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 |
|---|---|---|---|---|---|
6,295 | lean_file_chunk | 4813c37b139b3e33b7568bbb224888253191e7ffc0f34004b164a5014b1ee6de | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Scott Harper, Peiran Wu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Harper, Peiran Wu
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import LeanPool.OrderPQ.MonoidHom
import LeanPool.OrderPQ.TorsionBy
/-!
# LeanPool.OrderPQ.IsCycli... |
3,897 | lean_file_chunk | b6566144ded8a803424b440892fd2830c6561b18b26bb3cdaeca6e3514b6c203 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Scott Harper, Peiran Wu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Harper, Peiran Wu
-/
import LeanPool.OrderPQ.Basic
/-!
# LeanPool.OrderPQ.Main
-/
attribute [local implicit_reducible]
MulZMod instMulMulZMod instMulOneClassMulZMod... |
3,277 | lean_file_chunk | f234e576379e824be3739ecb9f2fba26855f65b6febb6c5a3fa72b31e7b4eb21 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Scott Harper, Peiran Wu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Harper, Peiran Wu
-/
import Mathlib.Algebra.Group.Hom.Defs
import Mathlib.Algebra.Group.Subgroup.Basic
import Mathlib.GroupTheory.OrderOfElement
import Mathlib.Data.ZMod... |
3,660 | lean_file_chunk | d334e266f1f4418d7dd0e074628f056e6e67cf7ae9e89c24729fda59762048fc | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Scott Harper, Peiran Wu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Harper, Peiran Wu
-/
import LeanPool.OrderPQ.PrimeOrder
import Mathlib.Data.ZMod.Aut
import Mathlib.RingTheory.ZMod.UnitsCyclic
/-!
# LeanPool.OrderPQ.MulZMod
-/
secti... |
2,587 | lean_file_chunk | e098bc9320034160b277a5c3b7cbde8bdfbbc329ec9cf1fc8cb5117bafea5fa3 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Scott Harper, Peiran Wu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Harper, Peiran Wu
-/
import LeanPool.OrderPQ.IsCyclic
/-!
# LeanPool.OrderPQ.PrimeOrder
-/
lemma ne_iff_eq_of_or_and_ne {α : Type*} {a b c : α} (h1 : a = b ∨ a = c) (h... |
5,139 | lean_file_chunk | dd36369545aca5303097f9f267e867cc96e8d20db354b1a076cff806a932a877 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Scott Harper, Peiran Wu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Harper, Peiran Wu
-/
import Mathlib.SetTheory.Cardinal.Finite
import Mathlib.GroupTheory.SemidirectProduct
import Mathlib.GroupTheory.GroupAction.ConjAct
import Mathlib.... |
1,228 | lean_file_chunk | fd33b70de2f86dac65197ab48c9056ceb4741d59e04f21567f7944c68f9c5273 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Scott Harper, Peiran Wu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Harper, Peiran Wu
-/
import Mathlib.Algebra.Group.Subgroup.Basic
import Mathlib.Tactic.Common
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.Ring
import Mathlib.Ta... |
1,044 | lean_file_chunk | 1dc6867f6ea287f6297b66f95591b5871837f1177cdbdaba04d775a73172eb5b | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Scott Harper, Peiran Wu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Harper, Peiran Wu
-/
import LeanPool.OrderPQ.Basic
import LeanPool.OrderPQ.IsCyclic
import LeanPool.OrderPQ.Main
import LeanPool.OrderPQ.MonoidHom
import LeanPool.Order... |
16,698 | lean_file_chunk | ca663a7a22fb19f898c641be1084b78278452cbbf7ad926497d7181004afda06 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 YnirPaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: YnirPaz
-/
import LeanPool.PCFTheory.Background.Cofinality
import LeanPool.PCFTheory.Background.Topology
/-!
# Club and stationary sets
This file sets up the basic theory of clubs (closed ... |
1,373 | lean_file_chunk | ae8577caaa910a3e13b3c23d2b1332df33e406e6e8e33f1742d553dcd1e82431 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 YnirPaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: YnirPaz
-/
import Mathlib.SetTheory.Cardinal.Cofinality.Ordinal
import LeanPool.PCFTheory.Background.Ordinal
/-!
# Cofinality results for indexed suprema
A more general universe version of... |
7,904 | lean_file_chunk | 8d596dac4599ded03a035f42f29d51861622f3a859bb602616b6e5e7d17946bc | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 YnirPaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: YnirPaz
-/
import Mathlib.SetTheory.Ordinal.Arithmetic
import Mathlib.SetTheory.Cardinal.Cofinality.Ordinal
import Mathlib.Order.SuccPred.Limit
/-!
