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 |
|---|---|---|---|---|---|
8,848 | lean_file_chunk | 0460daf4c4c99c8de34a1c3ed9f41acf0b4964b42dee5bd52f4e1270d7e4aab3 | 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.GroupWithZero.Canonical
public import Mathlib.Algebra.Order.Hom.Monoid
/-!
# Ordered monoid and group homomorphisms
This fil... |
13,577 | lean_file_chunk | 66cc1ace46ca3b368aa250e0b65580ffc7eb4f17dfea522324212e2edf83be2e | 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.GroupWithZero.Hom
public import Mathlib.Algebra.Order.Group.Abs
public import Mathlib.Algebra.Ring.Defs
/-!
# Algebraic order homom... |
569 | lean_file_chunk | 984d0721849abb725c4864b9d17c88cf2d70c9b85c4897b81fb22ffafe3b8dec | 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.Submonoid.Operations
public import Mathlib.Algebra.Order.Hom.Monoid
/-!
# Isomorphism of submonoids of ordered monoids
-/
@[expose... |
3,851 | lean_file_chunk | 86550eb12543584bccf2c23545abef902314b25586695da6fc2013eda8baa708 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
module
public import Mathlib.Algebra.Group.Equiv.TypeTags
public import Mathlib.Algebra.Order.Hom.Monoid
public import Mathlib.Algebra.Order.Monoid.Unbundled.TypeT... |
677 | lean_file_chunk | eb7c068454a8f258bdbddb08dc593987dfdabd6b88780773df3935c1fb83b86d | 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.Equiv
public import Mathlib.Algebra.Order.Hom.Monoid
public import Mathlib.Algebra.Order.Monoid.Units
/-! # Isomorphism of or... |
1,728 | lean_file_chunk | b228cb690000db12f7ee7e370fb2081e3eb7883fed48e77a950326e712c5bf6c | 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, Oliver Butterley, Lua Viana Reis
-/
module
public import Mathlib.Algebra.Order.SuccPred
public import Mathlib.Order.PartialSups
public import Mathlib.Order.SuccPred.Linear... |
1,199 | lean_file_chunk | 0725170064ace33ed27983d6fdcad3e35db6aae4413acc8e0c7b93b5c8cf0484 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.Order.Monoid.Unbundled.WithTop
public import Mathlib.Algebra.Order.SuccPred
public import Mathlib.Order.Su... |
2,089 | lean_file_chunk | bf74bb552684a424aeb9df49ee25770fa8f40c03371d447cabe81628cd6b927f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
module
public import Mathlib.Order.SuccPred.Archimedean
public import Mathlib.Algebra.Order.Monoid.Unbundled.TypeTags
/-!
# Successor and predecessor on type tags... |
2,994 | lean_file_chunk | 33c054e354f0543f3074cd187f7ef4f83df1900e928d839ac38fb21cfa0c54f4 | 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.Units.Equiv
public import Mathlib.Algebra.Order.Group.Unbundled.Basic
pub... |
4,512 | lean_file_chunk | 09772a86f6fc53232537e6d42cad71c2700e270abb2b2b275889b0c9e7934700 | 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.Defs
public import Mathlib.Algebra.Order.Group.Unbundled.Basic
publ... |
14,669 | lean_file_chunk | 04661ed1b296f1c2ec31e2f44a727d7e93f42783cd4c5167fafc4a815f5b4696 | 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, Yaël Dillies
-/
module
public import Mathlib.Algebra.Group.Defs
public import Mathlib.Order.OrderDual
public import Mathlib.Order.Lex
/-!
# Group structure on the o... |
2,453 | lean_file_chunk | 7d0b63d6624c5a8263b6c86b534d2af45545ecd59088060a50b05c90392301a2 | 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.Group.Opposite
public import Mathlib.Algebra.Order.Monoid.Defs
/-!
# Order instances for `MulOpposite`/`AddOpposite`
This file tra... |
710 | lean_file_chunk | 1afe8bb5d90461551b14aa54f8bee162334c77cf0d2b3732ffbf4461aa98cf34 | 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.Group.Int.Defs
public import Mathlib.Algebra.Order.Monoid.Defs
/-!
