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 |
|---|---|---|---|---|---|
23,925 | lean_file_chunk | 364283598424eb87193a92ddfeffff3897d60af277aa6b3a9d1e2624119e36f1 | lean_source_file | pkg_mathlib_source_file_chunks | Function.Embedding.encard_le ⟨fun ⟨⟨x, _⟩, hx⟩ ↦ ⟨x, hx⟩, fun _ _ h ↦ by
simpa [Subtype.coe_inj] using h⟩
set_option backward.isDefEq.respectTransparency false in
theorem Finite.exists_injOn_of_encard_le [Nonempty β] {s : Set α} {t : Set β} (hs : s.Finite)
(hle : s.encard ≤ t.encard) : ∃ (f : α → β), s ⊆ f ⁻¹'... |
12,711 | lean_file_chunk | a9b8f24ef13e41ee5ce7389341e42b0320eb208e4f786e397f10b3750d02615f | lean_source_file | pkg_mathlib_source_file_chunks | (hsc : sᶜ.Finite := by toFinite_tac) : sᶜ.ncard = Nat.card α - s.ncard := by
rw [← ncard_add_ncard_compl s hs hsc, Nat.add_sub_cancel_left]
theorem eq_univ_iff_ncard [Finite α] (s : Set α) :
s = univ ↔ ncard s = Nat.card α := by
rw [← compl_empty_iff, ← ncard_eq_zero, ← ncard_add_ncard_compl s, left_eq_add]
l... |
2,187 | lean_file_chunk | c29cd5ef26d953ffabf5fd7db6c424eb07dfad64b752d24e08e623f62eca75de | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
module
public import Mathlib.Data.Opposite
public import Mathlib.Data.Set.Operations
/-!
# The opposite of a set
The opposite of a set `s` is simply the set obtained... |
4,509 | lean_file_chunk | 626c440797da1f91e879c63b6b29308c024785154492d08cd905eea491598e72 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Miguel Marco. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Miguel Marco
-/
module
public import Mathlib.Data.Set.Function
public import Mathlib.Data.Set.Functor
/-!
# Sets in subtypes
This file is about sets in `Set A` when `A` is a set.
It ... |
1,367 | lean_file_chunk | fa468ef6ccde29fa505486c485d5459a7cfc7a2e8a3c94f23035137d3911abfc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Johannes Hölzl, Reid Barton, Kim Morrison, Patrick Massot, Kyle Miller,
Minchao Wu, Yury Kudryashov, Floris van Doorn
-/
module
public import Mathlib.Data.Set.Defs
/-!
... |
3,397 | lean_file_chunk | cbde6bc3a5a4ad7fe4198b6524f3e8b229cf16cda32ebb6a93d494195208d599 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Peter Pfaffelhuber. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Pfaffelhuber
-/
module
public import Mathlib.Data.Set.Accumulate
/-!
# Dissipate
The function `dissipate` takes `s : α → Set β` with `LE α` and returns `⋂ y ≤ x, s y`.
It... |
2,464 | lean_file_chunk | 6cbfece4b1d4473abee143be93d77ce9d8da159a763272c954f0f3ec103f8c5e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Data.Set.Image
public import Mathlib.Data.List.Defs
/-!
# Lemmas about `List`s and `Set.range`
In this file we prove lemmas about ra... |
10,161 | lean_file_chunk | ce337ba49fdb77d7bc276bd34558bf1e02e144d0cfd498fec2253bc790f209e7 | 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.Data.Set.NAry
public import Mathlib.Order.SupClosed
public import Mathlib.Order.UpperLower.Closure
/-!
# Set family operations
This file d... |
7,319 | lean_file_chunk | 996d737600a35153067dc4c503ae870c56d4ff2f82797be5c97f000974991404 | 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, Andrew Zipperer, Haitao Zhang, Minchao Wu, Yury Kudryashov
-/
module
public import Mathlib.Data.Set.Function
/-!
# Piecewise functions
This file contains basic results... |
3,574 | lean_file_chunk | 0d01475479231f5e5122847603f2d33353b896fa013ea62bfe304cca51a1f378 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 David Ledvinka. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Ledvinka
-/
module
public import Mathlib.Data.Set.Countable
public import Mathlib.Data.Finite.Prod
/-!
# Finite Exhaustions
This file defines a structure called `FiniteExhaust... |
1,650 | lean_file_chunk | ee65d63eabbaf042e200e83adb61807215e95c3550212787a7d8c6334b1a91e3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson, Leonardo de Moura
-/
module
public import Mathlib.Order.BooleanAlgebra.Set
/-!
# Indicator function valued in bool
See also `Set.indicator` and `Set.piecewise`.
... |
14,052 | lean_file_chunk | 5ee15b5ff6a245063d10749bf04e9a735eff1570ac604a18003509dd95e46ed7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
module
public import Mathlib.Data.Set.Prod
/-!
