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 |
|---|---|---|---|---|---|
3,985 | lean_file_chunk | 667b9ff7a4fbb75f142a0d72f73e32324a5abfda1cba9e2ce41c07a89dae70fe | 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.RingTheory.Ideal.BigOperators
public import Mathlib.RingTheory.FiniteType
/-!
# Rees algebra
The Rees algebra of an ideal `I` is the subalg... |
13,547 | lean_file_chunk | c021b4748b5701bccc44ffa92a5b4fd9413a8835cf0e31f920e7a3e88e36c88f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning, Yakov Pechersky
-/
module
public import Mathlib.Algebra.Module.LocalizedModule.Submodule
public import Mathlib.Order.Irreducible
public import Mathlib.RingTheory.Ide... |
2,076 | lean_file_chunk | 5ad4c246cc19efbaa7eb0e619c8db1abd12cc39818b29fdb704324ed220628f3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Alex J. Best. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex J. Best
-/
module
public import Mathlib.Algebra.Squarefree.Basic
public import Mathlib.Algebra.EuclideanDomain.Int
public import Mathlib.Data.ZMod.Basic
public import Mathlib.RingT... |
23,947 | lean_file_chunk | a1afe21fda8d3a226d283ccd312fcbbd16af39217553a1696089dc566f227fcd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 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.Algebra.Rat
public import Mathlib.Algebra.Group.Torsion
public import Mathlib.Algebra.Module.Rat
public import Mathlib.Algebra.P... |
400 | lean_file_chunk | 1050051230aa2e55428fb2a486ffe70a97c6a108082712e849d38c0e3ceb612a | lean_source_file | pkg_mathlib_source_file_chunks | mul_assoc _ (x.2.factorial : R), ← nsmul_eq_mul x.2.factorial]
simp [mul_assoc, descPochhammer_eq_factorial_smul_choose]
lemma map_choose {R S F : Type*} [Ring R] [Ring S] [BinomialRing R] [BinomialRing S]
[FunLike F R S] [RingHomClass F R S] (f : F) (a : R) (n : ℕ) :
f (Ring.choose a n) = Ring.choose (f a) ... |
4,416 | lean_file_chunk | 560d6d59c45290b25819e2704a940b0ae845e790a322eeb043e5d4423efe4704 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jz Pan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jz Pan
-/
module
public import Mathlib.Algebra.Module.TransferInstance
public import Mathlib.RingTheory.Finiteness.Cardinality
/-!
# Orzech property of rings
In this file we define the fol... |
11,841 | lean_file_chunk | 67143e00247f40d0e4f9d3da3fc8c7ae47716d3a97226203a433d3c61200ab9d | 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, Eric Wieser
-/
module
public import Mathlib.Algebra.Star.StarAlgHom
public import Mathlib.Data.Matrix.Basis
public import Mathlib.Data.Matrix.Composition
public import Mat... |
23,989 | lean_file_chunk | 2303ec0a22bb6355283ec6bee32ceabdfe6d5ceeb25774115a606bd6de2e83ef | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson, María Inés de Frutos-Fernández, Filippo A. E. Nuccio
-/
module
public import Mathlib.Data.Int.Interval
public import Mathlib.FieldTheory.RatFunc.AsPolynomial
public im... |
23,934 | lean_file_chunk | ca6c947ad9f95e9ae3fa39ba8711c91bbf252b8a6feb8b2db122d2ec995c0946 | lean_source_file | pkg_mathlib_source_file_chunks | rw [← log_le_iff_le_exp one_ne_zero, log_one]
lia
· obtain ⟨d, hd⟩ := Int.eq_ofNat_of_zero_le hDs.le
rw [← neg_neg (-D + ↑s), ← sub_eq_neg_add, neg_sub, hd]
apply (intValuation_le_iff_coeff_lt_eq_zero K F).mpr
intro n hn
rw [powerSeriesPart_coeff f n, hs]
apply h_va... |
5,169 | lean_file_chunk | b85230a0bb6f4935d40c57d3962dfe151ea8b59e931d51929e30d1d4012ccd5d | lean_source_file | pkg_mathlib_source_file_chunks | letI : UniformSpace (ratfuncAdicComplPkg (K := K).space) :=
ratfuncAdicComplPkg.uniformStruct
rw [← valuation_LaurentSeries_equal_extension, ← compare_comp_eq_compare ratfuncAdicComplPkg _]
· exact congr_fun (ratfuncAdicComplPkg.isDenseInducing.extend_unique
Valued.valuedCompletion_apply (Valued.continu... |
2,236 | lean_file_chunk | 8e6e04e6419cc4e38135dfa8acb633edab369ac5b93f5af14245da8c38f39299 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
module
public import Mathlib.RingTheory.Ideal.Oka
public import Mathlib.RingTheory.PrincipalIdealDomain
/-!
# Principal ideal domains and prime ideals
## Main results
... |
23,925 | lean_file_chunk | 5c9a85088756b301099f786851b34266d61a070c23e311eec15caeb492113382 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.Algebra.BigOperators.Fin
public import Mathlib.Algebra.Ring.GeomSum
public import Mathlib.RingTheory.Ideal.Quotient.Operations
/-!