# The integers form a linear ordered group
This file contains... |
7,857 | lean_file_chunk | cb93d1e45b92bf18ecd48f7e5773b3ea9c1636d6f70bbf581dbd699ad9ec5b21 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Algebra.Group.Indicator
public import Mathlib.Order.ConditionallyCompleteLattice.Indexed
public import Mathlib.Algebra.Order.Group.Syn... |
3,255 | lean_file_chunk | e29f3fb59a26a1ca601008bbd95e0e1ad9e2f8b34b4ead76ad1c354166a5518a | 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.Abs
public import Mathlib.Algebra.Order.Monoid.Unbundled.MinMax
/-... |
4,048 | lean_file_chunk | 4fcc43495f9ac4e84126afc6ebf3bd8dd5a7ef26008dbf124534e24006ec2fcc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 María Inés de Frutos-Fernández, Filippo A. E. Nuccio. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: María Inés de Frutos-Fernández, Filippo A. E. Nuccio
-/
module
public import Mathlib.Algebra.Order.Group.Basic
public import Mathlib.GroupTheory.... |
1,683 | lean_file_chunk | f5636b02911b45fcb97834fe5638a26ce8d8d09799995e92595163f6b3e5a688 | 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.Group.Nat.Defs
public import Mathlib.Algebr... |
5,389 | lean_file_chunk | 1b92745070d57979a404a9835963e16bafcb526837c229aceaaee5b69d46cbdd | 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, Kim Morrison, Artie Khovanov
-/
module
public import Mathlib.Algebra.Group.Subgroup.Defs
public import Mathlib.Algebra.Order.Group.Unbundled.Basic
public import Mathli... |
4,903 | lean_file_chunk | c84263e1676b3ba07d3efe281d26a64b42b0a8ea2b747fcb4dd81f7791386faa | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.Order.Group.OrderIso
public import Mathlib.Algebra.Order.Monoid.Canonical.Defs
public import Mathlib.Algeb... |
4,100 | lean_file_chunk | e88979aec2853e7dda6b64327d1e8519911e7652bf876505a35473659e51f037 | 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.Group.Unbundled.Basic
public import Mathlib.Algebra.Order.Monoid.Defs
public import Mathlib.Algebra.Order.M... |
6,149 | lean_file_chunk | 8c01bfd92f3898797c9ea3e94f6ff45c4d0630206ef0659b43a939b928db6428 | 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.Group.Hom.Defs
public import Mathlib.Algebra.Group.Nat.Defs
public import Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOf... |
816 | lean_file_chunk | ec984d1be7e80b5c79d9d760dfb9c84c8908fed629b7d4a84c41c6daddef64e8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Lua Viana Reis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lua Viana Reis
-/
module
public import Mathlib.Algebra.Order.Group.OrderIso
public import Mathlib.Order.PartialSups
/-!
# Results about `partialSups` of functions taking values in a ... |
2,524 | lean_file_chunk | b55a64737c48b47db8a686bc60e1e196e96bae49973d04c6a2900400a7061ecf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Dexin Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dexin Zhang
-/
module
public import Mathlib.Algebra.Group.Ideal
public import Mathlib.Algebra.Order.Monoid.Canonical.Defs
public import Mathlib.Order.WellFoundedSet
/-!
# Semigroup idea... |
2,232 | lean_file_chunk | 9bee623f3c1f563449242c7f3cb87b5ea79585201955aa198df129b64e17f755 | 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.Group.Defs
public import Mathlib.Order.RelIso.Basic
/-!
# Relation isomorphisms form a group
-/
@[expose] public section
asse... |
4,687 | lean_file_chunk | 6cb504eda7bb6e0ddc7ad40d7a66d1ce4225753d2610a5036109f6ef4a290d00 | 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.Unbundled.Basic
public import Mathlib.Algebra.Order.Monoid.Defs
pub... |
2,253 | lean_file_chunk | dc967f7f5ceae443558726df1f724c2862f3db1663a5bb19e4d6504d6be6108c | 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.Group.Action.Defs
public import Mathlib.Algebra.Order.Monoid.Unbundled.Defs
public import Mathlib.Order.ConditionallyCompleteLattice.B... |
1,296 | lean_file_chunk | 2596aae85d42b5df9e36c29bc3b941f9fc7dbad9eaf7538ee4b6e96688c68000 | 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
-/
module
public import Mathlib.Algebra.Group.Equiv.Defs
public import Mathlib.Algebra.Order.Group.Synonym
/-!
# Add/Mul equivalence for order type synonyms
-/
@[expose] publ... |
10,741 | lean_file_chunk | d6c048f3f5e21f7bbf6ab72910450dce394bc4e7a292d7904bf3b9aedfbef1ca | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin, Yaël Dillies
-/
module
public import Mathlib.Algebra.Order.Group.Unbundled.Abs
public import Mathlib.Algebra.Notation
/-!