# N-ary images of sets
This file defines `Set.image2`, the binary image of sets.
This is mostly useful to define... |
4,126 | lean_file_chunk | 1666ecfd390d6755fd9d2f64261cc50a4ba0181e73583e0167bbbb8119e3ef13 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
module
public import Mathlib.Data.Nat.Lattice
public import Mathlib.Order.PartialSups
/-!
# Accumulate
The function `accumulate` takes `s : α → Set β` with `L... |
8,893 | lean_file_chunk | 0785e7fa403e4a197920e514d3265706d9621d50c3ec4d5e03be9d4af71fec10 | 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.Data.Set.Image
public import Mathlib.Data.Set.BooleanAlgebra
/-!
# Sets in sigma types
This file defines `Set.sigma`, the indexed sum of s... |
3,911 | lean_file_chunk | 6652f2f459175039a9c43f7a1b77f6688db61dba82fd905432fd9dfeb9eb0a10 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Scott Carnahan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Carnahan
-/
module
public import Mathlib.Algebra.Order.AddTorsor
public import Mathlib.Order.WellFoundedSet
/-!
# Antidiagonal for scalar multiplication
Given partially ordere... |
23,992 | lean_file_chunk | 82533849f41f3eaaa15d966b2d4959dab00d4c26276642280f2d6c75a3b3b8cb | 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, Johannes Hölzl, Patrick Massot
-/
module
public import Mathlib.Data.Set.Image
public import Mathlib.Data.SProd
public import Mathlib.Data.Sum.Basic
/-!
# Sets in prod... |
14,448 | lean_file_chunk | 5de029b244445a18c91d1dcad044dacc23303ef2ecd5db557e8575ac8b7fcff2 | lean_source_file | pkg_mathlib_source_file_chunks | univ_pi_eq_empty_iff.2 <| h.elim fun x => ⟨x, rfl⟩
@[simp]
theorem disjoint_univ_pi : Disjoint (pi univ t₁) (pi univ t₂) ↔ ∃ i, Disjoint (t₁ i) (t₂ i) := by
simp only [disjoint_iff_inter_eq_empty, ← pi_inter_distrib, univ_pi_eq_empty_iff]
theorem Disjoint.set_pi (hi : i ∈ s) (ht : Disjoint (t₁ i) (t₂ i)) : Disjoint... |
7,270 | lean_file_chunk | 3cbb700c749cf8d02463147ba7552655a27b0054ee23193022b44176d67ea67b | 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.Set.Lattice
public import Mathlib.Order.Directed
/-!
# Union lift
This file defines `Set.iUnionLift` to glue together functions define... |
3,885 | lean_file_chunk | c29fae36b0e8b5f5966beebc5afd41b486a6190541091d1118b5a5b8c648f5b1 | 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.Data.Set.Basic
/-!
# Order structures and monotonicity lemmas for `Set`
-/
public section
open Function
universe u ... |
1,283 | lean_file_chunk | d635d88ddb135db47acd491b66b03b9e603a1659785ee944cbd43ca24dc6ba6a | 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, Johannes Hölzl, Mario Carneiro
-/
module
public import Mathlib.Order.CompleteBooleanAlgebra
/-!
# Sets are a complete atomic Boolean algebra.
This f... |
13,302 | lean_file_chunk | 64a46349e31df8594677cbe9a55d64b21917edb942a4d514101cfc6863fa9f20 | 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 Aesop
public import Mathlib.Data.Set.Disjoint
public import Mathlib.Tactic.Simproc.ExistsAndEq
/-!
# Lemmas about insertion, s... |
10,955 | lean_file_chunk | 6a3fa5c22dd6cd6510eb0ba4d4b9edd714e1c86e92b24d53db3d14e65f5ec3f8 | 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, Andrew Zipperer, Haitao Zhang, Minchao Wu, Yury Kudryashov
-/
module
public import Mathlib.Data.Set.Image
/-!