# Background lemmas on ordinals
Auxiliar... |
6,884 | lean_file_chunk | d860933d23e4df5ab70b5c02ebfa83714bfd15b13d91b77b7314894f6cec76db | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 YnirPaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: YnirPaz
-/
import Mathlib.SetTheory.Ordinal.Topology
import Mathlib.Topology.DerivedSet
import LeanPool.PCFTheory.Background.Ordinal
/-!
# Topological results on ordinals
A handful of orde... |
418 | lean_file_chunk | 32917bbd6dfcada74d35b390a15a2bbaddf0f2efbfff94dc78002d7e62ac3b50 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 YnirPaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: YnirPaz
-/
import LeanPool.PCFTheory.Background.Club
import LeanPool.PCFTheory.Background.Cofinality
import LeanPool.PCFTheory.Background.Ordinal
import LeanPool.PCFTheory.Background.Topolog... |
8,310 | lean_file_chunk | 03ef7626ea9de458c612b8870b8a1b17f1e68498755ffa8aa1415757a8290f21 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 YnirPaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: YnirPaz
-/
import LeanPool.PCFTheory.Background.Club
/-!
# Club guessing
This file formalizes `theorem 2.17` in the chapter "Cardinal Arithmetic" in the "Handbook
of set theory."
For `δ` ... |
1,613 | lean_file_chunk | f76b6dd9b73b68db857f3dcbc53bea954113f17ec7bc5feed75b9b0adaaed2e2 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 YnirPaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: YnirPaz
-/
import LeanPool.PCFTheory.Background
import LeanPool.PCFTheory.ClubGuessing
/-!
# PCF Theory
Source: doi:10.1007/978-1-4020-5764-9_15
Authors: YnirPaz
Status: verified
Main decl... |
23,979 | lean_file_chunk | b208c047bf2c11d0f8e4afa93678122a6020d0b0e4a15c40af7aee8c9b14b460 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.MorseBott.TubularProjection
import LeanPool.PLAcceleratedNesterovLean.Core.NesterovSeqGen
impor... |
21,537 | lean_file_chunk | 6d4962dbc04eb5d996f56b6dce6ab16b2a427b2123762d414e9730a0228418bc | lean_source_file | lean_pool_source_file_chunks | set L₀ := lyapunovOfState P μ' π f η s₀ with hL₀_def
have hL₀_nonneg : 0 ≤ L₀ :=
lyapunovOfState_nonneg P μ' π f η s₀ hμ' hη_pos hμη_lt1 hbdd
-- √L₀ ≤ δ
have hsqrt_L₀_le_δ : Real.sqrt L₀ ≤ δ := by
calc Real.sqrt L₀ ≤ Real.sqrt (δ ^ 2) := Real.sqrt_le_sqrt hL₀_small
_ = δ := Real.sqrt_sq (le_of_lt hδ... |
3,173 | lean_file_chunk | f00dba50f53bd75320868adff7a2410b4b95553b7f72bddcecb5de51099f6997 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Core.NesterovScheme
/-!
# Bootstrap Step 1: Geometric Decay by Induction
If Lₙ₊₁ ≤ c · Lₙ whe... |
2,123 | lean_file_chunk | 98e7e6719f68d6b29e0aa7e92e1aac8854d6a4226b5d38d5c49e460fddacafaa | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Core.NesterovScheme
/-!
# Bootstrap Step 2: Choosing α and Closing the Induction
## Base case... |
461 | lean_file_chunk | 4b6338d19e66a50a504c0cfde02c5afd13862372160b038cccf9e16d11ba2a49 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Convergence.Bootstrap.Main
import LeanPool.PLAcceleratedNesterovLean.Convergence.Bootstrap.Step... |
5,440 | lean_file_chunk | 4e0a4c036b3f255a75715a1a751d21df1425edd80835b5dd49b8970b4c0f8608 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Convergence.Coercivity.Step2
/-!
# Coercivity Core Bound
Proves that `(1 - a)² * (V² + μ' * E... |
15,560 | lean_file_chunk | 28e8e37af5e0c93894526c478df3c56a5adc5e79781bb58db1ce302a86ce83ac | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Convergence.Coercivity.Step1
import LeanPool.PLAcceleratedNesterovLean.Convergence.Coercivity.S... |
3,525 | lean_file_chunk | a55a374eb00dd27a43114d18b3c196b249fe85688ad6024ba3ebb4a87accb001 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Core.NesterovScheme
import LeanPool.PLAcceleratedNesterovLean.Core.NesterovSeqGen
/-!
# Coerci... |
1,820 | lean_file_chunk | d6bbc0ab01093c549fc7910ec222003728a04d38a8b79e08630d97d716ea1e7b | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Core.NesterovScheme
/-!
