chars int64 40 24k | content_type stringclasses 9
values | id stringlengths 13 64 | source stringclasses 5
values | subset stringclasses 31
values | text stringlengths 40 24k |
|---|---|---|---|---|---|
17,755 | lean_file_chunk | 79b9ecfab48a06718f5ae03eafa11833195ee5f92e33b7da9fa4c7782431c947 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Violeta Hernández Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Violeta Hernández Palacios
-/
module
public import Mathlib.Algebra.Order.Ring.Archimedean
public import Mathlib.Algebra.Ring.Subring.Order
public import Mathlib.Data.Real.... |
1,178 | lean_file_chunk | 2fada4b6d0b578ef0181a17277e0a231bd66e3e8b6dfbbcce73fd305e1623f09 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.Opposite
public import Mathlib.Algebra.Order.Ring.Defs
public import Mathlib.Algebra.Ring.Opposite
/-!
# Ordered ring i... |
3,879 | lean_file_chunk | 67dff2635337064acc8c3e1899116a074f7d59548fee507114e7b5cefa5c9427 | 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, Emirhan Duysak, Adem Alp Gök, Junyan Xu
-/
module
public import Mathlib.Algebra.Order.Group.Int
public import Mathlib.Algebra.Order.Group.Unbundled.Int
public import Mat... |
5,015 | lean_file_chunk | a4e3614923188df22a6dae087c6718950735bacdc33436a7b508adf6953a698a | 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, Leonardo de Moura, Mario Carneiro
-/
module
public import Mathlib.Algebra.Order.Monoid.Canonical.Defs
public import Mathlib.Algebra.Order.Ring.Defs
public import Mathlib... |
1,156 | lean_file_chunk | cb0065ae8a68ba794da3e3f0e0ab38e89af07ed18c3ac54fccad00038b37c4e9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
module
public import Mathlib.Algebra.Order.Ring.Defs
public import Mathlib.Algebra.Order.Ring.Unbundled.Rat
public import Mathlib.Algebra.Ring.Rat
/... |
2,005 | lean_file_chunk | 4b1e8bb43669382817afe484c32b244e364d386acee07c815e76043ed21f71f7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
module
public import Mathlib.Algebra.Order.Ring.Defs
public import Mathlib.Algebra.Order.Star.Basic
/-!
# Commutative star-ordered rings are ordered rings
A noncommu... |
1,559 | lean_file_chunk | 44a928e5e08947d0e9e4bec3845581b5ba07d6560f914441b70e7fe7b7c53851 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
module
public import Mathlib.Algebra.Order.Ring.Defs
public import Mathlib.Data.Int.Interval
import Mathlib.Algebra.Order.Ring.Cast
/-! # Intervals of integers in str... |
820 | lean_file_chunk | 0806ce7238a46df4ffcc813d4042cfab8b9c5ef6dba8d874e445f5ab820675e3 | 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.Monoid.Prod
public import Mathlib.Algebra.Order.Ring.Defs
public import Mathlib.Algebra.Ring.Prod
/-!
# Products of ordered r... |
1,289 | lean_file_chunk | 186a897b3a0ae5bd630fbb4fbf9d31a9e24938d3ca5d68694065bc6661f78066 | 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.Algebra.Order.Group.Nat
public import Mathlib.Algeb... |
11,924 | lean_file_chunk | 50e6715f31806491834782b323b70cd8ee4ae36e379a520503197aa9d8dbea46 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Weiyi Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Weiyi Wang, Violeta Hernández Palacios
-/
module
public import Mathlib.Algebra.Order.Archimedean.Class
public import Mathlib.Algebra.Order.Group.DenselyOrdered
public import Mathlib.Algeb... |
10,781 | lean_file_chunk | 4f39184f705487b0658921ecd9b90afe5aa287e1687ed1d99123a98cd7a04d33 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 María Inés de Frutos-Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: María Inés de Frutos-Fernández, Fabrizio Barroero
-/
module
public import Mathlib.Algebra.Module.NatInt
public import Mathlib.Algebra.Order.Hom.Basic
public import Mat... |
3,566 | lean_file_chunk | 456777327c4805864314c57e5248014991abf276138747381715c0536d07bd4c | 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, Leonardo de Moura, Mario Carneiro, Artie Khovanov
-/
module
public import Mathlib.Algebra.Order.Group.Cone
public import Mathlib.Algebra.Ring.Subsemiring.Order
/-!