# Restrict the domain of a function to a set
## Main defi... |
23,980 | lean_file_chunk | 423e298d8687c44b711bc0a04be57a66ebb6a50b9c1f3e29531bafa5baddc7ac | 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 Batteries.Tactic.Congr
public import Mathlib.Data.Option.Basic
public import Mathlib.Data.Prod.Basic
public import Mathlib.Data... |
23,998 | lean_file_chunk | 972c7505cd10320fe2b18e1afba9c100efcbb013d9b8eb0f05a29140f9eabec6 | lean_source_file | pkg_mathlib_source_file_chunks | theorem insert_image_compl_eq_range (f : α → β) (x : α) : insert (f x) (f '' {x}ᶜ) = range f := by
grind
theorem image_preimage_eq_range_inter {f : α → β} {t : Set β} : f '' (f ⁻¹' t) = range f ∩ t := by
grind
theorem image_preimage_eq_inter_range {f : α → β} {t : Set β} : f '' (f ⁻¹' t) = t ∩ range f := by
gri... |
2,953 | lean_file_chunk | aea655d78419ef9be8a19638ca11f46cbd950ee5ea4852c2c13b9302920d2bd4 | lean_source_file | pkg_mathlib_source_file_chunks | end Set
/-! ### Disjoint lemmas for image and preimage -/
section Disjoint
variable {α β γ : Type*} {f : α → β} {s t : Set α}
theorem Disjoint.preimage (f : α → β) {s t : Set β} (h : Disjoint s t) :
Disjoint (f ⁻¹' s) (f ⁻¹' t) :=
disjoint_iff_inf_le.mpr fun _ hx => h.le_bot hx
lemma Codisjoint.preimage (f : ... |
23,987 | lean_file_chunk | 3dd347455b9dae031a1402d3495b6d7a9ba25ac623a0f41ac459f786316741db | 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.Order.PropInstances
public import Mathlib.Tactic.Lift
/-!
# Basic properties of sets
Sets in Lean are homogeneous; al... |
10,652 | lean_file_chunk | 69170c11fd567d2ba9e55dd0b172541eddd6f185c2742d17a1ff29259fd42379 | lean_source_file | pkg_mathlib_source_file_chunks | inf_congr_left ht hu
theorem inter_congr_right (hs : t ∩ u ⊆ s) (ht : s ∩ u ⊆ t) : s ∩ u = t ∩ u :=
inf_congr_right hs ht
theorem inter_eq_inter_iff_left : s ∩ t = s ∩ u ↔ s ∩ u ⊆ t ∧ s ∩ t ⊆ u :=
inf_eq_inf_iff_left
theorem inter_eq_inter_iff_right : s ∩ u = t ∩ u ↔ t ∩ u ⊆ s ∧ s ∩ u ⊆ t :=
inf_eq_inf_iff_rig... |
3,680 | lean_file_chunk | d27b601514c0ffa4521fcf24074b0114a83b903026918720a5bb774c19aad320 | 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.Data.Set.Basic
/-!
# Theorems about the `Disjoint` relation on `Set`.
-/
public section
assert_not_exists HeytingAlg... |
13,156 | lean_file_chunk | 49575b08ee9b12a3fcc0e9a3f88b84beef094ed89542529775cd0e5f68d8b51a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Johannes Hölzl, Reid Barton, Kim Morrison, Patrick Massot, Kyle Miller,
Minchao Wu, Yury Kudryashov, Floris van Doorn
-/
module
public import Mathlib.Data.Set.CoeSort
pu... |
3,385 | lean_file_chunk | e1ef65f33e04106ca8609d3e7dfa7392fb4bfb48574de5628408ece837b31739 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
module
public import Mathlib.Data.Finset.Insert
public import Mathlib.Data.Set.Lattice
/-!
# Constructions involving sets of sets.
## Finite Intersections
We define a str... |
5,756 | lean_file_chunk | 21804d6aac85d00a0c46b0527a609224add48b5042e887e547a2fafa8e448079 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.Data.Set.Finite.Lattice
/-!
# Partitions based on membership of a sequence of sets
Let `f : ℕ → Set α` be a sequence of sets. For `n : ℕ`,... |
2,031 | lean_file_chunk | 45bfddf9b7a7569068b64a0d5629e6e0845ed132e23c0eaf56728d45d053d83e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson
-/
module
public import Mathlib.Util.Notation3
public meta import Mathlib.Lean.Expr.ExtraRecognizers
public import Mathlib.Data.Set.Operations
/-!
# Set Notation
This fil... |
10,720 | lean_file_chunk | 409f4f37726909342e8614bb2d3a224a53f9f17b55ac0273a1ea0d24c8298dc3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
module
public import Mathlib.Init
public import Batteries.Util.ExtendedBinder
import Mathlib.Tactic.ToDual
/-!
# Sets
This file sets up the theory of se... |
6,589 | lean_file_chunk | 5dce2c9ac481460bb3434d34142800261ccd76f1f38fd3d4e08799453558fecc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
module
public import Mathlib.Algebra.Order.Kleene
public import Mathlib.Algebra.Order.Ring.Canonical
public import Mathlib.Data.Set.BooleanAlgebra
public import ... |
23,962 | lean_file_chunk | a51142af9eb09b8b8e4a4d525987580f747ea64bcad29d69c4f12c2e92c037a2 | 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, Andrew Zipperer, Haitao Zhang, Minchao Wu, Yury Kudryashov
-/
module
public import Mathlib.Data.Set.Prod
public import Mathlib.Data.Set.Restrict
/-!