# Coercivity Step 2: Resolve Coupled Bounds on A_n and B_n
Given:
A... |
504 | lean_file_chunk | c5600de70a6841ac3921355d33e007bceeae0cb78db99ab7fe531ccdb5e565a2 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Convergence.Coercivity.Core
import LeanPool.PLAcceleratedNesterovLean.Convergence.Coercivity.Ma... |
6,006 | lean_file_chunk | 3ff65b5d466b6344cf6c50511857e89f2730949bb297574a3bb5f0174e3d08de | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Convergence.GenLocalArgument
import LeanPool.PLAcceleratedNesterovLean.Convergence.PhaseSchedul... |
9,014 | lean_file_chunk | 7cb8f867dba453d59a908e3bc3d21cbe284aebd7aff0fbaeec35f1febe70b072 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Core.NesterovScheme
/-!
# Curvature Absorption Helper Lemmas
Helper lemmas for the curvature... |
23,992 | lean_file_chunk | 0a35996adff43026dadb447a0105c2bce5e761ccfa8cc34ffb3766dcedf768e1 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
/-
Copyright (c) 2025. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
-/
import LeanPool.PLAcce... |
23,656 | lean_file_chunk | d2c82a0d4b95aa1c136ba2e876e0fcef26584a08544a3e64987047b2c252f8ff | lean_source_file | lean_pool_source_file_chunks | (Real.sqrt μ') ^ 2 / 2 * ‖ξn‖ ^ 2
let a := Real.sqrt (μ' * η)
let Ln := lyapunovOfState P μ' π f η sn
let proj_err := a * abs (@inner ℝ _ _ gn (P en))
δ_curv + proj_err ≤ θ * a * Ln := by
-- Derived positivity
have hη_nn : (0 : ℝ) ≤ η := le_of_lt hη_pos
have hμ'_pos : (0 : ℝ) < μ' ... |
372 | lean_file_chunk | 49ab91e07d92d63c89740704f86ed04fc20efc1226dbd8f18247ab0d228bd8d9 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Convergence.CurvAbsorb.Algebraic
import LeanPool.PLAcceleratedNesterovLean.Convergence.CurvAbso... |
23,983 | lean_file_chunk | dd0debf399fada4476df11ea6fe8484da2cec035c2cfc5ee42a4040941e04c98 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Core.EmbeddedManifold
import LeanPool.PLAcceleratedNesterovLean.Convergence.LocalGeometry.Main
... |
5,509 | lean_file_chunk | 4f5a100d4be93cce966e88d4ef7d7cfb3a66eca36da2452514545d0109286ddf | lean_source_file | lean_pool_source_file_chunks | = Real.sqrt η * ‖s'.v‖ := by
rw [norm_smul, Real.norm_eq_abs, abs_of_nonneg hsqrt_η_nn]
_ ≤ Real.sqrt η * (Cv' * Real.sqrt Ln) := by
exact mul_le_mul_of_nonneg_left hv'_bound hsqrt_η_nn
_ = (Real.sqrt η * Cv') * Real.sqrt Ln := by ring
_ ≤ Cmov * Real.sqrt Ln :=... |
23,949 | lean_file_chunk | 7e3ed2767b65afda7e4da153e945a5fb776d8c1533a2990448210fedfae8085c | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Core.EmbeddedManifold
import LeanPool.PLAcceleratedNesterovLean.Convergence.LocalGeometry.Main
... |
23,512 | lean_file_chunk | 52c74b36ec2fac323d6ee47b02953b564858a179f5f1ac572ddadd18bde98ce8 | lean_source_file | lean_pool_source_file_chunks | (le_of_lt (mul_pos (by linarith : (0:ℝ) < μ_minus) hη_pos))
hμη_lt1
have hlam : 0 ≤ (1 + Real.sqrt (μ_minus * η)) ^ 2 /
(2 * (1 - Real.sqrt (μ_minus * η))) :=
le_of_lt (div_pos (by positivity) (by linarith))
have h_Pv_sq := sq_nonneg ‖P (nesterovSeq f η ρ x₁ n_val).v‖
... |
10,904 | lean_file_chunk | 3754841799119f55063e15fa2d82759658b368bb7207527509c03bb1e6940eef | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Convergence.LocalGeometry.Step1
import LeanPool.PLAcceleratedNesterovLean.MorseBott.HessianPL
... |
23,968 | lean_file_chunk | 4c24ef38ac485ebdd2c6776265b080dea6c8c1e42cdd8aab08d1bade536c50ff | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Convergence.LocalGeometry.Step1
import LeanPool.PLAcceleratedNesterovLean.Convergence.LocalGeom... |
23,978 | lean_file_chunk | 2b4c9d6237636d2176abe8b9118ac61215847611cd5635611cc0c43385216265 | lean_source_file | lean_pool_source_file_chunks | rw [Metric.mem_sphere, dist_zero_right]; exact hξ₀_norm
-- fderiv ℝ π (π x) ξ₀ = 0 (linearity)
have hξ₀_normal : fderiv ℝ π (π x) ξ₀ = 0 := by
rw [hξ₀_def, map_smul, hξ_normal, smul_zero]
-- π(x) ∈ S
have hπ_in_S : π x ∈ S := (hπ_proj x hxU).1
-- Derive: dist(x, m_star)... |
