chars int64 40 24k | content_type stringclasses 9
values | id stringlengths 13 64 | source stringclasses 5
values | subset stringclasses 31
values | text stringlengths 40 24k |
|---|---|---|---|---|---|
10,674 | lean_file_chunk | 21dce3adb296d2545b9d6efc3641aacfdeac4cc54ce2eb39de50d4435f736860 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash, Jonathan Reich
-/
module
public import Mathlib.Data.Fin.Basic
public import Mathlib.LinearAlgebra.Matrix.Notation
public import Mathlib.GroupTheory.Perm.Cycle.Concrete
publi... |
7,770 | lean_file_chunk | 16d786d788f349abee862f85b8f262d52f26c5dd3682c5d46f4ef27a6fd5d56b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 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.Fin.Tuple.Reflection
public import Mathlib.LinearAlgebra.Matrix.Notation
/-!
# Lemmas for concrete matrices `Matrix (Fin m) (Fin n) α`
... |
6,665 | lean_file_chunk | 51164c76bb68d6f117b3d25a63e0f4f05ebb1ee6c628f6f9e8ca7706060541ff | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yunzhou Xie. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Yunzhou Xie, Eric Wieser
-/
module
public import Mathlib.Data.Matrix.Basic
public import Mathlib.Data.Matrix.Basis
/-!
# Composition of matrices
This file shows that `Mₙ... |
10,022 | lean_file_chunk | acff4911a9d7c8348e6a56d275959a16e8148b023a455ebcd9576eb39a0f80c6 | 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, Ahmad Alkhalawi
-/
module
public import Mathlib.LinearAlgebra.Matrix.ConjTranspose
public import Mathlib.Tactic.Abel
/-! # Extra lemmas about invertible matrices
A few of ... |
23,992 | lean_file_chunk | 13d9ffb5e7f717e5defe49262b9dc4c72caf412a9cc5cb8174a1bbfd43992d93 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Ellen Arlt. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ellen Arlt, Blair Shi, Sean Leather, Mario Carneiro, Johan Commelin, Lu-Ming Zhang
-/
module
public import Mathlib.Algebra.BigOperators.GroupWithZero.Action
public import Mathlib.Algebra.... |
20,136 | lean_file_chunk | d8748cad79f1c4dd983a7f6e3ef66a265b2c44da2796ad20d2d5b2db17094dbf | lean_source_file | pkg_mathlib_source_file_chunks | where `v` is seen as a column vector.
The notation has precedence 73, which comes immediately before ` ⬝ᵥ ` for `dotProduct`,
so that `A *ᵥ v ⬝ᵥ B *ᵥ w` is parsed as `(A *ᵥ v) ⬝ᵥ (B *ᵥ w)`.
-/
def mulVec [Fintype n] (M : Matrix m n α) (v : n → α) : m → α
| i => (fun j => M i j) ⬝ᵥ v
@[inherit_doc]
scoped infixr:73 ... |
23,981 | lean_file_chunk | 449c49d177b221ee419297aec9ea369d2565996dcf6afe559fa9c9d9b20805f3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Ellen Arlt. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ellen Arlt, Blair Shi, Sean Leather, Mario Carneiro, Johan Commelin, Lu-Ming Zhang
-/
module
public import Mathlib.Algebra.Algebra.Opposite
public import Mathlib.Algebra.Algebra.Pi
public... |
6,257 | lean_file_chunk | d45420fc12cb1a8dcd0a0a0607d00b0cdaa60d45d090ec6bee898f7cd9b1f84b | lean_source_file | pkg_mathlib_source_file_chunks | variable {R : Type*} [NonAssocSemiring R]
variable [Fintype n] [DecidableEq n]
/-- A version of `Set.matrix` for `Subsemiring`s.
Given a `Subsemiring` `S`, `S.matrix` is the `Subsemiring` of square matrices `m`
all of whose entries `m i j` belong to `S`. -/
@[simps!]
def matrix (S : Subsemiring R) : Subsemiring (Matri... |
5,572 | lean_file_chunk | 0089ad08a4ef7b8b3da1b95e5afd30b6fcd1ccd6638a3077399eb1837932caae | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 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.Group.Hom.Defs
public import Mathlib.Algebra.Group.Pi.Basic
/-!