# Idempot... |
2,621 | lean_file_chunk | 11ed178d8ed7dd04bde5348e92f20892012f9af224b0e07fd37579566024de56 | lean_source_file | pkg_mathlib_source_file_chunks | instance [NonUnitalSemiring R] (idem : IsIdempotentElem e) : Semiring idem.Corner where
__ : NonUnitalSemiring (NonUnitalSubsemiring.corner e) := inferInstance
one := ⟨e, e, by simp_rw [idem.eq]⟩
one_mul r := Subtype.ext ((Subsemigroup.mem_corner_iff idem).mp r.2).1
mul_one r := Subtype.ext ((Subsemigroup.mem_c... |
7,677 | lean_file_chunk | 299f5ef5e03ea617c57d78f4906b6289246b25ab843f6718bf61b6e14dfa5efd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Devon Tuma
-/
module
public import Mathlib.RingTheory.Jacobson.Ring
public import Mathlib.FieldTheory.IsAlgClosed.Basic
public import Mathlib.RingTheory.Spectrum.Prime.Basic
/-!
# Nullst... |
8,677 | lean_file_chunk | 82ca24e5a137ae0ab9e08c7860bbbba9d91eddeafaf8ea7b04564fc59277c923 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
module
public import Mathlib.LinearAlgebra.SModEq.Basic
public import Mathlib.LinearAlgebra.SModEq.Pow
public import Mathlib.RingTheory.AdicCompletion.Basic
public import Math... |
5,744 | lean_file_chunk | 4b16a9067054e94efed0a7849ea88f0dc99a57e3589267761c6517de7cf8b9f0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
module
public import Mathlib.Algebra.DualNumber
public import Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic
public import Mathlib.RingTheory.PrincipalIdealDomain... |
3,854 | lean_file_chunk | 6bd456db1534fb1db6a4508563dae565138bfc4a090ece5f50a6287dbc46c5f3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Johan Commelin
-/
module
public import Mathlib.Algebra.FreeMonoid.Basic
public import Mathlib.GroupTheory.FreeAbelianGroup
/-!
# Free rings
The theory of the free ring over a ... |
11,473 | lean_file_chunk | 84181b715e28e200aa6e3072cd63ab524fe02cbb892bb657a5c2d18db3ca0261 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.RingTheory.FiniteType
public import Mathlib.RingTheory.Localization.Defs
public import Mathlib.RingTheory.TensorProduct.Quotient
/-!
# Essent... |
117 | lean_file_chunk | 34bf4ee685bdaacd9da3ed232f470b80fc1eb9e5968cef31d9c4b4025798f947 | lean_source_file | pkg_mathlib_source_file_chunks | module -- shake: keep-all
public import Mathlib.RingTheory.Radical.NatInt
deprecated_module (since := "2026-03-04") |
1,232 | lean_file_chunk | e7905c703f65bc45e3e1b0323532341b5362b5fa671e20ef50af6366ff3fc11b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Stefan Kebekus. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefan Kebekus
-/
module
public import Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms
public import Mathlib.Topology.DiscreteSubset
/-!
# Theorems combining measure theory and top... |
10,160 | lean_file_chunk | bf779b90d4d369838b15ff3aea5fe4025916b81a3046bbd6d2d7316d67c8d6fb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Etienne Marion
-/
module
public import Mathlib.Data.Finite.Prod
public import Mathlib.MeasureTheory.SetSemiring
/-!
# Algebra of sets
In this file we define the notion of algebra of... |
23,976 | lean_file_chunk | 9ce434bf55789979800fc46e56039e9273dabf8761f1721a45b1503430090087 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Martin Zinkevich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Martin Zinkevich, Rémy Degenne
-/
module
public import Mathlib.Data.Set.Dissipate
public import Mathlib.Logic.Encodable.Lattice
public import Mathlib.MeasureTheory.M... |
7,487 | lean_file_chunk | 563ab890af68a72a6d7fed26f55e4aaa902c187bfb0da38c411d5e27bc2303f0 | lean_source_file | pkg_mathlib_source_file_chunks | theorem has_univ : d.Has univ := by simpa using d.has_compl d.has_empty
theorem has_iUnion {β} [Countable β] {f : β → Set α} (hd : Pairwise (Disjoint on f))
(h : ∀ i, d.Has (f i)) : d.Has (⋃ i, f i) := by
cases nonempty_encodable β
rw [← Encodable.iUnion_decode₂]
exact
d.has_iUnion_nat (Encodable.iUnion_... |
23,978 | lean_file_chunk | ab7f1c26381a7efca47445d27529b302834c714053060bc7a12adb8e2c3d226f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Peter Pfaffelhuber
-/
module
public import Mathlib.Data.Nat.Lattice
public import Mathlib.Data.Set.Accumulate
public import Mathlib.Data.Set.Pairwise.Lattice
public import... |
2,862 | lean_file_chunk | 3a8467eea64ba2444c2caa6f8ebf87a755687f30aec9c4276fa1569482005616 | lean_source_file | pkg_mathlib_source_file_chunks | lemma inter_mem (hC : IsSetRing C) (hs : s ∈ C) (ht : t ∈ C) : s ∩ t ∈ C := by
rw [← diff_diff_right_self]; exact hC.diff_mem hs (hC.diff_mem hs ht)
lemma isSetSemiring (hC : IsSetRing C) : IsSetSemiring C where
empty_mem := hC.empty_mem
inter_mem := fun _ hs _ ht => hC.inter_mem hs ht
diff_eq_sUnion' := by
... |
23,214 | lean_file_chunk | 47f000b385f0f1fe5c9ef7f0732e9d0a6d6a51c3d06f6d10c26b4f53b58ea57a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Alena Gusakov, Yaël Dillies
