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3ff0d687754c1b06d80fd93925a4833753f1c7de | 82b86ba2ae0d5aed0f01f49c46db5afec0eb2bd7 | /tests/lean/run/dollarProjIssue.lean | 82001be6bf204fc22c3d0bb4483c278f4df3eb97 | [
"Apache-2.0"
] | permissive | banksonian/lean4 | 3a2e6b0f1eb63aa56ff95b8d07b2f851072d54dc | 78da6b3aa2840693eea354a41e89fc5b212a5011 | refs/heads/master | 1,673,703,624,165 | 1,605,123,551,000 | 1,605,123,551,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 253 | lean |
def g (x : Nat) : List (Nat × List Nat) :=
[(x, [x, x]), (x, [])]
def h (x : Nat) : List (Nat × List Nat) :=
g x $.filter fun ⟨_, xs⟩ => xs.isEmpty
theorem ex1 : g 10 = [(10, [10, 10]), (10, [])] :=
rfl
theorem ex2 : h 10 = [(10, [])] :=
rfl
|
d9f9b5f3ac77cacc55e1e621815cb83a713c9c6c | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/multiset/fold.lean | 44feff6fa7eddd9a19f32297136537a946f6a297 | [
"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 | 3,794 | 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.multiset.erase_dup
/-!
# The fold operation for a commutative associative operation over a multiset.
-/
namespace multiset
variables {α β : Type*}
/-! ... |
2a549251f889acf8c0264e635930ee1989f3fabc | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/topology/sequences.lean | 273d64bc0f54aebee06a5a930b868ba987e58fbb | [
"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 | 16,508 | lean | /-
Copyright (c) 2018 Jan-David Salchow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Patrick Massot
-/
import topology.subset_properties
import topology.metric_space.basic
/-!
# Sequences in topological spaces
In this file we define sequences in... |
1bc419572407f968bfb9977d4267d7d696289fc8 | 367134ba5a65885e863bdc4507601606690974c1 | /src/algebra/algebra/subalgebra.lean | 003130d4176a3f426baac1962d5a00ea0c60ee69 | [
"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 | 24,648 | 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.operations
/-!
# Subalgebras over Commutative Semiring
In this file we define `subalgebra`s and the usual operations on them (`map`, `... |
dbdb8f76100db0b4ad69fed3607a4959e1342899 | bb31430994044506fa42fd667e2d556327e18dfe | /src/algebra/algebra/operations.lean | 7945baacf42300f18589350b516ede03a4ffe4ee | [
"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 | 24,497 | lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import algebra.algebra.bilinear
import algebra.algebra.equiv
import algebra.module.submodule.pointwise
import algebra.module.submodule.bilinear
import algebra.module.opposites
... |
14edb855052463d1f21660d960f347e6e18e197a | 3b15c7b0b62d8ada1399c112ad88a529e6bfa115 | /src/Lean/Meta/Tactic/Simp/Main.lean | 16b106701b659f91dddae93708e8a29e3bfbd33e | [
"Apache-2.0"
] | permissive | stephenbrady/lean4 | 74bf5cae8a433e9c815708ce96c9e54a5caf2115 | b1bd3fc304d0f7bc6810ec78bfa4c51476d263f9 | refs/heads/master | 1,692,621,473,161 | 1,634,308,743,000 | 1,634,310,749,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 20,581 | 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.Meta.Transform
import Lean.Meta.Tactic.Replace
import Lean.Meta.Tactic.Util
import Lean.Meta.Tactic.Clear
import Lean.Meta.Tactic.Simp.Types
imp... |
31f2bee6360ac2c5d634f2f674740b244e7b9f26 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/limits/shapes/strong_epi.lean | 01cfc4c59fcf49cd8bac524bbd91a2dc78586e5b | [
"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 | 7,433 | lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import category_theory.balanced
import category_theory.lifting_properties.basic
/-!