# Co... |
1,854 | lean_file_chunk | 1383c4cf4c0c312300e14985a9f42e4eac074bb3547449171e74e3f2018d88aa | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Eric Wieser, Yaël Dillies, Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Yaël Dillies, Andrew Yang
-/
module
public import Mathlib.Algebra.Order.Ring.Canonical
public import Mathlib.Data.Finset.Lattice.Fold
public impor... |
8,238 | lean_file_chunk | 0244ef0051da485dd584e8a8b51a5253d439c3e09fd2650204e9066b7c2a095c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis
-/
module
public import Mathlib.Algebra.Order.Ring.Defs
public import Mathlib.Algebra.Ring.Parity
public import Mathlib.Tactic.Bound.Attribute
/-!
# Bas... |
2,016 | lean_file_chunk | 60fa14eb6ad36c1ae617f83b6ce3a25b3a94ffbf57e747febd1e857261000603 | 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, Leonardo de Moura, Mario Carneiro
-/
module
public import Mathlib.Algebra.Order.Monoid.Basic
public import Mathlib.Algebra.Order.Ring.Defs
/-!
# Pulling back ordered ri... |
11,076 | lean_file_chunk | 46ec90bf2c2c6fc2f4d7a9c402988e45395194110f4569b53d9136ffde22d28d | 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, Leonardo de Moura, Mario Carneiro, Yaël Dillies, Yuyang Zhao
-/
module
public import Mathlib.Algebra.Order.Ring.Unbundled.Basic
public import Mathlib.Algebra.CharZero.De... |
7,915 | lean_file_chunk | 764e6534528022cdfcd58ae0d5409c4a62b768f5bd359570d09e70ab1e11f90e | 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.Order.BigOperators.Group.Finset
public import Mathlib.Algebra.Order.Ring.Defs
public import Mathlib.Algebra.Ring.GeomSum
/-!
... |
10,344 | lean_file_chunk | d136377c31c9389f97a91e0035c39ab9d787a4f83e8d3c975fd44a796ccd2a04 | 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, Leonardo de Moura, Mario Carneiro
-/
module
public import Mathlib.Algebra.Order.Group.Abs
public import Mathlib.Algebra.Order.Ring.Basic
public import Mathlib.Algebra.Or... |
586 | lean_file_chunk | 5188bdbee2e866577f52397a8dd8d32f46ff8b91d87c0952716710dd213d878a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.Algebra.Ring.Subring.Units
public import Mathlib.GroupTheory.Index
/-! # Lemmas about units of ordered rings -/
public section
lemma Units.... |
4,126 | lean_file_chunk | 3d0a60b35e964b26b3c2bcf380b9be3dfee0b09206004777a730bafc8fc690e5 | 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.Algebra.Order.Group.Abs
public import Mathlib.Algebra.Order.Ring.Int
public import Mathlib.Data.Nat.Cast.Order.Ring
public import Mathli... |
3,906 | lean_file_chunk | fb7af9790387269c2a3468b99566dba2cbf39d0efaea594b5ea6300e067d093d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.Monoid.Canonical.Defs
public import Mathlib.Data.Finset.Lattice.Fold
public import Mathlib.Algebra.Order.Sub.Unbundled.Basic
... |
10,165 | lean_file_chunk | 569e13359780bb2b1e8841c3baa7da46b6d737e787ea7521b65bb0a60e63a786 | 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, Leonardo de Moura, Mario Carneiro, Johannes Hölzl, Yuyang Zhao
-/
module
public import Mathlib.Algebra.Group.Units.Basic
public import Mathlib.Algebra.Order.Monoid.Defs
... |
23,982 | lean_file_chunk | 7dd5e82d06d8da9b72e55a21f3f8bb1b25a297b217b99dde66c10cc7598f06e7 | 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, Leonardo de Moura, Mario Carneiro, Johannes Hölzl
-/
module
public import Mathlib.Algebra.CharZero.Defs
public import Mathlib.Algebra.Group.Hom.Defs
public import Mathli... |
4,886 | lean_file_chunk | 0c7efeb2910c2615ea116a0dff8b763c8afa467f6643326ab037ab160f094df5 | lean_source_file | pkg_mathlib_source_file_chunks | inferInstanceAs <| AddZeroClass (WithTop α)
section AddMonoid
variable [AddMonoid α]
instance addMonoid : AddMonoid (WithBot α) :=
inferInstanceAs <| AddMonoid (WithTop α)
/-- Coercion from `α` to `WithBot α` as an `AddMonoidHom`. -/
def addHom : α →+ WithBot α where
toFun := WithTop.some
map_zero' := rfl
ma... |
10,132 | lean_file_chunk | 0dc2f648d7f6f4da18cd8f1f616245becbbe20d74bf4cda8814e4146d8e38b94 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis, Yury Kudryashov
-/
module
public import Mathlib.Algebra.Order.Monoid.Unbundled.Basic
public import Mathlib.Algebra.Order.Monoid.Unbundled.OrderDual
publ... |
1,451 | lean_file_chunk | 0b3507dfd10d46b169b63d1049c6ba3f23957709e67192252271412ae034d0ef | 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, Leonardo de Moura, Mario Carneiro, Johannes Hölzl
-/
module
public import Mathlib.Algebra.Order.Group.Synonym
public import Mathlib.Algebra.Order.Monoid.Unbundled.Defs
... |
3,647 | lean_file_chunk | c54adc01a854bbe50f205e41c41f6c9299b7af28dcbe8dc232d6304b10112396 | 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, Leonardo de Moura, Mario Carneiro, Johannes Hölzl
-/
module
public import Mathlib.Algebra.Order.Monoid.Unbundled.Basic
/-!