-/
module
public import Mathlib.Algebra.Order.Ring.GeomSum
public import Mathlib.Data.Finset.Slice
public import Mathlib.Data.Nat.BitIndices
pu... |
23,977 | lean_file_chunk | 7dea337cf36beb9b5a13bd3750fa4edc428da488a995af01c6e792287cf1b4d0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
module
public import Mathlib.Combinatorics.Hall.Basic
public import Mathlib.LinearAlgebra.Matrix.Rank
public import Mathlib.LinearAlgebra.Projectivization.Construc... |
111 | lean_file_chunk | 32a98466510ec3ca230e1122105c547d128598dc39f28497b87ea9f71592808e | lean_source_file | pkg_mathlib_source_file_chunks | mk K ![0, 1, 0] ?_, mk K ![0, 0, 1] ?_, ?_⟩ <;> simp [mem_iff, orthogonal_mk] }
end ofField
end Configuration |
4,354 | lean_file_chunk | 4c5f1a005b5e78791c780467957d6655cef35cf642595ed837804f4d12d8e9a1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Ching-Tsun Chou, Chris Wong, Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou, Chris Wong, Yaël Dillies
-/
module
public import Mathlib.Data.Finset.Density
public import Mathlib.Data.Fintype.Prod
public import Mathlib.... |
6,019 | lean_file_chunk | 6e78da0ecdef0b5ae3a09cd587060ea17e66ece4017915277a6df65f0927b0c8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
module
import Mathlib.Topology.Compactness.Compact
public import Mathlib.Data.Set.Finite.Basic
/-!
# Combinatorial compactness and the Rado selection lemma
This file c... |
22,369 | lean_file_chunk | 13b65e1d5ce43a00c52de1a2c0c43576acd81b4cc282154b38cbad44b4d5f89d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller, Yury Kudryashov
-/
module
public import Mathlib.Algebra.Module.BigOperators
public import Mathlib.Algebra.Order.Ring.Nat
public import Mathlib.Data.Nat.ModEq
public import M... |
12,504 | lean_file_chunk | 46ee46cdd178d511db24d80326b4dfae43105f72106abf32c63663864c2acc18 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
module
public import Mathlib.Data.Stream.Init
public import Mathlib.Topology.Algebra.Semigroup
public import Mathlib.Topology.Compactification.StoneCech
public import Mathli... |
11,168 | lean_file_chunk | 970df402aa6f96ebbb0d06a4d7deb7d602f0723cce90816e7e1197359a8c7d4a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
module
public import Mathlib.Algebra.MvPolynomial.Equiv
public import Mathlib.Algebra.Polynomial.Degree.Defs
public import Mathlib.Data.Finsupp.Monomia... |
23,935 | lean_file_chunk | 4b0d717765a02820dc6e374c3dbb6f9ee5ffcea51c782d7e5e4498b98c969159 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
module
public import Mathlib.Data.Fintype.Option
public import Mathlib.Data.Fintype.Shrink
public import Mathlib.Data.Fintype.Sum
public import Mathlib.Data.Finite.Prod
publ... |
416 | lean_file_chunk | 63f26bab19753130c58acfb177a2789679fa7242a83fcb765a876d1224657dc3 | lean_source_file | pkg_mathlib_source_file_chunks | ∃ n, ∀ C : (Fin n → α) → κ, ∃ l : Subspace η α (Fin n), l.IsMono C := by
obtain ⟨ι, ιfin, hι⟩ := exists_mono_in_high_dimension α κ η
refine ⟨Fintype.card ι, fun C ↦ ?_⟩
obtain ⟨l, c, cl⟩ := hι fun v ↦ C (v ∘ (Fintype.equivFin _).symm)
refine ⟨⟨l.idxFun ∘ (Fintype.equivFin _).symm, fun e ↦ ?_⟩, c, cl⟩
obtain ⟨... |
12,945 | lean_file_chunk | 1490485937a0972f7e26219ff282c799ac44bd7098e316162ddb11975c208675 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta, Doga Can Sertbas
-/
module
public import Mathlib.Algebra.Order.Ring.Abs
public import Mathlib.Data.Nat.ModEq
public import Mathlib.Data.Nat.Prime.Defs
public... |
23,987 | lean_file_chunk | dc184039884323e8d339b62edb71efcdf318933bfd0f0a5884234fd2bd5821d1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
module
public import Mathlib.Algebra.BigOperators.Fin
public import Mathlib.Algebra.Order.Algebra
public import Mathlib.Algebra.Ring.Subring.Units
public import Mathlib.... |
2,085 | lean_file_chunk | 908fc0ce77cf78697c030f8d8c7c9f276c99edb80fb486ffd25f9af9e1e64266 | lean_source_file | pkg_mathlib_source_file_chunks | · rw [div_eq_inv_mul, mul_smul, smul_add, H, ← add_smul, add_comm r₂, inv_smul_smul₀ h₁₂.ne']
/-- If vectors `v₁` and `v₂` are on the same ray, then they are nonnegative multiples of the same
vector. Actually, this vector can be assumed to be `v₁ + v₂`, see `SameRay.exists_eq_smul_add`. -/
theorem exists_eq_smul (h : ... |
23,911 | lean_file_chunk | 4e304f5329a3d3148e473204d6ec379f91e89cf1b986a827cb16a31cc38080a4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis, Eric Wieser
-/
module
public import Mathlib.LinearAlgebra.Multilinear.TensorProduct
public import Mathlib.Tactic.AdaptationNote
public import Mathlib.LinearAlgebra.M... |
12,702 | lean_file_chunk | 4456be322379e5bbe0c3a7f58b919b21eca956189268f177d8fc7e45143af4f9 | lean_source_file | pkg_mathlib_source_file_chunks | Then there is an `R`-linear map between `⨂ᵢ Hom(sᵢ, tᵢ)` and `Hom(⨂ᵢ sᵢ, ⨂ tᵢ)` defined by
`⨂ᵢ fᵢ ↦ ⨂ᵢ aᵢ ↦ ⨂ᵢ fᵢ aᵢ`.