# Strong epimorphisms
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to ... |
91517e2ad3d3e5cd17e395b0550077b751e463c1 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/topology/tietze_extension.lean | f3dac48a6df1f5a9e0a08e810dcd5ffe1934e235 | [
"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 | 22,823 | lean | /-
Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import topology.urysohns_bounded
import topology.algebra.ordered.monotone_continuity
import data.set.intervals.disjoint
import data.set.intervals.monotone
/-... |
e12eaa5f4aef454b5e39abcd004b76fb637e8e64 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/ring_theory/perfection.lean | 10a852b7914218311ca8fd4c5aedf78afae507c9 | [
"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 | 25,307 | 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 algebra.char_p
import algebra.ring.pi
import analysis.special_functions.pow
import field_theory.perfect_closure
import ring_theory.localization
import ring_theory.subri... |
932316890f4dfb549c09f30623c7d394ce47bde6 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/algebraic_topology/simplicial_object.lean | 650476a0471aef5e67293c0e382a0933892b6e60 | [
"Apache-2.0"
] | permissive | abentkamp/mathlib | d9a75d291ec09f4637b0f30cc3880ffb07549ee5 | 5360e476391508e092b5a1e5210bd0ed22dc0755 | refs/heads/master | 1,682,382,954,948 | 1,622,106,077,000 | 1,622,106,077,000 | 149,285,665 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 16,752 | lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Scott Morrison, Adam Topaz
-/
import algebraic_topology.simplex_category
import category_theory.category.ulift
import category_theory.limits.functor_category
import cat... |
7387072332b0e7025d7be2a30d8f3b48551bc723 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/limits/over_auto.lean | 8ac9cfe1a94df7c07954bb517705bedb94d6f351 | [] | 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 | 6,707 | lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Reid Barton, Bhavik Mehta
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.over
import Mathlib.category_theory.limits.prese... |
2d0db9ed88ce3cfb412e4db6557272215350f8c2 | 2b2a05a7af89c79da194505bf88205a6c4e05d68 | /src/game/world_10_inequality.lean | d096cfef107b40c5872a5dd748c6dde967b7ae36 | [] | no_license | lacrosse/natural_number_game | 6401a11a8c965da3903ae6695f84586edf6fac85 | 400179cde1d3fcc9744901dabff98813ba2b544f | refs/heads/master | 1,677,566,006,582 | 1,612,576,917,000 | 1,612,576,917,000 | 335,655,947 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,945 | lean | -- Game axiomatics
import game.world_09_advanced_multiplication
import mynat.le
namespace mynat
lemma one_add_le_self (x : mynat) : x ≤ 1 + x := begin[nat_num_game]
use 1,
apply add_comm,
end
lemma le_refl (x : mynat) : x ≤ x := begin[nat_num_game]
use 0,
refl,
end
attribute [refl] mynat.le_refl
theorem le... |
392193c774331754b99857836d5334e292710ddd | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/real/sqrt.lean | eef07e0a24594fb8f7f90e9912ed0fadebbea39a | [
"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 | 11,587 | lean | /-
Copyright (c) 2020 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Floris van Doorn, Yury Kudryashov
-/
import topology.instances.nnreal
import topology.algebra.ordered.monotone_continuity
/-!
# Square root of a real number
In this f... |
8fc137d2485e418d78234d2b90697783871010e3 | 5756a081670ba9c1d1d3fca7bd47cb4e31beae66 | /Mathport/Syntax/Translate/Expr.lean | 1dd1ef566596ff5d317419f3fecf9d622d983974 | [
"Apache-2.0"
] | permissive | leanprover-community/mathport | 2c9bdc8292168febf59799efdc5451dbf0450d4a | 13051f68064f7638970d39a8fecaede68ffbf9e1 | refs/heads/master | 1,693,841,364,079 | 1,693,813,111,000 | 1,693,813,111,000 | 379,357,010 | 27 | 10 | Apache-2.0 | 1,691,309,132,000 | 1,624,384,521,000 | Lean | UTF-8 | Lean | false | false | 18,695 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Daniel Selsam
-/
import Mathport.Syntax.Translate.Basic
namespace Mathport.Translate
open Lean hiding Expr Expr.app Expr.const Expr.sort Level Level.imax Level... |
fb30159dec3aca2904cb6400d0d21381edcaade9 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/reassoc_axiom.lean | cb1059e97c861b430a524e2b824f83a08222b461 | [] | 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 | 4,342 | lean | /-
Copyright (c) 2019 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author(s): Simon Hudon
