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8491825309cd1a239f29895be27f18e217925d75 | fcf3ffa92a3847189ca669cb18b34ef6b2ec2859 | /src/world8/level12.lean | 94bd14cf9de2b0fdc7dba18cf182e93546aab031 | [
"Apache-2.0"
] | permissive | nomoid/lean-proofs | 4a80a97888699dee42b092b7b959b22d9aa0c066 | b9f03a24623d1a1d111d6c2bbf53c617e2596d6a | refs/heads/master | 1,674,955,317,080 | 1,607,475,706,000 | 1,607,475,706,000 | 314,104,281 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 216 | lean | import mynat.definition
import mynat.add
import world2.level5
namespace mynat
theorem add_one_eq_succ (d : mynat) : d + 1 = succ(d) :=
begin [nat_num_game]
symmetry,
exact succ_eq_add_one d,
end
end mynat
|
625c09c8e0cdf4803915cd38376e56e559599850 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/category_theory/functor/left_derived.lean | 6f54af43a5929e26ae6002917ad07b27c9b8b0e7 | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 7,681 | 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 category_theory.preadditive.projective_resolution
/-!
# Left-derived functors
We define the left-derived functors `F.left_derived n : C ⥤ D` for any additive... |
ac168ae35572c71f758626fde4ea120c2077f028 | 798dd332c1ad790518589a09bc82459fb12e5156 | /set_theory/cardinal.lean | 48425e4df5927506431eeb44d4abc2ea16adf8f2 | [
"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 | 27,617 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl, Mario Carneiro
Cardinal arithmetic.
Cardinals are represented as quotient over equinumerous types.
-/
import data.set.finite data.quot logic.schroeder_bernstein logic... |
49ea73198ba966a40cce2798d98be08a5fbae1eb | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/root_name_in_ns.lean | e2d3483184c4b5f4203aa67214714c99fcf24c07 | [
"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 | 957 | lean | structure foo := (y : ℕ)
namespace foo
instance _root_.string.has_add : has_add string := ⟨(++)⟩
def _root_.string.frob (x : string) := x ++ x
def frob := "5".frob
meta mutual def _root_.string.meow, woof
with _root_.string.meow : string → ℕ
| s := if s.length = 0 then 0 else woof ⟨s.length⟩
with woof : foo → ℕ
| ... |
c43d88def5c958191f25eb621399fe6e677f153c | 0d2e44896897eda703992595d71a0b19ed30b8a1 | /uexp/src/uexp/rules/relationalAlgebra.lean | c9a0f665b1382eb354fedf54ff9e016d1edaa485 | [
"BSD-2-Clause"
] | permissive | wwombat/Cosette | a87312aabefdb53ea8b67c37731bd58c7485afb6 | 4c5dc6172e24d3546c9818ac1fad06f72fe1c991 | refs/heads/master | 1,619,479,568,051 | 1,520,292,502,000 | 1,520,292,502,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,175 | lean | import ..u_semiring
import ..sql
import ..tactics
open SQL
open Proj
open Expr
lemma commutativeSelect:
forall Γ s a slct0 slct1,
denoteSQL ((SELECT * FROM1 (SELECT * FROM1 a WHERE slct1) WHERE slct0): SQL Γ s) =
denoteSQL ((SELECT * FROM1 (SELECT * FROM1 a WHERE slct0) WHERE slct1): SQL Γ s) :=
begin
in... |
64877c4442c71e5fddd17b8602a9bfdd5004f180 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/int/dvd/basic.lean | 8b1da123a66206a5e41893f90da76f00e003ac46 | [
"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 | 2,207 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
import data.int.order.basic
import data.nat.cast.basic
/-!
# Basic lemmas about the divisibility relation in `ℤ`.
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any cha... |
57c06b4e4fee6bf67ac52882b37864059a7384b0 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/category_theory/abelian/opposite.lean | b768fdc5f48a587fdf04b0cbb085e3a06c0cd24e | [
"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 | 3,475 | 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 category_theory.abelian.basic
import category_theory.preadditive.opposite
import category_theory.limits.opposites
import category_theory.limits.constructions.l... |
c04cbba5d2c5bce09be4f2c8f82117f698e26726 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/analysis/inner_product_space/rayleigh.lean | 862b98632701654d9faaa67d7974b1d39fdda2bd | [
"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 | 12,729 | lean | /-
Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth, Frédéric Dupuis
-/
import analysis.inner_product_space.calculus
import analysis.inner_product_space.dual
import analysis.calculus.lagrange_multipliers
import linear_a... |
06a923e37e60c98e6dcfc5f2059f54ca54acdbc0 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/stream/basic.lean | 1143a8006aaaf4afcadb7ba33c5077e24db25f95 | [
"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 | 906 | lean | /-
Copyright (c) 2020 Gabriel Ebner, Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner, Simon Hudon
-/
import tactic.ext
import data.stream
import data.list.basic
import data.list.range
/-!
# Additional instances and attributes for streams
-/
... |
7b2bea393b6e8668500074ec0bdd027e299e8ca5 | f09e92753b1d3d2eb3ce2cfb5288a7f5d1d4bd89 | /src/for_mathlib/subrel.lean | ef459f5c66790cb4710bfd63b62ee8763433e5ad | [
"Apache-2.0"
] | permissive | PatrickMassot/lean-perfectoid-spaces | 7f63c581db26461b5a92d968e7563247e96a5597 | 5f70b2020b3c6d508431192b18457fa988afa50d | refs/heads/master | 1,625,797,721,782 | 1,547,308,357,000 | 1,547,309,364,000 | 136,658,414 | 0 | 1 | Apache-2.0 | 1,528,486,100,000 | 1,528,486,100,000 | null | UTF-8 | Lean | false | false | 329 | lean | import order.complete_lattice order.order_iso
namespace subrel
variables {α : Type*} [partial_order α] {p : α → Prop}
instance : partial_order {x // p x} :=
{ le := subrel (≤) p,
le_refl := λ x, le_refl x,
le_trans := λ x y z, le_trans,
le_antisymm := λ x y hx hy, subtype.eq $ le_antisymm hx hy }
end subrel
|
628b3ed75cbffd160dc490d70cdcc16abefc1958 | 6b2a480f27775cba4f3ae191b1c1387a29de586e | /group_rep_2/Tools/projector.lean | a788c26d5a53f84c830a9d12a46b0fcf1065c713 | [] | no_license | Or7ando/group_representation | a681de2e19d1930a1e1be573d6735a2f0b8356cb | 9b576984f17764ebf26c8caa2a542d248f1b50d2 | refs/heads/master | 1,662,413,107,324 | 1,590,302,389,000 | 1,590,302,389,000 | 258,130,829 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 7,589 | lean | import linear_algebra.basic
notation f ` ⊚ `:80 g:80 := linear_map.comp f g
set_option pp.generalized_field_notation false
universes u v v'
variables {R : Type u}[comm_ring R]{M : Type v}[add_comm_group M] [module R M ](f : M →ₗ[R]M)
open linear_map
open_locale big_operators
def is_projector (p : M →ₗ[R] M) := p * ... |
16957341f11e350691c354482122e5626948af86 | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/measure_theory/measurable_space.lean | 9bda3ab04083c9046c918aeab4e05dd039857b78 | [
"Apache-2.0"
] | permissive | jumpy4/mathlib | d3829e75173012833e9f15ac16e481e17596de0f | af36f1a35f279f0e5b3c2a77647c6bf2cfd51a13 | refs/heads/master | 1,693,508,842,818 | 1,636,203,271,000 | 1,636,203,271,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 49,038 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import measure_theory.measurable_space_def
import measure_theory.tactic
import data.tprod
import data.equiv.fin
/-!
# Measurable spaces and measurab... |
0f0e68a6a157695ebf639c9f5a1860c2a2f3ed69 | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/order/symm_diff.lean | 6d91db7d96ee2e50cc18c275f44a8cfbac1c9318 | [
"Apache-2.0"
] | permissive | ayush1801/mathlib | 78949b9f789f488148142221606bf15c02b960d2 | ce164e28f262acbb3de6281b3b03660a9f744e3c | refs/heads/master | 1,692,886,907,941 | 1,635,270,866,000 | 1,635,270,866,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,115 | lean | /-
Copyright (c) 2021 Bryan Gin-ge Chen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz, Bryan Gin-ge Chen
-/
import order.boolean_algebra
/-!
