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values | content stringlengths 3 6.12M |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
5f66f145dd85fd38f1e090d9a757869b0507eb5f | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/nat/upto.lean | bc1abd3632f9a0415b06873cc5b9db48ff6b8cbf | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 2,375 | lean | /-
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Simon Hudon
-/
import data.nat.basic
/-!
# `nat.upto`
`nat.upto p`, with `p` a predicate on `β`, is a subtype of elements `n : β` such that no value
(strictly) below `n` satisfies `p`.
... |
2f30b8d76aca246f31dfd05d54a5fed447a32063 | c3f2fcd060adfa2ca29f924839d2d925e8f2c685 | /library/data/nat/basic.lean | 1b0d870399de09918bb1a16d5efe0bbc8340c847 | [
"Apache-2.0"
] | permissive | respu/lean | 6582d19a2f2838a28ecd2b3c6f81c32d07b5341d | 8c76419c60b63d0d9f7bc04ebb0b99812d0ec654 | refs/heads/master | 1,610,882,451,231 | 1,427,747,084,000 | 1,427,747,429,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 12,395 | lean | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.nat.basic
Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad
Basic operations on the natural numbers.
-/
import logic.connectives data.num algebra.binary algebra.ring
... |
101a3b5f6b82bade00ba1c30b1928fbb1c45c375 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/namespaceHyg.lean | 55ec3afdbfa4a21e3d9767ec377aab83bf812100 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 60 | lean | macro "classical" : command => `(open Classical)
classical
|
0ce16620c8a89b0b58419ae68038ce7ebb427e0b | efce24474b28579aba3272fdb77177dc2b11d7aa | /src/homotopy_theory/topological_spaces/distrib.lean | 11e3203c81def34f87810e3fef2986b380241078 | [
"Apache-2.0"
] | permissive | rwbarton/lean-homotopy-theory | cff499f24268d60e1c546e7c86c33f58c62888ed | 39e1b4ea1ed1b0eca2f68bc64162dde6a6396dee | refs/heads/lean-3.4.2 | 1,622,711,883,224 | 1,598,550,958,000 | 1,598,550,958,000 | 136,023,667 | 12 | 6 | Apache-2.0 | 1,573,187,573,000 | 1,528,116,262,000 | Lean | UTF-8 | Lean | false | false | 4,385 | lean | import for_mathlib
import category_theory.colimit_lemmas
import .category
import .colimits
import .homeomorphism
import .inter_union
import .subspace
noncomputable theory
/-
The distributivity law in Top: X Γ Y β X Γ Z β
X Γ (Y β Z).
-/
open set
open category_theory
universe u
namespace homotopy_theory.topologic... |
4139d9ccdd5d539dd10f551398366dd0ac653246 | 037dba89703a79cd4a4aec5e959818147f97635d | /src/2021/sets/sheet4.lean | 0717654a66e6d925515287bc02ab1223b542a212 | [] | no_license | ImperialCollegeLondon/M40001_lean | 3a6a09298da395ab51bc220a535035d45bbe919b | 62a76fa92654c855af2b2fc2bef8e60acd16ccec | refs/heads/master | 1,666,750,403,259 | 1,665,771,117,000 | 1,665,771,117,000 | 209,141,835 | 115 | 12 | null | 1,640,270,596,000 | 1,568,749,174,000 | Lean | UTF-8 | Lean | false | false | 1,688 | lean | /-
Copyright (c) 2021 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author : Kevin Buzzard
-/
import tactic -- imports all the Lean tactics
/-!
# Sets in Lean, example sheet 4 : exists (`β`)
In this sheet we learn how to manipulate `β` in Lean. We will see
s... |
541ef2302cc8bf6d80df18f9dadae72a34778358 | 947b78d97130d56365ae2ec264df196ce769371a | /src/Lean/Compiler/NeverExtractAttr.lean | b5ee879daf91642a6683ffc81dc636d7cc034afe | [
"Apache-2.0"
] | permissive | shyamalschandra/lean4 | 27044812be8698f0c79147615b1d5090b9f4b037 | 6e7a883b21eaf62831e8111b251dc9b18f40e604 | refs/heads/master | 1,671,417,126,371 | 1,601,859,995,000 | 1,601,860,020,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 976 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Environment
import Lean.Attributes
namespace Lean
def mkNeverExtractAttr : IO TagAttribute :=
registerTagAttribute `neverExtract "instruct the... |
b72fba91d4eae1b0102084486ace2b81adbb95cf | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/funMatchIssue.lean | 36bf0213141309be5a5f679e5ab5f6a422ffb534 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 282 | lean | inductive T : Type 1 :=
| mkT : (forall {a : Type}, a -> a) -> T
open T
-- Works
def makeT (f : forall {a : Type}, a -> a) : T :=
mkT f
def makeT' : (forall {a : Type}, a -> a) -> T :=
fun x =>
let f := @x
mkT f
def makeT'' : (forall {a : Type}, a -> a) -> T
| f => mkT f
|
1e9e40f0071ee1db3859eabdc54e051cfec7acbc | 3d2a7f1582fe5bae4d0bdc2fe86e997521239a65 | /spatial-reasoning/spatial-reasoning-problem-14.lean | c4a9a38fdfaf9b101302e1abee72d171e64c8d9a | [] | no_license | own-pt/common-sense-lean | e4fa643ae010459de3d1bf673be7cbc7062563c9 | f672210aecb4172f5bae265e43e6867397e13b1c | refs/heads/master | 1,622,065,660,261 | 1,589,487,533,000 | 1,589,487,533,000 | 254,167,782 | 3 | 2 | null | 1,589,487,535,000 | 1,586,370,214,000 | Lean | UTF-8 | Lean | false | false | 183 | lean | /- Spatial Reasoning Problem 14 -/
/- It can be found at: SpatialQs.txt -/
/- (14) John is outside a circle and then crosses the border of the circle.
Is he inside the circle? -/
|
1c73dd01db77875ccfbb4d22c6dce23d11487d5c | bc0ebfde190bc1da50a425e63b8f44a50746ca42 | /src/misc_mathlib.lean | 69900a4d18668d4538efffba079a63cc775b43ba | [
"Apache-2.0"
] | permissive | Pazzaz/erdos-szekeres | d93996420d10aaa8c603379abdea3391295e8be2 | b6e53035340946602b9e4cc346314e541a5f3774 | refs/heads/master | 1,680,656,743,365 | 1,618,681,128,000 | 1,618,681,128,000 | 358,942,643 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,166 | lean | import data.list
import tactic
import data.finset
theorem sublist_take_mp_sublist
{X : Type*}
(A S: list X)
(n : β)
(h: S <+ A.take n)
: S <+ A
:= list.sublist.trans h (list.sublist_of_prefix (A.take_prefix n))
theorem nth_le_mem_take_succ
{X : Type*}
(A : list X)
(n : β)
(h : n < A.length)
: A.nth_le n h β A.take n.... |
eafec261cd833501294627d200d7632223fff33d | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /tests/lean/run/partial1.lean | c6602bb05a5f80343dbdf76938e1019a9bc08cfa | [
"Apache-2.0"
] | permissive | walterhu1015/lean4 | b2c71b688975177402758924eaa513475ed6ce72 | 2214d81e84646a905d0b20b032c89caf89c737ad | refs/heads/master | 1,671,342,096,906 | 1,599,695,985,000 | 1,599,695,985,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 538 | lean | new_frontend
partial def reverse {Ξ±} (as : List Ξ±) : List Ξ± :=
let rec loop : List Ξ± β List Ξ± β List Ξ±
| [], r => r
| a::as, r => loop as (a::r);
loop as []
#eval reverse [3, 2, 1]
#eval reverse [1, 2, 3, 4]
#print reverse
#print reverse.loop
#print reverse.loop._unsafe_rec
partial def appendRev {Ξ±} (extra : ... |
9e48e81c6bdbc9fe2dbb135739fee1cefc0852d9 | f313d4982feee650661f61ed73f0cb6635326350 | /Mathlib/Mem.lean | 7e7b47692c4ae158ede4f6e1b20b223b7a92becf | [
"Apache-2.0"
] | permissive | shingtaklam1324/mathlib4 | 38c6e172eec1385944db5a70a3b5545c924980ee | 50610c343b7065e8eec056d641f859ceed608e69 | refs/heads/master | 1,683,032,333,313 | 1,621,942,699,000 | 1,621,942,699,000 | 371,130,608 | 0 | 0 | Apache-2.0 | 1,622,053,166,000 | 1,622,053,166,000 | null | UTF-8 | Lean | false | false | 150 | lean | class Mem (Ξ± : outParam $ Type u) (Ξ³ : Type v) where
mem : Ξ± β Ξ³ β Prop
infix:50 " β " => Mem.mem
notation:50 x " β " s => Β¬ x β s
|
5b02c5a7630a84b3bda4442b6f3ae32d45a1b5a6 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/category_theory/limits/kan_extension.lean | 815218caa1dabf595143dfc1a6cac4cda349a4e2 | [
"Apache-2.0"
] | permissive | AntoineChambert-Loir/mathlib | 64aabb896129885f12296a799818061bc90da1ff | 07be904260ab6e36a5769680b6012f03a4727134 | refs/heads/master | 1,693,187,631,771 | 1,636,719,886,000 | 1,636,719,886,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,110 | lean | /-
Copyright (c) 2021 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Adam Topaz
-/
import category_theory.punit
import category_theory.structured_arrow
import category_theory.limits.functor_category
import category_theory.limits.shapes.termina... |
32f19e9b9d8b047f15e77e0368fe1d4800055b18 | fecda8e6b848337561d6467a1e30cf23176d6ad0 | /src/analysis/special_functions/trigonometric.lean | c9475e41137e5720a74a8eb5d67ba53537812f33 | [
"Apache-2.0"
] | permissive | spolu/mathlib | bacf18c3d2a561d00ecdc9413187729dd1f705ed | 480c92cdfe1cf3c2d083abded87e82162e8814f4 | refs/heads/master | 1,671,684,094,325 | 1,600,736,045,000 | 1,600,736,045,000 | 297,564,749 | 1 | 0 | null | 1,600,758,368,000 | 1,600,758,367,000 | null | UTF-8 | Lean | false | false | 74,223 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle SΓΆnne
-/
import analysis.special_functions.exp_log
/-!
