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 |
|---|---|---|---|---|---|
17,775 | lean_file_chunk | 42212f5656db52be3a5afa7bacb1b6b3782267ccfb6d8f1e005306bcdc5c38c9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
module
public import Mathlib.LinearAlgebra.Dimension.DivisionRing
public import Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition
public import Mathlib.LinearAl... |
23,936 | lean_file_chunk | 9debdddb949c6ec357b3ff33c03956bfb2514eb6c181d7bc7b494eeb1f6df142 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
module
public import Mathlib.Algebra.Module.Projective
public import Mathlib.LinearAlgebra.Dimension.Finite
public import Mathlib.LinearAlgebra.FiniteDimensional.Defs
pu... |
2,694 | lean_file_chunk | 0fddb187fbe374b06f4ba7b56a842fa78e2cab77c8053a4fbf040e96880e7088 | lean_source_file | pkg_mathlib_source_file_chunks | We now give characterisations of `finrank K V = 1` and `finrank K V ≤ 1`.
-/
section finrank_eq_one
/-- A vector space with a nonzero vector `v` has dimension 1 iff `v` spans.
-/
theorem finrank_eq_one_iff_of_nonzero (v : V) (nz : v ≠ 0) :
finrank K V = 1 ↔ span K ({v} : Set V) = ⊤ where
mp h := by simpa using... |
9,686 | lean_file_chunk | 9c6a93f0a8fc02f54bf39de6a96e1b56ef607d6311fc94643177822ce91a55df | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
module
public import Mathlib.LinearAlgebra.Basis.VectorSpace
public import Mathlib.LinearAlgebra.Dimension.Free
public import Mathlib.RingTheory.SimpleRing.Basic
/-!
# ... |
11,651 | lean_file_chunk | ba7d3da9e33f6b77c22f72536d5555642a079d5fe2b1f5b589c74d3533b1088b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.Data.Int.Order.Units
public import Mathlib.Data.ZMod.IntUnitsPower
public import Mathlib.RingTheory.TensorProduct.Basic
public import Mathlib.... |
15,426 | lean_file_chunk | 1439cdd213aa475d4deb3499c7ddd068d46442a508598b92fca2c693b39331f9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.LinearAlgebra.TensorProduct.Graded.External
public import Mathlib.RingTheory.GradedAlgebra.Basic
public import Mathlib.Tactic.SuppressCompilat... |
23,989 | lean_file_chunk | fe34b86e7e19d2134dd4e8c7e2cbd8dd01e14b112a3a90e452aa8bc5e8fa7d41 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
module
public import Mathlib.LinearAlgebra.AffineSpace.AffineEquiv
public import Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs
public import Mathlib.Algebra.NoZ... |
16,490 | lean_file_chunk | d96b5d15ca0c482b5f6e2316b954750a31310213264ac48beef779a9885ce601 | lean_source_file | pkg_mathlib_source_file_chunks | coe_injective <| image_image _ _ _
@[simp]
theorem map_direction (s : AffineSubspace k P₁) :
(s.map f).direction = s.direction.map f.linear := by
simp [direction_eq_vectorSpan, AffineMap.map_vectorSpan]
theorem map_span (s : Set P₁) : (affineSpan k s).map f = affineSpan k (f '' s) := by
rcases s.eq_empty_or_n... |
23,983 | lean_file_chunk | 3759406703ba1b2b2e06bd8ba8cdd0877892e2d0ea459ca0681b9cd98f928349 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
module
public import Mathlib.Order.Atoms
public import Mathlib.LinearAlgebra.Span.Defs
public import Mathlib.LinearAlgebra.AffineSpace.Defs
/-!
# Affine spaces
This fi... |
21,440 | lean_file_chunk | 0b3761eaca5e0f75891c6b3ad0b1c4e6a957ab47ef70c2a031a85f18d532ba68 | lean_source_file | pkg_mathlib_source_file_chunks | Nonempty (s₁ ⊔ s₂ : AffineSubspace k P) :=
.map (Set.inclusion <| SetLike.le_def.1 le_sup_left) ‹_›
instance nonempty_sup_right (s₁ s₂ : AffineSubspace k P) [Nonempty s₂] :
Nonempty (s₁ ⊔ s₂ : AffineSubspace k P) :=
.map (Set.inclusion <| SetLike.le_def.1 le_sup_right) ‹_›
variable (k V)
/-- The affine span ... |
23,960 | lean_file_chunk | da02b1221eb3072d62ff3a5cb62ff9eeb8eb442e540b8866e39ed4c23e72b14d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Chu Zheng
-/
module
public import Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic
public import Mathlib.LinearAlgebra.AffineSpace.Centroid
/-!