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.category.default
import Mathlib.PostPort
universes u_1
namespace Mathlib
/-... |
8106047b07827444a958d62aaecc2ebb2ab9b6eb | ebb7367fa8ab324601b5abf705720fd4cc0e8598 | /algebra/quotient_group.hlean | a00f26086516e2cd288501598edf892a53574a23 | [
"Apache-2.0"
] | permissive | radams78/Spectral | 3e34916d9bbd0939ee6a629e36744827ff27bfc2 | c8145341046cfa2b4960ef3cc5a1117d12c43f63 | refs/heads/master | 1,610,421,583,830 | 1,481,232,014,000 | 1,481,232,014,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 15,743 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Egbert Rijke
Constructions with groups
-/
import hit.set_quotient .subgroup ..move_to_lib
open eq algebra is_trunc set_quotient relation sigma sigma.ops prod tru... |
7e5275407b33df09835f2d24e3984350e99ee271 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /stage0/src/Lean/Server/Utils.lean | cc68564dbe9e1723877e94c4c04e3eedeb619f49 | [
"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 | 5,301 | lean | /-
Copyright (c) 2020 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki, Marc Huisinga
-/
import Lean.Data.Position
import Lean.Data.Lsp
import Lean.Server.InfoUtils
import Init.System.FilePath
namespace IO
def throwServerError (err... |
5ed47cba54be8c951f533746fdae4d64dcf9d409 | 2d041ea7f2e9b29093ffd7c99b11decfaa8b20ca | /ch6.lean | adf8b1b9878ed188f4ab8c87d856cd71edc2368c | [] | no_license | 0xpr/lean_tutorial | 1a66577602baa9a52c2b01130b9d70089653ea37 | 56ef609d8df9e392916012db5354bf182cbbb8d8 | refs/heads/master | 1,606,955,421,810 | 1,499,014,388,000 | 1,499,014,388,000 | 96,036,899 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,941 | lean | namespace hide
inductive nat : Type :=
| zero : nat
| succ : nat → nat
namespace nat
definition add (m n : nat) : nat :=
nat.rec_on n m (fun n add_m_n, succ add_m_n)
notation 0 := zero
infix `+` := add
theorem add_zero (m : nat) : m + 0 = m := rfl
theorem add_succ (m n : nat) : m + succ n = succ (m + n) := rfl
l... |
6862ff09eaeb6dbbd64f2ccc1ea5f758812f60a8 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/order_defaults.lean | 583086d34fd50233526dedfad4e80f8466323a89 | [
"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 | 589 | lean | example : preorder unit := {
le := λ _ _, true,
le_refl := λ _, trivial,
le_trans := λ _ _ _ _ _, trivial,
}
example : partial_order unit := {
le := λ _ _, true,
le_refl := λ _, trivial,
le_trans := λ _ _ _ _ _, trivial,
le_antisymm := by intros a b; intros; cases a; cases b; refl
}
exampl... |
d4315d19ca5c96a268b0cd0d35316e7410d3a6d7 | f57749ca63d6416f807b770f67559503fdb21001 | /library/theories/group_theory/finsubg.lean | 92c0be801e032a67174ed131d055d5dabc6ebecc | [
"Apache-2.0"
] | permissive | aliassaf/lean | bd54e85bed07b1ff6f01396551867b2677cbc6ac | f9b069b6a50756588b309b3d716c447004203152 | refs/heads/master | 1,610,982,152,948 | 1,438,916,029,000 | 1,438,916,029,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 20,694 | lean | /-
Copyright (c) 2015 Haitao Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author : Haitao Zhang
-/
-- develop the concept of finite subgroups based on finsets so that the properties
-- can be used directly without translating from the set based theory first
import d... |
93b2fd3e9831006309222460ff94497e4d5d8cdf | c3f2fcd060adfa2ca29f924839d2d925e8f2c685 | /tests/lean/hott/443_b.hlean | f7da256048e769289d7e79e62633f425a23536eb | [
"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 | 578 | hlean | import algebra.groupoid algebra.group
open eq sigma unit category path_algebra equiv
set_option pp.implicit true
set_option pp.universes true
set_option pp.notation false
context
parameters {D₀ : Type} [C : precategory D₀]
{D₂ : Π ⦃a b c d : D₀⦄ (f : hom a b) (g : hom c d)
(h : hom a c) (i : hom b d), Typ... |
345f3553b77b67b7714d6f38369a026a0a978dd4 | 26ac254ecb57ffcb886ff709cf018390161a9225 | /src/data/polynomial/induction.lean | 2f360982314dfd0d46209aa65121190b81d01a81 | [
"Apache-2.0"
] | permissive | eric-wieser/mathlib | 42842584f584359bbe1fc8b88b3ff937c8acd72d | d0df6b81cd0920ad569158c06a3fd5abb9e63301 | refs/heads/master | 1,669,546,404,255 | 1,595,254,668,000 | 1,595,254,668,000 | 281,173,504 | 0 | 0 | Apache-2.0 | 1,595,263,582,000 | 1,595,263,581,000 | null | UTF-8 | Lean | false | false | 4,450 | 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.degree.basic
/-!