# Trigonometric functions
## Main definitions
This file contains the foll... |
2b2178b96df19d2551f1b84af72b54c04e5ab035 | ddf69e0b8ad10bfd251aa1fb492bd92f064768ec | /src/data/int/basic.lean | a45414ee4f2854c9c64e9f937125019c2e74feae | [
"Apache-2.0"
] | permissive | MaboroshiChan/mathlib | db1c1982df384a2604b19a5e1f5c6464c7c76de1 | 7f74e6b35f6bac86b9218250e83441ac3e17264c | refs/heads/master | 1,671,993,587,476 | 1,601,911,102,000 | 1,601,911,102,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 47,928 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
The integers, with addition, multiplication, and subtraction.
-/
import data.nat.basic
import algebra.order_functions
open nat
namespace int
instance : inhabited β€ := ... |
2a5f632600dac8e162d9cf622166e61277193bfc | d8820d2c92be8052d13f9c8f8c483a6e15c5f566 | /src/M40002/M40002_C5.lean | 47800f312a010829baa4dbc61a7548834f8cac62 | [] | no_license | JasonKYi/M4000x_LEAN_formalisation | 4a19b84f6d0fe2e214485b8532e21cd34996c4b1 | 6e99793f2fcbe88596e27644f430e46aa2a464df | refs/heads/master | 1,599,755,414,708 | 1,589,494,604,000 | 1,589,494,604,000 | 221,759,483 | 8 | 1 | null | 1,589,494,605,000 | 1,573,755,201,000 | Lean | UTF-8 | Lean | false | false | 25,465 | lean | -- M40002 (Analysis I) Chapter 5. Continuity
import M40002.M40002_C4
import data.polynomial
namespace M40002
-- Definition of limits of functions (f(x) β b as x β a)
def func_converges_to (f : β β β) (a b : β) := β Ξ΅ > 0, β Ξ΄ > 0, β x : β, abs (x - a) < Ξ΄ β abs (f x - b) < Ξ΅
-- Definition of continuity at a point
d... |
adec776d696ade0760ec7ac2e50e5ce3ba02a08a | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/analysis/complex/basic.lean | fa49725857ba0279fa37463ec95ad4bc1e9e94fd | [
"Apache-2.0"
] | permissive | hamdysalah1/mathlib | b915f86b2503feeae268de369f1b16932321f097 | 95454452f6b3569bf967d35aab8d852b1ddf8017 | refs/heads/master | 1,677,154,116,545 | 1,611,797,994,000 | 1,611,797,994,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,339 | lean | /-
Copyright (c) SΓ©bastien GouΓ«zel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: SΓ©bastien GouΓ«zel
-/
import analysis.calculus.times_cont_diff
import analysis.normed_space.finite_dimension
/-!
# Normed space structure on `β`.
This file gathers basic facts on comple... |
1f6c347bed6ef1b77acc3098131373c5ce632e15 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/sheaves/sheaf_condition/sites.lean | d6692f330c357aa459dcf62c7f5a8bd32b57306e | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 8,118 | lean | /-
Copyright (c) 2021 Justus Springer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Justus Springer
-/
import category_theory.sites.spaces
import topology.sheaves.sheaf
import category_theory.sites.dense_subsite
/-!
# Coverings and sieves; from sheaves on sites an... |
e9bf69c26bff21a13001426642f5e9abb92433bb | 90edd5cdcf93124fe15627f7304069fdce3442dd | /src/Lean/Aesop/Config.lean | 99440c544295a424c9c4894c2e3cceb4dea23f27 | [
"Apache-2.0"
] | permissive | JLimperg/lean4-aesop | 8a9d9cd3ee484a8e67fda2dd9822d76708098712 | 5c4b9a3e05c32f69a4357c3047c274f4b94f9c71 | refs/heads/master | 1,689,415,944,104 | 1,627,383,284,000 | 1,627,383,284,000 | 377,536,770 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,725 | lean | /-
Copyright (c) 2021 Jannis Limperg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jannis Limperg, Asta Halkjær From
-/
import Lean.Aesop.RuleBuilder
open Lean
open Lean.Meta (SimpEntry getSimpLemmas)
namespace Lean.Aesop
namespace Parser.Attribute
declare_synta... |
e046043d96295bddbba09f23b67b964a4f4efe65 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/ptst.lean | f6b91b05fa9e1718d18d333ab4fdccb22fbb1560 | [
"Apache-2.0"
] | permissive | leanprover-community/lean | 12b87f69d92e614daea8bcc9d4de9a9ace089d0e | cce7990ea86a78bdb383e38ed7f9b5ba93c60ce0 | refs/heads/master | 1,687,508,156,644 | 1,684,951,104,000 | 1,684,951,104,000 | 169,960,991 | 457 | 107 | Apache-2.0 | 1,686,744,372,000 | 1,549,790,268,000 | C++ | UTF-8 | Lean | false | false | 77 | lean | open prod nat
-- Test tuple notation
#check ((3:nat), false, (1:int), true)
|
2511715fa6d08c2f0e7c2d973c6629e3e29387f3 | 88fb7558b0636ec6b181f2a548ac11ad3919f8a5 | /library/init/data/fin/ops.lean | 68b58636654fa81c4065e96b457a709ead651e64 | [
"Apache-2.0"
] | permissive | moritayasuaki/lean | 9f666c323cb6fa1f31ac597d777914aed41e3b7a | ae96ebf6ee953088c235ff7ae0e8c95066ba8001 | refs/heads/master | 1,611,135,440,814 | 1,493,852,869,000 | 1,493,852,869,000 | 90,269,903 | 0 | 0 | null | 1,493,906,291,000 | 1,493,906,291,000 | null | UTF-8 | Lean | false | false | 3,359 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import init.data.nat init.data.fin.basic
namespace fin
open nat
variable {n : nat}
def of_nat {n : nat} (a : nat) : fin (succ n) :=
β¨a % succ n, na... |
d60d51ffe34d9df4faaab0c67d5065cd707f6538 | 367134ba5a65885e863bdc4507601606690974c1 | /src/number_theory/pythagorean_triples.lean | b1c6851e86406c73f5ac33da9701b5f807b5bfd3 | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 26,046 | lean | /-
Copyright (c) 2020 Paul van Wamelen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Paul van Wamelen.
-/
import algebra.field
import ring_theory.int.basic
import algebra.group_with_zero.power
import tactic.ring
import tactic.ring_exp
import tactic.field_simp
/-!
# P... |
909448839e4d5084b2a5bf78f64e33919156f331 | f94866221d9fc3e2706d042c19de3c569d853531 | /src/main.lean | f1c77ae057e8ff5c0a0fc556ddba994c4c440d5f | [] | no_license | arthur-adjedj/proof_Q_denumerable | 1040647af48ffa7afe921b73a96c89e1a6896ba3 | 7a1059ea91cff929bb0c5fa3876c73b72ebee9f7 | refs/heads/main | 1,692,085,100,716 | 1,632,130,913,000 | 1,632,130,913,000 | 398,863,134 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,203 | lean | import init.data.nat.basic
import tactic.finish
import tactic.ext
import biject
import init.data.int.basic
import data.int.basic
import data.nat.parity
import tactic.hint
import data.nat.basic
universes u1 u2 u3 u4
def denombrable (Ξ± : Sort u1) : Prop :=
in_bijection β Ξ±
theorem tf_l {A : Sort u1} {B : Sort u2}... |
63433c18f2c159c73f2c107ea33bc30fde81258f | aa5a655c05e5359a70646b7154e7cac59f0b4132 | /tests/lean/run/concatElim.lean | f5ccc730c778afdedc692bf2aaa107400a04f63c | [
"Apache-2.0"
] | permissive | lambdaxymox/lean4 | ae943c960a42247e06eff25c35338268d07454cb | 278d47c77270664ef29715faab467feac8a0f446 | refs/heads/master | 1,677,891,867,340 | 1,612,500,005,000 | 1,612,500,005,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,992 | lean | universes u
def concat {Ξ±} : List Ξ± β Ξ± β List Ξ±
| [], a => [a]
| x::xs, a => x :: concat xs a
def last {Ξ±} : (xs : List Ξ±) β xs β [] β Ξ±
| [], h => absurd rfl h
| [a], h => a
| _::a::as, h => last (a::as) (fun h => by injection h)
def dropLast {Ξ±} : List Ξ± β List Ξ±
| [] => []
| [a] ... |
1f05422a4eb37c5f750fac42f68a73db152da722 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/ring_theory/euclidean_domain.lean | 83e3caea25d8affe6484642f7131b46912210be0 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 2,587 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Chris Hughes
-/
import ring_theory.coprime
import ring_theory.ideal.basic
/-!