# Dependent-typed matrices
-/
@[expose] public section
universe ... |
23,996 | lean_file_chunk | 092f087943afea6d2350ce49b6f081efecfb961130b690d18a1dc591fe9e5ba3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Ellen Arlt. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ellen Arlt, Blair Shi, Sean Leather, Mario Carneiro, Johan Commelin
-/
module
public import Mathlib.Data.Matrix.Basic
public import Mathlib.Data.Matrix.Composition
public import Mathlib.L... |
6,973 | lean_file_chunk | 76d1b4b0daced3d02e99efbd041ed82c7faf5cf980006bff3cefdb104e7873eb | lean_source_file | pkg_mathlib_source_file_chunks | @[simps]
def blockDiagonal'AddMonoidHom [AddZeroClass α] :
(∀ i, Matrix (m' i) (n' i) α) →+ Matrix (Σ i, m' i) (Σ i, n' i) α where
toFun := blockDiagonal'
map_zero' := blockDiagonal'_zero
map_add' := blockDiagonal'_add
end
@[simp]
theorem blockDiagonal'_neg [AddGroup α] (M : ∀ i, Matrix (m' i) (n' i) α) :
... |
2,266 | lean_file_chunk | 6b87635040840e75ca10ca57fe739c3cd2dc683a024fdb438793ca1f77128b44 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 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.Matrix.Mul
public import Mathlib.Algebra.Ring.Opposite
/-!
# Actions by matrices on vectors through `*ᵥ` and `ᵥ*`, cast as `Module`s
Th... |
15,114 | lean_file_chunk | 83786d28746c833d55e34d2d91378569bbaff857848c117cfbb00dabe9b649d9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Jalex Stark. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jalex Stark, Kim Morrison, Eric Wieser, Oliver Nash, Wen Yang
-/
module
public import Mathlib.Data.Matrix.Basic
/-!
# Matrices with a single non-zero element.
This file provides `Matri... |
7,365 | lean_file_chunk | 3dd42903862ec274da81a3fbd5f53ad014b14c90e811b84b5b1ca860c2f18ddc | 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.Data.Matrix.Mul
public import Mathlib.Data.PEquiv
/-!
# partial equivalences for matrices
Using partial equivalences to represent matrices... |
1,444 | lean_file_chunk | b3af4e8416734bf49b5866d80e1ec983b46af8058d95234801701e53ee57ebeb | 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.Algebra.DualNumber
public import Mathlib.Data.Matrix.Basic
/-!
# Matrices of dual numbers are isomorphic to dual numbers over matrices
Showi... |
7,015 | lean_file_chunk | f6b69877be42bb58a18df1c2b91683d74dc635a8871042a6110c432c5a3343f5 | 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, Minchao Wu
-/
module
public import Mathlib.Data.Sigma.Lex
public import Mathlib.Util.Notation3
public import Init.NotationExtra
public import Mathlib.Data.Sigma.Basic
publ... |
5,189 | lean_file_chunk | af32de4be611d405fc593bd7dfc3f6f6cd376471aa1bed899487baee93dd31fb | 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.Data.Countable.Defs
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Data.ENat.Defs
public import Mathlib.Logic.Equiv.... |
5,738 | lean_file_chunk | 5cb6c68b60ee0467817a9f08753a7f482a8f1fdef9c03d7a3d2fd534a47c9464 | 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.Data.Finite.Defs
public import Mathlib.Data.Bool.Basic
public import Mathlib.Data.Subtype
public import Mathlib.Tactic.MkIffOfInductiv... |
706 | lean_file_chunk | da49d22560efd0b01aca80a3f6de1011926a0bc4fa5d9a666f59e962d639cc47 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Logic.Small.Basic
public import Mathlib.Data.Countable.Defs
/-!
# All countable types are small.
That is, any countable type is equivalent... |
23,973 | lean_file_chunk | c77e90af256d78a636c649e4236e2cd08b63b73724438a97ce4e623a85fec919 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard
-/
module
public import Mathlib.Data.ENNReal.Operations
/-!
# The extended real numbers
This file defines `EReal`, `ℝ` with a top element `⊤` and a bottom element `⊥`, ... |
5,824 | lean_file_chunk | 9bdfd0e2c41eafc10695160d11bbc6bb3e718eb506791eeb45d151593e7740af | lean_source_file | pkg_mathlib_source_file_chunks | lemma toENNReal_eq_toENNReal {x y : EReal} (hx : 0 ≤ x) (hy : 0 ≤ y) :
x.toENNReal = y.toENNReal ↔ x = y := by
induction x <;> induction y <;> simp_all
lemma toENNReal_le_toENNReal {x y : EReal} (h : x ≤ y) : x.toENNReal ≤ y.toENNReal := by
induction x
· simp
· by_cases hy_top : y = ⊤
· simp [hy_top]
... |
23,970 | lean_file_chunk | 484ae7361a4613d4c4f90e81d04aabcb3b8bfb0ed04484d2565d2b5b03cd9975 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard
-/
module
public import Mathlib.Data.EReal.Basic
public import Batteries.Util.ProofWanted
/-!