# Lemmas about `min` and `max` in an ordered ... |
23,987 | lean_file_chunk | 31f8a51f1401e2012563fb086bf496cc2aec083e54e91fcb35bd43bc6c621408 | 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, Leonardo de Moura, Mario Carneiro, Johannes Hölzl, Damiano Testa,
Yuyang Zhao
-/
module
public import Mathlib.Algebra.Order.Monoid.Unbundled.Defs
public import Mathlib.D... |
23,974 | lean_file_chunk | 2baa479a5b2c05aa8af7bc0fa09adc5254bdb1a9f87dffb5d0b40aaef7305b3a | lean_source_file | pkg_mathlib_source_file_chunks | The lemma assuming right covariance is `Right.add_pos'`. -/]
theorem Left.one_lt_mul' [MulLeftMono α] {a b : α} (ha : 1 < a) (hb : 1 < b) :
1 < a * b :=
lt_mul_of_lt_of_one_lt' ha hb
/-! Lemmas of the form `a ≤ 1 → b ≤ c → a * b ≤ c`,
which assume right covariance. -/
@[to_additive]
theorem mul_le_of_le_one_of... |
1,926 | lean_file_chunk | 2f552f60295a8c0b7a3d25ceba2d849c0caf999347a854a57efec244885dfbc4 | lean_source_file | pkg_mathlib_source_file_chunks | protected theorem mul_le_mul_iff_right [Mul α] [IsMulCommutative α] [MulLeftMono α] {a b c : α}
(ha : MulLECancellable a) : b * a ≤ c * a ↔ b ≤ c := by
rw [mul_comm' b, mul_comm' c, ha.mul_le_mul_iff_left]
@[to_additive]
protected theorem le_mul_iff_one_le_right [MulOneClass α] [MulLeftMono α]
{a b : α} (ha ... |
22,317 | lean_file_chunk | fced058846824ee224e3e61c23c1614d785ecedae469f8edb1bf7c67880e7b7b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
module
public import Mathlib.Algebra.Group.Basic
public import Mathlib.Order.Basic
public import Mathlib.Order.Monotone.Defs
/-!
# Covariants and contravariants
Thi... |
4,849 | lean_file_chunk | 89137dc379c29a53037e41d5506489253527922ebd3560e52dea749fb186a58e | 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, Leonardo de Moura, Mario Carneiro, Johannes Hölzl
-/
module
public import Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE
public import Mathlib.Algebra.Group.TypeTags.... |
3,688 | lean_file_chunk | 4684414d3094bc93b6208257dc874b2a9e879d76f0189d6530baadd7054f03b5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson, Yaël Dillies
-/
module
public import Mathlib.Algebra.Order.Monoid.Unbundled.Basic
public import Mathlib.Order.MinMax
/-!
# Unbundled and weaker forms of canonically order... |
3,178 | lean_file_chunk | c8c2054c04cb8b4d0d7e3f68b1f98fba4de4965908ffd6fceb9c36e9d52b0831 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
module
public import Mathlib.Algebra.Group.Units.Basic
public import Mathlib.Algebra.Order.Monoid.Unbundled.Basic
/-!
# Lemmas for units in an ordered monoid
-/
public secti... |
3,194 | lean_file_chunk | dad6d3ec4888684f7f168a2fc74489e29da3a81de5f5645e66d1478f1e1570e0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jeremy Tan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
module
public import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
public import Mathlib.Data.Int.Interva... |
2,741 | lean_file_chunk | 74a78ef2b0a4c4fda0f8fa29c3521c88d38c2ff9bb171fd2e9cf764a2b6c7aa6 | 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.Group.Action.Defs
public import Mathlib.Algebra.Order.Group.Synonym
/-!
# Actions by and on order synonyms
This PR transfers group... |
735 | lean_file_chunk | 62cf062bb79e97355cd69416eafafc9a49d7517743a91cd0226e78982b085317 | 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.Group.Action.Pointwise.Set.Basic
public import Mathlib.Algebra.Order.Group.Action.End
public import Mathlib.Order.Preorder.Chain
/-... |
1,608 | lean_file_chunk | d137059d0d1af1ccba54ae1d5239a75e55b7cdf2ba06270ebffe21fb30c64da4 | 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.Group.Action.Faithful
public import Mathlib.Algebra.Order.Group.End
public import Mathlib.Order.RelIso.Basic
/-!