# Lemmas about Euclidean domains
Various about Euclidean domains are proved; all of them... |
349d7b287aad74d80f8d9f4a936d4313e088b755 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/finsupp/default.lean | 1864bbe881fa990b31ff6321cc653c554f86b699 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 288 | lean | /-
Copyright (c) 2020 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.finsupp.basic
import Mathlib.PostPort
namespace Mathlib
|
f3121de21b8bbf8013052d720334f4a68503d27c | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/group_theory/quotient_group.lean | 6d968723f6ab41d2308b257cf3c4c38be0a9210b | [
"Apache-2.0"
] | permissive | lacker/mathlib | f2439c743c4f8eb413ec589430c82d0f73b2d539 | ddf7563ac69d42cfa4a1bfe41db1fed521bd795f | refs/heads/master | 1,671,948,326,773 | 1,601,479,268,000 | 1,601,479,268,000 | 298,686,743 | 0 | 0 | Apache-2.0 | 1,601,070,794,000 | 1,601,070,794,000 | null | UTF-8 | Lean | false | false | 7,555 | lean | /-
Copyright (c) 2018 Kevin Buzzard and Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Patrick Massot.
This file is to a certain extent based on `quotient_module.lean` by Johannes HΓΆlzl.
-/
import group_theory.coset
universes u v
names... |
66f45cd66bc5089b4a208a664bd376d3f06f0de4 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/linear_algebra/affine_space/slope.lean | 18267ebaf02d16d3e742732027504aa75265129f | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 4,527 | lean | /-
Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import algebra.order.module
import linear_algebra.affine_space.affine_map
import tactic.field_simp
/-!
# Slope of a function
In this file we define the slop... |
d9c44209e7b00623b10a575944980b4594517ca4 | 8d65764a9e5f0923a67fc435eb1a5a1d02fd80e3 | /src/algebra/char_p/basic.lean | 616531f3aceefc393db17ed7ad80d4ddf44392e1 | [
"Apache-2.0"
] | permissive | troyjlee/mathlib | e18d4b8026e32062ab9e89bc3b003a5d1cfec3f5 | 45e7eb8447555247246e3fe91c87066506c14875 | refs/heads/master | 1,689,248,035,046 | 1,629,470,528,000 | 1,629,470,528,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 15,781 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Joey van Langen, Casper Putz
-/
import algebra.iterate_hom
import data.int.modeq
import data.nat.choose
import group_theory.order_of_element
/-!
# Characteristic of semirings
-/... |
6ba4871440d55fa2982f784b911b7ff80351386d | 75db7e3219bba2fbf41bf5b905f34fcb3c6ca3f2 | /library/data/list/sorted.lean | 112222f229238202cc732fae52381bcd4667fdd8 | [
"Apache-2.0"
] | permissive | jroesch/lean | 30ef0860fa905d35b9ad6f76de1a4f65c9af6871 | 3de4ec1a6ce9a960feb2a48eeea8b53246fa34f2 | refs/heads/master | 1,586,090,835,348 | 1,455,142,203,000 | 1,455,142,277,000 | 51,536,958 | 1 | 0 | null | 1,455,215,811,000 | 1,455,215,811,000 | null | UTF-8 | Lean | false | false | 5,767 | lean | /-
Copyright (c) 2015 Leonardo de Moura. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import data.list.comb data.list.perm
namespace list
variable {A : Type}
variable (R : A β A β Prop)
inductive locally_sorted : list A β Prop :=
| base0 : loca... |
bfa81a0cad879b0846d13a68d8c492fd8c7d340b | efa51dd2edbbbbd6c34bd0ce436415eb405832e7 | /20170116_POPL/super/usage.lean | ad38ae15f614326a883e3934bb9a3408b942f6b5 | [
"Apache-2.0"
] | permissive | leanprover/presentations | dd031a05bcb12c8855676c77e52ed84246bd889a | 3ce2d132d299409f1de269fa8e95afa1333d644e | refs/heads/master | 1,688,703,388,796 | 1,686,838,383,000 | 1,687,465,742,000 | 29,750,158 | 12 | 9 | Apache-2.0 | 1,540,211,670,000 | 1,422,042,683,000 | Lean | UTF-8 | Lean | false | false | 1,773 | lean | import tools.super
-- The super tactic takes two lists of lemmas as arguments:
-- super [normal lemmas] with [sos lemmas]
-- The sos lemmas ("set of support") are only used in a restricted way: we do
-- not perform inferences between sos lemmas, just with other clauses. (For
-- performance reasons.)
-- If the form... |
a3731214571b9bec62b0df92965896e81d2f0b21 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/noncomp_hott.hlean | 0a59b906be96e170119d03ba4db9f9ca98edd86e | [
"Apache-2.0"
] | permissive | soonhokong/lean | cb8aa01055ffe2af0fb99a16b4cda8463b882cd1 | 38607e3eb57f57f77c0ac114ad169e9e4262e24f | refs/heads/master | 1,611,187,284,081 | 1,450,766,737,000 | 1,476,122,547,000 | 11,513,992 | 2 | 0 | null | 1,401,763,102,000 | 1,374,182,235,000 | C++ | UTF-8 | Lean | false | false | 35 | hlean | noncomputable definition foo := 10
|
7a5cc9ac9daf38c9c3a3ba495c51dc02abc603c9 | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /tests/lean/run/infoTree.lean | bf034bebdde739c159f635ed41ab157ef97aa8c4 | [
"Apache-2.0"
] | permissive | williamdemeo/lean4 | 72161c58fe65c3ad955d6a3050bb7d37c04c0d54 | 6d00fcf1d6d873e195f9220c668ef9c58e9c4a35 | refs/heads/master | 1,678,305,356,877 | 1,614,708,995,000 | 1,614,708,995,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 769 | lean | import Lean
open Lean.Elab
elab "enableInfo!" : command => enableInfoTree
elab "showInfoTrees!" : command => do
let trees β getInfoTrees
trees.forM fun tree => do
logInfo f!"{β tree.format}"
structure A where
val : Nat β Nat
structure B where
pair : A Γ A
enableInfo!
def f (x : Nat) : Nat Γ Nat :=
... |
6dec208bfe35c040676453ef0ee36d13edf09b0d | 5ee26964f602030578ef0159d46145dd2e357ba5 | /src/for_mathlib/group.lean | 4b3b08138f8981a2f294a1c2421eec87ae689249 | [
"Apache-2.0"
] | permissive | fpvandoorn/lean-perfectoid-spaces | 569b4006fdfe491ca8b58dd817bb56138ada761f | 06cec51438b168837fc6e9268945735037fd1db6 | refs/heads/master | 1,590,154,571,918 | 1,557,685,392,000 | 1,557,685,392,000 | 186,363,547 | 0 | 0 | Apache-2.0 | 1,557,730,933,000 | 1,557,730,933,000 | null | UTF-8 | Lean | false | false | 1,735 | lean | import algebra.group data.equiv.basic
import group_theory.subgroup
import group_theory.quotient_group
import for_mathlib.equiv
variables {G : Type*} [group G]
open quotient_group
-- this one lemma is not PR'ed yet.
def group_equiv.quot_eq_of_eq {G1 : set G} [normal_subgroup G1] {G2 : set G} [normal_subgroup G2]
(h : ... |
3f7861bc0c065ab423212ed779c2c95ce11f0f2b | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /stage0/src/Lean/Meta/Coe.lean | e2d31c3f628a7835ad80d87ba80d70e2f0896aa0 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | EdAyers/lean4 | 57ac632d6b0789cb91fab2170e8c9e40441221bd | 37ba0df5841bde51dbc2329da81ac23d4f6a4de4 | refs/heads/master | 1,676,463,245,298 | 1,660,619,433,000 | 1,660,619,433,000 | 183,433,437 | 1 | 0 | Apache-2.0 | 1,657,612,672,000 | 1,556,196,574,000 | Lean | UTF-8 | Lean | false | false | 1,292 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.WHNF
import Lean.Meta.Transform
namespace Lean.Meta
/--
Return true iff `declName` is one of the auxiliary definitions/projections
us... |
ea2f85eee9c9889afdd9ebede59e70129861ef35 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/ring_theory/tensor_product.lean | 2ab4f3342304bc69c194dfd844ef57afbc01e335 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 19,420 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.linear_algebra.tensor_product
import Mathlib.algebra.algebra.basic
import Mathlib.PostPort
... |
27159ceb6a4e8e65577ed42aebc7627c78dbb63d | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/data/list/min_max.lean | aa32f329369938b46e0035302060ac8cf11f3bad | [
"Apache-2.0"
] | permissive | hikari0108/mathlib | b7ea2b7350497ab1a0b87a09d093ecc025a50dfa | a9e7d333b0cfd45f13a20f7b96b7d52e19fa2901 | refs/heads/master | 1,690,483,608,260 | 1,631,541,580,000 | 1,631,541,580,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 12,681 | lean | /-
Copyright (c) 2019 Minchao Wu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Minchao Wu, Chris Hughes
-/
import data.list.basic
/-!
# Minimum and maximum of lists
## Main definitions
The main definitions are `argmax`, `argmin`, `minimum` and `maximum` for lists.