# Functions over se... |
23,993 | lean_file_chunk | 23b7cea0ef1ab751520d1529daba3bfed8327cccd73d58087cf0c7805c158c84 | lean_source_file | pkg_mathlib_source_file_chunks | ⟨mapsTo_empty f ∅, injOn_empty f, surjOn_empty f ∅⟩
@[simp] theorem bijOn_empty_iff_left : BijOn f s ∅ ↔ s = ∅ :=
⟨fun h ↦ by simpa using h.mapsTo, by rintro rfl; exact bijOn_empty f⟩
@[simp] theorem bijOn_empty_iff_right : BijOn f ∅ t ↔ t = ∅ :=
⟨fun h ↦ by simpa using h.surjOn, by rintro rfl; exact bijOn_empty ... |
4,151 | lean_file_chunk | 7d266a7df6d0416a77fb489c81f4442ff7f062bb3a3a536a908b516d0022f324 | lean_source_file | pkg_mathlib_source_file_chunks | variable {p : β → Prop} [DecidablePred p] {f : α ≃ Subtype p} {g g₁ g₂ : Perm α} {s t : Set α}
protected lemma MapsTo.extendDomain (h : MapsTo g s t) :
MapsTo (g.extendDomain f) ((↑) ∘ f '' s) ((↑) ∘ f '' t) := by
rintro _ ⟨a, ha, rfl⟩; exact ⟨_, h ha, by simp_rw [Function.comp_apply, extendDomain_apply_image]⟩
... |
1,616 | lean_file_chunk | fbbdef8e3e593d3289b272cb107dc615582f9e29260017da901df56770f1c6f1 | 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.Order.BooleanAlgebra.Set
public import Mathlib.Order.SymmDiff
/-! # Symmetric differences of sets -/
public section
... |
4,520 | lean_file_chunk | 1c0e90d3dfdc9c1511498711eb3edcc1944dd84624d05859255fdde0e432cb81 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Floris van Doorn
-/
module
public import Mathlib.Order.WellFoundedSet
/-! # Multiplication antidiagonal -/
@[expose] public section
namespace Set
variable {α : Ty... |
5,647 | lean_file_chunk | e5a020b051f236294fc5cf1d8f7b5bc232498f3c207c713e9d071978bdffa5b7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2016 Leonardo de Moura. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
module
public import Batteries.Control.AlternativeMonad
public import Mathlib.Control.Basic
public import Mathlib.Data.Set.Defs
public import Mathlib.Data.Set.... |
6,671 | lean_file_chunk | a5ae204da29665a9330ae723a7d211cf8916502c4cc6cbcd155f19b59bbb5d73 | 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, Andrew Zipperer, Haitao Zhang, Minchao Wu, Yury Kudryashov
-/
module
public import Mathlib.Data.Set.Function
/-!
# Monotone functions over sets
-/
public section
vari... |
13,400 | lean_file_chunk | c2111a5c43f4a17df984a703280fd2ccacb1c4f686a4c594f33b49c851ff9c59 | 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.Data.Set.Insert
public import Mathlib.Tactic.ByContra
/-!
# Subsingleton
Defines the predicate `Subsingleton s : Prop... |
23,942 | lean_file_chunk | c6223d34e077ec6f3acf57a43fe0e6a2358c9fc7493ba9211524db5928cb865c | 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, Johannes Hölzl, Mario Carneiro
-/
module
public import Mathlib.Logic.Pairwise
public import Mathlib.Data.Set.BooleanAlgebra
/-!
# The set lattice
Th... |
23,993 | lean_file_chunk | 87351ec0cdf82ff90500748c5bb9355b55a226c340dad6d3d783fb27fccbba88 | lean_source_file | pkg_mathlib_source_file_chunks | @[simp] lemma biUnion_const {s : Set α} (hs : s.Nonempty) (t : Set β) : ⋃ a ∈ s, t = t :=
biSup_const hs
@[simp] lemma biInter_const {s : Set α} (hs : s.Nonempty) (t : Set β) : ⋂ a ∈ s, t = t :=
biInf_const hs
theorem iUnion_subtype (p : α → Prop) (s : { x // p x } → Set β) :
⋃ x : { x // p x }, s x = ⋃ (x) (... |
2,241 | lean_file_chunk | 551924a22adc190b08002ddc30cfb46e7c571ca53008f9be3e4802b67848d4ff | lean_source_file | pkg_mathlib_source_file_chunks | theorem iInter_ge_eq_iInter_nat_add (u : ℕ → Set α) (n : ℕ) : ⋂ i ≥ n, u i = ⋂ i, u (i + n) :=
iInf_ge_eq_iInf_nat_add u n
theorem _root_.Monotone.iUnion_nat_add {f : ℕ → Set α} (hf : Monotone f) (k : ℕ) :
⋃ n, f (n + k) = ⋃ n, f n :=
hf.iSup_nat_add k
theorem _root_.Antitone.iInter_nat_add {f : ℕ → Set α} (h... |
10,021 | lean_file_chunk | d20de0458c120b9f0e9038fe9a3908fd6be052af9455418e0461d2e127a62cc5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Daniel Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Morrison, Antoine Chambert-Loir
-/
module
public import Mathlib.Data.ENat.Lattice
public import Mathlib.Data.Finite.Card
public import Mathlib.Data.Set.Card
/-! # Combination... |
2,162 | lean_file_chunk | 74e8a9c98b2cb7760fc186d2b71c816290110a7ef588d8d9572ba02a81695f0f | 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.Data.Set.Basic
/-! # Lemmas about `inclusion`, the injection of subtypes induced by `⊆` -/
@[expose] public section
... |
13,126 | lean_file_chunk | 27bf26f75613253f1c26fac6402fd22cb2f374267d5c3fcabc67531ae3fcfab7 | 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.Data.Countable.Basic
public import Mathlib.Data.Set.Finite.Basic
public import Mathlib.Data.Set.Subsingleton
public import Mathlib.Logic... |
14,015 | lean_file_chunk | a739b90fe066110c81eead25a529b176514ed95053fd580d851c2d9b56d0836d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Neil Strickland
-/
module
public import Mathlib.Tactic.Ring
public import Mathlib.Data.PNat.Prime
/-!