# Tautological act... |
4,641 | lean_file_chunk | e37c59f48ae2acab39622aae0b6cbcc7a8d40ea656604e5dba3ef70b7fda482e | 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
-/
module
public import Mathlib.Algebra.Order.Group.Unbundled.Abs
public import Mathlib.Algebra.Group.Int.Defs
public import Mathlib.Data.Int.Basic
/-!
# Facts about `ℤ`... |
22,866 | lean_file_chunk | a4b72e58733544ec80a4b87c08a5d1c2594d9b4f186acba72814a228796ab31a | 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, Leonardo de Moura, Mario Carneiro, Johannes Hölzl
-/
module
public import Mathlib.Algebra.Order.Monoid.Unbundled.Basic
public import Mathlib.Algebra.Order.Sub.Defs
/-!
... |
11,766 | lean_file_chunk | b98ea6c6cf718628c8c92b1f2fe5c49f9b2b47ee1d034f99efb41398e94b54cb | 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, Leonardo de Moura, Mario Carneiro, Johannes Hölzl
-/
module
public import Mathlib.Algebra.Group.Even
public import Mathlib.Algebra.Group.Pi.Basic
public import Mathlib.A... |
23,985 | lean_file_chunk | 4f671406f5211c12a1b3857c145d66a4edfef659f91fb6f6e2ddfe272f0a8844 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Patrick Massot
-/
module
public import Mathlib.Algebra.Group.Action.Defs
public import Mathlib.Algebra.Group.Pointwise.Set.Scalar
public import Mathlib.Algebra.Order... |
8,485 | lean_file_chunk | 1f07a4e4edb4deed58aa4a705e221528264071a156626ce0220abf4e4d284076 | lean_source_file | pkg_mathlib_source_file_chunks | (c * ·) ⁻¹' Icc a b = Icc (a / c) (b / c) := by simp [← Ici_inter_Iic, h]
@[simp]
theorem preimage_const_mul_Iio₀ (a : G₀) (h : 0 < c) : (c * ·) ⁻¹' Iio a = Iio (a / c) :=
ext fun _x => (lt_div_iff₀' h).symm
@[simp]
theorem preimage_const_mul_Ioi₀ (a : G₀) (h : 0 < c) : (c * ·) ⁻¹' Ioi a = Ioi (a / c) :=
ext fun ... |
3,857 | lean_file_chunk | f1a0e511914858cfd3f0b3bc1de727c4a7702f45b2a9a9b2d7165750136e8527 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Algebra.Order.Group.Pointwise.Bounds
public import Mathlib.Order.ConditionallyCompleteLattice.Indexed
/-!
# Infima/suprema in ordered... |
4,434 | lean_file_chunk | fa06dec7a114f362729822a52bb4812954478ef1f11efdcdf6f166af04299a79 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Algebra.Order.Group.OrderIso
public import Mathlib.Algebra.Order.Monoid.Unbundled.OrderDual
public import Mathlib.Order.Bounds.OrderIs... |
9,200 | lean_file_chunk | f63d48a6dc5e2a297e7ea40ae829991bb1f3c3f3a90a18fccf9210aa9e75120b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 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.SuccPred
public import Mathlib.Order.Interval.Finset.SuccPred
/-!
# Finset intervals in an additive successor-predecessor ord... |
3,680 | lean_file_chunk | 3f944c139a27af595e08d402a906bc29693d186fee505359a1ff637f3e14d1fd | 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.Group.Embedding
public import Mathlib.Algebra.Order.Interval.Set.Monoid
public import Mathlib.Order.Interval.Finset.Defs
/-!
# Alge... |
11,235 | lean_file_chunk | 2fe2b4e633e9f76eda8391bda2e88c48c8c8d2766c06ef2253fbc37ac88677ce | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Stuart Presnell. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stuart Presnell, Eric Wieser, Yaël Dillies, Patrick Massot, Kim Morrison
-/
module
public import Mathlib.Algebra.GroupWithZero.InjSurj
public import Mathlib.Algebra.GroupWithZero.Hom... |
3,944 | lean_file_chunk | 53ab92bd186d812967c794fc1a815ef920dbc82e93e4a4b06ea077a2a6b73bfe | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Patrick Massot
-/
module
public import Mathlib.Algebra.Group.Basic
public import Mathlib.Data.Set.Function
public import Mathlib.Order.Interval.Set.Basic
public impo... |
8,921 | lean_file_chunk | 56b36665395cade2e960a7bb5403d4af01cb54f599f1a088aaf4882ab4febb39 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 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.SuccPred
public import Mathlib.Order.Interval.Set.SuccPred
/-!