# Addition, negation, subtraction and multiplication on extended real numbe... |
9,882 | lean_file_chunk | cf716e6189fdb4c538c0ab08639089bc755b996a83ee68d5c3ddfb57c445caf2 | lean_source_file | pkg_mathlib_source_file_chunks | | coe_coe x y => simp [← coe_mul, _root_.mul_pos_iff]
| zero_bot => simp
| neg_bot _ hx => simp [hx, EReal.coe_mul_bot_of_neg hx]
| bot_bot => simp
lemma mul_nonneg_iff {a b : EReal} : 0 ≤ a * b ↔ 0 ≤ a ∧ 0 ≤ b ∨ a ≤ 0 ∧ b ≤ 0 := by
simp_rw [le_iff_lt_or_eq, mul_pos_iff, zero_eq_mul (a := a)]
rcases lt_trich... |
22,420 | lean_file_chunk | a6c6839e45d3adadac1267cedf3a1abbb565e44ee7c48a14e27fa83eb378a20b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard
-/
module
public import Mathlib.Data.ENNReal.Inv
public import Mathlib.Data.EReal.Operations
public import Mathlib.Data.Sign.Basic
public import Mathlib.Data.Nat.Cast.Ord... |
6,723 | lean_file_chunk | bcee90a91abe25f0eb71dd2c2f98ac1a637891102aac9b1a02c9134af8ac4421 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 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.Finset.Lattice.Fold
public import Mathlib.Logic.Encodable.Pi
/-!
# W types
Given `α : Type` and `β : α → Type`, the W type determin... |
4,956 | lean_file_chunk | fb6c401c7acc019dde75705cb70a6362880119845aa4a316a47e5539b8cb4bed | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2015 Joseph Hua. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Hua
-/
module
public import Mathlib.Data.W.Basic
/-!
# Examples of W-types
We take the view of W types as inductive types.
Given `α : Type` and `β : α → Type`, the W type determi... |
3,660 | lean_file_chunk | 1a4ef74786a94c3410ccb85b19970ff8023c2582a4c05cd65d4bb091749554e8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
module
public import Mathlib.Data.W.Basic
public import Mathlib.SetTheory.Cardinal.Arithmetic
/-!
# Cardinality of W-types
This file proves some theorems about the car... |
468 | lean_file_chunk | 1b1618f42acf2289e9c608c57fca9ccb33f491210dad8855172f580bae494919 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Jannis Limperg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jannis Limperg
-/
module
public import Mathlib.Init
public import Aesop
/-!
# Sym2 Rule Set
This module defines the `Sym2` Aesop rule set. Aesop rule sets only become
visible once t... |
1,849 | lean_file_chunk | 879b26ee986bc3279129c692f13ff6db107d14fb5558409940b3d5b0540751f4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.Sym.Sym2
public import Mathlib.Order.Lattice
/-!
# Sorting the elements of `Sym2`
This file provides `Sym2.sortEquiv`, the forward dire... |
1,449 | lean_file_chunk | 0d999b691fcb18930fdb3f0a0b885bf1990ec697ccfb7062abb6fd4486b97955 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin
-/
module
public import Mathlib.Algebra.GroupWithZero.Basic
public import Mathlib.Data.Finset.Sym
public import Mathlib.Data.Finsupp.Defs
/-!
# Finitely suppor... |
9,061 | lean_file_chunk | 73b863355b8fb227013d30659c23c2e0bc4540f8f17753d3f8882a811c60fb23 | 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, Simon Hudon
-/
module
public import Mathlib.Data.PFunctor.Multivariate.Basic
/-!
# Multivariate quotients of polynomial functors.
Basic definition of multivariate QPF.... |
19,863 | lean_file_chunk | d3682922cd09818086472ede177efff23b3f98e63bed247bfeaec869bee51c67 | 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.PFunctor.Univariate.M
/-!
# Quotients of Polynomial Functors
We assume the following:
* `P`: a polynomial functor
* `W`: its W-ty... |
2,327 | lean_file_chunk | bd57fc897cbe752692d00c3ae4a326e016922bdef46915389af2924270562ae2 | 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, Simon Hudon
-/
module
public import Mathlib.Data.QPF.Multivariate.Basic
/-!
# The quotient of QPF is itself a QPF
The quotients are here defined using a surjective fun... |
2,639 | lean_file_chunk | e389500ce194b35a35898323ff442a74404b71ec819e1c067d0c9f6ec522e71c | 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, Simon Hudon
-/
module
public import Mathlib.Data.PFunctor.Multivariate.Basic
public import Mathlib.Data.QPF.Multivariate.Basic
/-!
# The composition of QPFs is itself a... |
2,944 | lean_file_chunk | 3e976e5c39c0b4be6066a28cc862172d74665757bfe8f3e6b83f9feb7cbc4623 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
module
public import Mathlib.Data.PFunctor.Multivariate.Basic
public import Mathlib.Data.QPF.Multivariate.Basic
/-!
# Dependent product and sum of QPFs are QPFs
-/
@[exp... |
1,881 | lean_file_chunk | 57f63da17f8d0e1817203a0b3f1ab9067a2d31683356aabe27c4a87cc7589aa8 | 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
-/
module
public import Mathlib.Control.Functor.Multivariate
public import Mathlib.Data.QPF.Multivariate.Basic
/-!