# Centroid of a simplex in ... |
4,422 | lean_file_chunk | 50fc40ea7f8e795e2baa425b8fe4b68d319d0e12352266d3b26a823097e36179 | lean_source_file | pkg_mathlib_source_file_chunks | have hp : p = (p -ᵥ s.centroid) +ᵥ s.centroid := by rw [vsub_vadd]
let s' : Finset (Fin (n + 1)) := {i₀}ᶜ
let u : s' → V := fun i => s.points i -ᵥ s.centroid
have h_span : ∀ i : s', p -ᵥ s.centroid ∈ (Submodule.span k ({u i} : Set V)) := by
intro i
have hi := h i
grind only [median_eq_line_point_centr... |
23,996 | lean_file_chunk | 7d18dd92d2dbc3632437e1e7d4e7f6d079c3d094e69a6970653901c40b32e7aa | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
module
public import Mathlib.Data.Finset.Sort
public import Mathlib.LinearAlgebra.AffineSpace.Independent
public import Mathlib.LinearAlgebra.AffineSpace.Restrict
/-!
#... |
3,986 | lean_file_chunk | 630f3dd2a4b8c25ca8cd93b53d9650ae94d5af0e7e638e5e060c407c0508b408 | lean_source_file | pkg_mathlib_source_file_chunks | refine ⟨fun i hi ↦ ?_, fun i hi ↦ by simp [hi]⟩
simp only [RelEmbedding.coe_toEmbedding, range_orderEmbOfFin, mem_coe, hi, Set.indicator_of_mem]
rw [← mem_coe, ← fs.range_orderEmbOfFin h] at hi
obtain ⟨j, rfl⟩ := hi
simp [(fs.orderEmbOfFin h).injective.extend_apply, hi]
· let w' : Fin (m + 1) → k := w... |
18,154 | lean_file_chunk | b7aac371e8a175bc21fe448a53a081077e87b595d997ee9c49f0fc2148d925e0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
module
public import Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear
public import Mathlib.LinearAlgebra.RootSystem.Reduced
public import Mathlib.LinearAlgebra.R... |
20,038 | lean_file_chunk | d828cf8137c4d0fa33871075254441176bd6295f9b76780f219b78689687334e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Scott Carnahan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Carnahan
-/
module
public import Mathlib.LinearAlgebra.BilinearForm.Basic
public import Mathlib.LinearAlgebra.BilinearForm.Orthogonal
public import Mathlib.LinearAlgebra.Dimensi... |
23,992 | lean_file_chunk | 406a2e0469f1fa5037067ea59593fd985c270f5412c767c64d19cbb9ee1e4061 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
module
public import Mathlib.LinearAlgebra.RootSystem.Base
public import Mathlib.LinearAlgebra.RootSystem.Chain
public import Mathlib.LinearAlgebra.RootSystem.Finite.Lemma... |
3,450 | lean_file_chunk | 269b5f983749b6423a7bab9c02d89056370599c7499056d1201f414b574792d6 | lean_source_file | pkg_mathlib_source_file_chunks | rw [show P.root '' {long P, short P} = {longRoot P, shortRoot P} by aesop] at this
refine this fun k hk ij hij ↦ ?_
replace hk : P.root k ∉ allRoots P :=
fun contra ↦ hk <| span_subset_span ℤ _ _ <| mem_span_of_mem_allRoots P contra
have aux := isOrthogonal_short_and_long P hk
rcases hij with rfl | rfl <;> ... |
16,686 | lean_file_chunk | bf653e6b4029183c29763a8fc106ae69a939080ad674e2a759ebadfc2ddd8055 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Scott Carnahan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Carnahan
-/
module
public import Mathlib.Algebra.Ring.SumsOfSquares
public import Mathlib.LinearAlgebra.RootSystem.RootPositive
/-!
# The canonical bilinear form on a finite ro... |
19,226 | lean_file_chunk | 4b94afb49013e58c378ebf569f00904d06847d2b4a75069737502da03fe706ea | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
module
public import Mathlib.LinearAlgebra.RootSystem.Base
public import Mathlib.LinearAlgebra.RootSystem.Chain
public import Mathlib.LinearAlgebra.RootSystem.Finite.G2
/... |
18,275 | lean_file_chunk | 564ae5b4283fb2c9b0e25ffd1e9fcf7f37440b3c6b1687a57f53431ddac0a5e1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
module
public import Mathlib.Algebra.Lie.Matrix
public import Mathlib.Algebra.Lie.OfAssociative
public import Mathlib.Algebra.Lie.Weights.Basic
public import Mathlib.Linea... |
16,751 | lean_file_chunk | ef1b46f9ee3fa71f56da7e3eb547a3280cefd23eb1a89519eb047824a08e0cb6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
module
public import Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic
public import Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Lemmas
public import Mathlib.A... |
4,209 | lean_file_chunk | d35f6427e6f6cc3d671242adad121d73fd64260719ca64833fee0d3b061a78c5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
module
public import Mathlib.Algebra.Lie.Basis
public import Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple
public import Mathlib.LinearAlgebra.RootSystem.Ge... |
17,837 | lean_file_chunk | 5fd78d4b1396e48049a48b076cf45a6d5aacb61283179bddca960e4276a68a36 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
module
public import Mathlib.Algebra.Lie.Matrix
public import Mathlib.Algebra.Lie.Semisimple.Lemmas
public import Mathlib.Algebra.Lie.Weights.Linear
public import Mathlib.... |
7,806 | lean_file_chunk | e22f3e6b5242907cbe9b3432a45b13906ae7fb1ed9aafb7c366c7ec19f76f4f4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.LinearAlgebra.QuadraticForm.TensorProduct
public import Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv
/-!