# Set intervals in an additive successor-predecessor order
Th... |
8,940 | lean_file_chunk | 6bc92979f992bbfe0f8e02470828c09d0cd60816618a5239f3081213d000da96 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot, Yury Kudryashov, Rémy Degenne
-/
module
public import Mathlib.Algebra.Order.Group.Abs
public import Mathlib.Algebra.Order.Group.Basic
p... |
10,922 | lean_file_chunk | 67b28dd73c1936cc84bc86f093bc19543cb930d4483e2e777b12b59eac78dfa0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
module
public import Mathlib.Algebra.Order.Monoid.Canonical.Defs
public import Mathlib.Algebra.Order.Monoid.Unbundled.OrderDual
public import Mathlib.Algebra.BigOp... |
23,913 | lean_file_chunk | efec5d1511fc11ccc39edac104f3a0303d7c41d97ddfc6f8c0240c5f85f3be1c | 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.Fintype.Card
public import Mathlib.Algebra.Order.BigOperators.Group.Multiset
public import Mathlib.Algebra.Order.Group.Nat
public i... |
6,865 | lean_file_chunk | 00fc63cee7a65f4694b8fc3d5129ee2a84b81e04e800396326892bfd555c9ec6 | lean_source_file | pkg_mathlib_source_file_chunks | rw [← mul_le_mul_iff_right, ← prod_union (disjoint_sdiff_inter _ _), sdiff_union_inter,
← prod_union, inter_comm, sdiff_union_inter]
simpa only [inter_comm] using disjoint_sdiff_inter t s
@[to_additive] lemma prod_sdiff_lt_prod_sdiff {ι M : Type*} [CommMonoid M] [PartialOrder M]
[IsOrderedCancelMonoid M] [Deci... |
7,424 | lean_file_chunk | ea09f2b7f8e218a8c701fd3dc7abc0cacc21c386a7dcb5870cd0629b1e2f3139 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
module
public import Mathlib.Algebra.BigOperators.Group.Multiset.Defs
public import Mathlib.Algebra.Order.BigOperators.Group.List
public import Mathlib.Algebra.Order... |
4,912 | lean_file_chunk | 10eb3e3d45aa6753166758d92f992b19d6ae23cea2600fa448cd8288e5714f5d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.BigOperators.Group.Finset.Sigma
public import Mathlib.Algebra.Order.Interval.Finset.SuccPred
public import Mathlib.Data.Nat.SuccPred... |
2,899 | lean_file_chunk | cef6efc46a8c2ea9e0034ef3edcca5bd7a061a58cf38d4559a4cb84e79495f87 | 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, Daniel Weber
-/
module
public import Mathlib.Algebra.BigOperators.Group.List.Defs
public import Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic
public import Mat... |
5,318 | lean_file_chunk | 64d210896fa69b1d20cb3c25766e6b6b55e7aa7040e0d3d78989910f99448907 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Michael Stoll, Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll, Floris van Doorn
-/
module
public import Mathlib.Algebra.BigOperators.Group.Finset.Basic
public import Mathlib.Algebra.Order.GroupWithZero.Unbundled.Ba... |
2,608 | lean_file_chunk | 2a4a7657134f3c946774bdcfb9325334f95b9db4af0e830b3ab81420d968b2fe | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Ruben Van de Velde. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ruben Van de Velde, Daniel Weber
-/
module
public import Mathlib.Algebra.BigOperators.Group.Multiset.Defs
public import Mathlib.Algebra.Order.BigOperators.GroupWithZero.List
/-!
... |
864 | lean_file_chunk | 0c7d0479d6cde27491c3e923d0e016ad8c8a4b6191c0a02362873b6410c9640f | 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.Ring.Canonical
public import Batteries.Data.List.Lemmas
/-!
# Big operators on a list in ordered rings
This file conta... |
11,450 | lean_file_chunk | 91ae1e0c1514d1209cb5f0573557b1e9867573c42ceb7763897dbfabd4dc0939 | 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
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.Order.AbsoluteValue.Basic
public import Mathlib.Algebra.Order.BigOper... |
2,460 | lean_file_chunk | e97473531205b093ee44e0943c37b5e525710b0d1d02d209b7b895f39128b075 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Ruben Van de Velde. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ruben Van de Velde
-/
module
public import Mathlib.Algebra.Order.BigOperators.GroupWithZero.Multiset
public import Mathlib.Algebra.Order.BigOperators.Ring.List
/-!
