductSpace.PiL2
/-!
# LeanPool.WhiteheadTheorem.Shapes.Disk
Imported Lean Pool materi... |
17,499 | lean_file_chunk | 00ec433e60d87787be7a4c2c7089947d0ec32ec70d94ed71eac54fa5e9b3b4a3 | 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.CWComplex
import LeanPool.WhiteheadTheorem.Auxiliary
import LeanPool.WhiteheadTheorem.Shapes.Disk
import LeanPool.WhiteheadTheorem.Shapes.Cube
i... |
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