# Linear equivalences of tensor... |
5,644 | lean_file_chunk | 37ef723a140fc11fa700ae88321b3b11fdf5fd2cb7874f90fa308b9ef75497fc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.CategoryTheory.Monoidal.Transport
public import Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic
public import Mathlib.LinearAlgebra.Quadrati... |
1,245 | lean_file_chunk | 61660a0eddc7a4c5cc3f0a64f546229b7999fc886c267ca1ef66b82f288083b5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Monoidal
public import Mathlib.Algebra.Category.ModuleCat.Monoidal.Symmetric
/-!
# The monoida... |
8,953 | lean_file_chunk | 46eb0c664434b9cb7350884cff761cc5ae47f46ba452782f3c4ee6b7f742f039 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.LinearAlgebra.Alternating.Curry
public import Mathlib.GroupTheory.Perm.Fin
public import Mathlib.Data.Fin.Parity
/-!
# Uncurrying alt... |
3,796 | lean_file_chunk | 6f17b51289f65e4285d08c3d3432fae18851151db2fad45efc79353efceee91d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
module
public import Mathlib.LinearAlgebra.FreeModule.StrongRankCondition
public import Mathlib.LinearAlgebra.Dimension.Finite
/-!
# Finite and free modules using... |
5,553 | lean_file_chunk | af1c97a4b1aeab2d1d208f6c411e63a8c51d5217ab068f1a333bab66a0e12b13 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Alex J. Best, Xavier Roblot
-/
module
public import Mathlib.Data.Int.Associated
public import Mathlib.Data.Int.NatAbs
public import Mathlib.LinearAlgebra.Determinant
publi... |
2,018 | lean_file_chunk | 054bd2f6ea3f937ea9344019b80e2024b2629545d1827a614145992eca63df86 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
module
public import Mathlib.LinearAlgebra.FreeModule.Basic
public import Mathlib.LinearAlgebra.Matrix.StdBasis
public import Mathlib.RingTheory.Finiteness.Cardina... |
5,956 | lean_file_chunk | 0344a486208d9d39f13617e8efe964be3404e6a6283b8732e04ae05dc602bd9a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Xavier Roblot
-/
module
public import Mathlib.Data.ZMod.QuotientRing
public import Mathlib.LinearAlgebra.Dimension.Constructions
public import Mathlib.LinearAlgebra.FreeMo... |
9,881 | lean_file_chunk | 7875da826d2c16db68f9073689e9dcc294c1f612e5e8a8754caacaa21c7f9799 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Matteo Cipollina. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matteo Cipollina
-/
module
public import Mathlib.Combinatorics.Quiver.ConnectedComponent
public import Mathlib.Combinatorics.Quiver.Path.Vertices
public import Mathlib.Data.Matrix.M... |
2,176 | lean_file_chunk | fb4ce97c4f30a5ef52d777f2c9b928b130f91ef2ecf98da043114148afa24ef0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Aaron Anderson, Jalex Stark. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson, Jalex Stark
-/
module
public import Mathlib.FieldTheory.Finite.Basic
public import Mathlib.LinearAlgebra.Matrix.Charpoly.Coeff
public import Mathlib.Linea... |
11,909 | lean_file_chunk | da3486a0494c3ebe30f8e991e2adab591fca1cc7ae06fc9c7431e6a8ad042b9f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Algebra.Polynomial.Eval.SMul
public import Mathlib.LinearAlgebra.Matrix.Adjugate
public import Mathlib.LinearAlgebra.Matrix.Block
public imp... |
4,262 | lean_file_chunk | 4ced5494a6c84f394c7018e98e353039f6ac555eeaa21c1a4ed946906b3e86bc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
module
public import Mathlib.Algebra.MvPolynomial.Equiv
public import Mathlib.LinearAlgebra.Matrix.Charpoly.Coeff
public import Mathlib.RingTheory.MvPolynomial.Homog... |
10,220 | lean_file_chunk | 9e610cd7225664dfe08d3a55a5622455e75439857f1f9a0c0bf0245c081bd139 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.LinearAlgebra.Matrix.Charpoly.Coeff
public import Mathlib.LinearAlgebra.Matrix.ToLin
/-!
# Cayley-Hamilton theorem for f.g. modules.
Given ... |
16,132 | lean_file_chunk | 225050f558e444ddb61730f774afc33977e0c01201a01a2461c8c3b55a34b8a1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Aaron Anderson, Jalex Stark. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson, Jalex Stark
-/
module
public import Mathlib.Algebra.Polynomial.Expand
public import Mathlib.Algebra.Polynomial.Laurent
public import Mathlib.Algebra.Polyn... |
1,236 | lean_file_chunk | 79e60070f733a08a09cb3d7a6e59ab82632477aabde62dc61a746f6c384ece5c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.LinearAlgebra.Matrix.Charpoly.Coeff
public import Mathlib.RingTheory.Polynomial.Resultant.Basic
/-!