# Positive & negative parts
Mathema... |
1,424 | lean_file_chunk | f79933e6bcded5f5a06f33e3c1463e4e3a750877be988223188dba7b34016da0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
module
public import Mathlib.Algebra.Order.Group.OrderIso
public import Mathlib.Order.ConditionallyCompleteLattice.Indexed
/-!
# Distributivity of group ope... |
10,257 | lean_file_chunk | 92c4999b48e61a9fb6d6a2dd9ea223b901d154b412e629eb3a32fdfbcb112a14 | 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.Defs
public import Mathlib.Algebra.Order.Group.Unbundled.Abs
public... |
4,276 | lean_file_chunk | e3d1e54797f0977b28d8d5c49d04a84bb9641cfd0fc143af879cad6aa60af368 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin, Yaël Dillies
-/
module
public import Mathlib.Algebra.Order.Group.OrderIso
/-!
# Lattice ordered groups
Lattice ordered groups were introduced by [Birkhoff][b... |
827 | lean_file_chunk | 8bfa37b98b3f251c866fa181a979d8706f9d5ee725153437aaa303b2106755d4 | 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.Defs
public import Mathlib.Algebra.Order.Monoid.Units
/-!
# The u... |
1,226 | lean_file_chunk | 35c30a118773c499e90afd05e0eacbcb7aa77aeb63f8bbd20515a9602da35093 | 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, Yury Kudryashov
-/
module
public import Mathlib.Order.Bounds.Basic
public import Mathlib.Algebra.Order.Monoid.Defs
public import Mathlib.Algebra.Order.Group.Unbundled.... |
1,172 | lean_file_chunk | 9ff8bd6721d56c6ef0eb06d6e90942d897474acefc6b60654ee54941a0858dcf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
module
public import Mathlib.Algebra.Group.Pi.Basic
public import Mathlib.Algebra.Order.Group.Synonym
public import Mathlib.Algebra.Order.Monoid.Defs
public import Mathl... |
17,161 | lean_file_chunk | eb5742854878a9f11b73d391b692c89ecd86d0d21bc4e797d65017b2d0570168 | 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.Ring.Prod
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
public import Mathlib.Algebra.Order.Ring.Canonical
public im... |
2,088 | lean_file_chunk | 05348841495b0d73655cbc6f2cbbabc3585aa682796b01c6c50e8241c0988725 | 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.Order.Interval.Finset.Basic
public import Mathlib.Order.Interval.Multiset
/-!
# Algebraic properties of multiset intervals
This fi... |
9,080 | lean_file_chunk | 25c8a70ed66d688415ddbddbe50fa00c5f157d44f14a0479375464c1156dac80 | 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.Expect
public import Mathlib.Algebra.Module.Rat
public import Mathlib.Algebra.Order.BigOperators.Ring.Finset
public imp... |
1,277 | lean_file_chunk | 35282ec96d5993daaac1026cb76397b7fa33ed88c3f1f6866dcced26b9bdf881 | 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.Module.Defs
public import Mathlib.Algebra.Order.GroupWithZero.Action.Synonym
public import Mathlib.Algebra.Order.Ring.Synonym
/-!
#... |
2,140 | lean_file_chunk | deceda1f13dfb0b9d8fc68d069f74ad4edd9cc7255a0c21cfd9cb9307fc64701 | 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.Module.Rat
public import Mathlib.Data.Rat.Cast.Order
public import Mathlib.Algebra.Order.Module.Defs
/-!