# Euclidean algorithm for ℕ
This file sets up a version of the Euclidean algor... |
3,367 | lean_file_chunk | b62544a859cddd836c3f093ea4ddd47f393538e8de58b63512b84617c820fdeb | 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.Order.Interval.Finset.Nat
public import Mathlib.Data.PNat.Defs
/-!
# Finite intervals of positive naturals
This file proves that `ℕ+` is a... |
14,754 | lean_file_chunk | de62381020ba53b8256b5fe3c8508fc152e226c52ee5e125495a1549f62339ff | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Neil Strickland
-/
module
public import Mathlib.Algebra.BigOperators.Group.Multiset.Basic
public import Mathlib.Data.PNat.Prime
public import Mathlib.Data.Nat.Factors
public import M... |
657 | lean_file_chunk | 8b8c4a85157c16011393f1e1013ccc613dc65010f2a3174ec19e4401013f5280 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Javier Burroni. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Javier Burroni
-/
module
public import Mathlib.Algebra.Order.SuccPred
public import Mathlib.Data.PNat.Basic
/-!
# Order related instances for `ℕ+`
-/
@[expose] public section
names... |
10,976 | lean_file_chunk | b0b0fe48efc83962e8b7753b74dce65b0174550baff2cacdb1f81dc32dea103e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Ralf Stephan, Neil Strickland, Ruben Van de Velde
-/
module
public import Mathlib.Algebra.GroupWithZero.Divisibility
public import Mathlib.Algebra.Order.Positiv... |
767 | lean_file_chunk | 3a2048678fee299627099697e1fd2ec8ea214fc7bac8895f48f2d6d904acf27c | 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, Simon Hudon, Yury Kudryashov
-/
module
public import Mathlib.Data.Nat.Notation
/-! # Definition and notation for positive natural numbers -/
@[expose] public section... |
6,385 | lean_file_chunk | b910fae12461a9a48303ae09fcac9796cf82cf5f5970f782ca8daabf5af49b35 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Neil Strickland
-/
module
public import Mathlib.Data.Int.Order.Basic
public import Mathlib.Data.Nat.Basic
public import Mathlib.Data.PNat.Notation
public import... |
645 | lean_file_chunk | 8e37dd0532b7792a4e4fd06b8895dfe45d6469de86832e4bbb9b61a616099eb5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Ralf Stephan, Neil Strickland, Ruben Van de Velde
-/
module
public import Mathlib.Data.PNat.Defs
public import Mathlib.Logic.Equiv.Defs
/-!
# The equivalence b... |
7,650 | lean_file_chunk | 0405599fa7106c378f0d90a626ad50c07648f24fb18ac3cc6fa193e05639b6b3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Neil Strickland
-/
module
public import Mathlib.Data.Nat.Prime.Defs
public import Mathlib.Data.PNat.Basic
/-!
# Primality and GCD on pnat
This file extends th... |
3,777 | lean_file_chunk | 44cc408ee113013073473e6cc78bb311cd53aa89510e2a1c3f4edb73a621d8bf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky, Floris van Doorn
-/
module
public import Mathlib.Data.Nat.Find
public import Mathlib.Data.PNat.Basic
/-!
# Explicit least witnesses to existentials on positive natu... |
7,094 | lean_file_chunk | d1028449004e62b607e07aa747fc0e5f200256eb309a7542bf6fe91f5c13bca0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Haitian Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Haitian Wang, Malvin Gattinger
-/
module
public import Mathlib.Algebra.Order.Sub.Unbundled.Basic
public import Mathlib.Data.Multiset.OrderedMonoid
/-!