... |
e244d99c7459495606eeca7f28c942780b439b4a | ce6917c5bacabee346655160b74a307b4a5ab620 | /src/ch6/ex0402.lean | e619da20b25e79a483ae28a44a141627b5551284 | [] | no_license | Ailrun/Theorem_Proving_in_Lean | ae6a23f3c54d62d401314d6a771e8ff8b4132db2 | 2eb1b5caf93c6a5a555c79e9097cf2ba5a66cf68 | refs/heads/master | 1,609,838,270,467 | 1,586,846,743,000 | 1,586,846,743,000 | 240,967,761 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 222 | lean | variable {Ξ± : Type*}
def is_prefix (lβ : list Ξ±) (lβ : list Ξ±) : Prop :=
β t, lβ ++ t = lβ
infix ` <+: `:50 := is_prefix
@[simp]
theorem list.is_prefix_refl (l : list Ξ±) : l <+: l :=
β¨[], by simpβ©
|
72299bb1a77f4a6ad84f26dea801eb21becdc5a1 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/mvar3.lean | 75acd1888f38d784969103f8148f009a6e60bf6b | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | cipher1024/lean4 | 6e1f98bb58e7a92b28f5364eb38a14c8d0aae393 | 69114d3b50806264ef35b57394391c3e738a9822 | refs/heads/master | 1,642,227,983,603 | 1,642,011,696,000 | 1,642,011,696,000 | 228,607,691 | 0 | 0 | Apache-2.0 | 1,576,584,269,000 | 1,576,584,268,000 | null | UTF-8 | Lean | false | false | 3,068 | lean | import Lean.MetavarContext
open Lean
def mkLambdaTest (mctx : MetavarContext) (ngen : NameGenerator) (lctx : LocalContext) (xs : Array Expr) (e : Expr)
: Except MetavarContext.MkBinding.Exception (MetavarContext Γ NameGenerator Γ Expr) :=
match MetavarContext.mkLambda xs e false true lctx { mctx := mctx, ngen := ... |
7f2e50990b63c6605975b5a44c11b93382373fd0 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/measure_theory/function/conditional_expectation.lean | 5157a106cbe4d300bcf1baa59da5168d8d62157e | [
"Apache-2.0"
] | permissive | AntoineChambert-Loir/mathlib | 64aabb896129885f12296a799818061bc90da1ff | 07be904260ab6e36a5769680b6012f03a4727134 | refs/heads/master | 1,693,187,631,771 | 1,636,719,886,000 | 1,636,719,886,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 86,989 | lean | /-
Copyright (c) 2021 RΓ©my Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: RΓ©my Degenne
-/
import analysis.inner_product_space.projection
import measure_theory.function.l2_space
import measure_theory.decomposition.radon_nikodym
/-! # Conditional expectation
... |
652677f468b85abf2c7779cc4ff716eaa05f56ca | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/topology/constructions.lean | b4ae819f0d3a4891ede1e1cc7aefb6c547b1fdaf | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 50,102 | lean | /-
Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl, Mario Carneiro, Patrick Massot
-/
import topology.maps
import order.filter.pi
import data.fin.tuple
/-!
# Constructions of new topological spaces from old ones
This f... |
14fb35f3a9efe0f9376c7010bf731a48281a1d14 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /tests/playground/sleep_save.lean | fb2724d6dea1f556d7459c3f66bd176b38b018c8 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | EdAyers/lean4 | 57ac632d6b0789cb91fab2170e8c9e40441221bd | 37ba0df5841bde51dbc2329da81ac23d4f6a4de4 | refs/heads/master | 1,676,463,245,298 | 1,660,619,433,000 | 1,660,619,433,000 | 183,433,437 | 1 | 0 | Apache-2.0 | 1,657,612,672,000 | 1,556,196,574,000 | Lean | UTF-8 | Lean | false | false | 795 | lean | macro "expensive_tactic" : tactic => `(sleep 5000)
example (hβ : x = y) (hβ : y = z) : z = x := by
expensive_tactic
save
have : y = x := hβ.symm
have : z = y := hβ.symm
trace "hello world"
apply this.trans
exact βΉy = xβΊ
example (hβ : p β¨ q) (hβ : p β x = 0) (hβ : q β y = 0) : x * y = 0 := by
expensive... |
3088dd5d7b5b0801f4036b31869a71c0d32e1140 | e030b0259b777fedcdf73dd966f3f1556d392178 | /tests/lean/elab_error_msgs.lean | 023a0a85aa604020c1f8718d971c2f6f4dfcc3af | [
"Apache-2.0"
] | permissive | fgdorais/lean | 17b46a095b70b21fa0790ce74876658dc5faca06 | c3b7c54d7cca7aaa25328f0a5660b6b75fe26055 | refs/heads/master | 1,611,523,590,686 | 1,484,412,902,000 | 1,484,412,902,000 | 38,489,734 | 0 | 0 | null | 1,435,923,380,000 | 1,435,923,379,000 | null | UTF-8 | Lean | false | false | 352 | lean | lemma ex1 (a b : Prop) : a β§ b β§ b β b β§ a :=
and.rec (Ξ» ha hb hb, ha)
@[elab_as_eliminator]
def bogus_elim {A : Type} {C : A β A β Prop} {a b : A} (h : C a a) : C a b :=
sorry
lemma ex2 (a b : Prop) : a β§ b :=
bogus_elim trivial
lemma ex1 (a b : Prop) : a β§ b β§ b β b β§ a :=
Ξ» h, and.rec
(Ξ» ha hb, ha + hb)
... |
ffd80f17e86932b303e239133d32f616a2923717 | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/ring_theory/multiplicity.lean | 89215f1d5e37d71b0fdc4b5120066d5bc365ae11 | [
"Apache-2.0"
] | permissive | ChrisHughes24/mathlib | 98322577c460bc6b1fe5c21f42ce33ad1c3e5558 | a2a867e827c2a6702beb9efc2b9282bd801d5f9a | refs/heads/master | 1,583,848,251,477 | 1,565,164,247,000 | 1,565,164,247,000 | 129,409,993 | 0 | 1 | Apache-2.0 | 1,565,164,817,000 | 1,523,628,059,000 | Lean | UTF-8 | Lean | false | false | 15,332 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Chris Hughes
-/
import algebra.associated data.int.gcd data.nat.enat
import tactic.converter.interactive
import tactic.norm_cast
variables {Ξ± : Type*}
open nat ropt... |
e8a261d37953a4dd4dadae0d2ab93657bf117eaa | efce24474b28579aba3272fdb77177dc2b11d7aa | /src/homotopy_theory/formal/i_category/cylinder_object.lean | 385cc263df18ccfb25e02a69c5d7a05969692f1a | [
"Apache-2.0"
] | permissive | rwbarton/lean-homotopy-theory | cff499f24268d60e1c546e7c86c33f58c62888ed | 39e1b4ea1ed1b0eca2f68bc64162dde6a6396dee | refs/heads/lean-3.4.2 | 1,622,711,883,224 | 1,598,550,958,000 | 1,598,550,958,000 | 136,023,667 | 12 | 6 | Apache-2.0 | 1,573,187,573,000 | 1,528,116,262,000 | Lean | UTF-8 | Lean | false | false | 2,139 | lean | import .homotopy_equivalences
import .lemmas
universes v u
open category_theory
open category_theory.category
local notation f ` β `:80 g:80 := g β« f
/-
We show that IA is a cylinder object for A, in the sense that
A β A β IA β A is a factorization of the fold map into a
cofibration followed by a homotopy equivalen... |
5f173285e3cf73473a54ec31a899551e451f854e | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/finset/fold.lean | 9ebaefe51cdc6c1d5eeb8939ed027d943b07018e | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 9,128 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import algebra.order.monoid.with_top
import data.finset.image
import data.multiset.fold
/-!
# The fold operation for a commutative associative operation over a finse... |
64a0c2f82d077950bd791f5ad8019a1da386f3cf | 0845ae2ca02071debcfd4ac24be871236c01784f | /tests/lean/string_imp2.lean | 77821577c6909abdfe8e01216435e44f917bde5f | [
"Apache-2.0"
] | permissive | GaloisInc/lean4 | 74c267eb0e900bfaa23df8de86039483ecbd60b7 | 228ddd5fdcd98dd4e9c009f425284e86917938aa | refs/heads/master | 1,643,131,356,301 | 1,562,715,572,000 | 1,562,715,572,000 | 192,390,898 | 0 | 0 | null | 1,560,792,750,000 | 1,560,792,749,000 | null | UTF-8 | Lean | false | false | 2,556 | lean | def f (s : String) : String :=
s ++ " " ++ s
def g (s : String) : String :=
s.push ' ' ++ s.push '-'
def h (s : String) : String :=
let itβ := s.mkIterator in
let itβ := itβ.next in
itβ.remainingToString ++ "-" ++ itβ.remainingToString
#exit -- Disabled until we implement new VM
def r (s : String) : String :=
let ... |
38495593c0d4b8723610703370d61560cb482e68 | c2d3fec70c4d83c328c648449c5f2b1c48e8c05c | /propositional.lean | f5ee24978f4e6c0bdfb176e176967315d757dbf9 | [] | no_license | agro1986/lean-proofs | d603364212d46c30601da94660f4f0133a47d793 | a11b42ec47dbb347b66547d7e72e5154e13b6e85 | refs/heads/master | 1,598,977,963,373 | 1,572,882,333,000 | 1,572,882,333,000 | 219,005,217 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,602 | lean | variables p q r s: Prop
-- commutativity of β§ and β¨
theorem and_switch (h: p β§ q): q β§ p :=
and.intro h.right h.left
example: p β§ q β q β§ p :=
iff.intro
(and_switch p q)
(and_switch q p)
theorem or_switch (h: p β¨ q): q β¨ p :=
or.elim h
(assume p, or.inr p)
(assume q, or.inl q)
example: p β¨ q ... |
9c08ea74b6bf8fcbb860c3586cc045d35f758a43 | 46125763b4dbf50619e8846a1371029346f4c3db | /src/order/complete_boolean_algebra.lean | 347f77593dc8dd6e3c02cc565c8fe97c7dfe113e | [
"Apache-2.0"
] | permissive | thjread/mathlib | a9d97612cedc2c3101060737233df15abcdb9eb1 | 7cffe2520a5518bba19227a107078d83fa725ddc | refs/heads/master | 1,615,637,696,376 | 1,583,953,063,000 | 1,583,953,063,000 | 246,680,271 | 0 | 0 | Apache-2.0 | 1,583,960,875,000 | 1,583,960,875,000 | null | UTF-8 | Lean | false | false | 4,647 | lean | /-
Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl
Theory of complete Boolean algebras.