This is `TensorProduct.homTensorHomMap` for an arbitrary family of modules.
Note that `PiTensorProduct.piTensorHomMap (tprod R f)` is equal to `PiTensorProduct.map f`.
-/
def piTensorHomMap : (⨂[R] i... |
1,446 | lean_file_chunk | eed1315ecafbf614d67c72a8bca0e232a3d0be1361fdd0d83987b87a6c5b5feb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Nailin Guan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nailin Guan
-/
module
public import Mathlib.Algebra.Exact
public import Mathlib.LinearAlgebra.BilinearMap
/-!
# The Left Exactness of Hom
If `M1 → M2 → M3 → 0` is an exact sequence of... |
6,743 | lean_file_chunk | 0151c867ca2b63baceeeff5053fe32c3b391f5c5315dda99f342cae8c897237a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Martin Dvorak. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Martin Dvorak, Kyle Miller, Eric Wieser
-/
module
public import Mathlib.Algebra.Lie.Basic
public import Mathlib.LinearAlgebra.BilinearMap
public import Mathlib.LinearAlgebra.LinearInde... |
7,341 | lean_file_chunk | 58fde69f4d96326e68285bef1275e88e936c1feb8112fb15d10937ec0e492e59 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Algebra.BigOperators.Finsupp.Basic
public import Mathlib.Algebra.Module.Defs
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
p... |
21,808 | lean_file_chunk | f56707315c93b176a09cc4baa29cf1e9edcf04eefa708f4d9b8ea03a9f1358d4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash, Deepro Choudhury, Mitchell Lee, Johan Commelin
-/
module
public import Mathlib.Algebra.EuclideanDomain.Basic
public import Mathlib.Algebra.EuclideanDomain.Int
public import ... |
6,714 | lean_file_chunk | 13ce8218dc8981f3c8f0899c5128cc03005f18e45eb3dd349b812ef9c8cde4ef | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Justin Thomas. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Justin Thomas
-/
module
public import Mathlib.FieldTheory.Minpoly.Field
public import Mathlib.RingTheory.PrincipalIdealDomain
public import Mathlib.Algebra.Polynomial.Module.AEval
/-!... |
130 | lean_file_chunk | 99a28915cc60eb301345f337560eafc2e72a5a5694fb2bc4568bc26ababaf7f5 | lean_source_file | pkg_mathlib_source_file_chunks | module -- shake: keep-all
public import Mathlib.LinearAlgebra.GeneralLinearGroup.Basic
deprecated_module (since := "2025-12-08") |
23,965 | lean_file_chunk | 9f5d1a0840d867370725a90ee22a31787f6d49d1d8276a9594c403ad9b7a9188 | 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, Mario Carneiro
-/
module
public import Mathlib.Algebra.Module.Submodule.Equiv
public import Mathlib.Algebra.Module.Torsion.Free
/-!
# Basics on bilinear maps
This file provide... |
945 | lean_file_chunk | b7629e05399a23f27bdcf64955688b3bf88799c66104f7aeb7e1ee88a1b34c3d | lean_source_file | pkg_mathlib_source_file_chunks | {G : Type*} [AddCommMonoid G] [Module R G]
-- TODO Also make a semi-linear version.
/-- Bundled statement of bilinearity for a function.
The bundled type `E →ₗ[R] F →ₗ[R] G` should be preferred in cases where that can be used.
`IsBilinearMap` can be useful to have `IsBilinearMap (myFunction ..)` as a hypothesis to a
... |
1,546 | lean_file_chunk | 9f6e11a4cde8cac4fa9f7681e1b0021cde30666e80b4a813bfae3b1d57ff412c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash, Deepro Choudhury
-/
module
public import Mathlib.GroupTheory.OrderOfElement
public import Mathlib.LinearAlgebra.Span.Defs
public import Mathlib.Algebra.Module.Equiv.Basic
/... |
5,872 | lean_file_chunk | eafac3776871cbe288be33f1edd22fcc0d0ad8b57222bee2cfeb66cc6a48a20c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Matej Penciak. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matej Penciak, Moritz Doll, Fabien Clery
-/
module
public import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
/-!