# Dershowitz-Manna ordering
In t... |
3,156 | lean_file_chunk | 4614cc2515639ee089febaa4d7a2ba4142208e7bf2c9e6638de6b9d00a305140 | 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.Algebra.Order.Group.Multiset
/-!
# Disjoint sum of multisets
This file defines the disjoint sum of two multisets as `Multiset (α ⊕ β)`. Be... |
12,301 | lean_file_chunk | 73ce577913c6452248200c8a9077ab1b8c69e728fe1d1578bad706f7b3d84614 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
module
public import Mathlib.Data.Fintype.Card
public import Mathlib.Algebra.BigOperators.Group.Finset.Basic
/-!
# Multiset coercion to type
This module defines a `CoeSo... |
7,544 | lean_file_chunk | ca8d799994dadce58bf46bc5573488f76342468549af4c1a7119832d926cf05d | 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: Mario Carneiro
-/
module
public import Mathlib.Data.List.Nodup
public import Mathlib.Data.Multiset.ZeroCons
/-!
# Counting multiplicity in a multiset
-/
@[expose] public sec... |
2,054 | lean_file_chunk | 44b3fac865943cb9798284888e11b4375e0391b9a68691a5a7a1f95b1bb5a72d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 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.Multiset.Bind
/-!
# Sections of a multiset
-/
@[expose] public section
assert_not_exists Ring
namespace Multiset
variable {α :... |
674 | lean_file_chunk | 37f588802d54562a4efd27fce7244d355fed206ab2cea4ee6bdc7f39bb2a46ed | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 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.List.Pairwise
public import Mathlib.Data.Multiset.Defs
/-!
# Pairwise relations on a multiset
This file provides basic results about ... |
20,566 | lean_file_chunk | 4795be96a44eec866ffc0e504842e24d2ee7aaf9275c5c043ee436d4524aee66 | 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: Mario Carneiro
-/
module
public import Mathlib.Data.Multiset.Defs
public import Mathlib.Order.BoundedOrder.Basic
/-!
# Definition of `0` and `::ₘ`
This file defines construct... |
14,145 | lean_file_chunk | 27fa68ec29f1d84e30263512ca0286afe27740e74a554484911a969c4e85c567 | 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, Rudy Peterson
-/
module
public import Mathlib.Algebra.BigOperators.Group.Multiset.Basic
/-!
# Bind operation for multisets
This file defines a few basic operations o... |
2,801 | lean_file_chunk | 1112d190324c288ac4b2266ed77b6c73b4d682351f9c981c858fe559491ae8b4 | 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.DFinsupp.Interval
public import Mathlib.Data.DFinsupp.Multiset
public import Mathlib.Order.Interval.Finset.Nat
public import Mathlib.Data... |
3,284 | lean_file_chunk | aabffc46268d7726c065a5a5026d689ec919581f320e78f58e5d1a494ddac5fa | 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
-/
module
public import Mathlib.Data.Multiset.Powerset
/-!
# The antidiagonal on a multiset.
The antidiagonal of a multiset `s` consists of all pairs `(t₁, t₂)`
such ... |
4,601 | lean_file_chunk | 93361992bcc9fa72200d30c2c41c2486da831faede0b0812ff65bc053a6de0d1 | 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
-/
module
public import Mathlib.Data.List.Dedup
public import Mathlib.Data.Multiset.UnionInter
/-!
# Erasing duplicates in a multiset.
-/
@[expose] public section
as... |
15,253 | lean_file_chunk | 3c953646ce9eb8193a6d9cea80960492dc192928d8bd6efa37bc2824a8200228 | 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: Mario Carneiro
-/
module
public import Mathlib.Data.Multiset.Count
public import Mathlib.Data.List.Count
/-!
# Sum and difference of multisets
This file defines the following... |
6,041 | lean_file_chunk | d73d6453158a6adc5cd66bcaf6cfd4c8ce0dbaa7997e310c527e163cc9c3fb08 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 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.Multiset.Bind
/-!
# The Cartesian product of multisets
## Main definitions
* `Multiset.pi`: Cartesian product of multisets index... |
5,692 | lean_file_chunk | 9d77fdf00a3dbfad3953c3ded55fb0ae11af02f7fa5dc28166727328e78d7c45 | 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: Mario Carneiro
-/
module
public import Mathlib.Data.Multiset.ZeroCons
/-!
# Basic results on multisets
-/
@[expose] public section
-- No algebra should be required
assert_n... |
3,180 | lean_file_chunk | 956d9aa3d4dd9db01a7ce8362457916bf8bf48416a39ddde250bcea1a2933941 | 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
-/
module
public import Mathlib.Data.List.Sort
public import Mathlib.Data.Multiset.Range
public import Mathlib.Util.Qq
public meta import Mathlib.Data.Multiset.Defs
/-... |
9,805 | lean_file_chunk | ca19a19f43edbb06e3bec75bc966b895cd39c2d34d7e57edcd91dcdcfaf0076c | 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
-/
module
public import Mathlib.Data.Multiset.Dedup
public import Mathlib.Data.List.Infix
/-!