# The discriminant of a matrix
-/
... |
4,226 | lean_file_chunk | 17b19c79b0a9fbda56a2763fc55b23a2f4b9675bccbb2435bc316ed142855402 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Mohanad Ahmed. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mohanad Ahmed
-/
module
public import Mathlib.Algebra.Algebra.Spectrum.Basic
public import Mathlib.Algebra.Polynomial.Basic
public import Mathlib.FieldTheory.IsAlgClosed.Basic
/-!
# E... |
2,714 | lean_file_chunk | 008821e3438fceb6377a5eb3f1e88a359142a6d2b2a7a82e191550e6b10a1953 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Aaron Anderson, Jalex Stark. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson, Jalex Stark, Eric Wieser
-/
module
public import Mathlib.LinearAlgebra.Matrix.Charpoly.Coeff
public import Mathlib.LinearAlgebra.Matrix.ToLin
public impor... |
3,690 | lean_file_chunk | 56db4d7f001b4278bf89fece68758ac9152ba862d7886157daab35a6b6aa591f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Thomas Lanard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck, Inna Capdeboscq, Johan Commelin, Thomas Lanard, Peiran Wu
-/
module
public import Mathlib.FieldTheory.Finiteness
public import Mathlib.LinearAlgebra.Matrix.GeneralLinea... |
2,813 | lean_file_chunk | 10cd65b7611374d7026e4c87d2567b756ea8502e2fe08527cc0ae8f5618ac798 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
module
public import Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Defs
/-!
# Basic lemmas about the general linear group $GL(n, R)$
This file lists various basi... |
12,360 | lean_file_chunk | b271dc66ce7a12d9a177df47f85be56e9674df6efb3af000f0a8f618505d48dc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
module
public import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
public import Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup
public import Mathlib.LinearAlgebr... |
3,606 | lean_file_chunk | 7eda01b18f681af956eab10f9bc573189886e8041915c0e38a3fd1827ef1c1bc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
module
public import Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Basic
public import Mathlib.Data.Sign.Basic
/-!
# Projective general linear group
In t... |
10,767 | lean_file_chunk | 59e71970c199cb888daf03c82039611d27e795245091e0012464067a5fd11c5f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Algebra.Group.AddChar
public import Mathlib.LinearAlgebra.Matrix.Charpoly.Disc
public import Mathlib.LinearAlgebra.Matrix.GeneralLinearG... |
23,960 | lean_file_chunk | 954466cc9f848baa603905cf3ac86a9fdddc94bb16753ee1acd1a62c6bd733a3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Chris Hughes, Anne Baanen
-/
module
public import Mathlib.Data.Matrix.Basic
public import Mathlib.Data.Matrix.Block
public import Mathlib.LinearAlgebra.Matrix.Notation
public im... |
12,668 | lean_file_chunk | 5ac9420cc4cff60b8fa1bfc7d7746332d9b8c5770077f6edd363815dbebb82ca | lean_source_file | pkg_mathlib_source_file_chunks | rw [hsucc, hc i (Fin.succ_pos _), zero_mul, add_zero]
set M' := updateRow M k.succ (N k.succ) with hM'
have hM : M = updateRow M' k.succ (M' k.succ + c k • M (Fin.castSucc k)) := by
ext i j
by_cases hi : i = k.succ
· simp [hi, hM', hsucc, updateRow_self]
rw [updateRow_ne hi, hM', updateRow_ne hi]
... |
4,553 | lean_file_chunk | 9cc02fbac7245808b28453e7843426475c4635f27d9d7e8ecd841c19a7af656c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
module
public import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
public import Mathlib.Algebra.Ring.NegOnePow
/-!
# Miscellaneous results about determinant
In thi... |
9,141 | lean_file_chunk | d1d5d1460acc6b4be619f13d8ab1f000d17ef83c815ed1c14dbb68c9d80dc11f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Martin Dvorak. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Martin Dvorak, Vladimir Kolmogorov, Ivan Sergeev, Bhavik Mehta
-/
module
public import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
public import Mathlib.Data.Matrix.ColumnRowPartiti... |
920 | lean_file_chunk | 2b18b8fd74f5a1e906a27e29bc6dc97e4459338a67779272c94d6269f4c92825 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Kim Morrison
-/
module
public import Mathlib.Algebra.Module.Torsion.Basic
public import Mathlib.LinearAlgebra.Dimension.Finite
/-!
# Re... |
1,166 | lean_file_chunk | ae4204540195b9ca60be5ed85cd7f3fbc856fdee6ff5e6c73f00f4b670fda74e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.Algebra.Module.Torsion.Basic
public import Mathlib.LinearAlgebra.Dimension.Constructions
public import Mathlib.LinearAlgebra.Dimension.Subs... |
9,368 | lean_file_chunk | 22839e12de2b669079a18275444069481921ae0898e74d5171bb7b5ed7c69fbc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Geometry.RingedSpace.PresheafedSpace
public import Mathlib.CategoryTheory.Limits.Final
public import Mathlib.Topology.Sheaves.Stalks
/-!