# The Symplectic Group
This file defines the symplectic group and... |
23,931 | lean_file_chunk | 9bd6378a45bcd8bda466835bf16a0f7bfef45f9982e57d1f9157a4041e35ca82 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov, Eric Wieser
-/
module
public import Mathlib.Algebra.Algebra.Prod
public import Mathlib.Algebra.Group.Graph
public impor... |
9,513 | lean_file_chunk | 88415766838e1a92493f50d60527e809b00382bdccee58fdf42e3f5b43c29061 | lean_source_file | pkg_mathlib_source_file_chunks | /-- Four-way commutativity of `prod`. The name matches `mul_mul_mul_comm`. -/
@[simps apply]
def prodProdProdComm : ((M × M₂) × M₃ × M₄) ≃ₗ[R] (M × M₃) × M₂ × M₄ :=
{ AddEquiv.prodProdProdComm M M₂ M₃ M₄ with
toFun := fun mnmn => ((mnmn.1.1, mnmn.2.1), (mnmn.1.2, mnmn.2.2))
invFun := fun mmnn => ((mmnn.1.1, m... |
5,255 | lean_file_chunk | e06560ec4e8c64fd894b32148d790b6c88f2e9e585b7bd37d172ce911356e495 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
module
public import Mathlib.GroupTheory.GroupAction.FixingSubgroup
public import Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup
public... |
1,997 | lean_file_chunk | b9940df8f3e3ab717e9de8494fbddf73bdcd54be8767a01692c71b3b9e0fe33e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 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.Trace
public import Mathlib.LinearAlgebra.FreeModule.PID
public import Mathlib.LinearAlgebra.FreeModule.Finite.Basic
/-!
# Line... |
23,974 | lean_file_chunk | a6afd14ad439822d9ae2638db268107847ef0d0165932cf3fa7394b0e7cee275 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov, Eric Wieser
-/
module
public import Mathlib.Algebra.Group.Fin.Tuple
public import Mathlib.Algebra.BigOperators.GroupWit... |
6,041 | lean_file_chunk | 0517c21cc811de54199a45c602e2d40e56774a3f381e132a7c71c0bb42a021c3 | lean_source_file | pkg_mathlib_source_file_chunks | { Function.ExtendByZero.hom R s with
toFun := fun f => Function.extend s f 0
map_smul' := fun r f => by simpa using Function.extend_smul r s f 0 }
end Extend
variable (R) in
/-- `Fin.consEquiv` as a continuous linear equivalence. -/
@[simps]
def Fin.consLinearEquiv
{n : ℕ} (M : Fin n.succ → Type*) [Semiri... |
9,895 | lean_file_chunk | 496aad156598050aed606f8f3a39bfbfa833f09d93f9d5bd99f075b7a51bdcd5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
module
public import Mathlib.LinearAlgebra.Transvection.Basic
/-!
# Center of the algebra of linear endomorphisms
If `V` is an `R`-module, we say th... |
16,372 | lean_file_chunk | 216ee7a3910485eb84dfec1553b2d3b73596809ce0dc002bf746215b138eb793 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 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.Ray
public import Mathlib.LinearAlgebra.Determinant
/-!
# Orientations of modules
This file defines orientations of modules.... |
8,537 | lean_file_chunk | debef8507a98c8e4ff45bd887375462e27c18011a67f0e35b834dae8560b704a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov
-/
module
public import Mathlib.LinearAlgebra.Quotient.Basic
public import Mathlib.LinearAlgebra.Quotient.Card
/-!
# Is... |
4,909 | lean_file_chunk | fd424860af38a3831114d3cffaad0ccebf594f34a23d6aab67b1588feb303ecd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
module
public import Mathlib.Dynamics.Newton
public import Mathlib.LinearAlgebra.Semisimple
public import Mathlib.LinearAlgebra.FreeModule.Finite.Matrix
/-!
# Jordan-Chev... |
11,829 | lean_file_chunk | ae4da48aa9e94fef36f583e117800ce7ee3b34ea2d880876e1fab80aa37e8984 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash, Antoine Labelle
-/
module
public import Mathlib.LinearAlgebra.Dual.Lemmas
public import Mathlib.LinearAlgebra.Matrix.ToLin
/-!