# Theory of univariate polynomials
The main results are `induction_on` and `as_s... |
9baed485be31d5a56b5ee777a596adeb6e0070f1 | e94d3f31e48d06d252ee7307fe71efe1d500f274 | /hott/types/trunc.hlean | f987e6f00fc0fdd10bf31efacf144d952c32eba0 | [
"Apache-2.0"
] | permissive | GallagherCommaJack/lean | e4471240a069d82f97cb361d2bf1a029de3f4256 | 226f8bafeb9baaa5a2ac58000c83d6beb29991e2 | refs/heads/master | 1,610,725,100,482 | 1,459,194,829,000 | 1,459,195,377,000 | 55,377,224 | 0 | 0 | null | 1,459,731,701,000 | 1,459,731,700,000 | null | UTF-8 | Lean | false | false | 22,895 | hlean | /-
Copyright (c) 2015 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
Properties of trunc_index, is_trunc, trunctype, trunc, and the pointed versions of these
-/
-- NOTE: the fact that (is_trunc n A) is a mere proposition is proved i... |
20a20b7f76cadcdb8c46fc0bd019beade5af3e5f | 798dd332c1ad790518589a09bc82459fb12e5156 | /linear_algebra/submodule.lean | e456bffc6aa512ed373dbfdc61615b5b401bed63 | [
"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 | 9,980 | lean | /-
Copyright (c) 2018 Mario Carneiro and Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro and Kevin Buzzard
-/
import order.order_iso
import tactic.tidy
import linear_algebra.subtype_module
import linear_algebra.quotient_module
import linea... |
1b732dd79425d0e6b628781f6bb3061fd4ff17c2 | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /stage0/src/Lean/HeadIndex.lean | 907279fcbc41d6ce4bf4db9095ecd6b3f25df304 | [
"Apache-2.0"
] | permissive | collares/lean4 | 861a9269c4592bce49b71059e232ff0bfe4594cc | 52a4f535d853a2c7c7eea5fee8a4fa04c682c1ee | refs/heads/master | 1,691,419,031,324 | 1,618,678,138,000 | 1,618,678,138,000 | 358,989,750 | 0 | 0 | Apache-2.0 | 1,618,696,333,000 | 1,618,696,333,000 | null | UTF-8 | Lean | false | false | 2,047 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
import Lean.Expr
namespace Lean
inductive HeadIndex where
| fvar (fvarId : FVarId)
| mvar (mvarId : MVarId)
| const (constName : Name)
| proj (stru... |
3cb1c13d06cc87892802b7dcc7ded65894efb91d | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/lift2.lean | 4c791dbef321f22ff43e4ddb38a018feed8c97f2 | [
"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 | 278 | lean | namespace test
inductive {u₁ u₂} lift (A : Type u₁) : Type (max 1 u₁ u₂)
| inj : A → lift
set_option pp.universes true
variables (A : Type 3) (B : Type 1)
check A = lift.{1 3} B
universe u
variables (C : Type (u+2)) (D : Type u)
check C = lift.{u u+2} D
end test
|
e7636cebe7207e4001ff41a00261758457d31076 | 0845ae2ca02071debcfd4ac24be871236c01784f | /library/init/lean/compiler/ir/checker.lean | 994120ffbe341e914420e5cd8a3dadb52e90b19c | [
"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 | 5,696 | 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.lean.compiler.ir.compilerm
namespace Lean
namespace IR
namespace Checker
structure Context :=
(env : Environment) (localCtx : LocalCo... |
a7b8708a4bd7e545a9a18c12444b4aed16d4ef78 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/order/filter/countable_Inter_auto.lean | 4581b705b1f0a2e2acb135d070a1ca6e3c0b4090 | [] | 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 | 8,969 | lean | /-
Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Yury G. Kudryashov
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.order.filter.basic
import Mathlib.data.set.countable
import Mathlib.PostPort
univer... |
085d14ed54194ec990e53d93ba869dae15e192b3 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/algebra/group/commute.lean | d0f93f754030cc48d5968cd668f3fa9d322a696e | [
"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 | 7,310 | lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Neil Strickland, Yury Kudryashov
-/
import algebra.group.semiconj
/-!
# Commuting pairs of elements in monoids
We define the predicate `commute a b := a * b = b * a` and provide som... |
38d939dddf4599d3a14fb5ebb7b7bf51d1a751f0 | b0d97c09d47e3b0a68128c64cad26ab132d23108 | /src/compcont/ex4.lean | 9bb0b0f1e9ecd85345dd9edf34e22829d2ffd41e | [] | no_license | jmvlangen/RIP-seminar | 2ad32c1c6fceb59ac7ae3b2251baf08f4c0c0caa | ed6771404dd4bcec298de2dfdc89d5e9cfd331bb | refs/heads/master | 1,585,865,817,237 | 1,546,865,823,000 | 1,546,865,823,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,029 | lean | import analysis.topology.topological_space
import analysis.topology.continuity
import analysis.topology.topological_structures
import ex3
open tactic expr function has_add
variables {X : Type*} {Y : Type*} {Z : Type*} {W : Type*}
{f f₁ f₂ : X → Y} {g : Y → Z} {h : Z → W}
variables [topological_space X] [topo... |
adb8e0211e73ad43f782c2e510149883e5ec647d | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/topology/algebra/affine.lean | 2b6d2b458b8de6d4ffaae9f57cb0ac36cab0ff08 | [
"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 | 1,414 | lean | /-
Copyright (c) 2020 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import topology.continuous_function.algebra
import linear_algebra.affine_space.affine_map
/-!