# ... |
11,075 | lean_file_chunk | 24b36f37361f59fb70d6964edf88fc16e708a86acc1ea7e55d9ae426427208b4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Geometry.RingedSpace.PresheafedSpace.HasColimits
public import Mathlib.Geometry.RingedSpace.Stalks
public import Mathlib.Topology.Sheaves.Fu... |
23,958 | lean_file_chunk | bd81a12bd783d56bbd7cb35f4cf0cbbffb09ebef8bc054c1ef6e5bab5dcddb9a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.Topology.Category.TopCat.Limits.Pullbacks
public import Mathlib.Geometry.RingedSpace.LocallyRingedSpace
/-!
# Open immersions of structured s... |
23,942 | lean_file_chunk | 2e1b44b3445382722acace15770a87a587307615ce4c5318b6b54ebb80b02cde | lean_source_file | pkg_mathlib_source_file_chunks | @[deprecated (since := "2025-12-18")] alias toSheafedSpaceHom_base := toSheafedSpaceHom_hom_base
@[deprecated (since := "2025-12-18")] alias toSheafedSpaceHom_c := toSheafedSpaceHom_hom_c
instance toSheafedSpace_isOpenImmersion : SheafedSpace.IsOpenImmersion (toSheafedSpaceHom Y f) :=
H
@[simp]
theorem sheafedSpace... |
7,954 | lean_file_chunk | a914f4ab24a5652fe1c14ea01f2f513c4a17495cc18136847903e8f41a2704a0 | lean_source_file | pkg_mathlib_source_file_chunks | (LocallyRingedSpace.forgetToSheafedSpace ⋙ SheafedSpace.forgetToPresheafedSpace) :=
preservesPullback_symmetry _ _ _
instance forget_reflectsPullback_of_right :
ReflectsLimit (cospan g f) LocallyRingedSpace.forgetToSheafedSpace :=
reflectsLimit_of_reflectsIsomorphisms _ _
instance forgetToPresheafedSpace_refl... |
19,465 | lean_file_chunk | 0a90632e105d4e11d9d62e95e03d227a594f044a2161930061de951f072f38b2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
module
public import Mathlib.Algebra.Category.Ring.Constructions
public import Mathlib.Geometry.RingedSpace.Basic
public import Mathlib.Geometry.RingedSpace.Stalks
... |
9,396 | lean_file_chunk | 1465ea7406adc7b6c55f50dd50cecfcb134e2fe4c9c77ff1eede0eea39ed4292 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Justus Springer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Justus Springer, Andrew Yang
-/
module
public import Mathlib.Algebra.Category.Ring.Colimits
public import Mathlib.Algebra.Category.Ring.FilteredColimits
public import Mathlib.Algebra... |
14,198 | lean_file_chunk | 5508f59bcc4464cd832256c187f874aacad09562b0f08cc5f722b9d2b7f2987b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Adjunction.FullyFaithful
public import Mathlib.CategoryTheory.Elementwise
public import Mathlib.Topology.Sheaves.Presheaf
/-... |
23,939 | lean_file_chunk | 200382bd050cf097bfc65fa8a58bb2c07752be6bf0044690805955405931cc92 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Ben Eltschig. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ben Eltschig
-/
module
public import Mathlib.Analysis.InnerProductSpace.EuclideanDist
/-!
# Diffeological spaces
A diffeological space is a concrete sheaf on the site of cartesian spa... |
5,789 | lean_file_chunk | c9596566347e7048324928a450db346c084f50f9e27f65a81506d8482936da5e | lean_source_file | pkg_mathlib_source_file_chunks | lemma self_subset_toPlots_generateFrom (g : Set ((n : ℕ) × (𝔼ⁿ → X))) :
g ⊆ (generateFrom g).toPlots :=
fun _ hd _ h ↦ h hd
lemma isPlot_generatedFrom_of_mem {g : Set ((n : ℕ) × (𝔼ⁿ → X))} {n : ℕ} {p : 𝔼ⁿ → X}
(hp : ⟨n, p⟩ ∈ g) : (@IsPlot _ (generateFrom g)) p :=
self_subset_toPlots_generateFrom g hp
i... |
14,130 | lean_file_chunk | c897cea0ff21228d986c1a38a1616925b71b733982f4a43497596c967d189b2e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
module
public import Mathlib.Geometry.Euclidean.Projection
public import Mathlib.Analysis.Normed.Module.Normalize
/-!