# Contractions
Given modules $M, N$ over a c... |
16,862 | lean_file_chunk | 7617f3d5a7f0b05b95b4e25d0e6e05f4d9774668fbad9a15648d4f339e98e39b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen, Antoine Labelle
-/
module
public import Mathlib.LinearAlgebra.Contraction
public import Mathlib.LinearAlgebra.Matrix.Charpoly... |
118 | lean_file_chunk | 56dfa93436dd9e4e820ccd1dc24d7d17281881a5c0ef445fecf147cace20112b | lean_source_file | pkg_mathlib_source_file_chunks | module -- shake: keep-all
public import Mathlib.LinearAlgebra.SModEq.Basic
deprecated_module (since := "2025-10-28") |
105 | lean_file_chunk | 689be18d1a4a2e02afa01bd30a20f726c1622470443895c65e78a27655107a6a | lean_source_file | pkg_mathlib_source_file_chunks | module
public import Mathlib.LinearAlgebra.Transvection.Basic
deprecated_module (since := "2026-03-27") |
23,997 | lean_file_chunk | e7c98e5c584c202c1529071615921a7d526634adc7f8fb10927acba9a045b7bd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Wrenna Robson
-/
module
public import Mathlib.Algebra.BigOperators.Group.Finset.Pi
public import Mathlib.Algebra.Polynomial.FieldDivision
public import Mathlib.LinearAlgebra.Van... |
5,887 | lean_file_chunk | 2c73843c95587c8e05031fc31f73f21a22c480d36ffd415e50ed5176ea7fd1bf | lean_source_file | pkg_mathlib_source_file_chunks | simp_rw [nodal, Finset.mul_prod_erase _ (fun x => X - C (v x)) hi]
theorem X_sub_C_dvd_nodal (v : ι → R) {i : ι} (hi : i ∈ s) : X - C (v i) ∣ nodal s v := by
classical
exact ⟨nodal (s.erase i) v, nodal_eq_mul_nodal_erase hi⟩
theorem nodal_insert_eq_nodal [DecidableEq ι] {i : ι} (hi : i ∉ s) :
nodal (insert i ... |
15,305 | lean_file_chunk | 2a53792972816ba81baf5ef963292b3f1aa85fcae652d16ee32f0d4c7f91a95c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Peter Nelson
-/
module
public import Mathlib.Data.Nat.Factorial.BigOperators
public import Mathlib.Data.Nat.Factorial.SuperFactorial
public import Mathlib.LinearAlgebra.Matr... |
7,731 | lean_file_chunk | f01e6e5d2c3fac2b491bfd4dccea87c5e735f755a6d1e60b04c58fbfaab37ede | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
module
public import Mathlib.Algebra.Algebra.Pi
public import Mathlib.LinearAlgebra.Finsupp.VectorSpace
public import Mathlib.LinearAlgebra.FreeModule.Basic
public i... |
13,928 | lean_file_chunk | a4090d888fc259617414ea5255fdde41a4758c7cd7594b2d6c89849ef4525212 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Kim Morrison
-/
module
public import Mathlib.RingTheory.Ideal.Quotient.Basic
public import Mathlib.RingTheory.Noetherian.Orzech
public import Mathlib.RingTheory.OrzechPr... |
23,923 | lean_file_chunk | f44df1c056014302a3032c61955433c16dba22363c1bdbf7f224f4e4c8f86438 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jz Pan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jz Pan
-/
module
public import Mathlib.LinearAlgebra.TensorProduct.Tower
public import Mathlib.LinearAlgebra.TensorProduct.Finiteness
public import Mathlib.LinearAlgebra.TensorProduct.Submodu... |
5,959 | lean_file_chunk | 5983927ad6ad89f3be20c6ba1bbc8566085f3ee88d8cfc22296e7a22f06d168d | lean_source_file | pkg_mathlib_source_file_chunks | /-- If `M` and `N` are linearly disjoint, if `N` is flat, then any two commutative
elements of `↥(M ⊓ N)` are not `R`-linearly independent (namely, their span is not `R ^ 2`). -/
theorem not_linearIndependent_pair_of_commute_of_flat_right [Module.Flat R N]
(a b : ↥(M ⊓ N)) (hc : Commute a.1 b.1) : ¬LinearIndependen... |
22,510 | lean_file_chunk | 4e58df774a69b8f0f36a201bfbd0bfe092b801fe0fdb7e3caed74ce3c436c3e5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
module
public import Mathlib.LinearAlgebra.Determinant
public import Mathlib.LinearAlgebra.Dual.Basis
public import Mathlib.LinearAlgebra.Matrix.Dual
p... |
13,022 | lean_file_chunk | 44adcd73ebbde3ec9a2b0c8b0f965f4c7afb3aa7191ca9fc780db93061d4d7ae | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Shing Tak Lam. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shing Tak Lam
-/
module
public import Mathlib.Algebra.Star.Unitary
public import Mathlib.Data.Matrix.Reflection
public import Mathlib.LinearAlgebra.GeneralLinearGroup.Basic
public impo... |
23,976 | lean_file_chunk | a11c5b7035f72e93be8dbcf043d7904b6e381800dc8cd4d9b9aea79d1f274e3a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Moritz Doll
-/
module
public import Mathlib.Algebra.Field.Basic
public import Mathlib.Algebra.Module.Torsion.Field
public import Mathlib.LinearAlgebra.Prod
/-!