# Symmetric difference
The symmetric difference or disjunctive union of sets `A` and `B` is the set of elements ... |
b8179451e0e5810a79d4608c66dcdbed7b119821 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/mv_polynomial/basic.lean | 8dac8e5c459bbc153b73737b92b8aff49fcbedfa | [
"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 | 53,009 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
-/
import algebra.algebra.tower
import algebra.monoid_algebra.support
import data.finsupp.antidiagonal
import order.symm_diff
import rin... |
385a45815a3154a4a435930bfd11d0fa962db9e0 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/matrix/rank.lean | 0e4d9dcf153640282b628f0e0830d81ce6e4acb3 | [
"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 | 3,722 | 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 linear_algebra.free_module.finite.rank
import linear_algebra.matrix.to_lin
/-!
# Rank of matrices
The rank of a matrix `A` is defined to be the rank of rang... |
2cd3b70f397146ae7c42922b0308df5db364a7c3 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/lvl1.lean | 256f08e98fe567b79666e9e297caf5e69fc52d72 | [
"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 | 1,345 | lean | import Lean.Level
namespace Lean
namespace Level
def mkMax (xs : Array Level) : Level :=
xs.foldl (start := 1) (init := xs[0]!) mkLevelMax
#eval toString $ normalize $ mkLevelSucc $ mkLevelSucc $ mkMax #[levelZero, mkLevelParam `w, mkLevelSucc (mkLevelSucc (mkLevelSucc (mkLevelParam `z))), levelOne, mkLevelSucc (mkL... |
a519fd3cba7c1361ee267b6840bb4fbd43298f57 | b00eb947a9c4141624aa8919e94ce6dcd249ed70 | /stage0/src/Lean/Elab/Binders.lean | 7ff554bdb0fbde4614aa8d83e1351d592744cecd | [
"Apache-2.0"
] | permissive | gebner/lean4-old | a4129a041af2d4d12afb3a8d4deedabde727719b | ee51cdfaf63ee313c914d83264f91f414a0e3b6e | refs/heads/master | 1,683,628,606,745 | 1,622,651,300,000 | 1,622,654,405,000 | 142,608,821 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 26,345 | 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.Elab.Quotation.Precheck
import Lean.Elab.Term
import Lean.Parser.Term
namespace Lean.Elab.Term
open Meta
open Lean.Parser.Term
/--
Given syn... |
177e12e2821c678eef690f633222251566ec1a76 | 4c630d016e43ace8c5f476a5070a471130c8a411 | /category/applicative.lean | 5e754c608e66a7a082224e14ce2dd92b386a5aef | [
"Apache-2.0"
] | permissive | ngamt/mathlib | 9a510c391694dc43eec969914e2a0e20b272d172 | 58909bd424209739a2214961eefaa012fb8a18d2 | refs/heads/master | 1,585,942,993,674 | 1,540,739,585,000 | 1,540,916,815,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,930 | lean | /-
Copyright (c) 2017 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Simon Hudon
Instances for identity and composition functors
-/
import category.functor
universe variables u v w
section lemmas
open function
variables {F : Type u → Type v}
variables... |
d1ffc72ff6abd3c9bde355dbee9435a95616a0a2 | e61a235b8468b03aee0120bf26ec615c045005d2 | /stage0/src/Init/Control/State.lean | 16154f491af00e2030ca350a8193c0b301dd2909 | [
"Apache-2.0"
] | permissive | SCKelemen/lean4 | 140dc63a80539f7c61c8e43e1c174d8500ec3230 | e10507e6615ddbef73d67b0b6c7f1e4cecdd82bc | refs/heads/master | 1,660,973,595,917 | 1,590,278,033,000 | 1,590,278,033,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,571 | 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, Sebastian Ullrich
The State monad transformer.
-/
prelude
import Init.Control.Alternative
import Init.Control.Lift
import Init.Control.Id
import Init.Control... |
11acb43e3b8cc2eb927fbccdeaa550788ce4a3c3 | 682dc1c167e5900ba3168b89700ae1cf501cfa29 | /src/basicmodal/syntax/syntax.lean | 3f6e006d9e294addb9f16f3b723a07e21a233319 | [] | no_license | paulaneeley/modal | 834558c87f55cdd6d8a29bb46c12f4d1de3239bc | ee5d149d4ecb337005b850bddf4453e56a5daf04 | refs/heads/master | 1,675,911,819,093 | 1,609,785,144,000 | 1,609,785,144,000 | 270,388,715 | 13 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 1,122 | lean | /-
Copyright (c) 2021 Paula Neeley. All rights reserved.
Author: Paula Neeley
-/
import basicmodal.language
---------------------- Proof System ----------------------
-- Define a context
@[reducible] def ctx : Type := set (form)
notation AX `∪` φ := set.insert φ AX
-- Proof system
inductive prfK : ctx → form → Pro... |
905a3a9bbe1cd27c462cb6e2d3598da1569f3967 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/hott/bug_struct_level.hlean | 5328258cae3992ec00c1bdb75cd05f8e6ef89ae9 | [
"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 | 1,181 | hlean | import algebra.category
open category
section
parameter {D₀ : Type}
parameter (C : precategory D₀)
parameter (D₂ : Π ⦃a b c d : D₀⦄ (f : hom a b) (g : hom c d) (h : hom a c) (i : hom b d), Type)
attribute comp [reducible]
definition comp₁_type [reducible] : Type :=
Π ⦃a b c₁ d₁ c₂ d₂ : D₀⦄
⦃f₁ : ho... |
251f0b8019c2513c3781ae4327da6216b0c9ed40 | f083c4ed5d443659f3ed9b43b1ca5bb037ddeb58 | /analysis/topology/continuity.lean | c567d50dd74e47dca077ad2d559c5326f3bc3948 | [
"Apache-2.0"
] | permissive | semorrison/mathlib | 1be6f11086e0d24180fec4b9696d3ec58b439d10 | 20b4143976dad48e664c4847b75a85237dca0a89 | refs/heads/master | 1,583,799,212,170 | 1,535,634,130,000 | 1,535,730,505,000 | 129,076,205 | 0 | 0 | Apache-2.0 | 1,551,697,998,000 | 1,523,442,265,000 | Lean | UTF-8 | Lean | false | false | 47,739 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot
Continuous functions.
Parts of the formalization is based on the books:
N. Bourbaki: General Topology
I. M. James: Topologies and U... |
e22232eff75070b70be6548e46a362a652d9bd52 | e429a7c31201d4c56a2716f77a99c4831967b0de | /distance.lean | e0d2f7e1f181f90339f0ed33fe79ecc8cb940c41 | [] | no_license | jthickstun/lean | cdb5ee8ec78294167d771a6167c0947419afa9eb | 8254b987f06be1f98ef2e0cc33b7d4655d77dc85 | refs/heads/master | 1,620,156,057,836 | 1,557,865,724,000 | 1,557,865,724,000 | 106,618,304 | 8 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 4,054 | lean | /-
Some useful facts about distances
(this helps us avoid reasoning about negative numbers)
-/
def dist : ℕ → ℕ → ℕ
| 0 m := m
| n 0 := n
| (n+1) (m+1) := dist n m
lemma dist_rfl (n : ℕ) : dist n n = 0 :=
begin
induction n with n ih,
{ reflexivity },
{ simp [dist, ih] }
end
lemma dist_zero_left (m :... |
3d3a62d0505f0962f902ad5243b7f0c263d3e67f | 6b45072eb2b3db3ecaace2a7a0241ce81f815787 | /data/nat/gcd.lean | 45631d38a1cf0b2bc3653b2c6f16eb434114ecad | [] | no_license | avigad/library_dev | 27b47257382667b5eb7e6476c4f5b0d685dd3ddc | 9d8ac7c7798ca550874e90fed585caad030bbfac | refs/heads/master | 1,610,452,468,791 | 1,500,712,839,000 | 1,500,713,478,000 | 69,311,142 | 1 | 0 | null | 1,474,942,903,000 | 1,474,942,902,000 | null | UTF-8 | Lean | false | false | 10,605 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
Definitions and properties of gcd, lcm, and coprime.