# Signed distance to an affine subspace in a Eucli... |
17,430 | lean_file_chunk | 5dba6e1ce4e0ee39c07733facffde8576f1ba76761bdb15fb3e7e48b7f900a22 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
module
public import Mathlib.Geometry.Euclidean.Projection
public import Mathlib.Analysis.InnerProductSpace.Projection.FiniteDimensional
public import Mathlib.Analysis.I... |
23,651 | lean_file_chunk | b3028e0871c3b9aae5b8654cb403bcf6ae1e46b55b5260c4062238d4b3914976 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Manuel Candales
-/
module
public import Mathlib.Analysis.Normed.Affine.AddTorsor
public import Mathlib.Geometry.Euclidean.Angle.Oriented.Affine
public import Mathlib.Geome... |
23,940 | lean_file_chunk | 017227ca88bd1ffa8c6c16b5de98eee7d5498900e9881ac1eedca25a7f273621 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
module
public import Mathlib.Geometry.Euclidean.Projection
public import Mathlib.Geometry.Euclidean.Sphere.Basic
public import Mathlib.LinearAlgebra.AffineSpace.Simplex.... |
15,487 | lean_file_chunk | b797dfc43c947d26e046e1435396b68631623e08d4197e1fe6868d9895414f4e | lean_source_file | pkg_mathlib_source_file_chunks | /-- The centroid of some vertices of a simplex, in terms of `pointsWithCircumcenter`. -/
theorem centroid_eq_affineCombination_of_pointsWithCircumcenter {n : ℕ} (s : Simplex ℝ P n)
(fs : Finset (Fin (n + 1))) :
fs.centroid ℝ s.points =
(univ : Finset (PointsWithCircumcenterIndex n)).affineCombination ℝ s.... |
4,747 | lean_file_chunk | 89e261aa9e1c5dce67379d4d312ccb32b3be657e104babb6e81e64f25e26715e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Chu Zheng
-/
module
public import Mathlib.Analysis.Normed.Affine.Simplex
public import Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine
public import Mathlib.LinearAlgeb... |
23,983 | lean_file_chunk | b0907f470b6137497af7607f928fade5a8c8f5279587038b818740b0c32564e6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
module
public import Mathlib.Geometry.Euclidean.Altitude
public import Mathlib.Geometry.Euclidean.Circumcenter
/-!
# Monge point and orthocenter
This file defines the ... |
9,844 | lean_file_chunk | 90d21e4b83b823e72a4e0607fd44f222cfb7f75692f30cddeaee4438873d99c5 | lean_source_file | pkg_mathlib_source_file_chunks | · have hu : (Set.univ : Set (Fin 3)) = {j₁, j₂, j₃} := by grind
rw [← Set.image_univ, hu, Set.image_insert_eq, Set.image_insert_eq, Set.image_singleton, h₁,
h₂, h₃, Set.insert_subset_iff, Set.insert_subset_iff, Set.singleton_subset_iff]
exact
⟨t₁.orthocenter_mem_affineSpan, mem_affineSpan ℝ ... |
10,684 | lean_file_chunk | 4d883d9862f743fb1cc13dadb2926d46a38fb33c823bb382b2460ab386b074d6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Weiyi Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Weiyi Wang
-/
module
public import Mathlib.Geometry.Euclidean.Circumcenter
public import Mathlib.Geometry.Euclidean.MongePoint
import Mathlib.Geometry.Euclidean.Angle.Sphere
import Mathli... |
8,174 | lean_file_chunk | ddf5f60b1f27da74bb411e5e376d51caf32a4a2f342a5a15a6751711533c2f5a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Manuel Candales
-/
module
public import Mathlib.Geometry.Euclidean.PerpBisector
public import Mathlib.Algebra.QuadraticDiscriminant
/-!
# Euclidean spaces
This file make... |
6,215 | lean_file_chunk | c16de5d1c9c02dc0c75e1732e1fd0bed462330aa175df17ea3affdbb1de5ba0c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Chu Zheng. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chu Zheng
-/
module
public import Mathlib.Geometry.Euclidean.Triangle
public import Mathlib.Topology.MetricSpace.Similarity
import Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle
/... |
23,994 | lean_file_chunk | 8c82c64d92ecce61aa638a94582f60f23a23839d36ca3a82f70079e06accfe76 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
module
public import Mathlib.Analysis.Convex.Side
public import Mathlib.Geometry.Euclidean.Altitude
public import Mathlib.Geometry.Euclidean.SignedDist
public import Mat... |
23,982 | lean_file_chunk | 289e3cc823b19db3deb10eea87e0d96d868d265b5d466f1bbf0a403aed17498f | lean_source_file | pkg_mathlib_source_file_chunks | (h : s.ExcenterExists signs) (i : Fin (n + 1)) :
s.signedInfDist i (s.excenter signs) =
(if i ∈ signs then -1 else 1) * (∑ j, s.excenterWeightsUnnorm signs j)⁻¹ := by
simp_rw [excenter_eq_affineCombination,
signedInfDist_affineCombination _ _ h.sum_excenterWeights_eq_one, excenterWeights,
Pi.smul_ap... |