# Monotonicity of the acti... |
23,960 | lean_file_chunk | 8566771f208c68c23bf876915e4255b279f3ade0435f8496b1f473b79eefa65a | 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
-/
module
public import Mathlib.Algebra.DirectSum.Decomposition
public import Mathlib.Algebra.DirectSum.Module
public import Mathlib.Algebra.Module.Submodule.Order
public impor... |
22,836 | lean_file_chunk | 7e9b97975e56ec9126d13c9b708d66151d3d3442b01801b8165f67edf55fc1ed | lean_source_file | pkg_mathlib_source_file_chunks | set_option backward.isDefEq.respectTransparency false in
/-- Evaluate coefficients of the `HahnSeries` given an arbitrary input that's not necessarily in
`f`'s domain. The coefficient is picked from `y` that is "close enough" to `x` (their difference
is in a higher `ArchimedeanClass`). If no such `y` exists (in other w... |
5,783 | lean_file_chunk | cc16d8d27ca33a49f2a1fc89698b7119d2da009aa0c91e4002d76bd7f9764519 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
module
public import Mathlib.Algebra.Module.LinearMap.Defs
public import Mathlib.Algebra.Order.Hom.Monoid
public import Mathlib.Tactic.ContinuousFunctionalCalculus... |
3,646 | lean_file_chunk | 01b900edf3055db56c03ce70511214d2cfac74d5670dadd4dcc20994b585ef32 | 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.Pointwise.Set.Scalar
public import Mathlib.Algebra.Order.Module.Field
public import Mathlib.Order.Bounds.OrderIso
public impor... |
6,866 | lean_file_chunk | ed79b331a1a5e5ed5c773dffa060fe09639e03e201f61832259de7e7f8551134 | 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
-/
module
public import Mathlib.Algebra.Module.Submodule.Basic
public import Mathlib.Algebra.Module.Submodule.Lattice
public import Mathlib.Algebra.Order.Archimedean.Class
publ... |
2,072 | lean_file_chunk | fc2399ae1913dc3c6b8929c0a237d7024b621f0737c7006502531a501dc5ec00 | 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
-/
module
public import Mathlib.Algebra.Field.Defs
public import Mathlib.Algebra.GroupWithZero.Invertible
public import Mathlib.Algebra.Order.Group.Unbundled.Abs
public import ... |
23,964 | lean_file_chunk | fafbc61253d632e38d3069361464a727d7acb5c18baa893adc4aa404c858b41f | 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.Module.Torsion.Free
public import Mathlib.Algebra.Order.Group.Basic
public import Mathlib.Algebra.Order.GroupWithZero.Action.Synonym... |
23,970 | lean_file_chunk | 7087511ba24e4c50d0f2611780b58ed4921c24aad400dbe21fbe239f866afa4e | lean_source_file | pkg_mathlib_source_file_chunks | lemma smul_nonneg [PosSMulMono α β] (ha : 0 ≤ a) (hb : 0 ≤ b₁) : 0 ≤ a • b₁ := by
simpa only [smul_zero] using smul_le_smul_of_nonneg_left hb ha
lemma smul_nonpos_of_nonneg_of_nonpos [PosSMulMono α β] (ha : 0 ≤ a) (hb : b ≤ 0) : a • b ≤ 0 := by
simpa only [smul_zero] using smul_le_smul_of_nonneg_left hb ha
lemma ... |
6,398 | lean_file_chunk | 18b1469a9ae70174d99d0b2767a05e5ba6661b1b1dc3f3cfb3be74e5f8c44752 | lean_source_file | pkg_mathlib_source_file_chunks | instance instSMulPosStrictMono [SMulPosStrictMono α β] [SMulPosStrictMono α γ] :
SMulPosStrictMono α (β × γ) where
smul_lt_smul_of_pos_right := by
simp_rw [lt_iff]
rintro a (⟨h₁, h₂⟩ | ⟨h₁, h₂⟩) _b₁ _b₂ hb
· exact .inl ⟨smul_lt_smul_of_pos_right hb h₁, smul_le_smul_of_nonneg_right hb.le h₂⟩
· exac... |
1,049 | lean_file_chunk | 57eb809257e6e184991240c7e707f21062b70142bdbaf442bfbd1c5abb3b526c | 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
-/
module
public import Mathlib.Algebra.Module.Equiv.Basic
public import Mathlib.Algebra.Order.Group.Equiv
public import Mathlib.Algebra.Order.Module.Synonym
/-!