-/
open well_founded decidable prod
namespace nat
/- gcd -/
theorem gcd_dvd (m n : ℕ) : (gcd m... |
f81abbe69deef1cfd2b89c89ad92f60282a34a1a | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /archive/imo/imo1988_q6.lean | ffceec71d3b10d83f592e2d91a10ea2aeb40c80c | [
"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 | 13,835 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import data.nat.prime
import data.rat.defs
import order.well_founded
import tactic.linarith
/-!
# IMO 1988 Q6 and constant descent Vieta jumping
Question 6 of IMO1... |
736b3c16381c1addc5c5d634aec46a0623a5b270 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/ring_theory/roots_of_unity.lean | 434bb677d31194ba6d3c25e095c9063e9b78389c | [] | 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 | 21,621 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.nat.parity
import Mathlib.data.polynomial.ring_division
import Mathlib.group_theory.or... |
4e8493f9faef77891435f64d6972d8cca801540c | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/ring_theory/adjoin_root.lean | a7da2bea5ea4ec577706edd15ac5062e3a16eea4 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 30,941 | 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 algebra.algebra.basic
import data.polynomial.field_division
import linear_algebra.finite_dimensional
import ring_theory.adjoin.basic
import ring_... |
4ef39d906c978addcda41cc6231b29fbecdb222f | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/rational.lean | 965f188545e8a3f456223d6ce07b4a837cde0425 | [
"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 | 590 | lean | structure Rat where
num : Int
den : Nat
pos : den > 0
instance (n : Nat) : OfNat Rat n where
ofNat := {
num := n
den := 1
pos := by decide
}
instance : Add Rat where
add a b := {
num := a.num * b.den + b.num * a.den
den := a.den * b.den
pos := sorry
}
instance : Coe Int Rat wher... |
0796dc86476fc9c348a0ce98c418d7a2a47be908 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Elab/Tactic/Conv/Rewrite.lean | a6d3ed840bb499ceca0badeae85835d02f8ef03a | [
"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 | 782 | 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.Tactic.Rewrite
import Lean.Elab.Tactic.Rewrite
import Lean.Elab.Tactic.Conv.Basic
namespace Lean.Elab.Tactic.Conv
open Meta
@[builtin_tac... |
5833ba3e2e4a4eeb032a835e227a5d3836ce78a8 | cc060cf567f81c404a13ee79bf21f2e720fa6db0 | /lean/category-theory2.lean | caa2bf4568053ef5dc80246782c23756a647e8d7 | [
"Apache-2.0"
] | permissive | semorrison/proof | cf0a8c6957153bdb206fd5d5a762a75958a82bca | 5ee398aa239a379a431190edbb6022b1a0aa2c70 | refs/heads/master | 1,610,414,502,842 | 1,518,696,851,000 | 1,518,696,851,000 | 78,375,937 | 2 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 5,985 | lean | import standard
import data.nat
structure Category : Type :=
(Obj : Type)
(Hom : Obj → Obj → Type)
(Id : Π A : Obj, Hom A A)
(compose : Π ⦃A B C : Obj⦄, Hom B C → Hom A B → Hom A C)
(Id_left : Π ⦃A B : Obj⦄ (f : Hom A B), compose !Id f = f)
(Id_right : Π ⦃A B : Obj⦄ (f : Hom A B), compose f !Id = f)
... |
67f2d3a92178ae94d530b0f4b89a12ec8b9de933 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/analysis/complex/abs_max.lean | 61a9eae8571e3c745be8b38f68bf58c9b53ef6ae | [
"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 | 22,752 | lean | /-
Copyright (c) 2022 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import analysis.complex.cauchy_integral
import analysis.normed_space.completion
import analysis.normed_space.extr
import topology.algebra.order.extr_closure
... |
0690780a0b15e704689b623cec562638217faf70 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/analysis/normed_space/finite_dimension.lean | 2b5c239e30de0743a9beb64952fd7df99b6a77e1 | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 35,895 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import analysis.asymptotics.asymptotic_equivalent
import analysis.normed_space.affine_isometry
import analysis.normed_space.operator_norm
import analysis.normed... |
266f318c641f995aa8ea44e37b172105d5cace8b | 30b012bb72d640ec30c8fdd4c45fdfa67beb012c | /category_theory/natural_transformation.lean | 0b30c72b4a41e94b85a0d5b1eb83ab84f0696921 | [
"Apache-2.0"
] | permissive | kckennylau/mathlib | 21fb810b701b10d6606d9002a4004f7672262e83 | 47b3477e20ffb5a06588dd3abb01fe0fe3205646 | refs/heads/master | 1,634,976,409,281 | 1,542,042,832,000 | 1,542,319,733,000 | 109,560,458 | 0 | 0 | Apache-2.0 | 1,542,369,208,000 | 1,509,867,494,000 | Lean | UTF-8 | Lean | false | false | 4,082 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tim Baumann, Stephen Morgan, Scott Morrison
Defines natural transformations between functors.
Introduces notations
`F ⟹ G` for the type of natural transformations between functors ... |
43ca93960cc74e6208375668c837f65b8079764e | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /tests/lean/run/liftMethodInMacrosIssue.lean | a4d411e7b39fddb946aff566537155b91041cdd2 | [
"Apache-2.0"
] | permissive | dupuisf/lean4 | d082d13b01243e1de29ae680eefb476961221eef | 6a39c65bd28eb0e28c3870188f348c8914502718 | refs/heads/master | 1,676,948,755,391 | 1,610,665,114,000 | 1,610,665,114,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 536 | lean | #lang lean4
def foo (x : Nat) : IO Bool := do
if x == 0 then
throw $ IO.userError "foo: unexpected zero"
pure (x == 1)
def tst (x : Nat) : IO Unit := do
if x == 0 then
IO.println "x is 0"
else if (← foo x) then
IO.println "x is 1"
else
IO.println "other"
#eval tst 0
#eval tst 1
#eval tst 2
syntax term "<|||... |
518239b60a138c39593b8ab1f374404b4d17d923 | 3dc4623269159d02a444fe898d33e8c7e7e9461b | /.github/workflows/geo/src/pfin/basic.lean | 8ecd564e9762a8cfc4aedc632ac1c522da3bad0d | [] | no_license | Or7ando/lean | cc003e6c41048eae7c34aa6bada51c9e9add9e66 | d41169cf4e416a0d42092fb6bdc14131cee9dd15 | refs/heads/master | 1,650,600,589,722 | 1,587,262,906,000 | 1,587,262,906,000 | 255,387,160 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,337 | lean | open nat
universe u
inductive pfin (n : nat) : Type u
| mk (val : nat) (is_lt : val < n) : pfin
namespace pfin
@[reducible]
def val {n} : pfin n → nat
| ⟨v, _⟩ := v
@[reducible]
def is_lt {n} : ∀ (a : pfin n), a.val < n
| ⟨_, h⟩ := h
protected def lt {n} (a b : pfin n) : Prop :=
a.val < b.val
protected def le {n... |
23bb09ab9496411feda6e3543f2e708e9d938a60 | ec62863c729b7eedee77b86d974f2c529fa79d25 | /7/b.lean | d39cf29866dad4111cc4264f2b7e2badc45bc138 | [] | no_license | rwbarton/advent-of-lean-4 | 2ac9b17ba708f66051e3d8cd694b0249bc433b65 | 417c7e2718253ba7148c0279fcb251b6fc291477 | refs/heads/main | 1,675,917,092,057 | 1,609,864,581,000 | 1,609,864,581,000 | 317,700,289 | 24 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,238 | lean | import Lean.Util.SCC
import Std.Data.HashMap
def solve (rules : Std.HashMap String (List (Int × String))) : Int := do
let sccs := Lean.SCC.scc (rules.toList.map Prod.fst) (λ bag => (rules.find! bag).map Prod.snd)
-- how many bags must a bag hold, including itself?
let mut size : Std.HashMap String Int := Std.HashMap.e... |
59abc13ab56862fb685bdac6d3e055fe637ccda5 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/combinatorics/simple_graph/regularity/bound.lean | b90bf7744f082e733527efd862ef102d480400f6 | [
"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 | 7,196 | lean | /-
Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import analysis.special_functions.pow
import order.partition.equipartition
/-!