# Preparations for defining operations on `Finset`.
The operations here ... |
12,768 | lean_file_chunk | ff39e2127eb56bd930192404e4f19ed04452f4087c6d4c98e625edec9cc70484 | 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.List.Sublists
public import Mathlib.Data.List.Zip
public import Mathlib.Data.Multiset.Bind
public import Mathlib.Data.Multiset.Rang... |
6,178 | lean_file_chunk | e4207112842d1616467c2946b4c473d5cdd73c8db242c3a06bbff374349ba18d | 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: Mario Carneiro
-/
module
public import Mathlib.Data.Multiset.AddSub
/-!
# Repeating elements in multisets
## Main definitions
* `replicate n a` is the multiset containing on... |
17,788 | lean_file_chunk | 4cc9e0238b40200f3a995a7589d002ee0ff1babc0828bcb20f049bda76925766 | 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: Mario Carneiro, Rudy Peterson
-/
module
public import Mathlib.Data.Multiset.MapFold
public import Mathlib.Data.Set.Function
public import Mathlib.Order.Hom.Basic
/-!
# Filteri... |
13,893 | lean_file_chunk | 5715ecb8fb737384ebfa4993b67d0656934a19ab911ded6c21ddd91b6498fdb0 | 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: Mario Carneiro
-/
module
public import Mathlib.Data.List.Perm.Subperm
public import Mathlib.Data.Nat.Basic
public import Mathlib.Data.Quot
public import Mathlib.Order.Monotone.... |
14,617 | lean_file_chunk | 3e7f768e166701518df578e4b810d4d3e376f07e0e68e5afe9fdf6213d37c3ca | 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: Mario Carneiro
-/
module
public import Mathlib.Data.List.Perm.Lattice
public import Mathlib.Data.Multiset.Filter
public import Mathlib.Order.MinMax
public import Mathlib.Logic.... |
3,442 | lean_file_chunk | 7cb044fbbc4cbb8d15c182881f762a3e8c533de6d6c903287c2d0d57d57fd7a8 | 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
-/
module
public import Mathlib.Data.Multiset.Dedup
/-!
# The fold operation for a commutative associative operation over a multiset.
-/
@[expose] public section
nam... |
4,446 | lean_file_chunk | bbcee8ef8c4257b5f5c23fd052cc11cf5ee046375a654e73a9e9f873bc311489 | 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: Mario Carneiro, Johannes Hölzl, Simon Hudon, Kenny Lau
-/
module
public import Mathlib.Data.Multiset.Bind
public import Mathlib.Control.Traversable.Lemmas
public import Mathlib.Control.T... |
2,018 | lean_file_chunk | 41947d53c410fd7fcad1927f3373b3f7175734433667ae8a0386537107cefbdd | 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: Mario Carneiro
-/
module
public import Mathlib.Data.Multiset.UnionInter
/-! # `Multiset.range n` gives `{0, 1, ..., n-1}` as a multiset. -/
@[expose] public section
assert_n... |
817 | lean_file_chunk | fee49a618c93dd081eece68410d10257f41933f928d80d6e990944295ba71523 | 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: Mario Carneiro
-/
module
public import Mathlib.Algebra.Order.Group.Multiset
public import Mathlib.Algebra.Order.Monoid.Canonical.Defs
/-!
# Multisets as ordered monoids
The `... |
2,790 | lean_file_chunk | 0e60951b83fec861b74a168b653435898b314ef2102d18ac816f6131e0d7dc13 | 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.Multiset.FinsetOps
public import Mathlib.Data.Multiset.Fold
/-!
# Lattice operations on multisets
This file defines `Multiset.sup... |
17,334 | lean_file_chunk | 4c76bee2606906b8ef1deba1287268a9ea6922258415667361d0733478758a63 | 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: Mario Carneiro
-/
module
public import Mathlib.Data.List.Perm.Basic
public import Mathlib.Data.Multiset.Replicate
public import Mathlib.Data.Set.List
/-!
# Mapping and folding... |
2,609 | lean_file_chunk | 8e60d64319bd93cd4646070944a8e926702641c06030b4476e3587be9cbd9beb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
module
public import Mathlib.Data.List.NatAntidiagonal
public import Mathlib.Data.Multiset.MapFold
/-!