# Big operator... |
3,177 | lean_file_chunk | d4f22d3953ff92e8d4ea7cad44e04d34bb48a9f7c3928e0833132c85808eb1c9 | 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.GroupWithZero.Action.Defs
public import Mathlib.Algebra.Order.Group.Action.Synonym
public import Mathlib.Algebra.Order.GroupWithZero... |
2,668 | lean_file_chunk | 0a77ba046a0fa19962037a9a98ae78efa0f3096a25c3bf4243a70d832a44a109 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic
public import Mathlib.Algebra.GroupWithZero.Units.Equiv
public import Mathlib.Order.Hom.Basic
/-!... |
23,995 | lean_file_chunk | ec2c1f41bf1b7d4b813dd728fba847370af710e7966effb5c17ec44bb694e193 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa, Yuyang Zhao
-/
module
public import Mathlib.Algebra.GroupWithZero.Units.Basic
public import Mathlib.Algebra.Notation.Pi.Defs
public import Mathlib.Algebra.Order.GroupWit... |
23,978 | lean_file_chunk | 43091571b9ad58a1b69a9eb0d86c7e4fb77d477286a72349136cbe98b887026b | lean_source_file | pkg_mathlib_source_file_chunks | lemma pow_lt_pow_right_of_lt_one₀ (h₀ : 0 < a) (h₁ : a < 1) (hmn : m < n) : a ^ n < a ^ m :=
(pow_lt_pow_iff_right_of_lt_one₀ h₀ h₁).2 hmn
lemma pow_lt_self_of_lt_one₀ (h₀ : 0 < a) (h₁ : a < 1) (hn : 1 < n) : a ^ n < a := by
simpa only [pow_one] using pow_lt_pow_right_of_lt_one₀ h₀ h₁ hn
end strict_mono
variable... |
11,823 | lean_file_chunk | c7e6a5a4fb4f73002fb5050b02d9a7d95f3e45bddc5de189943b25dd059a5fa5 | lean_source_file | pkg_mathlib_source_file_chunks | · rwa [mul_inv_le_iff₀ hb]
/-- One direction of `le_div_iff₀` where `c` is allowed to be `0` (but `b` must be nonnegative). -/
lemma mul_le_of_le_div₀ (hb : 0 ≤ b) (hc : 0 ≤ c) (h : a ≤ b / c) : a * c ≤ b :=
mul_le_of_le_mul_inv₀ hb hc (div_eq_mul_inv b _ ▸ h)
/-- One direction of `div_le_iff₀` where `b` is allowed... |
21,648 | lean_file_chunk | c9bbc7a5425e497102b33e4c899148ab6928545bef3ca18923f23a328a2720fc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa, Yuyang Zhao
-/
module
public import Mathlib.Algebra.Order.Monoid.Unbundled.Defs
public import Mathlib.Tactic.MkIffOfInductiveProp
public import Mathlib.Util.Notation3
/... |
11,115 | lean_file_chunk | e5d1149829e10dc0a230f8fe6b99c1e38c540708e13c7a63164cb97a7b2282f2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 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.Sub.Defs
public import Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE
/-!
# Lemmas about subtraction in an unbundl... |
2,523 | lean_file_chunk | 91df108bb42489bf4a145538a837383ba05cf0f051dee1df81374eca07605954 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 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.Group.Equiv.Defs
public import Mathlib.Algebra.Order.Sub.Unbundled.Basic
public import Mathlib.Algebra.Ring.Basic
public imp... |
5,643 | lean_file_chunk | 50fa40c3aaa1b3cef2630bf690703e4a2882b92a66f4efd0e4b36b6c35e92596 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Florent Schaffhauser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Florent Schaffhauser, Artie Khovanov
-/
module
public import Mathlib.Algebra.Field.IsField
public import Mathlib.Algebra.Order.Ring.Ordering.Defs
public import Mathlib.Algebra.R... |
6,138 | lean_file_chunk | e80aee3a50e28e1f01b817fe961072f4b319b42d01efc120634145502804783b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Florent Schaffhauser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Florent Schaffhauser, Artie Khovanov
-/
module
public import Mathlib.Algebra.Ring.Subsemiring.Defs
public import Mathlib.RingTheory.Ideal.Prime
public import Mathlib.Algebra.Gro... |
5,850 | lean_file_chunk | 41be128654e7232ad0c2698e5708e705bbca348b6b799e126a27c754d7cbf9b1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
module
public import Mathlib.Algebra.Order.Group.Unbundled.Abs
public import Mathlib.Algebra.Order.Group.Unbundled.Basic
public import Mathlib.Algebr... |
23,963 | lean_file_chunk | 41277fb722ed2572270f8d8345b5cdd91890684224261142bdd1322c4fd4ec4b | 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, Leonardo de Moura, Mario Carneiro, Yaël Dillies
-/
module
public import Mathlib.Algebra.Group.Units.Basic
public import Mathlib.Algebra.GroupWithZero.NeZero
public impor... |