# Topological properties of affine spaces and maps
For now, this con... |
42738f9ae4ab5a1c7c1020979672f0e02a38da1c | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/tactic12.lean | 13d33a88e703c116f3fc15225e645f51498a3326 | [
"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 | 287 | lean | import logic
open tactic
theorem tst (a b : Prop) (H : ¬ a ∨ ¬ b) (Hb : b) : ¬ a ∧ b
:= begin
apply and.intro,
exact
(assume Ha, or.elim H
(assume Hna, @absurd _ false Ha Hna)
(assume Hnb, @absurd _ false Hb Hnb)),
assumption
end
|
cc720188e809c4e45cb6e6599c7fbfe4d0754858 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/linear_algebra/matrix/ldl.lean | 4c5ba1efe552510b5010bb584298de514b026815 | [
"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 | 4,722 | lean | /-
Copyright (c) 2022 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp
-/
import analysis.inner_product_space.gram_schmidt_ortho
import linear_algebra.matrix.pos_def
/-! # LDL decomposition
This file proves the LDL-decomposition o... |
a79acfae581e33c255fab17651733a41da30a38a | ff5230333a701471f46c57e8c115a073ebaaa448 | /library/init/category/lawful.lean | 61e75201f48a0414f1039f9a6cb7c874b6025bfc | [
"Apache-2.0"
] | permissive | stanford-cs242/lean | f81721d2b5d00bc175f2e58c57b710d465e6c858 | 7bd861261f4a37326dcf8d7a17f1f1f330e4548c | refs/heads/master | 1,600,957,431,849 | 1,576,465,093,000 | 1,576,465,093,000 | 225,779,423 | 0 | 3 | Apache-2.0 | 1,575,433,936,000 | 1,575,433,935,000 | null | UTF-8 | Lean | false | false | 11,145 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
-/
prelude
import init.category.monad init.meta.interactive
import init.category.state init.category.except init.category.reader init.category.option
universes... |
b57666d1f00f0b7f47ba2fd591d49a9804465c62 | a7eef317ddec01b9fc6cfbb876fe7ac00f205ac7 | /src/data/nat/basic.lean | a8fc81c5d32e4e6bcca8abc43b2fe27694ca82ed | [
"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 | 66,566 | lean | /-
Copyright (c) 2014 Floris van Doorn (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
import algebra.ordered_ring
import algebra.order_functions
/-!
# Basic operation... |
05d838b41076854ced1104f4817f349bb26d177e | 4727251e0cd73359b15b664c3170e5d754078599 | /src/category_theory/limits/shapes/strict_initial.lean | f75fb39581491dce5f0ad9d77eb4660ddca9727e | [
"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 | 8,297 | lean | /-
Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import category_theory.limits.shapes.terminal
import category_theory.limits.shapes.binary_products
import category_theory.epi_mono
/-!
# Strict initial objects
This fi... |
625ecad1dd96f6273f76ec424183e3d8321e86ce | 6afa22d5eee6e9a56b6a2f1210eca8f7a1067466 | /library/init/meta/expr.lean | 0929cc5ab124a5b71e6105f8be8f7547e1b7346c | [
"Apache-2.0"
] | permissive | giordano/lean | 72a1fabfeb2f1ccfd38673e2719a719cd6ffbb40 | 56f8877f1efa22215aca0b82f1c0ce2ff975b9c3 | refs/heads/master | 1,663,091,511,168 | 1,590,688,082,000 | 1,590,688,082,000 | 268,183,678 | 0 | 0 | Apache-2.0 | 1,590,885,425,000 | 1,590,885,424,000 | null | UTF-8 | Lean | false | false | 22,203 | 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
-/
prelude
import init.meta.level init.control.monad init.meta.rb_map
universes u v
open native
/-- Column and line position in a Lean source file. -/
structur... |
2b08067a976ddb1bc6f87756293d9ac5d7faa2be | 649957717d58c43b5d8d200da34bf374293fe739 | /src/category_theory/endomorphism.lean | be54941d8ec723cd6dd88e6d7cc21fb43cc1bd3b | [
"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 | 3,190 | lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Scott Morrison, Simon Hudon
Definition and basic properties of endomorphisms and automorphisms of an object in a category.