-/
import order.complete_lattice order.boolean_algebra data.set.basic
set_option old_structure_cmd true
universes u v w
variables... |
7689c06965945ce8546aa02458694b2012dd64aa | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/ring_theory/jacobson.lean | c4f252cd949d89537e8db70a06391d636e06c717 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 34,288 | lean | /-
Copyright (c) 2020 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Devon Tuma
-/
import ring_theory.localization.away
import ring_theory.ideal.over
import ring_theory.jacobson_ideal
/-!
# Jacobson Rings
The following conditions are equivalent for a ring ... |
31dd0d376ee0e910de881d6c45499bf0b6407c27 | 437dc96105f48409c3981d46fb48e57c9ac3a3e4 | /src/topology/separation.lean | d05aa19ea7532ed0ef315e5a49faf51c7cfda027 | [
"Apache-2.0"
] | permissive | dan-c-k/mathlib | 08efec79bd7481ee6da9cc44c24a653bff4fbe0d | 96efc220f6225bc7a5ed8349900391a33a38cc56 | refs/heads/master | 1,658,082,847,093 | 1,589,013,201,000 | 1,589,013,201,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 16,717 | lean | /-
Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl, Mario Carneiro
Separation properties of topological spaces.
-/
import topology.subset_properties
open set filter
open_locale topological_space
local attribute [instan... |
642a7e055cb93e8aec981156814039a0e668bca3 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/multiset/pi.lean | f47ac224b1f7b60cef754b04a60d7b06a2648c68 | [
"Apache-2.0"
] | permissive | AntoineChambert-Loir/mathlib | 64aabb896129885f12296a799818061bc90da1ff | 07be904260ab6e36a5769680b6012f03a4727134 | refs/heads/master | 1,693,187,631,771 | 1,636,719,886,000 | 1,636,719,886,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,888 | lean | /-
Copyright (c) 2018 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl
-/
import data.multiset.nodup
/-!
# The cartesian product of multisets
-/
namespace multiset
section pi
variables {Ξ± : Type*}
open function
/-- Given `Ξ΄ : Ξ± β Type*`... |
54d481b82678a3ffd238287355c2ebbee5fccd5e | 798dd332c1ad790518589a09bc82459fb12e5156 | /analysis/normed_space.lean | 9ff8669af12d5bcd54833a5ee429794f5204f6b7 | [
"Apache-2.0"
] | permissive | tobiasgrosser/mathlib | b040b7eb42d5942206149371cf92c61404de3c31 | 120635628368ec261e031cefc6d30e0304088b03 | refs/heads/master | 1,644,803,442,937 | 1,536,663,752,000 | 1,536,663,907,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,813 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Normed spaces.
Authors: Patrick Massot, Johannes HΓΆlzl
-/
import algebra.pi_instances
import linear_algebra.prod_module
import analysis.nnreal
variables {Ξ± : Type*} {Ξ² : Type*} {Ξ³ : Type*} {ΞΉ... |
8f3e9f22b105ac20ee1be6b741727b44278625d5 | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /library/data/unit/insts.lean | 6f7cf442e4dea2cbaee1348b96da232d9fb4f297 | [
"Apache-2.0"
] | permissive | codyroux/lean | 7f8dff750722c5382bdd0a9a9275dc4bb2c58dd3 | 0cca265db19f7296531e339192e9b9bae4a31f8b | refs/heads/master | 1,610,909,964,159 | 1,407,084,399,000 | 1,416,857,075,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 582 | lean | -- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Author: Leonardo de Moura
import data.unit.decl data.unit.thms logic.decidable logic.inhabited
open decidable
namespace unit
protected theorem subsingleton [instance] : subsingl... |
34ed4aac3369873202141164a07550c928f392b9 | c9b68131de1dfe4e7f0ea5749b11e67a774bc839 | /src/memory.lean | a150075d17565eae21b5542e9c8e538e5f55ddd1 | [] | no_license | congge666/formal-proofs | 2013f158f310abcfc07c156bb2a5113fb78f7831 | b5f6964d0220c8f89668357f2c08e44861128fe3 | refs/heads/master | 1,691,374,567,671 | 1,632,704,604,000 | 1,632,706,366,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,971 | lean | /-
The organization of information in the memory.
-/
import memory_aux constraints
noncomputable theory
open_locale classical
open_locale big_operators
open_locale disable_subsingleton_simps
/- the data -/
variables {F : Type*}
variable {T : β} -- the number of steps in the execution
variables {pc inst
... |
6718e568cbf54b93a1818aa3657798e8e6e1998c | d72901cc240bd78b8b0384565e4f4dee8abd3a86 | /src/topology/metric_space/gromov_hausdorff.lean | 0dbc1521a14bf85b20d38c8937904f4571c695aa | [
"Apache-2.0"
] | permissive | leon-volq/mathlib | 513b24765349bb5187df9d898b92beadf96124d9 | 0cc93a137e9b2e243f8ae1f808fa7225ce0fe143 | refs/heads/master | 1,676,294,376,990 | 1,610,838,688,000 | 1,610,838,688,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 55,682 | lean | /-
Copyright (c) 2019 SΓ©bastien GouΓ«zel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: SΓ©bastien GouΓ«zel
-/
import topology.metric_space.closeds
import set_theory.cardinal
import topology.metric_space.gromov_hausdorff_realized
import topology.metric_space.completion
/... |
3bf3f8f138fc1db9b338f94d8f16618d41133b93 | 8930e38ac0fae2e5e55c28d0577a8e44e2639a6d | /computability/halting.lean | f2332cfc0a39e8242be1443764e6a0084503377b | [
"Apache-2.0"
] | permissive | SG4316/mathlib | 3d64035d02a97f8556ad9ff249a81a0a51a3321a | a7846022507b531a8ab53b8af8a91953fceafd3a | refs/heads/master | 1,584,869,960,527 | 1,530,718,645,000 | 1,530,724,110,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,733 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
More partial recursive functions using a universal program;
Rice's theorem and the halting problem.
-/
import computability.partrec_code
open encodable denumerable
nam... |
ece5d25ee85d78f03eecdbfde0e46a9020215915 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/monoidal/opposite.lean | fcb952d416984d0f37b1d3099b6d56a2144614a2 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 5,217 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.monoidal.coherence
/-!
# Monoidal opposites
We write `Cα΅α΅α΅` for the monoidal opposite of a monoidal category `C`.
-/
universes vβ vβ uβ uβ
... |
23eed55ef89df68776add5f3c2a52a464e361522 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/monad/default_auto.lean | 5b5af04ffd45a63304447b7e4257ef125b636b8e | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 202 | lean | import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.monad.limits
import Mathlib.category_theory.monad.types
import Mathlib.PostPort
namespace Mathlib
end Mathlib |
f4ef3829de0de2b3b3014b02fbadaa4d4a172c80 | 9b9a16fa2cb737daee6b2785474678b6fa91d6d4 | /src/ring_theory/algebra.lean | 1e34dd1e140417e3e0465566e8d7cc530dfabef1 | [
"Apache-2.0"
] | permissive | johoelzl/mathlib | 253f46daa30b644d011e8e119025b01ad69735c4 | 592e3c7a2dfbd5826919b4605559d35d4d75938f | refs/heads/master | 1,625,657,216,488 | 1,551,374,946,000 | 1,551,374,946,000 | 98,915,829 | 0 | 0 | Apache-2.0 | 1,522,917,267,000 | 1,501,524,499,000 | Lean | UTF-8 | Lean | false | false | 18,606 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
Algebra over Commutative Ring (under category)
-/
import data.polynomial data.multivariate_polynomial
import linear_algebra.tensor_product
import ring_theory.subring
universes ... |
6be97ac2197fb6dbcd1731da5db1fea2b1b24ad1 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/algebra/quadratic_discriminant.lean | c409916124bd78b96e7c206e1d416915feb065b5 | [
"Apache-2.0"
] | permissive | gebner/mathlib | eab0150cc4f79ec45d2016a8c21750244a2e7ff0 | cc6a6edc397c55118df62831e23bfbd6e6c6b4ab | refs/heads/master | 1,625,574,853,976 | 1,586,712,827,000 | 1,586,712,827,000 | 99,101,412 | 1 | 0 | Apache-2.0 | 1,586,716,389,000 | 1,501,667,958,000 | Lean | UTF-8 | Lean | false | false | 6,906 | lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
-/
import algebra.ordered_field
import tactic.linarith tactic.ring
/-!
# Quadratic discriminants and roots of a quadratic
This file defines the discriminant of a quadra... |
7bd0b39a8489866b94916b6548be4e8175c4da3a | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/tactic/replacer.lean | 34b8100493c2318abf44207cbcbb23ac87ad1cc6 | [
"Apache-2.0"
] | permissive | fpvandoorn/mathlib | b21ab4068db079cbb8590b58fda9cc4bc1f35df4 | b3433a51ea8bc07c4159c1073838fc0ee9b8f227 | refs/heads/master | 1,624,791,089,608 | 1,556,715,231,000 | 1,556,715,231,000 | 165,722,980 | 5 | 0 | Apache-2.0 | 1,552,657,455,000 | 1,547,494,646,000 | Lean | UTF-8 | Lean | false | false | 4,773 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
A mechanism for defining tactics for use in auto params, whose
meaning is defined incrementally through attributes.