13,175 | lean_file_chunk | ab2264d85c9635db2ecc69cd4c714c3d7ef45422c1ba40023e4f467bcbe6554e | lean_source_file | pkg_mathlib_source_file_chunks | theorem mul_self_lt_mul_self_iff [PosMulStrictMono R] [MulPosMono R]
{a b : R} (h1 : 0 ≤ a) (h2 : 0 ≤ b) : a < b ↔ a * a < b * b :=
((@strictMonoOn_mul_self R _).lt_iff_lt h1 h2).symm
theorem mul_self_inj [PosMulStrictMono R] [MulPosMono R]
{a b : R} (h1 : 0 ≤ a) (h2 : 0 ≤ b) : a * a = b * b ↔ a = b :=
(@s... |
2,183 | lean_file_chunk | 4726264f5ae7b5110685f4171d39e7a17b8b1ff6f3e9dec07f4a691809644e0a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yaël Dillies, Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Andrew Yang
-/
module
public import Mathlib.Algebra.Category.Grp.Basic
public import Mathlib.Algebra.Group.Pi.Lemmas
public import Mathlib.CategoryTheory.Yone... |
4,576 | lean_file_chunk | 0ece2ed4f57f871fa3f5c01b22360f0ad24ee84823de0e2689f22f1d8689d407 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Algebra.Group.Pi.Lemmas
public import Mathlib.Algebra.Category.Grp.Preadditive
public import Mathlib.CategoryTheory.Preadditive.Biproducts
p... |
5,858 | lean_file_chunk | 52e1c26dd07edecb70f229a5a8464398f25b739172cd2a8b8e14cb3b1ff1e21d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
module
public import Mathlib.Algebra.Category.Grp.Biproducts
public import Mathlib.Algebra.Category.Grp.Zero
public import Mathlib.Algebra.Ring.PUnit
public import Mat... |
12,851 | lean_file_chunk | aa6fff50d78b2b27228636a3f4b53901488a4d9049dbbc7888b2e19a973f56ac | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
module
public import Mathlib.Algebra.Category.Grp.EquivalenceGroupAddGroup
public import Mathlib.CategoryTheory.ConcreteCategory.EpiMono
public import Mathlib.CategoryTh... |
1,920 | lean_file_chunk | b9f6f19f33a16835f3f3de365420967ed0e235c3af17eeb2fdd52777e49a0864 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.Algebra.Category.Grp.Abelian
public import Mathlib.Algebra.Category.Grp.EpiMono
public import Mathlib.Algebra.Category.Grp.Zero
public import Math... |
1,458 | lean_file_chunk | 218fafa50f0dc3724a0aa496c26730c2a1e2e6098af2db61d8d8e14b9dd8f3d5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
module
public import Mathlib.Algebra.Category.Grp.Colimits
public import Mathlib.Algebra.Category.Grp.Limits
public import Mathlib.Algebra.Category.Grp.ZModuleEquivale... |
1,773 | lean_file_chunk | aaf2fcb901fb08e81ce9902dc44f3e37dde6dea47bba31589fa64ba8a310fc6e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Junyan Xu
-/
module
public import Mathlib.Algebra.Module.CharacterModule
public import Mathlib.Algebra.Category.Grp.EquivalenceGroupAddGroup
public import Mathlib.Algebra.... |
2,128 | lean_file_chunk | a93c29fe92c1a105727c8245f6214229fa13b956d75ae7dfb15980fe2976d7c3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Nailin Guan, Yuyang Zhao
-/
module
public import Mathlib.Data.Finite.Defs
public import Mathlib.Algebra.Category.Grp.Basic
/-!
## Main definitions and results
* `Finite... |
1,849 | lean_file_chunk | c3891a361cb4b26ab24461d903ee6df6a538e8a8894c842966c2fc20af7bc2b9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
module
public import Mathlib.Algebra.Category.Grp.Basic
public import Mathlib.CategoryTheory.Preadditive.Basic
/-!
# The category of additive commutative groups is pr... |
21,290 | lean_file_chunk | 768deae5b346270554373ccfbd8fc503819389fb303f7d89bc75eef18198dfe6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
module
public import Mathlib.Algebra.Category.MonCat.Basic
public import Mathlib.Algebra.Group.End
public import Mathlib.CategoryTheory.Endomorphism
public import Ma... |
9,643 | lean_file_chunk | 893124ff00356917466b0aefc011b2190a7da6106264119b4bb3373f836fbf20 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Sophie Morel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sophie Morel
-/
module
public import Mathlib.Algebra.Category.Grp.LargeColimits
public import Mathlib.Algebra.Category.Grp.Limits
public import Mathlib.Algebra.Module.CharacterModule
pu... |
8,906 | lean_file_chunk | 5e19b093a46af4fe096c4c1665376caa1570ef55236ea941e950631afae6559b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Justus Springer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Justus Springer
-/
module
public import Mathlib.Algebra.Category.Grp.Basic
public import Mathlib.Algebra.Category.MonCat.FilteredColimits
/-!