# Antidiagonals in ℕ × ℕ as multisets
This file defines the ... |
3,209 | lean_file_chunk | d79042329529c59d4365c73c620d42a0bd3da333d456015704138daabc47d1b1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
module
public import Mathlib.Data.List.Sym
/-! # Unordered tuples of elements of a multiset
Defines `Multiset.sym` and the specialized `Multiset.sym2` for computing mult... |
1,383 | lean_file_chunk | 5bf76270433ddadc2a10b0adfdc407fb4d31901cbdc0860d2361e332e2c95b7e | 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.Data.Vector.Basic
/-!
# The `zipWith` operation on vectors.
-/
@[expose] public section
namespace List
namespace Vector
section ZipWith... |
4,592 | lean_file_chunk | 8c33ead02bbe2b67e7086a0d4360f5dce38cce31d9252885b242c946984a01b7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Alex Keizer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Keizer
-/
module
public import Mathlib.Data.Vector.Basic
/-!
This file establishes a `snoc : Vector α n → α → Vector α (n+1)` operation, that appends a single
element to the ba... |
23,971 | lean_file_chunk | b2219699989bdda03842a9d9ef1fa78af6eb308f7ae8af0fa52be2e2c5cfb5de | 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.Vector.Defs
public import Mathlib.Data.List.Nodup
public import Mathlib.Control.Applicative
public import Mathlib.Control.Traversab... |
2,048 | lean_file_chunk | f49a1cc64dab5b60248c52ae1e62a87aa3e594d2d1b7461a0aab89f57ad12be6 | lean_source_file | pkg_mathlib_source_file_chunks | η (x.traverse f) = x.traverse (@η _ ∘ f) := by
induction x with
| nil => simp! [functor_norm, cast, η.preserves_pure]
| cons ih =>
rw [Vector.traverse_def, Vector.traverse_def, ← ih, η.preserves_seq, η.preserves_map]
rfl
end Traverse
instance : Traversable.{u} (flip Vector n) where
traverse := @Vector... |
8,580 | lean_file_chunk | b15702c0bbcafb3f04e496afc86a431270f9e62817da940a3db661741b38b63c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
module
public import Mathlib.Data.List.Defs
public import Mathlib.Tactic.Common
/-!
The type `List.Vector` represents lists with fixed length.
TODO: The ... |
2,848 | lean_file_chunk | ea635eb2bb9ec29b8645e73cc30663354b31ff5cdf0b2f9d8b60f5cb13caf396 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Devon Tuma
-/
module
public import Mathlib.Data.Vector.Basic
/-!
# Theorems about membership of elements in vectors
This file contains theorems for membership in a `v.toList` for a vect... |
14,872 | lean_file_chunk | 9b15cb3cdd9530991c55a0cffadf700c8e2cb70bedba1627e3d38f5c50c1bdd5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Alex Keizer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Keizer
-/
module
public import Mathlib.Data.Vector.Basic
public import Mathlib.Data.Vector.Snoc
/-!
This file establishes a set of normalization lemmas for `map`/`mapAccumr` oper... |
7,301 | lean_file_chunk | eaf7512a6d93c31acf750d64c68c520b158eb597fbb6233157138c0812c1f5b8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Eric Rodriguez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Rodriguez
-/
module
public import Mathlib.Algebra.GroupWithZero.Units.Lemmas
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
public import Mathlib.Algebra.Order.Rin... |
9,859 | lean_file_chunk | 4872388c12df71dd3d9f2100c7ad430864f5dc71aa546abe8deeaabe2c890d15 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Eric Rodriguez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Rodriguez
-/
module
public import Mathlib.Algebra.GroupWithZero.Defs
public import Mathlib.Algebra.Ring.Defs
public import Mathlib.Algebra.Order.Ring.Defs
public import Mathlib.T... |
1,157 | lean_file_chunk | ccc98b3c9d6325b75871fabbebe818afd2351675a188fb35ac9f53a198a13b33 | 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.Finset.Attr
public import Mathlib.Tactic.Bound.Init
public import Mathlib.Tactic.Common
public import Mathlib.Tactic.Finiteness.Attr
publ... |
6,651 | lean_file_chunk | f97fb35bf0671bba1e8f43fab20fb84812868dca00e8660333d51715c9cbbda4 | 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.Algebra.Module.LinearMap.End
public import Mathlib.Data.Matrix.Mul
public import Mathlib.Data.Matrix.Basis
public import Mathlib.Algebra.Algeb... |
12,157 | lean_file_chunk | 975e42887760a7bf1651975a081ffafe381a4879cf3b8598b3ed19971f187d8e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Mohanad ahmed. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mohanad Ahmed
-/
module
public import Mathlib.Data.Matrix.Block
public import Mathlib.LinearAlgebra.Matrix.SemiringInverse
/-! # Block Matrices from Rows and Columns
This file provid... |
13,431 | lean_file_chunk | 835a717f11158efb201cf21194e52b756830697cac33527beb4ba682769f965c | 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.Data.Int.Cast.Basic
public import Mathlib.Data.Int.Cast.Pi
public import... |
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