# Pa... |
15,151 | lean_file_chunk | 10276e36cbcc397c0fa0bb1fef860eb13a75e04e46bd8ec084dc85c6bd2fc111 | lean_source_file | pkg_mathlib_source_file_chunks | (DirectedOn.mono_comp LinearPMap.domain_mono.monotone hc)]
simp
protected theorem le_sSup {c : Set (E →ₛₗ.[σ] F)} (hc : DirectedOn (· ≤ ·) c) {f : E →ₛₗ.[σ] F}
(hf : f ∈ c) : f ≤ LinearPMap.sSup c hc :=
Classical.choose_spec (sSup_aux c hc) hf
protected theorem sSup_le {c : Set (E →ₛₗ.[σ] F)} (hc : DirectedOn... |
23,999 | lean_file_chunk | 6352b7800d36322e4098a8d5d484d1262aaf57ee7da052e51053871e16695315 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 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.Quotient.Basic
public import Mathlib.LinearAlgebra.Prod
public import Mathlib.Algebra.Module.Submodule.Invariant
public ... |
5,133 | lean_file_chunk | e283a1f180ae2b374b4188c75e6d7a928b421264c384ca950c76c35124fb7373 | lean_source_file | pkg_mathlib_source_file_chunks | fun ⟨hT, h⟩ => h.symm ▸ hT.projection_isIdempotentElem⟩
open LinearMap in
/-- Given an idempotent linear operator `q`,
we have `q ∘ p = p` iff `range p ⊆ range q` for all `p`. -/
theorem IsIdempotentElem.comp_eq_right_iff {q : M →ₗ[S] M} (hq : IsIdempotentElem q)
{E : Type*} [AddCommMonoid E] [Module S E] (p : E →... |
6,294 | lean_file_chunk | e8d134d5c086097a8ac525e61508b92c67d00382e88e5eee9b7c2fc787d76508 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.GroupTheory.Goursat
public import Mathlib.LinearAlgebra.Prod
public import Mathlib.LinearAlgebra.Quotient.Basic
/-!
# Goursat's lemma f... |
23,944 | lean_file_chunk | 6b5c97c6b8022fefaf680d667fe12d4d659eaaefff38efba33d9cd442663f2d7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-/
module
public import Mathlib.LinearAlgebra.Dual.Basis
public import Mathlib.LinearAlgebra.FreeModule.StrongRankCondition
pu... |
10,515 | lean_file_chunk | c70a1cfcb46023e038d563c7f83587a8ff9889b6ff7a5ac7fa99cdcf2180b9b9 | lean_source_file | pkg_mathlib_source_file_chunks | suffices Associated (LinearMap.det (f' ∘ₗ ↑e)) (LinearMap.det f') by
convert this using 2
ext x
exact h x
rw [← mul_one (LinearMap.det f'), LinearMap.det_comp]
exact Associated.mul_left _ (associated_one_iff_isUnit.mpr e.isUnit_det')
theorem LinearMap.associated_det_comp_equiv {N : Type*} [AddCommGroup... |
15,711 | lean_file_chunk | a0e2d9b6b9a6a434099b4e60d9e5e90a6af7dd3c021d62bb06393fddf53d062d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.Module.Torsion.Basic
public import Mathlib.FieldTheory.Perfect
public import Mathlib.LinearAlgebra.AnnihilatingPolynomial
public impor... |
23,981 | lean_file_chunk | 34a7909c1120a33771f1aa3f7b3b0296969367068d895f893ee667074af8d881 | 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: Johannes Hölzl, Kenny Lau
-/
module
public import Mathlib.Data.DFinsupp.Submonoid
public import Mathlib.Data.DFinsupp.Sigma
public import Mathlib.Data.Finsupp.ToDFinsupp
public import Math... |
4,120 | lean_file_chunk | 43bc8ef7f63a8c91b508ba11c5ded41a1decd0e278e275a944b34959880534af | lean_source_file | pkg_mathlib_source_file_chunks | · intro h s v hv hv0
specialize h s v 0
simp_all
/-- A family of additive subgroups over an additive group are independent if and only if
`DFinsupp.sumAddHom` applied with `AddSubgroup.subtype` is injective. -/
theorem iSupIndep_iff_dfinsuppSumAddHom_injective (p : ι → AddSubgroup N) :
iSupIndep p ↔ Functi... |
3,828 | lean_file_chunk | 218374669535fab3b820a02631f422da6f47fc263738438f26ebe1a92367cd9b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer
-/
module
public import Mathlib.LinearAlgebra.Contraction
/-!
# The coevaluation map on finite-dimensional vector spaces
Given a finite-dimensional vector space `... |
1,465 | lean_file_chunk | 8a2238c55a532f96af46b118eb3f385461612f9a0bbb5464106a90aed0e954b7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
module
public import Mathlib.Data.Finsupp.Encodable
public import Mathlib.Data.Set.Countable
public import Mathlib.LinearAlgebra.Finsupp.LinearCombination
public imp... |
2,138 | lean_file_chunk | 28d3494dc6b88ee51b4ed2ed7905a92a2af02ebdee12419a5db50e010d52a7f3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.Algebra.FreeAlgebra
public import Mathlib.LinearAlgebra.Basis.Cardinality
public import Mathlib.LinearAlgebra.Dimension.StrongRankCondition
pu... |
13,754 | lean_file_chunk | 8e02e5692695c791aa9c3158d84583c817b367ddb2e2000490e5a984f4fe7fda | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Wrenna Robson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wrenna Robson
-/
module
public import Mathlib.Analysis.Normed.Group.Basic
/-!