# The forgetful functor from (commutati... |
600 | lean_file_chunk | 45e4d22f5fb117c03a970298c6ee4c7f23c73a74022661ae3007c3a77d4f0367 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
module
public import Mathlib.Algebra.Category.Grp.ZModuleEquivalence
public import Mathlib.Algebra.Category.ModuleCat.Subobject
/-!
# The category of abelian groups i... |
1,753 | lean_file_chunk | eae5017a75e1be6522d7c1f80b3fcc0f7e89c8d0ec6fccfe602a099866553a9f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Algebra.Category.ModuleCat.Basic
/-!
The forgetful functor from ℤ-modules to additive commutative groups is
an equivalence of categories.
... |
3,015 | lean_file_chunk | 4e26e7b309ce490330dc340fede11d6a5d6a711a94e26bb925b23c08a40226b3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
module
public import Mathlib.Algebra.Category.Grp.Basic
public import Mathlib.CategoryTheory.Yoneda
/-!
# The forget functor is corepresentable
It is shown that the forget f... |
1,957 | lean_file_chunk | 444901b6da1fa0e21e6e9820068be800beedf4f868f6c9917e856f69273cbac4 | 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: David Kurniadi Angdinata, Moritz Firsching, Nikolas Kuhn
-/
module
public import Mathlib.Algebra.Category.Grp.EpiMono
public import Mathlib.Algebra.Category.Grp.Preadditive
public i... |
1,771 | lean_file_chunk | 520243210ce8cecf7cf45d443609892367b46c99020d8cbc3a0d7966452046e2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.Algebra.Category.Grp.Basic
public import Mathlib.CategoryTheory.ShrinkYoneda
public import Mathlib.Algebra.Group.Shrink
/-!
# Shrin... |
5,870 | lean_file_chunk | 0ebe2b4478d793bbf51a6704f5f43bb79920d91a25fb959c0fbd24b4a77b152f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
module
public import Mathlib.Algebra.Category.Grp.CartesianMonoidal
public import Mathlib.Algebra.Category.Grp.EquivalenceGroupAddGroup
public import Mathlib.CategoryT... |
2,088 | lean_file_chunk | 454b00b96fb5e3edbc9b56bbb28aa0e773ee5724390e1ae751b2ab3655cb123d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
module
public import Mathlib.Algebra.Category.Grp.ZModuleEquivalence
public import Mathlib.Algebra.Category.ModuleCat.Injective
public import Mathlib.Algebra.EuclideanDo... |
12,275 | lean_file_chunk | b1389484dd3497fc7429e82d1e56c43d63d8ff4b50b7f9772a1230467db52f2d | 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, Sophie Morel
-/
module
public import Mathlib.Algebra.Category.Grp.Preadditive
public import Mathlib.Algebra.Group.Shrink
public import Mathlib.CategoryTheory.ConcreteCateg... |
4,992 | lean_file_chunk | c17ece8895b1c403617c203074990991c9f774e84dc84bc9763ba647fedd9f9c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata, Moritz Firsching, Nikolas Kuhn, Amelia Livingston
-/
module
public import Mathlib.Algebra.Category.Grp.Biproducts
public import Mathlib.Algebra.Cat... |
2,626 | lean_file_chunk | e1e3fe04a92d2e3ce5de11fd82129cee42bffd7d203ddfa5ba582e34f5e8dc01 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Sophie Morel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sophie Morel
-/
module
public import Mathlib.Algebra.Category.Grp.Colimits
public import Mathlib.Algebra.Module.CharacterModule
public import Mathlib.Algebra.Group.Equiv.Basic
/-!
# Ex... |
20,767 | lean_file_chunk | 58a2a9dd4178dbc010f3bb9696363685d33f7db7fcbe751abdc80fdc400cc6ae | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Algebra.Category.Grp.ForgetCorepresentable
public import Mathlib.Algebra.Category.Grp.Preadditive
public import Mathlib.Algebra.Category.Mon... |
7,885 | lean_file_chunk | 53fce6d6e1191554cb01c1b4452e2110d47e31c114b79bc3c8dc2307d682c591 | 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, Johannes Hölzl
-/
module
public import Mathlib.Algebra.Category.Grp.Preadditive
public import Mathlib.GroupTheory.FreeAbelianGroup
public import Mathlib.CategoryTheory.Adj... |
3,292 | lean_file_chunk | 0e99ee7f12a6465693728b5eadbd4ea553ae05cb63fd7b2feb387baf756c7af9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Algebra.Category.Grp.Abelian
public import Mathlib.CategoryTheory.Limits.Shapes.Images
/-!
# The category of commutative additive groups ha... |
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