16,272 | lean_file_chunk | ef703a3893136766ca8105d27b59cedfeccc81bfcca72e87a23d2d708775b750 | lean_source_file | pkg_mathlib_source_file_chunks | (s.signedInfDist j (AffineMap.lineMap (s.excenter signs) (s.touchpoint signs i) t)))
(Set.Icc 0 1) := by
refine continuousOn_of_forall_continuousAt
fun t ht ↦ ((continuousAt_sign_of_ne_zero ?_).comp
(((s.signedInfDist j).cont.comp ?_).continuousAt))
· intro h0
rw [← abs_eq_zero, abs_si... |
9,137 | lean_file_chunk | 0903d4bb7a3e44c0d4a9eb5a12e72cb9a147e2f7f44811a647b241c32d9fd68c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Joseph Myers
-/
module
public import Mathlib.Analysis.InnerProductSpace.Orthogonal
public import Mathlib.Analysis.Normed.Group.AddTorsor
public import Mathlib.Analys... |
23,919 | lean_file_chunk | e411275b708ec0eb185d5a26be4ff9e118faccae7e2924db2ad69c0a8334f05c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Manuel Candales
-/
module
public import Mathlib.Analysis.InnerProductSpace.Projection.Reflection
public import Mathlib.Analysis.InnerProductSpace.Projection.Submodule
publ... |
8,907 | lean_file_chunk | fe5f2b523d49e2218bb2819db1f60139c3bbef7aec769a41cc4249c8a4a4afdb | lean_source_file | pkg_mathlib_source_file_chunks | [Nonempty s₂] [s₁.direction.HasOrthogonalProjection] [s₂.direction.HasOrthogonalProjection]
(p : P) :
reflection s₁ p = reflection s₂ p ↔
(orthogonalProjection s₁ p : P) = orthogonalProjection s₂ p := by
rw [reflection_apply', reflection_apply']
constructor
· intro h
rw [← @vsub_eq_zero_iff_eq V... |
5,595 | lean_file_chunk | f6dd4b2a5248d0392cfb72960cf248a5787b866b9974983c1457468705bf6c26 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Jovan Gerbscheid. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jovan Gerbscheid, Chu Zheng
-/
module
public import Mathlib.Topology.MetricSpace.Congruence
public import Mathlib.Analysis.InnerProductSpace.Basic
public import Mathlib.Analysis.Nor... |
5,405 | lean_file_chunk | 794a6cf3e826edf3db3c3e9a05439f6a1b2c6f7e9621c3b06e910724417e562a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 A. M. Berns. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: A. M. Berns
-/
module
public import Mathlib.Analysis.Convex.Between
public import Mathlib.Algebra.Ring.Defs
public import Mathlib.Tactic.Continuity
/-!
# Polygons
This file defines pol... |
23,960 | lean_file_chunk | cbd681f097983eca1dd758f17e131175d7c7efb382e25c5db3e8c9c22014f4e7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Floris van Doorn
-/
module
public import Mathlib.Geometry.Manifold.MFDeriv.Tangent
public import Mathlib.Geometry.Manifold.ContMDiffMap
public import Mathlib.Geo... |
4,391 | lean_file_chunk | 0829c8dbb092b438888c680409aa338a35601877d2899aec0cd82e732d8e760f | lean_source_file | pkg_mathlib_source_file_chunks | PartialEquiv.prod_source, Set.mem_prod, TangentBundle.mem_chart_source_iff] at hp
let φ (x : E) := I ((chartAt H a.proj) ((chartAt H p.1.proj).symm (I.symm x)))
have D0 : DifferentiableWithinAt 𝕜 φ (Set.range I) (I ((chartAt H p.1.proj) p.1.proj)) := by
apply ContDiffWithinAt.differentiableWithinAt _ one... |
23,943 | lean_file_chunk | 590847832710a2f7fd6d7e9c481694e5e96472ca51cbbd164666fd38d4f06686 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
module
public import Mathlib.Geometry.Manifold.StructureGroupoid
public import Mathlib.Topology.Connected.LocPathConnected
public import Mathlib.Topology.OpenP... |
7,595 | lean_file_chunk | ba16602d2db832930ecfbe87b14b7befd91b94276507757497ab8836e7ae05c4 | lean_source_file | pkg_mathlib_source_file_chunks | variable [TopologicalSpace H] [TopologicalSpace M] [TopologicalSpace M']
[cm : ChartedSpace H M] [cm' : ChartedSpace H M']
/-- The disjoint union of two charted spaces modelled on a non-empty space `H`
is a charted space over `H`. -/
@[implicit_reducible]
def ChartedSpace.sum_of_nonempty [Nonempty H] : ChartedSpac... |
12,543 | lean_file_chunk | 3f5d0e6b72ea1963e494162b07cc0b00bc577869a78178efa06ebfdc36820316 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Michael Rothgang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Rothgang
-/
module
public import Mathlib.Geometry.Manifold.IsManifold.Basic
/-! # Local properties of smooth functions which depend on both the source and target
In this f... |
3,856 | lean_file_chunk | 9b5fdb7a7eb91d3409f22bc174033f32e4fd8962f1cc68d57ba4929628a5d7ff | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri
-/
module
public import Mathlib.Geometry.Manifold.ContMDiff.NormedSpace
public import Mathlib.Geometry.Manifold.Notation
/-!