-/
import tactic.basic data.string.defs data.list.def... |
8e3b4ba7c69b54e710b3283d2cb3df661bd5813b | d0f9af2b0ace5ce352570d61b09019c8ef4a3b96 | /hw8/hw8_turn_in/associativity_and_precedence.lean | b3d9b016a494c4043144ccc0189307133d31b638 | [] | no_license | jngo13/Discrete-Mathematics | 8671540ef2da7c75915d32332dd20c02f001474e | bf674a866e61f60e6e6d128df85fa73819091787 | refs/heads/master | 1,675,615,657,924 | 1,609,142,011,000 | 1,609,142,011,000 | 267,190,341 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,945 | lean | import .propositional_logic_syntax_and_semantics
open pExp
#check 2 + 3 + 4
#check (2 + 3) + 4
#check 2 + (3 + 4)
/-
Motivation: Can't overlad β. First
attempt at a solution: overload >
to mean pImp, as follows.
notation e1 > e2 := pImp e1 e2
Problem: > is a reserved notation
in Lean. We can overload it but we
c... |
6fbe5e25a2d747f7fb7847a49183d8e1521f5c3a | f68ef9a599ec5575db7b285d4960e63c5d464ccc | /Exercises/Lista 2/capitulo-04-LucasMoschen.lean | f222f8079b9b7a84447428fb118e97ce22e50bad | [] | no_license | lucasmoschen/discrete-mathematics | a38d5970cc571b0b9d202bf6a43efeb8ed6f66e3 | 0f1945cc5eb094814c926cd6ae4a8b4c5c579a1e | refs/heads/master | 1,677,111,757,003 | 1,611,500,097,000 | 1,611,500,097,000 | 205,903,359 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,306 | lean | variables A B C D : Prop
example : A β§ (A β B) β B :=
assume : A β§ (A β B),
show B, from (and.right this) (and.left this)
example : A β Β¬ (Β¬ A β§ B) :=
assume h: A,
assume hβ : Β¬A β§ B,
show false, from (and.left hβ) h
example : Β¬ (A β§ B) β (A β Β¬ B) :=
assume h: Β¬ (A β§ B),
assume hβ : A,
assume hβ : B,
show false, f... |
df25909008834d13c231864a221b0872409e9e52 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/psigma/order.lean | 28fcd68846249a1929517da2831ade841eb65191 | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 3,743 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Minchao Wu
-/
import data.sigma.lex
import order.synonym
/-!
# Lexicographic order on a sigma type
This file defines the lexicographic order on `Ξ£β' i, Ξ± i`. `a` is l... |
24a6fb2c15a786d3fd41ac367bfdee87c7ebae13 | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /doc/demo/nnf.lean | 518b40f50dff8db7b795c5d1cfbb12627feae584 | [
"Apache-2.0"
] | permissive | codyroux/lean0.1 | 1ce92751d664aacff0529e139083304a7bbc8a71 | 0dc6fb974aa85ed6f305a2f4b10a53a44ee5f0ef | refs/heads/master | 1,610,830,535,062 | 1,402,150,480,000 | 1,402,150,480,000 | 19,588,851 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 509 | lean | rewrite_set NNF
add_rewrite not_not_eq not_true not_false not_neq not_and not_or not_iff not_implies not_forall
not_exists forall_and_distribute exists_and_distributer exists_and_distributel : NNF
variable p : Nat β Nat β Bool
variable f : Nat β Nat
variable g : Nat β Nat β Nat
(*
local t1 = parse_lea... |
b637c5a889bf053c7d17689719efbb5f564c327c | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/ring_theory/perfection_auto.lean | 7570085f3e46cf9de16687c9caf3806552be09f7 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 24,840 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.char_p.default
import Mathlib.algebra.ring.pi
import Mathlib.analysis.special_functions.pow
i... |
c97fc0e641ab3828f15fdb5e9a7df0b8f635bf5b | 0851884047bb567d19e188e8f1ad959c5ae9c5ce | /src/Euclid/axioms.lean | 0af862667e98b7ff09b37cf9762ba9aad7a1c235 | [
"Apache-2.0"
] | permissive | yz5216/xena-UROP-2018 | 00d3f71a831324966d40d302544ed2cbbec3fd0f | 5e9da9dc64dc51897677f8b73ab9f94061a8d977 | refs/heads/master | 1,584,922,436,989 | 1,531,487,250,000 | 1,531,487,250,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,415 | lean | class Euclidean_plane (point : Type) :=
-- Equidistance of 4 Points
(eqd : point β point β point β point β Prop)
-- Between A B C means B is on the line segment AC
(B : point β point β point β Prop)
(eqd_refl : β a b : point, eqd a b b a)
(eqd_trans : β a b p q r s, eqd a b p q β eqd a b r s β eqd p q r s)
(id_eqd : β... |
eded654cea0bdca70ec678a1333a620e597bea0c | bb31430994044506fa42fd667e2d556327e18dfe | /src/set_theory/ordinal/natural_ops.lean | 526bc5ea3d49ce01dcd65050a181a3bf13a470e8 | [
"Apache-2.0"
] | permissive | sgouezel/mathlib | 0cb4e5335a2ba189fa7af96d83a377f83270e503 | 00638177efd1b2534fc5269363ebf42a7871df9a | refs/heads/master | 1,674,527,483,042 | 1,673,665,568,000 | 1,673,665,568,000 | 119,598,202 | 0 | 0 | null | 1,517,348,647,000 | 1,517,348,646,000 | null | UTF-8 | Lean | false | false | 12,041 | lean | /-
Copyright (c) 2022 Violeta HernΓ‘ndez Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Violeta HernΓ‘ndez Palacios
-/
import set_theory.ordinal.arithmetic
/-!
# Natural operations on ordinals
The goal of this file is to define natural addition and multiplic... |
fcd7ee8d87b3e89e61f24e870b0750d2ae1eb472 | 40ad357bbd0d327dd1e3e7f7beb868bd4e5b0a9d | /src/temporal_logic/scheduling.lean | e8cf088bb93919bdaadba03bafaf099a3ed5a530 | [] | no_license | unitb/temporal-logic | 9966424f015976d5997a9ffa30cbd77cc3a9cb1c | accec04d1b09ca841be065511c9e206b725b16e9 | refs/heads/master | 1,633,868,382,769 | 1,541,072,223,000 | 1,541,072,223,000 | 114,790,987 | 5 | 3 | null | null | null | null | UTF-8 | Lean | false | false | 19,351 | lean |
import .lemmas
import .spec
import data.set.basic
import util.data.minimum
import util.data.ordering
import util.data.order
import util.function
import util.logic
import tactic.norm_num
open temporal function predicate nat set
local infix ` β `:75 := v_eq
local prefix `β― `:0 := cast (by simp)
universes u v
namesp... |
341d94c18c1cc016a9b675d795c0c12abd60a4f4 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/blast_ematch5.lean | 5a8e8c45bc3cc608b1f2e8bc9884a5978c47fcc6 | [
"Apache-2.0"
] | permissive | soonhokong/lean | cb8aa01055ffe2af0fb99a16b4cda8463b882cd1 | 38607e3eb57f57f77c0ac114ad169e9e4262e24f | refs/heads/master | 1,611,187,284,081 | 1,450,766,737,000 | 1,476,122,547,000 | 11,513,992 | 2 | 0 | null | 1,401,763,102,000 | 1,374,182,235,000 | C++ | UTF-8 | Lean | false | false | 248 | lean | constant subt : nat β nat β Prop
lemma subt_trans [forward] {a b c : nat} : subt a b β subt b c β subt a c :=
sorry
set_option blast.strategy "ematch"
example (a b c d : nat) : subt a b β subt b c β subt c d β subt a d :=
by blast
|
bec4ac5fea3824ccc2611e9da7d442116d85237a | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/analysis/calculus/iterated_deriv.lean | 57637f6b3ffd904beb184e0d756398636eab0aff | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 14,346 | lean | /-
Copyright (c) 2020 SΓ©bastien GouΓ«zel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: SΓ©bastien GouΓ«zel
-/
import analysis.calculus.deriv
import analysis.calculus.cont_diff
/-!