3,622 | lean_file_chunk | 6573908f61051e6d60b7056084fda8f13d9ac5ee9b1afe9a329a2b93da157254 | lean_source_file | lean_pool_source_file_chunks | -- e = x − π(x), so the inner products match; convert (c/2) form
have : μ' * ‖e‖ ^ 2 / 2 = μ' / 2 * ‖e‖ ^ 2 := by ring
linarith
-- ----------------------------------------------------------------
-- (d) Hessian lower bound D²f(x) ≽ −ε₀·I: inherited from V₂
-- ----------------------------------------------... |
8,090 | lean_file_chunk | 8d4af32bbdef70dc602eb7bf4fe90f63627604bdc74d29dc94c5aa49ae10ba77 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Convergence.LocalGeometry.Step2
import Mathlib.Analysis.InnerProductSpace.Calculus
import Mathl... |
10,566 | lean_file_chunk | bed2c3f9e7d9ef4668cff769d98e889a4fc730f0c9845a2a35b994eea99de563 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Core.NesterovScheme
import Mathlib.Analysis.Calculus.Deriv.MeanValue
/-!
# Local Geometry Step... |
9,037 | lean_file_chunk | 5cf945bb6458cd0fba2cd0d8ab38cb96f8d61a44c1c480bc8725598119a0563b | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Core.NesterovScheme
import Mathlib.Analysis.Calculus.Deriv.Comp
import Mathlib.Analysis.Calculu... |
603 | lean_file_chunk | bb872d92fea856d1853f1fb5dbaf4e04256d872b6b56a5708666202c65fb9ae4 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Convergence.LocalGeometry.HessianBound
import LeanPool.PLAcceleratedNesterovLean.Convergence.Lo... |
8,380 | lean_file_chunk | df11c88ccc0e265589e499f0e59abe0393f9c260cec06accc06c7fd86ceb40fe | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Convergence.LyapunovContraction.Step1
/-!
# Auxiliary Variable Recursion for Lyapunov Contract... |
5,125 | lean_file_chunk | 0d761514af65df8408677da2a4eb286ae5bdf6f663c5034df8f4ca2bd5f114c1 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import Mathlib.Data.Real.Basic
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.FieldSimp
/-!
# Flat-Case Lyapunov Contraction: Arit... |
4,188 | lean_file_chunk | a86b48569853f108ce5ec2c8d22968dc56e785b2e699d9ab2c4e077818a92242 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Core.NesterovScheme
/-!
# Algebraic helper lemmas for the flat-case Lyapunov bound
Provides n... |
23,993 | lean_file_chunk | 2644b58bfbbb00f4330492b55dcbd935ac44eab2bfb115114bfedd15bde3a58d | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Convergence.LyapunovContraction.Step1
import LeanPool.PLAcceleratedNesterovLean.Convergence.Lya... |
15,909 | lean_file_chunk | adf223ee2455910b66b1abd3ef3e165e54f39ad52820d1873ed9f0681f32ef6c | lean_source_file | lean_pool_source_file_chunks | intro t ht0 ht1
exact hΩp_sub_Up (hΩ_sub_Ωp
((convex_ball m_star (min (r₀ / 9) R_abs)) hx_in hx'_in
(by linarith : (0 : ℝ) ≤ 1 - t) ht0 (by linarith : (1 : ℝ) - t + t = 1)))
have h_seg_raw := hSegment x'n sn.x hx'n_Up hxn_Up h_path
have h_diff_eq : x'n - sn.x = Real.sqrt η • sn... |
23,979 | lean_file_chunk | f560e9cdd6825512b62032e816a3f6fa9b6278581e378c064997f024e3084ae3 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Convergence.LyapunovContraction.Step1
import LeanPool.PLAcceleratedNesterovLean.Convergence.Lya... |
15,857 | lean_file_chunk | 11afdaaa747c842fafe036db3fbe630c63c6ef8f23265a5b885434bef4559280 | lean_source_file | lean_pool_source_file_chunks | (1 - t) • sn.x + t • x'n ∈ U_plus := by
intro t ht0 ht1
exact hΩp_sub_Up (hΩ_sub_Ωp
((convex_ball m_star (min (r₀ / 9) R_abs)) hx_in hx'_in
(by linarith : (0 : ℝ) ≤ 1 - t) ht0 (by linarith : (1 : ℝ) - t + t = 1)))
have h_seg_raw := hSegment x'n sn.x hx'n_Up hxn_Up h_path
... |
9,261 | lean_file_chunk | 5dc6529179bdf7167cc642fb6c1d2d558c068feafd97f1653039ef7157a9ed9b | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Core.NesterovScheme
import Mathlib.Analysis.Calculus.Deriv.Comp
import Mathlib.Analysis.Calculu... |
1,985 | lean_file_chunk | c52bcd39a13b76456966bfd8f680b846fa79fee2f5e441ad5527d2b91ba63bec | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Core.NesterovScheme
/-!