# Constant functors are QPFs
Constant functors map every ... |
1,488 | lean_file_chunk | 81ee606fd814ced8024340750edbcefaaef926b5ef62e854e44218a842f5b488 | 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
-/
module
public import Mathlib.Control.Functor.Multivariate
public import Mathlib.Data.QPF.Multivariate.Basic
/-!
Projection functors are QPFs. The `n`-ary projection funct... |
19,906 | lean_file_chunk | 97200c396935a63ea29f51668f83a0ce55dadffaf396e98f6bffa6cef77062e6 | 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, Simon Hudon
-/
module
public import Mathlib.Control.Functor.Multivariate
public import Mathlib.Data.PFunctor.Multivariate.Basic
public import Mathlib.Data.PFunctor.Multi... |
11,671 | lean_file_chunk | 57c44ce0153a2c6d8c34be93c5c68570b87a7693a1488a390afe65491c4c62eb | 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, Simon Hudon
-/
module
public import Mathlib.Data.PFunctor.Multivariate.W
public import Mathlib.Data.QPF.Multivariate.Basic
/-!
# The initial algebra of a multivariate q... |
2,398 | lean_file_chunk | 4b374c736e591f170f89cfbff61cb1b8b92a55af80fb43c4cd5b3910efc27ac5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.Data.Fin.Tuple.Sort
public import Mathlib.Order.WellFounded
public import Mathlib.Order.PiLex
public import Mathlib.Data.Finite.Prod
/-!
... |
5,096 | lean_file_chunk | 6510a3a561f52dbf263f93ec229c67265daebb481a9182668fcee34a42a37b5e | 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, Brendan Murphy
-/
module
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Logic.Equiv.Fin.Basic
public import Mathlib.Logic.Function.OfArity
/-!
# Currying ... |
8,152 | lean_file_chunk | dab9a971f316e0dc0896e4774c95e418a2c8e625b526db144ccc9c2ed7eeb9ba | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 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.Fin.VecNotation
public import Mathlib.Algebra.BigOperators.Fin
/-!
# Lemmas for tuples `Fin m → α`
This file contains alternative defin... |
6,341 | lean_file_chunk | ef23e419b7302b998646c5ee83905ccc709af72b9c2e79a02a7bfe1b4fd5634b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
module
public import Mathlib.Data.Fin.Tuple.Basic
/-!
# Take operations on tuples
We define the `take` operation on `n`-tuples, which restricts a tuple to its first `m` elem... |
4,623 | lean_file_chunk | b9fd6028f1984d5d8266929d33da76bb33ccb507141eb9ad328b76fc7beb2923 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Bolton Bailey. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bolton Bailey
-/
module
public import Mathlib.Data.Finset.Prod
public import Mathlib.Data.Fintype.Pi
/-!
# Fin-indexed tuples of finsets
-/
public section
open Fin Fintype
namespac... |
23,967 | lean_file_chunk | 7dc5600115c5aa3c5cd9132819e3e64e2bc407a17dd07c4e276c75052c9eb0e3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Yury Kudryashov, Sébastien Gouëzel, Chris Hughes, Antoine Chambert-Loir
-/
module
public import Mathlib.Data.Fin.Rev
public import Mathlib.Data.Nat.Find
public imp... |
23,980 | lean_file_chunk | ff8eb6aba5442385a00b5fd6a92cb3e560e1f34ef5a8e1ef86df6e24b7553403 | lean_source_file | pkg_mathlib_source_file_chunks | theorem comp_snoc {α : Sort*} {β : Sort*} (g : α → β) (q : Fin n → α) (y : α) :
g ∘ snoc q y = snoc (g ∘ q) (g y) := by
ext j
by_cases h : j.val < n
· simp [h, snoc, castSucc_castLT]
· rw [eq_last_of_not_lt h]
simp
/-- Appending a one-tuple to the right is the same as `Fin.snoc`. -/
theorem append_righ... |
5,132 | lean_file_chunk | 30a4de7bc8a68903136cc4eaeed9d1f79fe92e131db27e85d8cd62fe94a4b383 | lean_source_file | pkg_mathlib_source_file_chunks | 0 < Fin.find p h ↔ ¬p 0 := Fin.pos_iff_ne_zero.trans (Fin.find_eq_zero _).not
lemma find_of_find_le {p : Fin (m + n) → Prop} [DecidablePred p]
{hᵢ : ∃ i, p i} (hm : m ≤ Fin.find p hᵢ) :
Fin.find p hᵢ = (Fin.find (fun j => p (j.natAdd m))
⟨(Fin.cast (Nat.add_comm _ _) (Fin.find p hᵢ)).subNat _ hm, by
... |
8,180 | lean_file_chunk | 9f7dea9aa569aa334f302a98ea972eb7a24772db30c15a5e17816ceebd4a2a6c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