# Linear equi... |
4,960 | lean_file_chunk | 2350af78d51c9a52f3c4b3ccda789b309247400cbec5f87ecb71c8edcfa20ddb | 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.Order.Module.Defs
public import Mathlib.Algebra.Field.Defs
public import Mathlib.Tactic.Positivity.Core
public import Mathlib.Algebr... |
363 | lean_file_chunk | 533480ef3d6a28f3c8f5d61d44258c4b49d1ff8a6ea442b5b2be3db12cf23269 | 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 -- shake: keep-all
public import Mathlib.Algebra.Order.Algebra
deprecated_module (since := "2025-12-16")
public section
@[deprecated (since := "2025-12-16")] a... |
14,505 | lean_file_chunk | 8060faf2857b5f884f9e69a3caf627e959bdb9856abfdca0c6d095afc98970a9 | 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, Robert Y. Lewis
-/
module
public import Mathlib.Algebra.Order.CauSeq.Basic
public import Mathlib.Algebra.Ring.Action.Rat
public import Mathlib.Tactic.FastInstance
/-!... |
23,986 | lean_file_chunk | 17735e59afb89425c3d362644bdb115a4366085b33be7fda24b31c42e0e5e190 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
public import Mathlib.Algebra.Group.Action.Pi
public import Mathlib.Algebra.Order.AbsoluteValue.Basic
public import Mathlib.Algebra.Order.Field.Basic
public i... |
8,183 | lean_file_chunk | 3ef722e35dfc23776935bc773bf761a9c5672eb09a0e38acfdb2ab243663e153 | lean_source_file | pkg_mathlib_source_file_chunks | | Or.inl fg, Or.inr gh => Or.inl <| lt_of_lt_of_eq fg gh
| Or.inr fg, Or.inl gh => Or.inl <| lt_of_eq_of_lt fg gh
| Or.inr fg, Or.inr gh => Or.inr <| Setoid.trans fg gh
lt_iff_le_not_ge _ _ :=
⟨fun h => ⟨Or.inl h, not_or_intro (mt (lt_trans h) lt_irrefl) (not_limZero_of_pos h)⟩,
fun ⟨h₁, h₂⟩ => h₁.r... |
9,699 | lean_file_chunk | fe965631e2bd30f06dce7b733de342297184f938e77dc1b9a190653a18681639 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Yaël Dillies
-/
module
public import Mathlib.Algebra.Field.GeomSum
public import Mathlib.Algebra.Order.Archimedean.Basic
public import Mathlib.Algebra.Order.BigOperators.R... |
8,028 | lean_file_chunk | 222fb5ea5beb968f112641dee786af2cabcc3113c80471bff85e9a657ed1b29d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Antoine Chambert-Loir and María Inés de Frutos-Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir, María Inés de Frutos-Fernández, Bhavik Mehta, Eric Wieser
-/
module
public import Mathlib.Algebra.Order.Monoid.Canonic... |
12,608 | lean_file_chunk | 3ca75d61e3ff1072a9ffb3fc724f3b86de8ce263a45197b6719c5c55d3577426 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Arend Mellendijk. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Arend Mellendijk
-/
module
public import Mathlib.Algebra.Order.Antidiag.Pi
public import Mathlib.Algebra.Order.BigOperators.Ring.Finset
public import Mathlib.NumberTheory.Arithmetic... |
10,817 | lean_file_chunk | 9971fa1220f471e90ef36aadcfeaf445a2c4964dbabedd99c74f253c24437817 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Antoine Chambert-Loir and María Inés de Frutos-Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir, María Inés de Frutos-Fernández, Eric Wieser, Bhavik Mehta,
Yaël Dillies
-/
module
public import Mathlib.Algebra.Grou... |
2,986 | lean_file_chunk | 6aa7a00a1817251e237bd975291770e2dd0744963bc1eb3471473fc8081ce87f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Weiyi Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Weiyi Wang
-/
module
public import Mathlib.Algebra.Order.Antidiag.Finsupp
public import Mathlib.Data.Finsupp.Basic
public import Mathlib.Data.Finsupp.Multiset
import Mathlib.Data.Sym.Card... |
6,348 | lean_file_chunk | adaaaaf00e87c23970bc3ff71afe547e94361bd92f53a45e3677e89c708f4ad2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Antoine Chambert-Loir and María Inés de Frutos-Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir, María Inés de Frutos-Fernández, Eric Wieser, Bhavik Mehta,
Yaël Dillies
-/
module
public import Mathlib.Algebra.BigO... |
3,968 | lean_file_chunk | 0cfc13406296ecab61b7c4dd113658a55301175bfbaa357c6ede9e83047cb606 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Stefan Kebekus. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefan Kebekus
-/
module
public import Mathlib.Algebra.Order.AddGroupWithTop
public import Mathlib.Algebra.Order.Ring.WithTop
/-!
# Conversion from WithTop to Base Type
For types α ... |
2,420 | lean_file_chunk | 450115f077372b44437b4428bf4c3191ad47b9c940420bd830e739f558b7d083 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
module
public import Mathlib.Algebra.GroupWithZero.Defs
public import Mathlib.Algebra.Order.Group.Synonym
/-!
# Group with zero structure on the order type synonyms... |
2,904 | lean_file_chunk | 9b42bef419471e9343d82261b70549f56a31e36310699581231a9177cb0cdaf0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard
-/
module
public import Mathlib.Algebra.Order.GroupWithZero.Canonical
public import Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic
/-!