# One-dimensional iterated derivatives
We define the `n`-th derivative of a function `f ... |
9032350100a7e4b01f066f77b75d1a60baca4c2f | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/data/nat/sqrt.lean | 98ca8aa9232a1328ae6172a4037d12844fd19638 | [
"Apache-2.0"
] | permissive | soonhokong/lean-osx | 4a954262c780e404c1369d6c06516161d07fcb40 | 3670278342d2f4faa49d95b46d86642d7875b47c | refs/heads/master | 1,611,410,334,552 | 1,474,425,686,000 | 1,474,425,686,000 | 12,043,103 | 5 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 7,106 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
Very simple (sqrt n) function that returns s s.t.
s*s β€ n β€ s*s + s + s
-/
import data.nat.order data.nat.sub
namespace nat
open decidable
-- This is th... |
ea55de95e165d60b221dd58371fab71c8be30795 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/data/ordering/lemmas_auto.lean | 314d44834dbf7ecd85e9cb092d54edd7396caae6 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,499 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.data.ordering.basic
import Mathlib.Lean3Lib.init.meta.default
import Mathlib.Lean3Lib.init.algebra.class... |
4ff2e338de4d4030b77ffdef2d5bcbb5741568b0 | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /src/Lean/Data/RBMap.lean | 22221ec697e8bd4264b14adb1c0f9142f10bf244 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | tobiasgrosser/lean4 | ce0fd9cca0feba1100656679bf41f0bffdbabb71 | ebdbdc10436a4d9d6b66acf78aae7a23f5bd073f | refs/heads/master | 1,673,103,412,948 | 1,664,930,501,000 | 1,664,930,501,000 | 186,870,185 | 0 | 0 | Apache-2.0 | 1,665,129,237,000 | 1,557,939,901,000 | Lean | UTF-8 | Lean | false | false | 15,405 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
namespace Lean
universe u v w w'
inductive Rbcolor where
| red | black
inductive RBNode (Ξ± : Type u) (Ξ² : Ξ± β Type v) where
| leaf ... |
4ca428fc43eea25a826bccd438324881976747bd | 737dc4b96c97368cb66b925eeea3ab633ec3d702 | /tests/lean/run/multiTargetCasesInductionIssue.lean | fa1f6147f563abbd22238ec10b617e01536c7f9b | [
"Apache-2.0"
] | permissive | Bioye97/lean4 | 1ace34638efd9913dc5991443777b01a08983289 | bc3900cbb9adda83eed7e6affeaade7cfd07716d | refs/heads/master | 1,690,589,820,211 | 1,631,051,000,000 | 1,631,067,598,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,657 | lean | def Vec (Ξ± : Type u) (n : Nat) : Type u := { a : List Ξ± // a.length = n }
def Vec.nil : Vec Ξ± 0 := β¨[], rflβ©
def Vec.cons (a : Ξ±) (as : Vec Ξ± n) : Vec Ξ± (n+1) := β¨a :: as.val, by simp [as.property]β©
set_option pp.analyze false
def Vec.casesOn
(motive : (n : Nat) β Vec Ξ± n β Sort v)
(n : Nat)
(as : Vec... |
2744b3ed2949983dd5e69f81809cdde8569f7079 | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /stage0/src/Lean/Meta/Tactic/Apply.lean | 539bb1d9aa8ca69cb85fb8ad03df0539b2af1dcf | [
"Apache-2.0"
] | permissive | williamdemeo/lean4 | 72161c58fe65c3ad955d6a3050bb7d37c04c0d54 | 6d00fcf1d6d873e195f9220c668ef9c58e9c4a35 | refs/heads/master | 1,678,305,356,877 | 1,614,708,995,000 | 1,614,708,995,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,287 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Util.FindMVar
import Lean.Meta.ExprDefEq
import Lean.Meta.SynthInstance
import Lean.Meta.CollectMVars
import Lean.Meta.Tactic.Util
namespace Le... |
cf8f606251d1453fefa207469f56e74ade9da060 | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/topology/algebra/monoid.lean | f62e5682e9756b2d5d8dd1fb7c71a0c1579a657e | [
"Apache-2.0"
] | permissive | ilitzroth/mathlib | ea647e67f1fdfd19a0f7bdc5504e8acec6180011 | 5254ef14e3465f6504306132fe3ba9cec9ffff16 | refs/heads/master | 1,680,086,661,182 | 1,617,715,647,000 | 1,617,715,647,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,122 | lean | /-
Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl, Mario Carneiro
-/
import topology.continuous_on
import group_theory.submonoid.operations
import algebra.group.prod
import algebra.pointwise
/-!
# Theory of topological... |
53acf7364ffdea2b3547f6f4f05ed23f84479a37 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/analysis/normed_space/int.lean | 786f3f7d5fe07ea264f3a5fde8a934f999cd9890 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 1,522 | lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import analysis.normed.field.basic
/-!
# The integers as normed ring
This file contains basic facts about the integers as normed ring.
Recall that `βnβ` denotes th... |
73fa391622e85ab3b5b4f3f78722bcf6c3387a97 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/ring_theory/coprime.lean | 5701c20d9d0f9df26c3c4c956cacded9b9bf8cd6 | [
"Apache-2.0"
] | permissive | hikari0108/mathlib | b7ea2b7350497ab1a0b87a09d093ecc025a50dfa | a9e7d333b0cfd45f13a20f7b96b7d52e19fa2901 | refs/heads/master | 1,690,483,608,260 | 1,631,541,580,000 | 1,631,541,580,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,669 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Ken Lee, Chris Hughes
-/
import algebra.big_operators.basic
import data.fintype.basic
import data.int.gcd
import data.set.pairwise
import tactic.ring
/-!
# Coprime elements of a... |
bd59cdfe19d178e60cc6f9a2ca0e64e5665ada8b | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /tests/lean/run/expandAbbrevAtIsClass.lean | 575c3921315236dfc39d8c4e5aa9f41aa6c6e860 | [
"Apache-2.0"
] | permissive | williamdemeo/lean4 | 72161c58fe65c3ad955d6a3050bb7d37c04c0d54 | 6d00fcf1d6d873e195f9220c668ef9c58e9c4a35 | refs/heads/master | 1,678,305,356,877 | 1,614,708,995,000 | 1,614,708,995,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 193 | lean | def one (Ξ± : Type u) [OfNat Ξ± (natLit! 1)] : Ξ± := 1
abbrev HasOne (Ξ± : Type u) := OfNat Ξ± (natLit! 1)
def one' (Ξ± : Type u) [HasOne Ξ±] : Ξ± := 1
example : HasOne Nat := inferInstance
|
bd49a080b3652b54b0b596d118d3092ff58a9983 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/dynamics/periodic_pts.lean | 353804e7661ea24df3c0467e62730b3c2138c21a | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 24,673 | lean | /-
Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import algebra.hom.iterate
import data.list.cycle
import data.pnat.basic
import data.nat.prime
import dynamics.fixed_points.basic
import group_theory.group_ac... |
acbfac4a77dcd79b846720a366eaddcb01c66f07 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/data/list/perm.lean | 1d73362be795d7e162959b77aaccdfa2f0df620a | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 54,298 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
import data.list.erase_dup
import data.list.lattice
import data.list.permutation
import data.list.zip
import logic.relation
... |
abe6ca25b01eac508d295aa9c6b0f932c57e3979 | 367134ba5a65885e863bdc4507601606690974c1 | /src/tactic/omega/int/preterm.lean | 3936d85c9df91c7dcc0b85384400e2ffa35b5c37 | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 2,814 | lean | /-
Copyright (c) 2019 Seul Baek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Seul Baek
-/
/-
Linear integer arithmetic terms in pre-normalized form.
-/
import tactic.omega.term
namespace omega
namespace int
/-- The shadow syntax for arithmetic terms. All constant... |
83dadc76048b45b161d96ff5d3530f18b55c8872 | 5d166a16ae129621cb54ca9dde86c275d7d2b483 | /tests/lean/run/record10.lean | e5168c0fcf5e6a50b296d65960b3e37667e296af | [
"Apache-2.0"
] | permissive | jcarlson23/lean | b00098763291397e0ac76b37a2dd96bc013bd247 | 8de88701247f54d325edd46c0eed57aeacb64baf | refs/heads/master | 1,611,571,813,719 | 1,497,020,963,000 | 1,497,021,515,000 | 93,882,536 | 1 | 0 | null | 1,497,029,896,000 | 1,497,029,896,000 | null | UTF-8 | Lean | false | false | 487 | lean | set_option old_structure_cmd true
#print prefix semigroup
#print "======================="
structure [class] has_two_muls (A : Type) extends has_mul A renaming mulβmul1,
private has_mul A renaming mulβmul2
#print prefix has_two_muls
#print "======================="
struct... |
c785520c0a6f807a3b6f75cf51d202cf7da21680 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/data/zmod/quotient.lean | 3fd7a8587f6841ecfa01145d6d142196578e1b17 | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 2,369 | lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import data.zmod.basic
import group_theory.quotient_group
import ring_theory.int.basic
/-!
# `zmod n` and quotient groups / rings
This file relates `zmod n` to the quotie... |
dd81138b1b3870d821b9b5af2c4fc8a61bf298b3 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/category_theory/functor/epi_mono.lean | cb3bff689fb2a6f8dc52d256876754c5bc4f3fc7 | [
"Apache-2.0"
] | permissive | ramonfmir/mathlib | c5dc8b33155473fab97c38bd3aa6723dc289beaa | 14c52e990c17f5a00c0cc9e09847af16fabbed25 | refs/heads/master | 1,661,979,343,526 | 1,660,830,384,000 | 1,660,830,384,000 | 182,072,989 | 0 | 0 | null | 1,555,585,876,000 | 1,555,585,876,000 | null | UTF-8 | Lean | false | false | 8,747 | lean | /-
Copyright (c) 2022 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import category_theory.epi_mono
/-!
# Preservation and reflection of monomorphisms and epimorphisms
We provide typeclasses that state that a functor preserves or refl... |
50804f9b21fc6817eaafa246addbe68d1dde9d80 | f3849be5d845a1cb97680f0bbbe03b85518312f0 | /old_library/init/datatypes.lean | 23ef9cbdae74df805de09da4a750b77e8e4e3343 | [
"Apache-2.0"
] | permissive | bjoeris/lean | 0ed95125d762b17bfcb54dad1f9721f953f92eeb | 4e496b78d5e73545fa4f9a807155113d8e6b0561 | refs/heads/master | 1,611,251,218,281 | 1,495,337,658,000 | 1,495,337,658,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,565 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
Basic datatypes
-/
prelude
notation `Prop` := Type 0
notation `Typeβ` := Type 2
notation `Typeβ` := Type 3
universe variables u v
inductive poly_unit : Ty... |
e333775a5040d15f62c397902fe91f0bd397325e | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/algebra/homology/additive.lean | 11f29707270ed3b231cd09ed9d8cb28694ebd7a8 | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 8,617 | lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import algebra.homology.homology
import algebra.homology.single
import category_theory.preadditive.additive_functor
/-!