module
public import Mathlib.Algebra.Group.End
public import Mathlib.Data.Finset.Sort
public import Mathlib.Data.Prod.Lex
public import Mathlib.Order.Interval.Finset.Fin
p... |
4,539 | lean_file_chunk | e4e662ed55674ad3a0778a739af7e79d9bcdf1fca75bac9f20396d52adcebc35 | 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.Data.Fin.Tuple.Basic
public import Mathlib.Order.Fin.Basic
/-! # Constructions of embeddings of `Fin n` into a type
* `F... |
8,348 | lean_file_chunk | 9ef9df32a22430bf8b1475aaca439b6526f379da1ac0c748096ac6de421dc084 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 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.BigOperators.Fin
public import Mathlib.Algebra.Group.Fin.Tuple
public import Mathlib.Data.Finset.NatAntidiagonal
public import Mathlib... |
9,295 | lean_file_chunk | b7e5d0308db6a0134100b651210c8bf740500d25bd897ba69b5c8697f97348d1 | 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.Group.TransferInstance
public import Mathlib.Data.Finsupp.MonomialOrder
public import Mathlib.Data.Finsupp.Weight
... |
6,081 | lean_file_chunk | 41d308d464478bfa0076374aa6a23d1d2e4d6626b9b4d7931c0bbe52a4a30c89 | 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, Simon Hudon
-/
module
public import Mathlib.Control.Functor.Multivariate
public import Mathlib.Data.PFunctor.Univariate.Basic
/-!
# Multivariate polynomial functors.
M... |
10,184 | lean_file_chunk | 5826a0fd94b895e4843fb64714aa51119e3b8220874894ad9570d137c5b56201 | 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, Simon Hudon
-/
module
public import Mathlib.Data.PFunctor.Multivariate.Basic
/-!
# The W construction as a multivariate polynomial functor.
W types are well-founded tr... |
11,150 | lean_file_chunk | 5063482542382f4b3b47eb45c9d26274b1a36604d37036fa06a9935d02db2cf0 | 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, Mario Carneiro, Simon Hudon
-/
module
public import Mathlib.Data.PFunctor.Multivariate.Basic
public import Mathlib.Data.PFunctor.Univariate.M
/-!
# The M construction a... |
6,577 | lean_file_chunk | 2ed017d0fb66a04ccc294efe6a73df083750c665af6dbde7cab1fc868285e2de | 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.W.Basic
/-!
# Polynomial Functors
This file defines polynomial functors and the W-type construction as a polynomial functor.
(For t... |
20,570 | lean_file_chunk | 944a0e7f5449dda17bc3da68f4d81a4f30b987b7b517a6029d58dea9469ea5f9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
module
public import Mathlib.Data.PFunctor.Univariate.Basic
/-!
# M-types
M types are potentially infinite tree-like structures. They are defined
as the greatest fixpoin... |
6,389 | lean_file_chunk | 17c7a375d416f20cf585cdec269642b18df27aef98b149fc560fc2438f0d7128 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Minchao Wu, Mario Carneiro
-/
module
public import Mathlib.Data.Finset.Insert
public import Mathlib.Data.Finset.Lattice.Basic
/-!
# Lemmas ab... |
4,154 | lean_file_chunk | 1e4e76fec969a348985bc40189a8772233c2b36227a2769b35f327a7fba50778 | 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.Data.Finset.Lattice.Fold
public import Mathlib.Data.Finset.Prod
/-!
# Lattice operations on finsets of products
This file is concerned... |
2,105 | lean_file_chunk | 9df8306ccba95b645211bdd8f4e4a235c25390eaf30514668a5289b65368a4a1 | 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.Data.Finset.Lattice.Fold
public import Mathlib.Data.Finset.Union
/-!
# Relating `Finset.biUnion` with lattice operations
This file sho... |
2,168 | lean_file_chunk | 5f59d918ebc8f7caf30ad8fae4b2fa64e442371ffe085ef35b7d4d9c3ae32776 | 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.Data.Finset.Lattice.Prod
public import Mathlib.Data.Finset.Pi
/-!
# Lattice operations on finsets of functions
This file is concerned ... |
10,621 | lean_file_chunk | af8108e6e7c90c20aff46f25a1648815fbea72b7ed65ab337b70bdec9558cc1e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Minchao Wu, Mario Carneiro
-/
module
public import Mathlib.Data.Finset.Defs
public import Mathlib.Data.Multiset.FinsetOps
/-!