# Covariant instances on `Wit... |
23,527 | lean_file_chunk | d8e00c6ebbf1c824630d8720ea199c9efbd4628ab32404437e7d765257d1f632 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Johan Commelin, Patrick Massot
-/
module
public import Mathlib.Algebra.Group.WithOne.Map
public import Mathlib.Algebra.GroupWithZero.InjSurj
public import Mathlib.Algebra.GroupW... |
5,109 | lean_file_chunk | c2b47afc235270ea7de21ba121c4b6ef7a2841efd6ca0e68f538b1384f6860a4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 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.GroupWithZero.ProdHom
public import Mathlib.Algebra.Order.Group.Equiv
public import Mathlib.Algebra.Order.Monoid.Lex
public im... |
3,006 | lean_file_chunk | 5bb5827be6692b2ef71fbff62c31981595350a88b387d8547e03460c8faac331 | 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, Yaël Dillies, Andrew Yang
-/
module
public import Mathlib.Algebra.Order.GroupWithZero.Canonical
public import Mathlib.Algebra.Order.GroupWithZero.Unbundled.OrderIso
public i... |
799 | lean_file_chunk | 4a0670ebbd41a0d898fcdaaf770522d21abd826ca8e66679f17dd34c4ef9b41d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
module
public import Mathlib.Algebra.Group.Submonoid.Defs
public import Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic
public import Mathlib.Order.Interval.Set.... |
2,267 | lean_file_chunk | be2d62f4302d4642ac910f390eaab996a833fe9a5c495c828814aed93ca0f424 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Filippo A. E. Nuccio. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: María Inés de Frutos-Fernández, Filippo A. E. Nuccio
-/
module
public import Mathlib.Algebra.GroupWithZero.Range
public import Mathlib.Algebra.Order.GroupWithZero.WithZero
publi... |
1,761 | lean_file_chunk | fcd94d3224ac500e152092f27797b7bf5e07370932ffd85329ca09a4e10bb63d | 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
-/
module
public import Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic
public import Mathlib.Order.Bounds.Basic
public import Math... |
1,114 | lean_file_chunk | c2e39d6d4b3809ae2794afaa35012cb0e0c5ac4fedda10ddcc27a7852d7727b4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Leonardo de Moura, Mario Carneiro, Floris van Doorn
-/
module
public import Mathlib.Algebra.Field.Defs
public import Mathlib.Algebra.Order.GroupWithZero.Canonical
pu... |
726 | lean_file_chunk | cffdeaf4e94ab1a105b3051f6689fc3ae334668a4e1a1aa5f2b640673d778a36 | 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.Field.Rat
public import Mathlib.Algebra.Order.Nonneg.Field
public import Mathlib.Algebra.Order.Ring.Rat
/-!
# T... |
678 | lean_file_chunk | 872d722dfb5d81a86bbb28e4af2f00403b9a5ea3ede949f41298fc5b9a1668f2 | 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.Field.Subfield.Defs
public import Mathlib.Algebra.Order.Ring.InjSurj
/-!
# Ordered instances on subfields
-/
@[expose] public se... |
1,583 | lean_file_chunk | eb6af1f27a68ad84e4e70461a765e7e308a865ad9dbb1f5f38505c526510f5f3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Alex J. Best. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex J. Best, Yaël Dillies
-/
module
public import Mathlib.Algebra.Field.Defs
public import Mathlib.Algebra.Group.Pointwise.Set.Scalar
public import Mathlib.Algebra.GroupWithZero.Action... |
1,410 | lean_file_chunk | a9a579ba88d5ff830ad0447024bd4f8a708f1db3c3da93f2e566cc4515b4b67b | 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.Notation.Pi.Defs
public import Mathlib.Algebra.Order.Monoid.Defs
public import Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE
pub... |
23,949 | lean_file_chunk | 5ba5a70c97e9a77581856e5d22cba6378b7332af2cd3b2553f7d0bfbce8111db | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Leonardo de Moura, Mario Carneiro, Floris van Doorn
-/
module
public import Mathlib.Algebra.Field.Basic
public import Mathlib.Algebra.GroupWithZero.Units.Lemmas
publ... |
8,375 | lean_file_chunk | 60af361de88375b01b59359f9bce11c68868e504cdae794f3ebda90d14f6d9a9 | lean_source_file | pkg_mathlib_source_file_chunks | theorem le_of_forall_sub_le (h : ∀ ε > 0, b - ε ≤ a) : b ≤ a := by
contrapose! h
simpa only [@and_comm ((0 : α) < _), lt_sub_iff_add_lt, gt_iff_lt] using
exists_add_lt_and_pos_of_lt h
private lemma exists_lt_mul_left_of_nonneg {a b c : α} (ha : 0 ≤ a) (hc : 0 ≤ c) (h : c < a * b) :
∃ a' ∈ Set.Ico 0 a, c < ... |
648 | lean_file_chunk | e6b08bb53aa92caef4e6e1236403cda357711790fcbbc780df4a0a28b40a7672 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Leonardo de Moura, Mario Carneiro, Floris van Doorn
-/
module -- shake: keep-all
public import Mathlib.Tactic.Linter.DeprecatedModule
public import Mathlib.Tactic.Ba... |
2,225 | lean_file_chunk | 91c03b45eebb5223daea12df79207d7cfc7d41af3e6f5928c45ec98a8ffb7259 | 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.Field.GeomSum
public import Mathlib.Algebra.Order.Ring.Defs
/-!