# Numerical bounds for Szemerédi Regularity Lemma
This file g... |
50a59090eebab2d71b419f6681115a0426121b72 | b147e1312077cdcfea8e6756207b3fa538982e12 | /ring_theory/ideals.lean | e9d4c74fd81aaeee8619a921c4f4317eff8fa1a7 | [
"Apache-2.0"
] | permissive | SzJS/mathlib | 07836ee708ca27cd18347e1e11ce7dd5afb3e926 | 23a5591fca0d43ee5d49d89f6f0ee07a24a6ca29 | refs/heads/master | 1,584,980,332,064 | 1,532,063,841,000 | 1,532,063,841,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,597 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Chris Hughes
-/
import algebra.module tactic.ring linear_algebra.quotient_module
universes u v
variables {α : Type u} {β : Type v} [comm_ring α] {a b : α}
open set function
loc... |
30c3fcc7f49f454f11734ae38373d404b74c6fe6 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/data/equiv/basic.lean | adff2330764c9b216d1dbb0e19bc818b160ae98c | [
"Apache-2.0"
] | permissive | waynemunro/mathlib | e3fd4ff49f4cb43d4a8ded59d17be407bc5ee552 | 065a70810b5480d584033f7bbf8e0409480c2118 | refs/heads/master | 1,693,417,182,397 | 1,634,644,781,000 | 1,634,644,781,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 85,937 | 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, Mario Carneiro
-/
import data.prod
import data.sum
import data.subtype
import data.sigma.basic
import data.option.basic
import logic.function.basic
import log... |
f396a86b3e315b4857c83ada0b610183302dd733 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/PostPort/Coe.lean | 12c62d75c93e4577262962de5d1de74e9fc19678 | [] | 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 | 877 | lean | import Mathlib.Lean3Lib.init.coe
universes u v
variable {α : Sort u} {β : Sort v}
noncomputable instance hasCoe [inst : Mathlib.has_coe α β] : Coe α β := {
coe := @Mathlib.has_coe.coe _ _ inst
}
-- TODO: why does mathlib declare these instances directly?
-- topology/algebra/open_subgroup.lean:42:instance has_coe_s... |
9f967d91abc0bff6fbae565ef0cd11d3f2e5f837 | fe25de614feb5587799621c41487aaee0d083b08 | /src/Lean/PrettyPrinter/Delaborator/Builtins.lean | 6caaa51e03ad6096a23fee378a23cc517a12ad32 | [
"Apache-2.0"
] | permissive | pollend/lean4 | e8469c2f5fb8779b773618c3267883cf21fb9fac | c913886938c4b3b83238a3f99673c6c5a9cec270 | refs/heads/master | 1,687,973,251,481 | 1,628,039,739,000 | 1,628,039,739,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 29,786 | lean | /-
Copyright (c) 2020 Sebastian Ullrich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
-/
import Lean.PrettyPrinter.Delaborator.Basic
import Lean.PrettyPrinter.Delaborator.SubExpr
import Lean.PrettyPrinter.Delaborator.TopDownAnalyze
import Lean.Pars... |
298425a5db4b23e007577e8b26832fb43bc2feea | a7eef317ddec01b9fc6cfbb876fe7ac00f205ac7 | /src/ring_theory/power_series.lean | 5777bb2d54074250c855b359b01a05255e1a9be5 | [
"Apache-2.0"
] | permissive | kmill/mathlib | ea5a007b67ae4e9e18dd50d31d8aa60f650425ee | 1a419a9fea7b959317eddd556e1bb9639f4dcc05 | refs/heads/master | 1,668,578,197,719 | 1,593,629,163,000 | 1,593,629,163,000 | 276,482,939 | 0 | 0 | null | 1,593,637,960,000 | 1,593,637,959,000 | null | UTF-8 | Lean | false | false | 57,817 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Kenny Lau
-/
import data.mv_polynomial
import ring_theory.ideal_operations
import tactic.linarith
/-!
# Formal power series
This file defines (multivariate) formal po... |
4655f65297ddd989e72d125b3b94eae220d28ab9 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/algebra/algebra/restrict_scalars.lean | 217969d7b7f4e8c2119adb4df550180f223bb859 | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 7,622 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov
-/
import algebra.algebra.tower
/-!
# The `restrict_scalars` type alias
See the documentation attached to the `restrict_scalars` definition for advice on how a... |
bd1593858180f50890b7b3e46760cbc19ae552bd | d642a6b1261b2cbe691e53561ac777b924751b63 | /src/algebra/group/to_additive.lean | fa823c4dc1f944d6d77e05a6535794c0ba116de4 | [
"Apache-2.0"
] | permissive | cipher1024/mathlib | fee56b9954e969721715e45fea8bcb95f9dc03fe | d077887141000fefa5a264e30fa57520e9f03522 | refs/heads/master | 1,651,806,490,504 | 1,573,508,694,000 | 1,573,508,694,000 | 107,216,176 | 0 | 0 | Apache-2.0 | 1,647,363,136,000 | 1,508,213,014,000 | Lean | UTF-8 | Lean | false | false | 9,721 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Yury Kudryashov.
-/
import tactic.basic tactic.transport tactic.algebra
/-!
# Transport multiplicative to additive
This file defines an attribute `to_additive` that ... |
292e3db972343e6e16ad40333d92922942da9ca5 | 4f065978c49388d188224610d9984673079f7d91 | /constructive_tensor_product.lean | cff8fc387181a597afa336e8bb715bc24e8abe2f | [] | no_license | kckennylau/Lean | b323103f52706304907adcfaee6f5cb8095d4a33 | 907d0a4d2bd8f23785abd6142ad53d308c54fdcb | refs/heads/master | 1,624,623,720,653 | 1,563,901,820,000 | 1,563,901,820,000 | 109,506,702 | 3 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 18,657 | lean | import group_theory.coset
import group_theory.free_group
import linear_algebra.basic
universes u v w u₁ v₁
variable (α : Type u)
def is_add_group_hom {α : Type u} {β : Type v} [add_group α] [add_group β] (f : α → β) : Prop :=
@is_group_hom (multiplicative α) (multiplicative β) _ _ f
attribute [class] is_add_group_ho... |
8659597a951b12041f6d4b3dee1e36ca8a9f944a | 4727251e0cd73359b15b664c3170e5d754078599 | /src/logic/function/basic.lean | 1e1ff8e49485438a90ce44945be52069316b67d9 | [
"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 | 32,091 | lean | /-
Copyright (c) 2016 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import data.option.defs
import logic.nonempty
import tactic.cache
/-!
# Miscellaneous function constructions and lemmas
-/
universes u v w
namespac... |
2b8933ba428675ba203ded79a3e44eb265835355 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Compiler/LCNF/MonoTypes.lean | 0d90433ac41c1726e2bc7830da64f2fde3fdd3c0 | [
"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 | 4,623 | lean | /-
Copyright (c) 2022 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.InferType
import Lean.Compiler.LCNF.Util
import Lean.Compiler.LCNF.BaseTypes
import Lean.Compiler.LCNF.CompilerM
namespace Lean.Compiler.L... |
945d36d979c8f568b3ef2cf545e63c5f5c7e0b94 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/tactic/interactive.lean | 7ece8deb106021a70b59d961a97b831ad4294851 | [
"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 | 38,002 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Simon Hudon, Sébastien Gouëzel, Scott Morrison
-/
import tactic.lint
import tactic.dependencies
open lean
open lean.parser
local postfix `?`:9001 := optional
local po... |
f62a14cb9b8ebfb4c649f411ce3bb92a6de0d2d5 | 00de0c30dd1b090ed139f65c82ea6deb48c3f4c2 | /src/algebra/ring.lean | 843991b8ab959dbe5153bdf49cf422b63688fdeb | [
"Apache-2.0"
] | permissive | paulvanwamelen/mathlib | 4b9c5c19eec71b475f3dd515cd8785f1c8515f26 | 79e296bdc9f83b9447dc1b81730d36f63a99f72d | refs/heads/master | 1,667,766,172,625 | 1,590,239,595,000 | 1,590,239,595,000 | 266,392,625 | 0 | 0 | Apache-2.0 | 1,590,257,277,000 | 1,590,257,277,000 | null | UTF-8 | Lean | false | false | 38,532 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Amelia Livingston
-/
import algebra.group.hom
import algebra.group.units
import tactic.norm_cast
import tactic.split_ifs
import algeb... |
ca17868dd8e6f2e98e2b1f32d815bc4b7d85a0c6 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/number_theory/pell.lean | 4094d815b558c1ad914bc4ffb4eabbc070db6344 | [
"Apache-2.0"
] | permissive | stjordanis/mathlib | 51e286d19140e3788ef2c470bc7b953e4991f0c9 | 2568d41bca08f5d6bf39d915434c8447e21f42ee | refs/heads/master | 1,631,748,053,501 | 1,627,938,886,000 | 1,627,938,886,000 | 228,728,358 | 0 | 0 | Apache-2.0 | 1,576,630,588,000 | 1,576,630,587,000 | null | UTF-8 | Lean | false | false | 39,439 | 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 data.nat.modeq
import number_theory.zsqrtd.basic
/-!