# Lattice struc... |
23,951 | lean_file_chunk | e0eda04b9f56dc95beada772b93881226e7c151a2147a5f425db3f9a96a41ae0 | 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.Data.Finset.Fold
public import Mathlib.Data.Finset.Sum
public import Mathlib.Data.Multiset.Lattice
public import Mathlib.Data.Set.Boolea... |
6,101 | lean_file_chunk | 2da7608fde3ab3305c14c26fdd5714dbf2148cb4fbebcbf98a9e685bead8fe27 | lean_source_file | pkg_mathlib_source_file_chunks | Also, this lemma assumes that `s` is nonempty instead of assuming that its image is nonempty. -/]
lemma sup'_comp_eq_map {s : Finset γ} {f : γ ↪ β} (g : β → α) (hs : s.Nonempty) :
s.sup' hs (g ∘ f) = (s.map f).sup' (map_nonempty.2 hs) g :=
.symm <| sup'_map _ _
@[to_dual (attr := gcongr)]
theorem sup'_mono {s₁ ... |
1,684 | lean_file_chunk | 4c002dccf6624a29ff7786691970b9b4f7aa7b4326d6172277db36f86e8d8662 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Concordance Inc. dba Harmonic. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Init
/-!
# Definition of `Nat.nthRoot`
In this file we define `Nat.nthRoot n a` to be the floor of the `n`th root of `... |
1,804 | lean_file_chunk | 62134f0c6a8e6ac6b4f639ee44c5cbba12af532f88743289159fb1a99b771d16 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Floris van Doorn (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
module
public import Mathlib.Data.Nat.Find
public import Mathlib.Data.Set.Basic
... |
12,481 | lean_file_chunk | 01a6234a0a14bda0338ad2777be3f1fd5146626dd43f6779bc71b16ed465635d | 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: Chris Hughes, Patrick Stevens
-/
module
public import Mathlib.Algebra.BigOperators.Intervals
public import Mathlib.Algebra.BigOperators.NatAntidiagonal
public import Mathlib.Algebra.Big... |
1,429 | lean_file_chunk | 5e819487c93abfc7da067f77889d0db251096c6af7121f3bc36baffef2e58ab3 | 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: Chris Hughes, Patrick Stevens
-/
module
public import Mathlib.Data.Nat.Choose.Basic
public import Mathlib.Data.Nat.Prime.Factorial
/-!
# Divisibility properties of binomial coefficient... |
338 | lean_file_chunk | 67bb904a64032d0c8ec3e92ef6c1d40743d6851fc6c841f2e76c07397e7826ae | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Antoine Chambert-Loir & María-Inés de Frutos—Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir, María-Inés de Frutos—Fernández
-/
module -- shake: keep-all
public import Mathlib.Tactic.Common
deprecated_module (sinc... |
18,660 | lean_file_chunk | 9693598bf4cabe1de5260ffcd7e07496dfd2ab52008eedaf04010117eecc0cc7 | 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: Chris Hughes, Bhavik Mehta, Stuart Presnell, Antoine Chambert-Loir,
María-Inés de Frutos—Fernández
-/
module
public import Mathlib.Data.Nat.Factorial.Basic
public import Mathlib.Order... |
6,374 | lean_file_chunk | c5af02c95da5a1add23f53be12021ff87a8694027a25387d50ba4c47c77c87b5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Gareth Ma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gareth Ma
-/
module
public import Mathlib.Algebra.CharP.Lemmas
public import Mathlib.Data.ZMod.Basic
public import Mathlib.RingTheory.Polynomial.Basic
meta import Mathlib.Tactic.GRewrite
... |
14,259 | lean_file_chunk | 5e4d2715ebf7ecbebc8b1b1cf881087da3d116a8f48fecd47c064014abe1bfd5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Bolton Bailey. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bolton Bailey, Patrick Stevens, Thomas Browning
-/
module
public import Mathlib.Algebra.Order.Ring.GeomSum
public import Mathlib.Data.Nat.Choose.Central
public import Mathlib.Data.Nat.... |
1,416 | lean_file_chunk | b094c58053711bc95174dc15932ef6694050a4dc229cc24708c45dc5a111fa01 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 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.Polynomial.Coeff
public import Mathlib.Data.Nat.Choose.Basic
/-!