# Partial sums of geometric series in an ordered field
This ... |
7,553 | lean_file_chunk | e594999bd6a6e446e88382d8f94094b23b5dc8e91a1ca1db5f2144e328a0e970 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Leonardo de Moura, Mario Carneiro, Floris van Doorn, Sabbir Rahman
-/
module
public import Mathlib.Algebra.GroupWithZero.Units.Lemmas
public import Mathlib.Algebra.O... |
2,600 | lean_file_chunk | 86c8c82af4d878c092120cc88ceda426ac81d35f9dfd1ef1ab53a823bee5a48a | 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.WithTop
/-!
# Lemma about subtraction in ordered monoid... |
1,013 | lean_file_chunk | 47dd04b8c8bf5a84a049cafcd8a095d5574a31d95d4011e593a2337d24ff5f00 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 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.Order.Sub.Defs
public import Mathlib.Algebra.Notation.Pi.Defs
public import Mathlib.Algebra.Notation.Prod
/-!
# Products of `Ordere... |
8,181 | lean_file_chunk | b88ba383e230657a01e46c4251a738de207d053450988a9a274b500959da5fd2 | 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.Monoid.Unbundled.ExistsOfLE
public import Mathlib.Algebra.Order.Monoid.Canonical.Defs
public import Mathlib.Algebra.Or... |
14,414 | lean_file_chunk | 963ce417ba2394f6ac5f9774e5ee1eb547e7c15a9f3e43f6816a67ccd28c7317 | 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.Basic
public import Mathlib.Algebra.Order.Monoid.Unbundled.Basic
public import Mathlib.Order.Lattice
/-!
# Ordered Su... |
1,202 | lean_file_chunk | d3de079fe17731ee61dfb7320abd9df0d147da67b76e208d3686dbb95eb449cf | 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.Order.Star.Basic
public import Mathlib.Algebra.Star.Prod
public import Mathlib.Algebra.Ring.Prod
/-!
# Products of star-ordered rings... |
1,455 | lean_file_chunk | 63048c19666ec00fb0a439b3e221172019df2d89752299783939df00f5e5112e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
module
public import Mathlib.Algebra.Group.Submonoid.Finite
public import Mathlib.Algebra.Order.Star.Basic
public import Mathlib.Algebra.Star.Pi
/-!
# Pi-types of star-or... |
20,283 | lean_file_chunk | 7f0fcdb7d79daae0bba41ddedb5bcc8033af1ab80e39f917b3073c113a6fee4b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 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.Submonoid.Membership
public import Mathlib.Algebra.GroupWithZero.Regular
public import Mathlib.Algebra.Order.Module.Defs
publi... |
1,162 | lean_file_chunk | 3dcf910e0c7e193126ca8b8ff79ee69f9ea0f50a2820be79d79cd5d54df6f7d5 | 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.Pi
public import Mathlib.Algebra.Order.Star.Basic
public import Mathlib.Algebra.Star.Conjneg
/-!
# Order properties of conjug... |
2,257 | lean_file_chunk | d942c915b1cc25337ac796bf695a8253154babb470cabcc6897811ffb3fc7e7b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
module
public import Mathlib.Algebra.Order.AbsoluteValue.Basic
public import Mathlib.Algebra.EuclideanDomain.Int
/-!