# Lyapunov Contraction Step 2: Normal Terms and Perturbation Absorptio... |
18,203 | lean_file_chunk | c79672b4dc32945b671a055ade0e6f4dc092742af6cae904052d9f0b204b095f | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Convergence.LyapunovContraction.Step1
import LeanPool.PLAcceleratedNesterovLean.Convergence.Lya... |
887 | lean_file_chunk | 8b3bb7edeb075174d6ce9e1bf8385060af26d3570bb40a464fc792b4e83a9bcf | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Convergence.LyapunovContraction.AuxVar
import LeanPool.PLAcceleratedNesterovLean.Convergence.Ly... |
23,991 | lean_file_chunk | e67e9cf65c26fd34c32de0a36d9b5edfbc5f0f7a63f9d540e0652aaf4f15a834 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Convergence.NesterovConvergence
import LeanPool.PLAcceleratedNesterovLean.Core.EmbeddedManifold... |
5,579 | lean_file_chunk | 675799250428de01bef31eb549d59ed8d3bdc8e0b891b41be878d79777b783d8 | lean_source_file | lean_pool_source_file_chunks | ∀ (f : E d → ℝ),
∀ (n : ℕ),
∀ (M : Type*) [TopologicalSpace M] [ChartedSpace (ManifoldModel n) M]
[IsManifold (modelI n) 2 M] [Nonempty M]
(ι : M → E d),
IsSmoothEmbedding (modelI n) (modelWithCornersSelf ℝ (E d)) 2 ι →
Set.range ι = argminSet f →
∀ (U : Set (E d)),
IsOpen U →
... |
2,006 | lean_file_chunk | e433a3499c1bfe265e0c3ab2b64736233fac4101e3bd967faa7989706bd86460 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Core.NesterovScheme
/-!
# Motion Error Step 1: Gradient Bound from L-Smoothness
Since π(x'_n)... |
286 | lean_file_chunk | df4b3e74f481297b573a075be380e2d0c599735cdedb0da1311359333259ec8e | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Convergence.MotionError.Main
/-!
# Motion error estimates
-/ |
16,751 | lean_file_chunk | 1077c8e167eb7c202c5ec666c60903e1720a8bff47540b73b6249eb4643e32a8 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Convergence.GenLocalArgument
import LeanPool.PLAcceleratedNesterovLean.Convergence.RateArithmet... |
6,035 | lean_file_chunk | c3476d4903acbda285b8d689a8f1699f1996869894d5a537133c3c2034435548 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import Mathlib.Analysis.SpecialFunctions.Pow.Real
import Mathlib.Analysis.SpecialFunctions.Log.Basic
import Mathlib.Topology.Algebra.Infi... |
4,498 | lean_file_chunk | 2dffc1b87d34dfe862cfee9f35043a75574287c6801c7fb76ae6cac9ff3536eb | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Convergence.PhaseSchedule
import LeanPool.PLAcceleratedNesterovLean.Core.Defs
import Mathlib.An... |
6,575 | lean_file_chunk | 83838757a7e39fce28031421bd5ee71e90d9558442d6f0baca3b11c0547201b7 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Core.NesterovSeqGen
import LeanPool.PLAcceleratedNesterovLean.Convergence.LyapunovContraction.S... |
307 | lean_file_chunk | 3917f1206c84f03efd75322788e157300659c8ae7eeb29c61b7580c25684fa0f | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Convergence.StateContraction.AuxVarRecursion
/-!