-/
import category_theory.category catego... |
da7e23fc7d7111af4f3fe916bedef77361bc308d | 5d76f062116fa5bd22eda20d6fd74da58dba65bb | /src/snarks/babysnark/knowledge_soundness.lean | cd0096d2541456ad074496538faed78ec996de5f | [] | no_license | brando90/formal_baby_snark | 59e4732dfb43f97776a3643f2731262f58d2bb81 | 4732da237784bd461ff949729cc011db83917907 | refs/heads/master | 1,682,650,246,414 | 1,621,103,975,000 | 1,621,103,975,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,183 | lean | /-
Author: Bolton Bailey
-/
import data.mv_polynomial.basic
import data.polynomial.div
import data.polynomial.field_division
import algebra.polynomial.big_operators
import ...general_lemmas.polynomial_mv_sv_cast
import ...general_lemmas.mv_divisability
import ...general_lemmas.single_antidiagonal
import ...general_lemm... |
ab3cd6762ef60302dd0ade4e66eb4ffea3a67e4c | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/calculus/affine_map.lean | 1d7e83abaa361dfa241cfba9e5c4afda3d011ecf | [
"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 | 1,018 | lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import analysis.normed_space.continuous_affine_map
import analysis.calculus.cont_diff
/-!
# Smooth affine maps
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to... |
ebc866fbdd79629d2de4c492bc093b9a9cacd6e0 | a1179fa077c09acc49e4fbc8d67084ba89ac4f4c | /tutorials/src/solutions/tuto_lib.lean | 7e35e383114918b622b5cf68f5b87b0bb67b66f7 | [] | no_license | Seeram/Lean-proof-assistant | 11ca0ca0e0446bacdd1773c4c481a3653b2f1074 | e672d46e0e5f39d8de2933ad4f4cac095ca6094f | refs/heads/master | 1,682,754,224,366 | 1,620,959,431,000 | 1,620,959,431,000 | 299,000,950 | 0 | 1 | null | 1,620,680,462,000 | 1,601,200,258,000 | Lean | UTF-8 | Lean | false | false | 6,807 | lean | import analysis.specific_limits
import data.int.parity
import topology.sequences
attribute [instance] classical.prop_decidable
/-
Lemmas from that file were hidden in my course, or restating things which
were proved without name in previous files.
-/
notation `|`x`|` := abs x
-- The mathlib version is unusable bec... |
2a5c7b7b0fb4ceb272860b4abef919813520f10e | 4727251e0cd73359b15b664c3170e5d754078599 | /src/ring_theory/polynomial/tower.lean | 39c38f58e0d03cf7700db6500429448fdb7f2fd0 | [
"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 | 2,572 | 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 algebra.algebra.tower
import data.polynomial.algebra_map
/-!
# Algebra towers for polynomial
This file proves some basic results about the algebra tower structure for... |
25fdee8305d99babf6b34388e4efc1cff0d4918c | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/field_theory/finite/basic.lean | 4e30307e77c12fa04f2a75e8cbdb35b54d7cc173 | [
"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 | 16,291 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Joey van Langen, Casper Putz
-/
import tactic.apply_fun
import data.equiv.ring
import data.zmod.algebra
import linear_algebra.finite_dimensional
import ring_theory.integral... |
6dc0427a52a8fe59cfd2daae5aa56187da9d11d9 | aa2345b30d710f7e75f13157a35845ee6d48c017 | /order/zorn.lean | 5ce232dfb5cf71fb978f7756cb154c15ec6c6ed3 | [
"Apache-2.0"
] | permissive | CohenCyril/mathlib | 5241b20a3fd0ac0133e48e618a5fb7761ca7dcbe | a12d5a192f5923016752f638d19fc1a51610f163 | refs/heads/master | 1,586,031,957,957 | 1,541,432,824,000 | 1,541,432,824,000 | 156,246,337 | 0 | 0 | Apache-2.0 | 1,541,434,514,000 | 1,541,434,513,000 | null | UTF-8 | Lean | false | false | 10,968 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Zorn's lemmas.
Ported from Isabelle/HOL (written by Jacques D. Fleuriot, Tobias Nipkow, and Christian Sternagel).
-/
import data.set.lattice
noncomputable theory
univ... |
9a262784b8604f89018e1a8e70faa998179d08c4 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /library/algebra/group.lean | b29259caeb1112e1ce3650cbaa306055f3a0b4ef | [
"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 | 23,334 | 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
Various multiplicative and additive structures. Partially modeled on Isabelle's library.