# Vandermonde's identity
In this file we prove Vandermonde's... |
5,762 | lean_file_chunk | 07d6446fca4daaceb1890d6496c4ed59d794b8f8004c482094beca71be979e5d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Patrick Stevens. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Stevens, Thomas Browning
-/
module
public import Mathlib.Data.Nat.Choose.Bounds
public import Mathlib.Data.Nat.GCD.Basic
public import Mathlib.Tactic.Ring
public import Mathl... |
19,955 | lean_file_chunk | 5b0da94b058542b44c3cde361af3f3add628d5db07ec3d23b18af784772bbf99 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Pim Otte. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller, Pim Otte
-/
module
public import Mathlib.Algebra.Order.Antidiag.Pi
public import Mathlib.Data.Finsupp.Multiset
public import Mathlib.Data.List.ToFinsupp
public import Mathlib.D... |
1,422 | lean_file_chunk | 3b679ca9cfb6bec743588e45991c89d8ef0d30bc91365793535c1de31f52a2e6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Algebra.Field.Defs
public import Mathlib.Algebra.GroupWithZero.Units.Basic
public import Mathlib.Data.Nat.Choose.Basic
public import Mathlib... |
3,032 | lean_file_chunk | b0d917b71eff819daa988dee32b5d048c492852e17c39d73de9227633dbd6a33 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Eric Rodriguez
-/
module
public import Mathlib.Algebra.Field.Defs
public import Mathlib.Algebra.Order.Ring.Defs
public import Mathlib.Data.Nat.Cast.Order.Basic
public impo... |
1,858 | lean_file_chunk | 89e6ac1cc1c063d3d2a39609f89e03f14dc5bd4a8c1e8ee2d52cfad96e019a6f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Algebra.Ring.Int.Defs
public import Mathlib.Data.Nat.Cast.Order.Basic
public import Mathlib.Order.Interval.Set.OrdConnected
public imp... |
712 | lean_file_chunk | 8569911388ce339fc729d4f81f3397442cd28a82bcd7cf7b5517e72d0246aea2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 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.Ring.Nat
public import Mathlib.Algebra.Order.Monoid.Unbundled.WithTop
/-!
# Lemma about the coercion `ℕ → WithBot ℕ`.
An orpha... |
1,151 | lean_file_chunk | ed070660e0137f5abc9c86e13d26f1ab9b946fd389856feedceeee0e0786d38e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
public import Mathlib.Data.Nat.Cast.Defs
public import Mathlib.Order.OrderDual
public import Mathlib.Order.Lex
/-!
# Cast of natural numbers (additional theo... |
1,137 | lean_file_chunk | 2ab3ee25be0fa9582f7ba492000b8b8c8aba31c0afdbb12e111af39d821b7057 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 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.Group.Prod
public import Mathlib.Data.Nat.Cast.Defs
/-!
# The product of two `AddMonoidWithOne`s.
-/
@[expose] public section
... |
2,233 | lean_file_chunk | adc106bf6f6ee00cec329a5d9ce2ae5e19d129729082208f7b572903753bc238 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 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.GroupWithZero.Commute
public import Mathlib.Algebra.Ring.Commute
/-!
# Cast of natural numbers: lemmas about `Commute`
-/
pub... |
6,670 | lean_file_chunk | 2b4d78d367484c0e0a06023f2d948ce4a9d69baf3e2676d4508a5c6e7c5fde0e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 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.Divisibility.Hom
public import Mathlib.Algebra.Group.Even
public import Mathlib.Algebra.Group.Nat.Hom
public import Mathlib.Alge... |
6,711 | lean_file_chunk | 910ab25a53d35f6af9ff50e5e16599b3e2b90d7ed4efe9425437649192f21ca8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Gabriel Ebner
-/
module
public import Mathlib.Algebra.Group.Defs
public import Mathlib.Data.Nat.Init
public import Mathlib.Tactic.SplitIfs
/-!
# Cast of natural numbe... |
1,441 | lean_file_chunk | 3e221a7c20415be6c55ba4752d2cdb417ad4db18d4a0ec64ce40d9dbd8d28c93 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Yaël Dillies, Patrick Stevens
-/
module
public import Mathlib.Algebra.CharZero.Defs
public import Mathlib.Data.Nat.Cast.Basic
public import Mathlib.Tactic.Common
publi... |
782 | lean_file_chunk | 5514df8d8102488cc2fdfbcf16107949359ca64dfd4d4f58a5e7db52f6b68ded | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Gabriel Ebner
-/
module
public import Mathlib.Data.Nat.Cast.Defs
/-!
# Lemmas about nonzero elements of an `AddMonoidWithOne`
-/
public section
open Nat
namespace ... |
8,401 | lean_file_chunk | e3bc844f32a87fec7786cc4336670b107ea702077483cd9b21c4b506a6b0ad7c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
module
public import Mathlib.Algebra.IsPrimePow
public import Mathlib.Data.Nat.Factorization.Basic
public import Mathlib.Data.Nat.Prime.Pow
public import Mathlib.NumberT... |
6,998 | lean_file_chunk | 59a44e03de6c851741cd8acd18a1dbb82aa00cb63b717dbe7663fadd548fe968 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Algebra.Order.Floor.Div
public import Mathlib.Algebra.Order.Ring.Nat
public import Mathlib.Data.Nat.Factorization.Defs
/-!
# Roots of natur... |
3,904 | lean_file_chunk | 3b5b8e8c0ab07a09b5e2a5f278c57a8f40ae8bc2a2413767fa47474f639637fe | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Paul Lezeau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Lezeau
-/
module
public import Mathlib.Data.Nat.Factorization.Basic
public import Mathlib.Data.Nat.GCD.BigOperators
/-!