# State contraction estimates
-/ |
1,220 | lean_file_chunk | 9525959e2409371d3c033e482f251b9466ad05940051934a7daa886c518f4522 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Convergence.Bootstrap
import LeanPool.PLAcceleratedNesterovLean.Convergence.Coercivity
import L... |
5,144 | lean_file_chunk | 54deba3e931770e6d86e4a81887629335deaa89f0902bed99ff5cbb25100f4b5 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import Mathlib.Analysis.Calculus.Gradient.Basic
import Mathlib.Analysis.InnerProductSpace.PiL2
import Mathlib.Topology.EMetricSpace.Lipsc... |
23,986 | lean_file_chunk | 41be7c3270264c283412d56c6529160481d58fb03b31b58d844baa8a1f645656 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Core.Defs
import LeanPool.PLAcceleratedNesterovLean.MorseBott.NormalHessianBound
import LeanPoo... |
23,989 | lean_file_chunk | ce0e405cd46525c49284e4ccb975dc08b3047d6d5d435bb4091bc2c2dbfad3e6 | lean_source_file | lean_pool_source_file_chunks | y ∈ S ↔ ∃ v : V, y = m + (v : E d) + (φ v : E d))
{x p : E d}
(hp_dist : dist x p = Metric.infDist x S)
(hp_graph : p = m + (u_p : E d) + (φ u_p : E d))
(hp_ball : p ∈ Metric.ball m δ) :
IsLocalMin (fun v : V => ‖(x - m) - (v : E d) - (φ v : E d)‖ ^ 2) u_p := by
have hcont : ContinuousAt (fun v : ... |
8,253 | lean_file_chunk | 1f4f209d298e860130add523ca4e1d49f54b308c3e8a246031e2efeb75ad14a0 | lean_source_file | lean_pool_source_file_chunks | ExternalThm3.pl_to_muPL f μ U m hm (hU_open.mem_nhds hm_U) hPL_ext
obtain ⟨_, Uloc, hUloc, φ_raw, hφ_raw_C2, hφ_raw0, hDφ_raw0, hGraph⟩ :=
MuPL.implies_submanifold_C2_chart f μ m hPL.1 hf3_at hmin hmuPL
have hφ_raw_ev : ∀ᶠ v in 𝓝 (0 : V), ContDiffAt ℝ 2 φ_raw v :=
hφ_raw_C2.eventually (by norm_num)
obtai... |
4,852 | lean_file_chunk | 07e96889687ed354102e0e701b79cf7b87f3b56a1519b895fe91fb5de677c99a | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Core.Defs
import Mathlib.Geometry.Manifold.MFDeriv.Basic
/-!
# Modified Nesterov Scheme and Su... |
5,487 | lean_file_chunk | 744794c66d7f3332cede1b9e9b2febbfe306c6590424ae25ab128f7c3d180a87 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Core.NesterovScheme
/-!
# Generalized Nesterov Sequence and State-Based Definitions
Extends t... |
489 | lean_file_chunk | 5aa54f9122e4c34dc64d7ff2de8a4af60dba98d7c0b1e12b852d26322a590da9 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Core.Defs
import LeanPool.PLAcceleratedNesterovLean.Core.EmbeddedManifold
import LeanPool.PLAcc... |
3,749 | lean_file_chunk | db4e13327131ca65a42122fe2e0c9ff9bc70d213d65cd175efe872e81d08906b | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Convergence.MainTheoremInternal
/-!
# Public main theorem wrappers
-/
noncomputable section
... |
14,095 | lean_file_chunk | f66b622093344740a3f7d2ee5ca8f18ec7e4db6d82feb963fa9de2c74f7b9ef6 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.MorseBott.TubularProjection
import LeanPool.PLAcceleratedNesterovLean.MorseBott.NormalHessianBo... |
1,997 | lean_file_chunk | 823cacefc661d6e74da56b2bd03a47cf65dbdd3d347bf9c6f30834ded6479203 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.MorseBott.Defs
import Mathlib.Analysis.InnerProductSpace.PiL2
import Mathlib.Analysis.InnerProd... |
6,234 | lean_file_chunk | 2492f3af07e520994dd75ce8a6eac42e6d187d6bbab1b9a6b5383adfb08daef1 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import Mathlib.Analysis.Calculus.FDeriv.Basic
import Mathlib.Analysis.Calculus.ContDiff.Defs
import Mathlib.Analysis.InnerProductSpace.Pr... |
12,880 | lean_file_chunk | 5c0746eb32baa2e328dcfcbb022ced894c22d36736d2c26ea3728284e4d02de2 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.MorseBott.Defs
import Mathlib.Analysis.Calculus.MeanValue
import Mathlib.Analysis.InnerProductS... |
9,710 | lean_file_chunk | 83797ec34349ecb08e85e16a93fdaa9712c48c71fa297641e8172b493e79c689 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.MorseBott.Defs
import Mathlib.Analysis.Calculus.FDeriv.Symmetric
import Mathlib.Analysis.Calcul... |
19,986 | lean_file_chunk | 257a9d5e6b726fe79dd9917b4cfaf480da7b231d43fd8e75724b6f73ab28f062 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.MorseBott.HessianPL.Basics
import Mathlib.Topology.Order.Compact
/-!