# Pell's equation and Matiyasevic's theorem
This file solves Pell's equation, i.e. integer solutions to... |
8bb5abdea8ebc64c240f2fef2c116bfe79f4be49 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/tactic/protected.lean | a9126f790658112f349703708ebec151249bc004 | [
"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 | 3,811 | 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 tactic.core
/-!
## `protected` and `protect_proj` user attributes
`protected` is an attribute to protect a declaration.
If a declaration `foo.bar` is marked prote... |
735a05f48e855c21fcb9c00573c44e9bc87dba79 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/monoidal/braided.lean | b46afa9e8ca1d5edd9b8946d5c1a974a22bd65d4 | [
"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 | 34,776 | 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_lemmas
import category_theory.monoidal.natural_transformation
import category_theory.monoidal.discrete
/-!
# Braided and sy... |
557fcdfbf0c20504f1f29f7b493b0cf5ade80649 | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /stage0/src/Lean/Compiler/Specialize.lean | ecdfd6f33b82b963d483469fdb8da552a3d4a5ad | [
"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 | 5,105 | 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.Meta.Basic
import Lean.Attributes
namespace Lean.Compiler
inductive SpecializeAttributeKind where
| specialize | nospecialize
deriving Inh... |
d40f2e4c3558c6dfc045331da86aa05a21b4d26d | 8d65764a9e5f0923a67fc435eb1a5a1d02fd80e3 | /src/group_theory/coset.lean | 387cd77a531885ecbc936570f93ce3b8cf3568bb | [
"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 | 16,835 | lean | /-
Copyright (c) 2018 Mitchell Rowett. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Rowett, Scott Morrison
-/
import group_theory.subgroup
/-!
# Cosets
This file develops the basic theory of left and right cosets.
## Main definitions
* `left_coset a s`:... |
dd04ec9ff5ef02db4938ad6a06a3968330081467 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/normed_space/extend.lean | 1b12d11cc1e0c7717ef20105cf042b1f6e8104da | [
"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 | 6,814 | lean | /-
Copyright (c) 2020 Ruben Van de Velde. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ruben Van de Velde
-/
import analysis.normed_space.operator_norm
import algebra.algebra.restrict_scalars
import data.is_R_or_C.basic
/-!
# Extending a continuous `ℝ`-linear map t... |
b24c17c8a00f8636db831e2d8011858dccf32403 | 90bd8c2a52dbaaba588bdab57b155a7ec1532de0 | /src/covering_space/lift.lean | 4da5c4ab5362f74aae8bd5fbb2a3ab2da48f3aeb | [
"Apache-2.0"
] | permissive | shingtaklam1324/alg-top | fd434f1478925a232af45f18f370ee3a22811c54 | 4c88e28df6f0a329f26eab32bae023789193990e | refs/heads/master | 1,689,447,024,947 | 1,630,073,400,000 | 1,630,073,400,000 | 381,528,689 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,993 | lean | import covering_space.def
variables {X X' Y : Type _} [topological_space X] [topological_space X'] [topological_space Y]
lemma is_open_f₀_eq_f₁ {p : C(X', X)} (hp : is_covering_map p) {f : C(Y, X)} {f₀ f₁ : C(Y, X')}
(hf₀ : p.comp f₀ = f) (hf₁ : p.comp f₁ = f) :
is_open {y | f₀ y = f₁ y} :=
begin
let S := {y ... |
30afff7f308f1debb75b5b72baf8571d391a5cfc | cabd1ea95170493667c024ef2045eb86d981b133 | /src/super/utils.lean | 518545570fc109e4227db48774298b9f8cf9542f | [] | no_license | semorrison/super | 31db4b5aa5ef4c2313dc5803b8c79a95f809815b | 0c6c03ba9c7470f801eb4d055294f424ff090308 | refs/heads/master | 1,630,272,140,541 | 1,511,054,739,000 | 1,511,054,756,000 | 114,317,807 | 0 | 0 | null | 1,513,304,776,000 | 1,513,304,775,000 | null | UTF-8 | Lean | false | false | 4,843 | lean | /-
Copyright (c) 2017 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner
-/
open tactic expr list native
meta def get_metas : expr → list expr
| (var _) := []
| (sort _) := []
| (const _ _) := []
| (mvar n pp_n t) := expr.mvar pp_n n t :: get_... |
f7d43efb4551370c5ca1392ea1bce6fd81c489d3 | 958488bc7f3c2044206e0358e56d7690b6ae696c | /lean/attribute.lean | 571ab0502f08a2083ca694467fe0614f0fa59159 | [] | no_license | possientis/Prog | a08eec1c1b121c2fd6c70a8ae89e2fbef952adb4 | d4b3debc37610a88e0dac3ac5914903604fd1d1f | refs/heads/master | 1,692,263,717,723 | 1,691,757,179,000 | 1,691,757,179,000 | 40,361,602 | 3 | 0 | null | 1,679,896,438,000 | 1,438,953,859,000 | Coq | UTF-8 | Lean | false | false | 747 | lean | variable {α : Type*}
def isPrefix (xs : list α) (ys : list α) : Prop :=
∃ (t : list α), xs ++ t = ys
--#check @isPrefix
--#print isPrefix
infix ` <+: `:50 := isPrefix
attribute [simp]
lemma list.isPrefixRefl : ∀ (xs : list α), xs <+: xs :=
assume xs, ⟨[], by simp⟩
lemma L1 : [1,2,3] <+: [1,2,3] := by simp
--#... |
4f947b5a3d2f72b1a647a482a129336cee310ba4 | 367134ba5a65885e863bdc4507601606690974c1 | /src/topology/category/Top/opens.lean | 4eafcf3d107e28c555bc4ff5b911c16f3062c5b9 | [
"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 | 7,943 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import topology.category.Top.basic
import category_theory.eq_to_hom
/-!
# The category of open sets in a topological space.
We define `to_Top : opens X ⥤ Top` and
`... |
e61b895a0b914570db7bbf213a2c7fab5688a62a | 271e26e338b0c14544a889c31c30b39c989f2e0f | /stage0/src/Init/Lean/Declaration.lean | 4f8b67929de250e2b5c86e14d623b1b0af032214 | [
"Apache-2.0"
] | permissive | dgorokho/lean4 | 805f99b0b60c545b64ac34ab8237a8504f89d7d4 | e949a052bad59b1c7b54a82d24d516a656487d8a | refs/heads/master | 1,607,061,363,851 | 1,578,006,086,000 | 1,578,006,086,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,050 | lean | /-
Copyright (c) 2018 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import Init.Lean.Expr
namespace Lean
/--
Reducibility hints are used in the convertibility checker.
When trying to solve a constraint such a
... |
84dd3a30a577ae3a090a4b5394e943485474555a | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /stage0/src/Lean/Compiler/CompilerM.lean | 5bbb7751a02ea14d3f1cc3c0cfae57e94e0616a0 | [
"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 | 6,622 | lean | /-
Copyright (c) 2022 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Util.ForEachExpr
import Lean.Compiler.InferType
namespace Lean.Compiler
/--
The state managed by the `CompilerM` `Monad`.