-/
import logic.eq data.unit data.sigma data.prod
import alge... |
c868b0a10614ed3ed9c0c696503a5df077e93cca | e21db629d2e37a833531fdcb0b37ce4d71825408 | /src/parlang/lemmas_exec.lean | 3879a0f3b72058d79aec66915c1fc9d1ef5137f8 | [] | no_license | fischerman/GPU-transformation-verifier | 614a28cb4606a05a0eb27e8d4eab999f4f5ea60c | 75a5016f05382738ff93ce5859c4cfa47ccb63c1 | refs/heads/master | 1,586,985,789,300 | 1,579,290,514,000 | 1,579,290,514,000 | 165,031,073 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,168 | lean | import parlang.defs
import parlang.lemmas_active_map
import parlang.lemmas_thread_state
import parlang.lemmas_state
namespace parlang
variables {n : ℕ} {σ : Type} {ι : Type} {τ : ι → Type} [decidable_eq ι]
@[simp]
lemma exec_skip {n} {ac : vector bool n} {s} : exec_state (kernel.compute id : kernel σ τ) ac s s := beg... |
616dc30b9abd48ea92c43728d4e2134a3aba283a | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/case_let.lean | 0bf142b6716b1c29d9a237ca136a9c2f71ff9231 | [
"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 | 177 | lean |
example (n m : ℕ) : n + m = m + n :=
begin
let s := n + m,
induction n,
case nat.zero : {sorry}, -- error: could not find open goal of given case
case nat.succ : {sorry}
end
|
b507a711497d971e73e61cb8c7e9dd8f11cf7e21 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/category_theory/limits/preserves/shapes/equalizers.lean | 00d6dbb5f11821cf16febc78783485be0bde7555 | [
"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 | 7,218 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import category_theory.limits.shapes.split_coequalizer
import category_theory.limits.preserves.basic
/-!
# Preserving (co)equalizers
Constructions to relate the notions... |
a75a1203d48e064800b7ca162be7ea8d2a334bdb | f20db13587f4dd28a4b1fbd31953afd491691fa0 | /leanpkg/leanpkg/resolve.lean | a8d28f66f4edf25ca098ff72dfc633184add23f4 | [
"Apache-2.0"
] | permissive | AHartNtkn/lean | 9a971edfc6857c63edcbf96bea6841b9a84cf916 | 0d83a74b26541421fc1aa33044c35b03759710ed | refs/heads/master | 1,620,592,591,236 | 1,516,749,881,000 | 1,516,749,881,000 | 118,697,288 | 1 | 0 | null | 1,516,759,470,000 | 1,516,759,470,000 | null | UTF-8 | Lean | false | false | 3,870 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Gabriel Ebner
-/
import leanpkg.manifest system.io leanpkg.proc leanpkg.git
namespace leanpkg
def assignment := list (string × string)
namespace assignment
def empty : assignm... |
742b003ecdfa96e9cccc7da6b788e3ca55e01308 | 92b50235facfbc08dfe7f334827d47281471333b | /hott/algebra/category/constructions/functor.hlean | b6407dc16306cafdf64301c478a0c1ed716ecbdb | [
"Apache-2.0"
] | permissive | htzh/lean | 24f6ed7510ab637379ec31af406d12584d31792c | d70c79f4e30aafecdfc4a60b5d3512199200ab6e | refs/heads/master | 1,607,677,731,270 | 1,437,089,952,000 | 1,437,089,952,000 | 37,078,816 | 0 | 0 | null | 1,433,780,956,000 | 1,433,780,955,000 | null | UTF-8 | Lean | false | false | 6,144 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Jakob von Raumer
Functor precategory and category
-/
import ..nat_trans ..category
open eq functor is_trunc nat_trans iso is_equiv
namespace category
definit... |
2f03f17eeaa6e56bde543efdf9f8b993a3f00352 | 618003631150032a5676f229d13a079ac875ff77 | /src/data/real/hyperreal.lean | a670a4df4bb36ad40bf660dcf80eab8d63e32239 | [
"Apache-2.0"
] | permissive | awainverse/mathlib | 939b68c8486df66cfda64d327ad3d9165248c777 | ea76bd8f3ca0a8bf0a166a06a475b10663dec44a | refs/heads/master | 1,659,592,962,036 | 1,590,987,592,000 | 1,590,987,592,000 | 268,436,019 | 1 | 0 | Apache-2.0 | 1,590,990,500,000 | 1,590,990,500,000 | null | UTF-8 | Lean | false | false | 36,765 | lean | /-
Copyright (c) 2019 Abhimanyu Pallavi Sudhir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Abhimanyu Pallavi Sudhir
Construction of the hyperreal numbers as an ultraproduct of real sequences.
-/
import order.filter.filter_product
import analysis.specific_limits
op... |
c10b1f8858b01e9e46706074cb0521da0f4adf9c | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/probability/probability_mass_function/constructions.lean | 01c74b53850eb20615ee66e3218acefb2af520e4 | [
"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 | 9,235 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Devon Tuma
-/
import probability.probability_mass_function.monad
/-!