# Hessian coercivity from... |
318 | lean_file_chunk | a73f2bbaa168c2b655c389e169a88826b3c9c72aeec6807f7552190299dc6a68 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.MorseBott.HessianPL.Basics
import LeanPool.PLAcceleratedNesterovLean.MorseBott.HessianPL.Main |
23,946 | lean_file_chunk | 5811818ef858a27af7dd5a488024a565b26225f68ae6798fea02f7d10e2d9619 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.MorseBott.Defs
import Mathlib.Analysis.Calculus.LocalExtr.Basic
import Mathlib.Analysis.Calculu... |
378 | lean_file_chunk | 17fa48b278d5c8a757a25ad329cd239e0d4c26e330544dcd10ebf1218aff73a3 | lean_source_file | lean_pool_source_file_chunks | have hFx' : compR (fderiv ℝ f (x₀ + ι (orthogonalProjectionOnto T (x - x₀),
orthogonalProjectionOnto N (x - x₀)))) = 0 := hFx
rw [h_decomp] at hFx'
exact (restrictToN_eq_zero_iff N (fderiv ℝ f x)).mp hFx' w
obtain ⟨U, hU, hUprop⟩ := h_iff.exists_mem
exact ⟨U, hU, φ, hφ_smooth, hφ_zero, hφ_deri... |
12,156 | lean_file_chunk | 0b12969cc27ba587082dd48b8007b47b825080695b30f82ef55c6315cb3f7f84 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.MorseBott.HessianPL
import Mathlib.Analysis.InnerProductSpace.Dual
/-!
Copyright (c) 2025. All... |
2,893 | lean_file_chunk | 3428f9514a5a19840877e5aec5a237c3d52886b8d7279c342e862c0825001d3f | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.MorseBott.HessianPL
import LeanPool.PLAcceleratedNesterovLean.MorseBott.Submanifold
/-!
Copyri... |
15,385 | lean_file_chunk | 037d478b3ac57c9aafe2264c31a0e41280f3be327bd77dbf89d5674625f5fa08 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.MorseBott.IFTProof
import LeanPool.PLAcceleratedNesterovLean.MorseBott.GradAlign
import LeanPoo... |
14,595 | lean_file_chunk | 8eb70e606fa264361b4aed0e26cddd5d4398a239cbc46b42bba7bf8b1d5b150c | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.MorseBott.Defs
import Mathlib.Analysis.Calculus.FDeriv.Congr
import Mathlib.Analysis.Calculus.C... |
23,974 | lean_file_chunk | 4adb6ae31eb304d0ec83dac8c9239d7089013575b628b42d3e5907b0a4591428 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.MorseBott.TubularProjection.Defs
import LeanPool.PLAcceleratedNesterovLean.MorseBott.TubularPro... |
6,804 | lean_file_chunk | 2f411b9bc43d528dad84729844721aec23b0c558835bc722ec44e3120eaaa882 | lean_source_file | lean_pool_source_file_chunks | obtain ⟨ε, hε_pos, hε_sub⟩ := Metric.isOpen_iff.mp hTN.isOpen m (hTN.subset hm_S)
refine ⟨ε / 3, by linarith, fun x hx hx_ball t ht => ?_⟩
obtain ⟨h0, h1⟩ := ht
have hπS := (tubularProj_mem hTN hne x hx).1
have hπdist := (tubularProj_mem hTN hne x hx).2
-- dist(x, m) < ε/3 by hx_ball
have hxm : ... |
23,976 | lean_file_chunk | cf431cf7ac9818a69b78ffeca3149611b4097961262d2218c9e48877ba6d3252 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.MorseBott.TubularProjection.Defs
import Mathlib.Analysis.Calculus.ImplicitContDiff
import Mathl... |
316 | lean_file_chunk | 92e7c6ffcededa35458fd26d18055c57a7676f06d1c86bb455b4dca0b4ba2e20 | lean_source_file | lean_pool_source_file_chunks | have hπ_chart := h_repr hy_U hπ_ball
change π y = m + (v_star y : E) + (φ (v_star y) : E)
change π y = m + (v_impl (y - m) : E) + (φ (v_impl (y - m)) : E)
rw [h_impl_eq]; exact hπ_chart
-- ── Step 7: Transfer C¹ from χ to π ──
exact hχ_cd.congr_of_eventuallyEq hπ_eq_χ
end PLAcceleratedNesterovLean |
412 | lean_file_chunk | ee58fd045cd2b5ad87159f8a79cfaa78fc46bb96d4cea5d9c3d5d4868d8660a5 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.MorseBott.TubularProjection.Defs
import LeanPool.PLAcceleratedNesterovLean.MorseBott.TubularPro... |
891 | lean_file_chunk | c055fb2c402dc6d488b5b50361932bdbff3ae97bf052de1ab337b92c4027527c | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.MorseBott.Bridge
import LeanPool.PLAcceleratedNesterovLean.MorseBott.BridgeDefs
import LeanPool... |
1,016 | lean_file_chunk | e5f7c38b76beafc1ba962e8cfb112937b53bdd3b3a5c305e5cfd94fd108358bd | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 M1ngXU. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Max Obreiter, Tobias Steinbrecher, Robert Foerster
-/
import LeanPool.PLAcceleratedNesterovLean.Core
import LeanPool.PLAcceleratedNesterovLean.MorseBott
import LeanPool.PLAcceleratedNesterovL... |
1,134 | lean_file_chunk | 63ff852f676222e846dd3de677871dca041503abce5799b4bcc926f7d99f2871 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Andrej Bauer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrej Bauer
-/
import Mathlib.Data.Part
/-!