# Homology is an additive functor
When `V` i... |
2083a341f6d088139204b072e010ced6c8739bbe | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /tests/bench/frontend_test.lean | 6506251a5a463429288510635be672b1cf53fa1d | [
"Apache-2.0"
] | permissive | mhuisi/lean4 | 28d35a4febc2e251c7f05492e13f3b05d6f9b7af | dda44bc47f3e5d024508060dac2bcb59fd12e4c0 | refs/heads/master | 1,621,225,489,283 | 1,585,142,689,000 | 1,585,142,689,000 | 250,590,438 | 0 | 2 | Apache-2.0 | 1,602,443,220,000 | 1,585,327,814,000 | C | UTF-8 | Lean | false | false | 61,186 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
notation, basic datatypes and type classes
-/
prelude
notation `Prop` := Sort 0
notation f ` $ `:1 a:0 := f a
/- Logical operations and relations -/
reserv... |
a3fe2b5e8da2e26660d1cb5562e9837e6ff1048e | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/463.lean | dfc856b4f216a23d697adfd3234593f5042b166a | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 263 | lean | structure A := (a b : Nat)
structure B extends A := (c : Nat)
structure C := (a b c : Nat)
structure D := (toA : A) (c : Nat)
def foo (s : C) : B := {s with} -- works in lean 4, works in lean 3
def bar (s : D) : B := {s with} -- works in lean 4, fails in lean 3
|
e393a64f8fdddb15b42a11f3dce5bf13169c043d | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/evalTacticBug.lean | 24435e9a58a0158d7d64ee36ed6827f99f5da932 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 378 | lean | syntax "foo" : tactic
macro_rules | `(tactic| foo) => `(tactic| assumption)
macro_rules | `(tactic| foo) => `(tactic| apply Nat.pred_lt; assumption)
macro_rules | `(tactic| foo) => `(tactic| contradiction)
example (i : Nat) (h : i - 1 < i) : i - 1 < i := by
foo
example (i : Nat) (h : i β 0) : i - 1 < i := by
foo... |
436e3e76bb737960e17ce36c8f1caf0804db61c7 | 35960c5b117752aca7e3e7767c0b393e4dbd72a7 | /src/occurs.lean | 58339bc8f332c984605265a0005ef509d2ac0254 | [
"Apache-2.0"
] | permissive | spl/tts | 461dc76b83df8db47e4660d0941dc97e6d4fd7d1 | b65298fea68ce47c8ed3ba3dbce71c1a20dd3481 | refs/heads/master | 1,541,049,198,347 | 1,537,967,023,000 | 1,537,967,029,000 | 119,653,145 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 963 | lean | import data.equiv.basic
namespace tts ------------------------------------------------------------------
/-- An enumeration of the states in which a variable can occur with respect to
bindings. `occurs` is isomorphic to `bool` but more descriptive in naming. -/
@[derive decidable_eq]
inductive occurs : Type
| bound :... |
edc18f8cd4862becde36eb9c0cc7a70c4151257e | 0c9c1ff8e5013c525bf1d72338b62db639374733 | /library/init/data/nat/lemmas.lean | e1fb94474959d99714b64cd4439b834d86155061 | [
"Apache-2.0"
] | permissive | semorrison/lean | 1f2bb450c3400098666ff6e43aa29b8e1e3cdc3a | 85dcb385d5219f2fca8c73b2ebca270fe81337e0 | refs/heads/master | 1,638,526,143,586 | 1,634,825,588,000 | 1,634,825,588,000 | 258,650,844 | 0 | 0 | Apache-2.0 | 1,587,772,955,000 | 1,587,772,954,000 | null | UTF-8 | Lean | false | false | 49,238 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad
-/
prelude
import init.data.nat.basic init.data.nat.div init.meta init.algebra.functions
universes u
namespace nat
attribute [pre_smt] nat_zero... |
e02ca922817dd379178383da78d1d5e64884f0d3 | d29d82a0af640c937e499f6be79fc552eae0aa13 | /src/ring_theory/derivation.lean | 67aabe1bbedd4a20f126e38747c1f077135ff3c0 | [
"Apache-2.0"
] | permissive | AbdulMajeedkhurasani/mathlib | 835f8a5c5cf3075b250b3737172043ab4fa1edf6 | 79bc7323b164aebd000524ebafd198eb0e17f956 | refs/heads/master | 1,688,003,895,660 | 1,627,788,521,000 | 1,627,788,521,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,026 | lean | /-
Copyright Β© 2020 NicolΓ² Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: NicolΓ² Cavalleri
-/
import algebra.lie.of_associative
import ring_theory.algebra_tower
/-!
# Derivations
This file defines derivation. A derivation `D` from the `R`-algebra `A` to t... |
d1213893d0040d85e03e9d5e02c67c7831d5542d | 9954952c821fe205cf4a343886fef5c7b6f070bf | /lean/intro.lean | 1cba65b49c6a18bb3096b3253136f37de0960da4 | [] | no_license | gaorongjia/cs-dm | cc81c43a56e4e3861de4779ae63d74378d64f03b | e50adcf6120d985c93075fa36d4f0211589779a3 | refs/heads/master | 1,584,030,132,304 | 1,524,251,414,000 | 1,524,251,414,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 33,431 | lean | /-
At this point, we've proposed and validated
(using truth tables) a set of fundamental
inference rules. Unfortunately, using truth
tables doesn't scale well. We thus play an
important game, now, where we simply accept
the inference rules as valid transformation
between sets of premises and conclusions. We
view the Ps... |
8a5e77619f98fb9543df79a1ef257f0b03d1d070 | 4fa118f6209450d4e8d058790e2967337811b2b5 | /src/sheaves/presheaf_of_topological_rings.lean | d441ddb31c3256caf801e7678c7945d06ee7cc92 | [
"Apache-2.0"
] | permissive | leanprover-community/lean-perfectoid-spaces | 16ab697a220ed3669bf76311daa8c466382207f7 | 95a6520ce578b30a80b4c36e36ab2d559a842690 | refs/heads/master | 1,639,557,829,139 | 1,638,797,866,000 | 1,638,797,866,000 | 135,769,296 | 96 | 10 | Apache-2.0 | 1,638,797,866,000 | 1,527,892,754,000 | Lean | UTF-8 | Lean | false | false | 2,075 | lean | /-
Presheaf of toplogical rings.
-/
import topology.algebra.ring
import sheaves.presheaf_of_rings
universes u v
open topological_space
-- Definition of a presheaf of topological rings.
structure presheaf_of_topological_rings (Ξ± : Type u) [topological_space Ξ±]
extends presheaf_of_rings Ξ± :=
(Ftop : β (U), topolo... |
22e216e8255f58c448e761e5b91fcf1d13805fa4 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/computability/turing_machine.lean | 05d26c6f167eff3f48162b256b9ae322da624abc | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 109,678 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.fintype.basic
import data.pfun
import logic.function.iterate
import order.basic
import tactic.apply_fun
/-!
# Turing machines
This file defines a sequen... |
5a129dd6b1a4f3f9445c40bfc59c2654e2914c5d | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/category_theory/eq_to_hom.lean | c7a18834f100c69b23d82b75e675ac3b6dcfa629 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 5,116 | lean | /-
Copyright (c) 2018 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Scott Morrison
-/
import category_theory.opposites
universes vβ vβ uβ uβ -- morphism levels before object levels. See note [category_theory universes].
namespace category_t... |
dd90ab58aea3843461b8daaaeff3fd97bf3743d3 | 54d7e71c3616d331b2ec3845d31deb08f3ff1dea | /library/tools/super/cdcl_solver.lean | acd8b16311b889c04209097618c570aa3af85535 | [
"Apache-2.0"
] | permissive | pachugupta/lean | 6f3305c4292288311cc4ab4550060b17d49ffb1d | 0d02136a09ac4cf27b5c88361750e38e1f485a1a | refs/heads/master | 1,611,110,653,606 | 1,493,130,117,000 | 1,493,167,649,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,976 | lean | /-
Copyright (c) 2016 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner
-/
import .clause
open tactic expr monad super
namespace cdcl
@[reducible] meta def prop_var := expr
@[reducible] meta def proof_term := expr
@[reducible] meta def proof... |
3ac314a274111ac7a7e236b13c16d5ff54217180 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/algebra/category/Module/basic.lean | e53b48f7d24a92e6dedcc728eca95f7a06402cb2 | [
"Apache-2.0"
] | permissive | dupuisf/mathlib | 62de4ec6544bf3b79086afd27b6529acfaf2c1bb | 8582b06b0a5d06c33ee07d0bdf7c646cae22cf36 | refs/heads/master | 1,669,494,854,016 | 1,595,692,409,000 | 1,595,692,409,000 | 272,046,630 | 0 | 0 | Apache-2.0 | 1,592,066,143,000 | 1,592,066,142,000 | null | UTF-8 | Lean | false | false | 5,619 | lean | /-
Copyright (c) 2019 Robert A. Spencer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert A. Spencer, Markus Himmel
-/
import algebra.category.Group.basic
import category_theory.concrete_category
import category_theory.limits.shapes.kernels
import category_theory.... |
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