# Euclidean absolute values
This file defines a pred... |
17,422 | lean_file_chunk | 6947ab1b7c6bd4bb55c672f52710c753ac03a65ceaf41e6bfecdefe50b2a579d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Anne Baanen
-/
module
public import Mathlib.Algebra.GroupWithZero.Regular
public import Mathlib.Algebra.GroupWithZero.Units.Lemmas
public import Mathlib.Algebra.Order.Hom... |
10,574 | lean_file_chunk | 86247c68bfbc4f82d88cebf9a0eb9313383ca4ee12dafd391443242911e2732d | 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.GroupWithZero.Action.Pi
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order.Module.Defs
public import ... |
23,963 | lean_file_chunk | 5d924125bd253bb344bde85a41aa8c6aa395b7eeb245643a88551809fe7a7c7f | 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, Kevin Kappelmann
-/
module
public import Mathlib.Algebra.Order.Field.Basic
public import Mathlib.Algebra.Order.Floor.Semiring
public import Mathlib.Tactic.Abel
public ... |
6,844 | lean_file_chunk | cd0d548d59d220a3081d5aeeda02bffb276034789e56e7b0372023ed4254a354 | lean_source_file | pkg_mathlib_source_file_chunks | · have h0 := ((floor_eq_self_iff_mem _).mpr ht).trans ((ceil_eq_self_iff_mem _).mpr ht).symm
rw [h, cast_add, cast_one, left_eq_add] at h0
exact one_ne_zero h0
· apply le_antisymm (Int.ceil_le_floor_add_one _)
rw [add_one_le_iff, lt_ceil]
exact lt_of_le_of_ne (Int.floor_le a) ((iff_false_right h).mp (... |
5,683 | lean_file_chunk | e8a8e2929821beeee2f09dcf09cca47248f5830a5c85485b06c219d5755423bb | 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, Kevin Kappelmann
-/
module
public import Mathlib.Algebra.Order.Field.Basic
public import Mathlib.Algebra.Order.Floor.Semiring
public import Mathlib.Tactic.Linarith
/-... |
10,144 | lean_file_chunk | bd65485ef7e545e0b3cbb0e0d108c17fd99f481dcca294d12d1e1b9afcbe8672 | 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, Kevin Kappelmann
-/
module
public import Mathlib.Algebra.Order.Ring.Cast
public import Mathlib.Data.Nat.Cast.Basic
import Mathlib.Data.Int.LeastGreatest
/-!
# Floor ... |
14,634 | lean_file_chunk | 00a925584b730a7018b5d13b7407eb16c9f01ce8e0b8fb773bce450377ef5582 | 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, Kevin Kappelmann
-/
module
public import Mathlib.Algebra.Order.Floor.Defs
public import Mathlib.Order.Interval.Set.Defs
/-!
# Lemmas on `Nat.floor` and `Nat.ceil` for... |
9,351 | lean_file_chunk | cf4b0c368920b69f5e5b0c83b9b638664bf452b53bc438dbe21e770c88d7e9f6 | 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.Data.ENat.Lattice
public import Mathlib.Data.NNReal.Basic
public import Mathlib.Data.Real.ENatENNReal
import Mathlib.Data.ENNReal.Operation... |
18,348 | lean_file_chunk | 2e6fa8377683fa12fe5ad780afcc6e567bf2e21356c14e8e8ed8c8be1118d4da | 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.GroupWithZero.Synonym
public import Mathlib.Algebra.Order.Ring.Canonical
public import Ma... |
4,118 | lean_file_chunk | faba7d6e1e8a1610e8ea5d105d5e33b128c6f85ffa144a1c17f7dc01a0681b88 | 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, Yaël Dillies
-/
module
public import Mathlib.Algebra.Order.Group.Synonym
public import Mathlib.Algebra.Ring.Defs
/-!
# Ring structure on the order type synonyms
Tr... |
7,092 | lean_file_chunk | 28c86aaa752762aa96d7f621a03b6d19599d213a3f410332ec9328bc8e816401 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu
-/
module
public import Mathlib.Algebra.Ring.Idempotent
public import Mathlib.Order.BooleanAlgebra.Defs
public import Mathlib.Order.Hom.Basic
/-!
# Boolean algebra structure on ... |
5,390 | lean_file_chunk | 2b9414418f41192d7e45c108f1dceb28116c49493f3152e8c108ad2d3b7ae1f2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 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.Nat.Cast.Commute
public import Mathlib.Data.Nat.Cast.Order.Ring
public import Mathlib.Tactic.Abel
/-! # Bernoulli's inequality
... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.