# Notation and core classes for partial combinatory algebras
A notation for totality of a partial element, a generic class for a
left-assoc... |
3,088 | lean_file_chunk | bc82b655f8d1132bb3df5f3b8a665d746bbd8d22b3b6ca5525adfc24cfe29fde | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Andrej Bauer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrej Bauer
-/
import Mathlib.Tactic.NthRewrite
import Mathlib.Data.Part
import LeanPool.PartialCombinatoryAlgebras.Basic
import LeanPool.PartialCombinatoryAlgebras.PartialCombinatoryAl... |
1,999 | lean_file_chunk | d4ae39caa998b5a6d13703f6392b01b71946d67fa6c4a16aeef832faed704dc1 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Andrej Bauer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrej Bauer
-/
import LeanPool.PartialCombinatoryAlgebras.Basic
import LeanPool.PartialCombinatoryAlgebras.CombinatoryAlgebra
/-! # Free (total) combinatory algebra -/
namespace LeanP... |
13,751 | lean_file_chunk | f4238da2cfe6954f431e43a0dab865538dbcaadbbf1a40e47d161c09643152f4 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Andrej Bauer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrej Bauer
-/
import Mathlib.Data.SetLike.Basic
import LeanPool.PartialCombinatoryAlgebras.Basic
import LeanPool.PartialCombinatoryAlgebras.CombinatoryAlgebra
/-! We derive from a giv... |
9,790 | lean_file_chunk | 0a26f7eca8664379c1f36fcc34eea5a55e1cca72412d3dea06eb454e67808b66 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Andrej Bauer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrej Bauer
-/
import Mathlib.Data.Finset.Basic
import LeanPool.PartialCombinatoryAlgebras.Basic
/-!
# Partial combinatory algebras
A partial combinatory algebra is a set equipped wit... |
9,525 | lean_file_chunk | 80a5c2a53c9702d7a7d53ff1c02a249b7d601c72cdc1f8391bd62e0486b67c1d | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Andrej Bauer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrej Bauer
-/
import LeanPool.PartialCombinatoryAlgebras.Basic
import LeanPool.PartialCombinatoryAlgebras.PartialCombinatoryAlgebra
/-! ## Programming with PCAs
A (non-trivial) PCA... |
3,022 | lean_file_chunk | 77994277b5fcfa012923e3c5b1a96aebe6dbcf37c8a1e722d10771a2f1d65a12 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Andrej Bauer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrej Bauer
-/
import LeanPool.PartialCombinatoryAlgebras.Basic
import LeanPool.PartialCombinatoryAlgebras.PartialCombinatoryAlgebra
import LeanPool.PartialCombinatoryAlgebras.Combinat... |
23,967 | lean_file_chunk | c68101e7f216a34b5899140cf538c87e0ab7457154bd8a5b18eac10d8b4dfcae | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Evan Chen, Kenny Lau, Seewoo Lee, Ken Ono, Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Evan Chen, Kenny Lau, Seewoo Lee, Ken Ono, Jujian Zhang
-/
import Mathlib.Algebra.Ring.GeomSum
import Mathlib.Analysis.Asymptotics.SpecificAsym... |
7,966 | lean_file_chunk | 37107dbe24978e051afc2f18b16ec4045b6032989c13a96a35fc37fa8dac44ce | lean_source_file | lean_pool_source_file_chunks | have hy_pos : 0 < y := lt_of_lt_of_le hexp_pos hy
have hy_gt_one : 1 < y := Real.one_lt_exp_iff.mpr h2α_pos |>.trans_le hy
have hlogy_pos : 0 < Real.log y := Real.log_pos hy_gt_one
have hgy_pos : 0 < Real.log y / y ^ (1 / (2 * α)) :=
div_pos hlogy_pos (Real.rpow_pos_of_pos hy_pos _)
have hanti_xy :
Re... |
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