# `C^n` bundled maps
In this file we ... |
13,886 | lean_file_chunk | 806f0f2d5fad876763245ddcefe8737983510776484f0de9c39cb5ed41df5793 | lean_source_file | pkg_mathlib_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
-/
module
public import Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension
public import Mathlib.Geometry.Manifold.ContMDiff.Atlas
public import Mathlib.Geometry.... |
13,538 | lean_file_chunk | 74c8ed815bf5df2a96700de9c67350363ecfaef09a4886e72ceb1301735b0610 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
module
public import Mathlib.Algebra.Lie.Basic
public import Mathlib.Geometry.Manifold.Algebra.LieGroup
public import Mathlib.Geometry.Manifold.VectorField.Lie... |
1,082 | lean_file_chunk | 6b1afa71c3c76a5b6c917968dec25ed54e27681c847f9ece276b6cc2ba0d2484 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yourong Zang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yourong Zang
-/
module
public import Mathlib.Analysis.Calculus.Conformal.NormedSpace
public import Mathlib.Geometry.Manifold.StructureGroupoid
/-!
# Conformal Groupoid
In this file we... |
1,234 | lean_file_chunk | fdc5e99564d3432f1b9c69151ed8ed7e41c333214a25301ee868e2316e6a7658 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Analysis.Normed.Module.FiniteDimension
public import Mathlib.Geometry.Manifold.IsManifold.Basic
public import Mathlib.Topology.Compact... |
12,032 | lean_file_chunk | ef8f7630abeb22c3b00c6f2bb06f7a533a69cc62d84b2a380b98e46e679866ed | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Michael Rothgang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Rothgang
-/
module
public import Mathlib.Analysis.SpecialFunctions.Pow.NNReal
public import Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary
/-!
## (Unoriented) bordis... |
6,086 | lean_file_chunk | 23f3ede15a7fda468c1e1ee241597648cc13eadb4fa7a1bd0ba5c17e1b986a27 | lean_source_file | pkg_mathlib_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
-/
module
public import Mathlib.FieldTheory.Finiteness
public import Mathlib.Geometry.Manifold.Diffeomorph
public import Mathlib.Geometry.Manifold.Instances.Real
publ... |
6,477 | lean_file_chunk | be4ce89896d519327c6b369c976cafd5d228fc919c9617718dc86929b3261717 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri
-/
module
public import Mathlib.Geometry.Manifold.Algebra.SmoothFunctions
public import Mathlib.RingTheory.Derivation.Basic
/-!
# Derivation bundle
In this file ... |
23,985 | lean_file_chunk | d621831354475e52c94ba424eca88b11613161944259500f8280eb2f755ac19d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Michael Rothgang, Thomas Murrills
-/
module
public import Mathlib.Geometry.Manifold.ContMDiff.Defs
public import Mathlib.Geometry.Manifold.MFDeriv.Defs
/-!
# Elaborat... |
23,978 | lean_file_chunk | 4a770963d65a8d5a5646d58f68e0bb94b0173848fdfa439d2c19be958168359c | lean_source_file | pkg_mathlib_source_file_chunks | trace[Elab.DiffGeo.MDiff] "`{e}` is a charted space over `{H}` via `{inst}`"
return some H else
if ← withReducible (pureIsDefEq H e) then
trace[Elab.DiffGeo.MDiff] "`{e}` is the charted space of `{M}` via `{inst}`"
return some H else return none
| _ => return none
... |
7,303 | lean_file_chunk | 8dd8cbb18d8ddac152d658c97303320b67b0579a5e1dc9e22492ab032a8d1134 | lean_source_file | pkg_mathlib_source_file_chunks | trying to determine `I` and `J` from the local context. -/
scoped elab:max "mfderiv[" s:term "]" ppSpace t:term:arg : term => do
let es ← Term.elabTerm s none
let e ← ensureIsFunction <| ← Term.elabTerm t none
let (srcI, tgtI) ← findModels e es
mkAppM ``mfderivWithin #[srcI, tgtI, e, es]
/-- `mfderiv% f x` ela... |
23,994 | lean_file_chunk | 2cd09fbcfc8bf6ed762716afda37fa3ba6774f2882171726c07b52716b203907 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri, Yury Kudryashov
-/
module
public import Mathlib.Geometry.Manifold.ContMDiffMap
public import Mathlib.Geometry.Manifold.MFDeriv.UniqueDifferential
/-!
# Diffeomorp... |
1,093 | lean_file_chunk | 7c2dc14ce00d7a4c3f0561fcadb8b4ce9eb4b4d0726a7f55f66ad5c720bde58e | lean_source_file | pkg_mathlib_source_file_chunks | contMDiff_invFun := by
apply ContMDiff.sumElim
· exact ContMDiff.inl.comp ContMDiff.inl
· exact ContMDiff.inr.sumMap contMDiff_id
@[simp]
theorem sumAssoc_coe :
(sumAssoc I M n M' M'' : (M ⊕ M') ⊕ M'' → M ⊕ (M' ⊕ M'')) = Equiv.sumAssoc M M' M'' := rfl
variable (I M n) in
/-- The canonical diffeomorphi... |
17,844 | lean_file_chunk | 05a8b9893388bc1aa5916dba95c45e6d76525f79a90b134280d89694a75128c1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Michael Rothgang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Rothgang
-/
module
public import Mathlib.Geometry.Manifold.Diffeomorph
public import Mathlib.Topology.IsLocalHomeomorph
/-!
# Local diffeomorphisms between manifolds
In th... |
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