-/
structure Compile... |
f6209ef9fac5acd94d8c46b2f2b253bc5efef202 | bb31430994044506fa42fd667e2d556327e18dfe | /src/geometry/euclidean/angle/sphere.lean | 9293c24e9f52a9a6899cee9d47fcca60ce2af472 | [
"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 | 25,050 | lean | /-
Copyright (c) 2022 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import geometry.euclidean.angle.oriented.right_angle
import geometry.euclidean.circumcenter
/-!
# Angles in circles and sphere.
This file proves results about angles in... |
e2b4c303803d414f2a74859b49cba8b54d1deec5 | 26b8b0964ca8e1c2e203585ba5940f83fe05e48a | /src/tidy/rewrite_search.lean | 0b228bf07e1bf451da1c31368f6471416d0247dc | [] | no_license | jcommelin/lean-tidy | ef3cd32a3804221d93f0dff9e180bb2c52f4b143 | 9cecf497e90db64b5ea140ad6ae1603976dcd402 | refs/heads/master | 1,585,129,919,276 | 1,533,512,680,000 | 1,533,512,680,000 | 143,677,361 | 0 | 0 | null | 1,616,803,481,000 | 1,533,530,576,000 | Lean | UTF-8 | Lean | false | false | 13,207 | lean | -- Copyright (c) 2018 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Daniel Barter, Louis Carlin, Scott Morrison, Sam Quinn, Simon Hudon
import data.list
import data.option
import .edit_distance
import .pretty_print
import .rewrite_all
namespace... |
a5e0705718c7048406c84732e562e95d0801c494 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/sites/dense_subsite.lean | 8a2498b39b1599fcc560b196a847c939c31cfde2 | [
"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 | 19,480 | lean | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import category_theory.sites.sheaf
import category_theory.sites.cover_lifting
import category_theory.adjunction.fully_faithful
/-!
# Dense subsites
> THIS FILE IS SYNCHRO... |
dfb35f9ad04ac523f86073fd54f4f75d7140925f | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/complex/basic.lean | 9644405e9b04f6aa15180586158fbf0727f5b3dc | [
"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 | 30,922 | lean | /-
Copyright (c) 2017 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Mario Carneiro
-/
import data.real.sqrt
/-!
# The complex numbers
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to ma... |
fdfde96ea31e937f035ca2d01edffc179b5da023 | 5749d8999a76f3a8fddceca1f6941981e33aaa96 | /test/tactics.lean | 8dc13e65cd6c4dd6bf81cc9673fb67bdeb5963ab | [
"Apache-2.0"
] | permissive | jdsalchow/mathlib | 13ab43ef0d0515a17e550b16d09bd14b76125276 | 497e692b946d93906900bb33a51fd243e7649406 | refs/heads/master | 1,585,819,143,348 | 1,580,072,892,000 | 1,580,072,892,000 | 154,287,128 | 0 | 0 | Apache-2.0 | 1,540,281,610,000 | 1,540,281,609,000 | null | UTF-8 | Lean | false | false | 13,858 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Scott Morrison
-/
import tactic.interactive tactic.finish tactic.ext tactic.lift tactic.apply
tactic.reassoc_axiom tactic.tfae tactic.elide tactic.ring_exp
tac... |
99e7526b7acf90c7cc1b55c01dc8c4e6284a6593 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/add_torsor.lean | 600aab44b6cf819b40c9a3253213fd260c5a0b6c | [] | 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 | 23,259 | lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Yury Kudryashov.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.group.prod
import Mathlib.algebra.group.type_tags
import Mathlib.alge... |
f9881e6c5f035215df282caecf3077989f978ee3 | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /tests/lean/run/catchThe.lean | 9b3cb3e39575b2eaa65342f38a11c72b9141db36 | [
"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 | 821 | lean | import Lean.Meta
open Lean
open Lean.Meta
universes u v w
abbrev M := ExceptT String $ MetaM
def testM {α} [HasBeq α] [HasToString α] (x : M α) (expected : α) : MetaM Unit := do
r ← x;
match r with
| Except.ok a => unless (a == expected) $ throwError ("unexpected result " ++ toString a)
| Except.error e => throw... |
ecfbca1b7391b38735385de3877e74cacb3b6b1e | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/algebra/semiconj.lean | c210678f9b8cca6f81148b98e4804382d761233c | [
"Apache-2.0"
] | permissive | rmitta/mathlib | 8d90aee30b4db2b013e01f62c33f297d7e64a43d | 883d974b608845bad30ae19e27e33c285200bf84 | refs/heads/master | 1,585,776,832,544 | 1,576,874,096,000 | 1,576,874,096,000 | 153,663,165 | 0 | 2 | Apache-2.0 | 1,544,806,490,000 | 1,539,884,365,000 | Lean | UTF-8 | Lean | false | false | 8,761 | lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
Some proofs and docs came from `algebra/commute` (c) Neil Strickland
-/
import algebra.ring algebra.group_power data.equiv.algebra
/-!
# Semiconjugate elements of a ... |
98155b55a1c9bfdd092c2295219badf15539d0ca | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/topology/separation.lean | 661e182f0e5d0edaf40ad6440538faecaf738602 | [
"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 | 12,410 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
Separation properties of topological spaces.
-/
import topology.order
open set filter lattice
local attribute [instance] classical.prop_decidable
uni... |
ee7225b51f51b0e6e7933bb2a53738ee682fd461 | bce603343785d07c32cb8b35950aba0b4d9415ae | /lean3/src/all.lean | 27203bcf1164e704063b0532fd3a384f31354d9d | [] | no_license | fpvandoorn/cryptomorphism | db00cf0b12c8fd561a6200eee6a6ff2a023f1228 | d486419ecced54de3db759dae81110be44b7c28b | refs/heads/master | 1,693,198,883,854 | 1,636,562,038,000 | 1,636,562,038,000 | 363,219,330 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 49,570 | lean | /-
A file importing all Lean files.
Import this file if you want to run a program on all declarations in Lean.
Automatically generated by `scripts/mk_all.sh` in `mathlib`.