# Hamming spaces
The Hamming metric counts the number of places two members of a (finite) Pi type
differ... |
15,494 | lean_file_chunk | 668c5d9f4becd9bdd9815a475a512e69731b5bea5234886e5b49394010d39b0e | 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
-/
module
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order.Monoid.NatCast
public import Mathlib.Algebra.Ring.Nat
public import Mathlib.... |
7,605 | lean_file_chunk | f5e259cfd08dd02e7a27431c0989a37d151890de1e60f9a009b36465988f0b00 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
module
public import Mathlib.Logic.Function.Basic
public import Mathlib.Tactic.AdaptationNote
public import Mathlib.Tactic.Simps.Basic
/-!
# Subtypes
This file pro... |
2,816 | lean_file_chunk | 2abb458909166275dbac0513a9b3b9a09124e890e4651dd2c1bbca936e643302 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
-/
module
public import Mathlib.Lean.Expr.Basic
/-!
# `Ineq` datatype
This file contains an enum `Ineq` (whose constructors are `eq`, `le`, `lt`), and operations
in... |
23,968 | lean_file_chunk | 9b7ea8cb6f6f7d3a26e0df7b8df794a5aac9f15bfd91a90f0fc07d500fdc430d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
module
public import Mathlib.Logic.Relation
public import Mathlib.Logic.Unique
public import Mathlib.Util.Notation3
/-!
# Quotient types
This module extends the co... |
6,169 | lean_file_chunk | 81a34505bb8a9ad220c5211c65b5a068f8dd7439857f04de007a92d413412714 | lean_source_file | pkg_mathlib_source_file_chunks | instead of instance arguments. -/
@[elab_as_elim]
protected theorem ind₂' {p : Quotient s₁ → Quotient s₂ → Prop}
(h : ∀ a₁ a₂, p (Quotient.mk'' a₁) (Quotient.mk'' a₂))
(q₁ : Quotient s₁) (q₂ : Quotient s₂) : p q₁ q₂ :=
Quotient.ind₂ h q₁ q₂
/-- A version of `Quotient.inductionOn` taking `{s : Setoid α}` as a... |
23,955 | lean_file_chunk | e3b5ddd8e72c5bfd1bfe0feba0fdce3eb255b17efca5e9a20765dc2922ecf4f9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Jeremy Avigad, Simon Hudon
-/
module
public import Mathlib.Algebra.Notation.Defs
public import Mathlib.Data.Set.Subsingleton
public import Mathlib.Logic.Equiv.Defs
/-... |
2,137 | lean_file_chunk | af68fb1bf770171619bae52a9be4c94a6a131a225aac3194cd8af673d324cb0b | lean_source_file | pkg_mathlib_source_file_chunks | a.get (left_dom_of_append_dom hab) ++ b.get (right_dom_of_append_dom hab) := by
simp [append_def]; aesop
theorem some_append_some [Append α] (a b : α) : some a ++ some b = some (a ++ b) := by
simp [append_def]
theorem inter_mem_inter [Inter α] (a b : Part α) (ma mb : α) (ha : ma ∈ a) (hb : mb ∈ b) :
ma ∩ mb ∈... |
3,323 | lean_file_chunk | 3c2e83a29a66c8999f9fd3c8358d0d42e49b68dac85c42e398170f276dae8a80 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Reid Barton, Simon Hudon, Kenny Lau
-/
module
public import Mathlib.Logic.Equiv.Defs
public import Mathlib.Logic.Small.Defs
/-!
# Opposites
In this file we define a stru... |
23,332 | lean_file_chunk | cd7bbb775b33b1fa9570366dc9339c516a8a9ebc5e68b1c83ea771c2e217f48a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
module
public import Mathlib.Data.Set.Prod
public import Mathlib.Order.RelIso.Basic
public import Mathlib.Order.SetNotation
/-!
# Relations as sets of pairs
This fil... |
4,007 | lean_file_chunk | 4f3a8cd0bfd570406ca2b5162883cf166e8335ddc72e81bcffd85f2bb3986f76 | 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
-/
module
public import Mathlib.Logic.Equiv.Defs
/-!
# A type for VM-erased data
This file defines a type `Erased α` which is classically isomorphic to `α`,
but erase... |
22,099 | lean_file_chunk | d7a754e97d66fe9275cdc3989af3b6462cd5b05692d1bf51659674855d3c321c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Jeremy Avigad, Simon Hudon
-/
module
public import Batteries.Tactic.GeneralizeProofs
public import Mathlib.Data.Part
public import Mathlib.Data.Rel
/-!
# Partial func... |
3,532 | lean_file_chunk | d1e95d3c4c40add34b2a3097cc067eab50a19cb49490170374ba8224eabac29b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Logic.Nontrivial.Defs
public import Mathlib.Logic.Nonempty
public import Mathlib.Tactic.Simps.Basic
public import Batteries.Logic
/-!
# Two... |
3,168 | lean_file_chunk | db69904c6c38e58750bc74cdb63d68a4b1a0ebab0512dda733aeb93120d70bc6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Harun Khan, Alex Keizer
-/
module
public import Mathlib.Algebra.Ring.InjSurj
public import Mathlib.Algebra.Ring.Equiv
public import Mathlib.Data.ZMod.Defs
public import Math... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.