# Lemmas about `factorizationLCMLeft`
This file contains so... |
23,999 | lean_file_chunk | d0cc2fec3637f8bacedc8fbc9259ed4f135d4bc67ab2265d722fa89ee8d46af9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Stuart Presnell. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stuart Presnell
-/
module
public import Mathlib.Algebra.Order.Interval.Finset.SuccPred
public import Mathlib.Data.Nat.Factorization.Defs
public import Mathlib.Order.Interval.Finset.N... |
453 | lean_file_chunk | 5e4e5882c2be7c2b729333b1d46d8a0bdd6dbdd9b6500b2d2e89ffa1815cb1fc | lean_source_file | pkg_mathlib_source_file_chunks | conv_lhs at h => rw [show m = m' * g from (Nat.div_mul_cancel (gcd_dvd_left m n)).symm]
conv_rhs at h => rw [show n = n' * g from (Nat.div_mul_cancel (gcd_dvd_right m n)).symm]
rw [pow_mul, pow_mul] at h
have : g ≠ 0 := by
rcases hmn with hm | hn
· exact gcd_ne_zero_left hm
· exact gcd_ne_... |
3,654 | lean_file_chunk | fd80016eeed02db65065aad6af342754654650cb78c168dc30cb5a0b94f3bbe6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Snir Broshi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Snir Broshi
-/
module
public import Mathlib.Data.Finsupp.Interval
public import Mathlib.Data.Nat.Factorization.Defs
public import Mathlib.NumberTheory.Divisors
/-!
# Results about divis... |
14,808 | lean_file_chunk | 45e104eac0f29199d19b8b0bce0e22305727ed4ec72a5c716385d3b9973881dd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Stuart Presnell. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stuart Presnell
-/
module
public import Batteries.Data.List.Count
public import Mathlib.Data.Finsupp.Multiset
public import Mathlib.Data.Finsupp.Order
public import Mathlib.Data.Nat.... |
5,427 | lean_file_chunk | 0be8a9e03bf29c4f736c175eca64ceac654bb045a0e4cd2b58a8cb88d5856689 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Stuart Presnell. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stuart Presnell
-/
module
public import Mathlib.Data.Nat.Factorization.Defs
/-!
# Induction principles involving factorizations
-/
@[expose] public section
open Nat Finset List Fi... |
21,860 | lean_file_chunk | c6cc86956169b60479cb4be7815a9711638935f4dd2961d03b268bee2fb7fcd6 | 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, Chris Hughes, Floris van Doorn, Yaël Dillies
-/
module
public import Mathlib.Data.Nat.Basic
public import Mathlib.Tactic.Common
public import Mathlib.Tactic.Monotonici... |
2,377 | lean_file_chunk | 1a020823a8f9f0c91447a2ee2409d3b7117efc81eb70193778f054c2aca0a6e1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Moritz Firsching. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Firsching
-/
module
public import Mathlib.Algebra.BigOperators.Intervals
public import Mathlib.Tactic.Ring
/-!
# Superfactorial
This file defines the [superfactorial](https... |
3,638 | lean_file_chunk | 50784307bed9ce78bb959f81f002f063115dc918d82794ec1c8a1d810aff8a7d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Antoine Chambert-Loir, María Inés de Frutos-Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir, María Inés de Frutos-Fernández
-/
module
public import Mathlib.Algebra.Algebra.Defs
public import Mathlib.Algebra.CharP.I... |
2,352 | lean_file_chunk | 186b6695c24aa3b239f807605232162028008403f9562d0cdffeb31d8c8d1732 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Pim Otte. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller, Pim Otte
-/
module
public import Mathlib.Algebra.Order.BigOperators.Ring.Finset
public import Mathlib.Tactic.Zify
/-!
# Factorial with big operators
This file contains some l... |
2,793 | lean_file_chunk | c38dbba7d980819a3b3b2a805d6b4ace649e59c51fa0ad0906110413ae5f0c0a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Jake Levinson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jake Levinson
-/
module
public import Mathlib.Data.Nat.Factorial.Basic
public import Mathlib.Tactic.Ring
public import Mathlib.Tactic.Positivity.Core
public import Mathlib.Algebra.BigO... |
1,140 | lean_file_chunk | 37e59c8aeeccfa529f2ea378f66ff513bbacb49491692ae78ffb285b6e09c95b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Data.Nat.Cast.Basic
public import Mathlib.Data.Nat.Factorial.Basic
/-!
# Cast of factorials
This file allows calculating factorials (inclu... |
10,364 | lean_file_chunk | acf52846f165f82e014c8681e5267146553b8de9c1e0d5ba293e22fe9af3a5f4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
-/
module
public import Mathlib.Algebra.Group.Nat.Units
public import Mathlib.Algebra.GroupWithZero.Divisibility
public import Mathlib.Algebra.GroupWit... |
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