-/
import algebra.add_torsor
import algebra.algebra.basic
import algebra.algebra.operations
import algebra.algebra.ordered
import algebra.algebra.su... |
a41fa45831fc21cddd19ce73db478f9be4685ea7 | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /stage0/src/Lean/Server/FileWorker/RequestHandling.lean | 1a3d515b9444aba928c4d5cae72c91b07ad9cc5e | [
"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 | 23,339 | lean | /-
Copyright (c) 2021 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki, Marc Huisinga
-/
import Lean.DeclarationRange
import Lean.Data.Json
import Lean.Data.Lsp
import Lean.Server.FileWorker.Utils
import Lean.Server.Requests
import... |
9e982445443df62d73768c1a1015b3a767949d28 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/data/sigma/basic.lean | 9a770cee046ee19c970c703edd0fe0cd440bbb00 | [
"Apache-2.0"
] | permissive | agjftucker/mathlib | d634cd0d5256b6325e3c55bb7fb2403548371707 | 87fe50de17b00af533f72a102d0adefe4a2285e8 | refs/heads/master | 1,625,378,131,941 | 1,599,166,526,000 | 1,599,166,526,000 | 160,748,509 | 0 | 0 | Apache-2.0 | 1,544,141,789,000 | 1,544,141,789,000 | null | UTF-8 | Lean | false | false | 5,470 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
-/
import tactic.lint
import tactic.ext
section sigma
variables {α α₁ α₂ : Type*} {β : α → Type*} {β₁ : α₁ → Type*} {β₂ : α₂ → Type*}
namespace sigma
instance [inhabit... |
d4172ad5fdb0c7175155fd39149a467323f226ed | 4950bf76e5ae40ba9f8491647d0b6f228ddce173 | /src/data/int/basic.lean | 006d9fc78f1d080937e6d5c3b779ba0ea26d2396 | [
"Apache-2.0"
] | permissive | ntzwq/mathlib | ca50b21079b0a7c6781c34b62199a396dd00cee2 | 36eec1a98f22df82eaccd354a758ef8576af2a7f | refs/heads/master | 1,675,193,391,478 | 1,607,822,996,000 | 1,607,822,996,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 51,252 | 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 ℤ := ... |
1adf9071483f8adf15aad5be09fa6b411ead3fc5 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /src/Init/Lean/Environment.lean | 8e08a933bc90bea8d035414845dd65209f922601 | [
"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 | 28,046 | 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
-/
prelude
import Init.System.IO
import Init.Util
import Init.Data.ByteArray
import Init.Lean.Data.SMap
import Init.Lean.Declaration
import Init.Lean.LocalCont... |
909e760687cfc2cc04b531f37270dbceeeb56ea3 | 3f1a1d97c03bb24b55a1b9969bb4b3c619491d5a | /library/data/rbtree/min_max.lean | db587ede4b9b07d35d7ab8fc6835139d79c6476f | [
"Apache-2.0"
] | permissive | praveenmunagapati/lean | 00c3b4496cef8e758396005013b9776bb82c4f56 | fc760f57d20e0a486d14bc8a08d89147b60f530c | refs/heads/master | 1,630,692,342,183 | 1,515,626,222,000 | 1,515,626,222,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,772 | 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 data.rbtree.basic
universe u
namespace rbnode
variables {α : Type u} {lt : α → α → Prop}
lemma mem_of_min_eq (lt : α → α → Prop) [is_irrefl α lt] {... |
1aa6f96994a5f7df3309a02992404d879ccc5938 | 86f6f4f8d827a196a32bfc646234b73328aeb306 | /examples/logic/unnamed_194.lean | d32c01414b06d38bfef13172d878a9ce9352ab9f | [] | no_license | jamescheuk91/mathematics_in_lean | 09f1f87d2b0dce53464ff0cbe592c568ff59cf5e | 4452499264e2975bca2f42565c0925506ba5dda3 | refs/heads/master | 1,679,716,410,967 | 1,613,957,947,000 | 1,613,957,947,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 169 | lean | import data.real.basic
-- BEGIN
def fn_ub (f : ℝ → ℝ) (a : ℝ) : Prop := ∀ x, f x ≤ a
def fn_lb (f : ℝ → ℝ) (a : ℝ) : Prop := ∀ x, a ≤ f x
-- END |
7e19116c9fd472de528e3d97181e74a4bdff70c2 | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/algebra/module/basic.lean | d92cc5737062446b0d3844afda10f96b3616802f | [
"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 | 19,820 | lean | /-
Copyright (c) 2015 Nathaniel Thomas. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nathaniel Thomas, Jeremy Avigad, Johannes Hölzl, Mario Carneiro
-/
import algebra.big_operators.basic
import algebra.group.hom
import algebra.ring.basic
import data.rat.cast
import g... |
ceb3c426c9590ab589122524579913db25f3e2be | 432d948a4d3d242fdfb44b81c9e1b1baacd58617 | /src/topology/sheaves/sheaf_condition/pairwise_intersections.lean | 874fd164666a16087c51ee08918605905362c1dc | [
"Apache-2.0"
] | permissive | JLimperg/aesop3 | 306cc6570c556568897ed2e508c8869667252e8a | a4a116f650cc7403428e72bd2e2c4cda300fe03f | refs/heads/master | 1,682,884,916,368 | 1,620,320,033,000 | 1,620,320,033,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,417 | 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 topology.sheaves.sheaf
import category_theory.limits.preserves.basic
import category_theory.category.pairwise
/-!
# Equivalent formulations of the sheaf cond... |
67db90871af8121e5e278fab261120fc20901174 | 4376c25f060c13471bb89cdb12aeac1d53e53876 | /Lean Game/world1_addition.lean | 7623424ce918cbd0724908e79d19f5913126d487 | [
"MIT"
] | permissive | RaitoBezarius/projet-maths-lean | 8fa7df563d64c256561ab71893c523fc1424b85c | 42356e980e021a20c3468f5ca1639fec01bb934f | refs/heads/master | 1,613,002,128,339 | 1,589,289,282,000 | 1,589,289,282,000 | 244,431,534 | 0 | 1 | MIT | 1,584,312,574,000 | 1,583,169,883,000 | TeX | UTF-8 | Lean | false | false | 6,780 | lean | import mynat.definition -- Imports the natural numbers.
/- Here's what you get from the import:
1) The following data:
* a type called `mynat`
* a term `0 : mynat`, interpreted as the number zero.
* a function `succ : mynat → mynat`, with `succ n` interpreted as "the number after n".
* Usual numerical notatio... |
8286390a14410c8f0b83324616ac4c3f332fcb59 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/topology/sheaves/stalks.lean | bdf85bff10616e39eb73af7e01d523fc9b205ef2 | [
"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 | 6,799 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import topology.category.Top.open_nhds
import topology.sheaves.presheaf
import category_theory.limits.limits
import category_theory.limits.types
noncomputable theory... |
39b60cc8c2c4859f9311ff684e56934156e6689c | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/tactic/solve_by_elim.lean | 71104257a31a162365a23137b546f23e41d3fde9 | [
"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 | 15,184 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Scott Morrison
-/
import tactic.core
/-!
# solve_by_elim
A depth-first search backwards reasoner.
`solve_by_elim` takes a list of lemmas, and repeating tries to `apply` th... |
97c7d8ef3171b9207b5296a7d086d9936a1afd5d | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/data/lazy_list.lean | f3feb33b4baa307ddfbd54d140b79d29c7c83225 | [] | 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 | 1,604 | 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
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
universes u l v w
namespace Mathlib
inductive lazy_list (α : Type u)
where
| nil : lazy_li... |
d3e47ad47529f1399bc77fb15a4cb62906a073a2 | 592ee40978ac7604005a4e0d35bbc4b467389241 | /Library/generated/mathscheme-lean/MoufangIdentity.lean | 9d16e4e9b402c123c9d9d16c7ef11a0a4cc9105c | [] | no_license | ysharoda/Deriving-Definitions | 3e149e6641fae440badd35ac110a0bd705a49ad2 | dfecb27572022de3d4aa702cae8db19957523a59 | refs/heads/master | 1,679,127,857,700 | 1,615,939,007,000 | 1,615,939,007,000 | 229,785,731 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,136 | lean | import init.data.nat.basic
import init.data.fin.basic
import data.vector
import .Prelude
open Staged
open nat
open fin
open vector
section MoufangIdentity
structure MoufangIdentity (A : Type) : Type :=
(op : (A → (A → A)))
(moufangId : (∀ {x y z : A} , (op (op z x) (op y z)) = (op (op z (op x y)) z... |
388b9e39253241e061bdd891f13749331f5869b6 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/analysis/normed_space/hahn_banach/extension.lean | 1210370615d58b57dd92a798d100ea79c0a95e86 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 6,818 | lean | /-
Copyright (c) 2020 Yury Kudryashov All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Heather Macbeth
-/
import analysis.convex.cone.basic
import analysis.normed_space.is_R_or_C
import analysis.normed_space.extend
/-!
# Extension Hahn-Banach theorem
I... |
d230e0fc3d7d0562e7d8609af43727101d8aad9a | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/finset/pointwise.lean | 0f441be5a12ecb9d376d307b8c39a8b645a914f6 | [
"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 | 57,506 | lean | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Yaël Dillies
-/
import data.finset.n_ary
import data.finset.preimage
import data.set.pointwise.finite
import data.set.pointwise.smul
import data.set.pointwise.list_... |
d636610b3893bad1748410291657813329dc67b7 | 2c41ae31b2b771ad5646ad880201393f5269a7f0 | /Lean/Qualities/Resilient.lean | 4228155bdb85a0d23b751673eee9a3642f004f19 | [] | no_license | kevinsullivan/Boehm | 926f25bc6f1a8b6bd47d333d936fdfc278228312 | 55208395bff20d48a598b7fa33a4d55a2447a9cf | refs/heads/master | 1,586,127,134,302 | 1,488,252,326,000 | 1,488,252,326,000 | 32,836,930 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 824 | lean | import SystemModel.System
import Qualities.Dependable
import Qualities.Flexible
import Qualities.Changeable
/- Resilient -/
/-
Boehm stipulates that [Resiliency] is a composite quality comprising [Dependability]
and [Flexibility]. That is, a system can be deemed to be resilient across stakeholders,
operational context... |
e1aa29884c39dabe4f3e5f64f93d0510fa5eed6b | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/simp_iota_eqn.lean | e4accdcac5f95aeb7eec905a0a2a6e7004975f31 | [
"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 | 475 | lean | def f {α : Type} (a : α) : α :=
a
example (a : nat) (h : a = 3) : [1,2].map nat.succ = [2, f a] :=
begin
simp!,
guard_target nat.succ 2 = f a,
simp [f, h]
end
def foo : bool → bool → bool
| tt tt := tt
| ff ff := tt
| _ _ := ff
example : foo tt tt = f tt :=
begin
simp!,
guard_target tt = f tt,
simp [f]... |
d6bb2771ab9d12c9d00fe00e16cb08c2fd08ca6f | a4673261e60b025e2c8c825dfa4ab9108246c32e | /tests/lean/run/suffices.lean | bf17ccd3e8cf609854394c0ccf149410a78d238f | [
"Apache-2.0"
] | permissive | jcommelin/lean4 | c02dec0cc32c4bccab009285475f265f17d73228 | 2909313475588cc20ac0436e55548a4502050d0a | refs/heads/master | 1,674,129,550,893 | 1,606,415,348,000 | 1,606,415,348,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 440 | lean | variables {a b c : Prop}
theorem ex1 (Ha : a) (Hab : a → b) (Hbc : b → c) : c :=
suffices b from Hbc this
suffices a from Hab this
Ha
theorem ex2 (Ha : a) (Hab : a → b) (Hbc : b → c) : c :=
suffices b by apply Hbc; assumption
suffices a by apply Hab; exact this
Ha
theorem ex3 (Ha : a) (Hab : a → b) (Hbc ... |
b4b3c3aa571fa14311c53efd988d433004c821e5 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/unfold1.lean | 702ee1ee886d04127afad502fbe722781bb9443c | [
"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 | 618 | lean | mutual
def isEven : Nat → Bool
| 0 => true
| n+1 => isOdd n
def isOdd : Nat → Bool
| 0 => false
| n+1 => isEven n
end
termination_by' measure fun | PSum.inl n => n | PSum.inr n => n
decreasing_by apply Nat.lt_succ_self
theorem isEven_double (x : Nat) : isEven (2 * x) = true := by
induction x with... |
4afc8ee0919223bade919c455f268be1ccc7395e | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/number_theory/number_field.lean | 0317ff7dc52c909409e93c039f6040b1c2bc5abd | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 9,812 | lean | /-
Copyright (c) 2021 Ashvni Narayanan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ashvni Narayanan, Anne Baanen
-/
import ring_theory.dedekind_domain.integral_closure
import algebra.char_p.algebra
/-!
# Number fields
This file defines a number field, the ring of... |
78cab2b780223ac4b681083e57df1eac96552262 | 947b78d97130d56365ae2ec264df196ce769371a | /stage0/src/Lean/Compiler/IR/RC.lean | 45d8d73131f88df9771cd842ec366823fbf32bec | [
"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 | 12,620 | 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.Runtime
import Lean.Compiler.IR.CompilerM
import Lean.Compiler.IR.LiveVars
namespace Lean
namespace IR
namespace ExplicitRC
/- Insert explicit ... |
99d886d3b55452a4391f435786eed2a41856f478 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/omega/misc_auto.lean | 88f31880d82a78fa5a92d23ec48b59d198c37504 | [] | 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 | 2,002 | lean | /-
Copyright (c) 2019 Seul Baek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Seul Baek
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.tactic.localized
import Mathlib.PostPort
namespace Mathlib
/-
Miscellaneous.
-/
namespace omega
t... |
eab5588aea32a7c8c3b31dcafb08d2e09f5dc82e | 649957717d58c43b5d8d200da34bf374293fe739 | /src/category_theory/limits/shapes/binary_products.lean | 3add0eb183ebd300b25457f27cfb6a16865306b9 | [
"Apache-2.0"
] | permissive | Vtec234/mathlib | b50c7b21edea438df7497e5ed6a45f61527f0370 | fb1848bbbfce46152f58e219dc0712f3289d2b20 | refs/heads/master | 1,592,463,095,113 | 1,562,737,749,000 | 1,562,737,749,000 | 196,202,858 | 0 | 0 | Apache-2.0 | 1,562,762,338,000 | 1,562,762,337,000 | null | UTF-8 | Lean | false | false | 1,120 | lean | -- Copyright (c) 2018 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Scott Morrison
import category_theory.limits.cones
import category_theory.discrete_category
universes v u
open category_theory
namespace category_theory.limits
@[derive deci... |
5b173a2e982cf1987045020168d64625e4d04d90 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/topology/uniform_space/compare_reals_auto.lean | dd747ab840e24fab965fcea78e1d64f8d8aefa14 | [] | 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 | 4,176 | lean | /-
Copyright (c) 2019 Patrick MAssot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.topology.uniform_space.absolute_value
import Mathlib.topology.instances.real
import Mathlib... |
8a134845f27dc9a9bc71623f3cafa99d99172013 | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/calc1.lean | b439bfadb86f376c32ba17bad93d94bfddf1484e | [
"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 | 254 | lean | import tactic.
infixl 50 => : implies
variables a b c d e : Bool.
axiom H1 : a → b.
axiom H2 : b = c.
axiom H3 : c → d.
axiom H4 : d = e.
theorem T : a → e
:= calc a => b : H1
... = c : H2
... => d : H3
... = e : H4.
|
0a3b8239ee3b99ab8adff1ddbe9db81c07f19187 | 7b89826c26634aa18c0110f1634f73027851edfe | /natural-number-game/src/world01/level02.lean | 9a09a304ae0c9b90ea6c63686cdeb5febff5a2df | [
"MIT"
] | permissive | marcofavorito/leanings | b7642344d8c9012a1cec74a804c5884297880c4d | 581b83be66ff4f8dd946fb6a1bb045d2ddf91076 | refs/heads/master | 1,672,310,991,244 | 1,603,031,766,000 | 1,603,031,766,000 | 279,163,004 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 222 | lean | import mynat.mul -- imports definition of multiplication on the natural numbers.
namespace mynat
lemma example2 (x y : mynat) (h : y = x + 7) : 2 * y = 2 * (x + 7) :=
begin [nat_num_game]
rw h,
refl
end
end mynat
|
94bae92b3a5d9fa0c5088d2a74b1877e4bd676bb | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/data/real/cau_seq.lean | ac4d8c0606bff1079092f0348ea9abc95942c4f4 | [
"Apache-2.0"
] | permissive | rmitta/mathlib | 8d90aee30b4db2b013e01f62c33f297d7e64a43d | 883d974b608845bad30ae19e27e33c285200bf84 | refs/heads/master | 1,585,776,832,544 | 1,576,874,096,000 | 1,576,874,096,000 | 153,663,165 | 0 | 2 | Apache-2.0 | 1,544,806,490,000 | 1,539,884,365,000 | Lean | UTF-8 | Lean | false | false | 24,598 | 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 algebra.big_operators algebra.ordered_field
/-!
# Cauchy sequences
A basic theory of Cauchy sequences, used in the construction of the reals and p-adic numb... |
1af3602f0422faeabb8d21ac0efc27e8c19b3c32 | 8b9f17008684d796c8022dab552e42f0cb6fb347 | /tests/lean/run/ftree_brec.lean | a05f61155a6f85c5bd9ada8963032cd979d65d83 | [
"Apache-2.0"
] | permissive | chubbymaggie/lean | 0d06ae25f9dd396306fb02190e89422ea94afd7b | d2c7b5c31928c98f545b16420d37842c43b4ae9a | refs/heads/master | 1,611,313,622,901 | 1,430,266,839,000 | 1,430,267,083,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,000 | lean | import data.unit data.prod
inductive ftree (A : Type) (B : Type) : Type :=
| leafa : ftree A B
| node : (A → B → ftree A B) → (B → ftree A B) → ftree A B
set_option pp.universes true
check @ftree
namespace ftree
namespace manual
definition below.{l l₁ l₂} {A : Type.{l₁}} {B : Type.{l₂}} (C : ftree A B → Type.{l+1}... |
cf9f5ba61692c6317436bab05405027032e2fd39 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/data/polynomial/field_division.lean | 1cf0e9b7e7a3c35028c3a2b75f450e9c0f7f81fc | [
"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 | 13,365 | lean |
/-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
-/
import data.polynomial.ring_division
import data.polynomial.derivative
import algebra.gcd_domain
/-!
# Theory of univari... |
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