# Specific Constructions of Probability Mass Functions
This file gives a number of different `pmf... |
f9cc8e10f2ed82ebd806f96f9b8d672ff9ece217 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/linear_algebra/free_module/ideal_quotient.lean | e41849fa71da7303da0887acb510b68c471cd1db | [
"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 | 6,095 | lean | /-
Copyright (c) 2022 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import data.zmod.quotient
import linear_algebra.free_module.finite.rank
import linear_algebra.free_module.pid
import linear_algebra.free_module.strong_rank_condition
impor... |
327409c9f705c564ab6481884c39fda3a130102a | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/computability/partrec_code.lean | 2fdafb679e60d992fad93613f77c14c41cae6f82 | [
"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 | 37,860 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
Godel numbering for partial recursive functions.
-/
import computability.partrec
open encodable denumerable
namespace nat.partrec
open nat (mkpair)
theorem rfind' {f}... |
8239829365608cdf9cabc37e195e8e8ccec36590 | 9dd3f3912f7321eb58ee9aa8f21778ad6221f87c | /tests/lean/run/nateq.lean | bf5661eea964cf2e9c038aeedf6b5e3d7f16e94d | [
"Apache-2.0"
] | permissive | bre7k30/lean | de893411bcfa7b3c5572e61b9e1c52951b310aa4 | 5a924699d076dab1bd5af23a8f910b433e598d7a | refs/heads/master | 1,610,900,145,817 | 1,488,006,845,000 | 1,488,006,845,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 896 | lean | open bool nat
attribute [reducible] nat.rec_on
definition is_eq (a b : nat) : bool :=
nat.rec_on a
(λ b, nat.cases_on b tt (λb₁, ff))
(λ a₁ r₁ b, nat.cases_on b ff (λb₁, r₁ b₁))
b
example : is_eq 3 3 = tt :=
rfl
example : is_eq 3 5 = ff :=
rfl
theorem eq.to_is_eq (a b : nat) (H : a = b) : is_eq a b = tt :=
ha... |
89bdf68a08cc9d557213f8b40aaf0c6e80b8bb28 | 5ca7b1b12d14c4742e29366312ba2c2ef8201b21 | /src/game/world7/level10.lean | 976964075bf546055e2661a1de194f6739563674 | [
"Apache-2.0"
] | permissive | MatthiasHu/natural_number_game | 2e464482ef3001863430b0336133b6697b275ba3 | 2d764f72669ae30861f6a1057fce0257f3e466c4 | refs/heads/master | 1,609,719,110,419 | 1,576,345,737,000 | 1,576,345,737,000 | 240,296,314 | 0 | 0 | Apache-2.0 | 1,581,608,357,000 | 1,581,608,356,000 | null | UTF-8 | Lean | false | false | 1,996 | lean | import game.world6.level8 -- hide
import tactic.tauto
local attribute [instance, priority 10] classical.prop_decidable -- hide
/-
# Advanced proposition world.
## Level 10: `exfalso` and proof by contradiction.
It's certainly true that $(P\land(\lnot P)\implies Q$ for any propositions $P$
and $Q$, because the left... |
905383aa472ac23c5f27a899d3e3bfe43b3c02c0 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /test/norm_num_ext.lean | ef6d5a3d196fe1587cb3152d5d126523a72a9e6c | [
"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 | 11,485 | lean | /-
Copyright (c) 2021 Mario Carneiro All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import algebra.big_operators.norm_num
import data.nat.squarefree
import data.int.gcd
import data.nat.fib
import data.nat.prime
import data.nat.sqrt_norm_num
import ana... |
0e267218b466729d90dee6ec347d7970c7d3017a | ce4db867008cc96ee6ea6a34d39c2fa7c6ccb536 | /src/m154.lean | 1526bd6f82c9c56ac6fa9dbc70ac0e4df4227654 | [] | no_license | PatrickMassot/lean-bavard | ab0ceedd6bab43dc0444903a80b911c5fbfb23c3 | 92a1a8c7ff322e4f575ec709b8c5348990d64f18 | refs/heads/master | 1,679,565,084,665 | 1,616,158,570,000 | 1,616,158,570,000 | 348,144,867 | 1 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 3,594 | lean | import data.int.parity
import tactic.apply_fun
import data.real.basic
import algebra.group.pi
import tactiques
namespace tactic.interactive
setup_tactic_parser
open tactic
meta def verifie : tactic unit :=
`[ { repeat { unfold limite_suite},
repeat { unfold continue_en },
push_neg,
try { simp only [exists_... |
1cd9f76b43604a9137eca6516828c58298750271 | 26ac254ecb57ffcb886ff709cf018390161a9225 | /src/data/fintype/card.lean | 0a78f3689e70ca5aae82edb7c74ce5b3e955924c | [
"Apache-2.0"
] | permissive | eric-wieser/mathlib | 42842584f584359bbe1fc8b88b3ff937c8acd72d | d0df6b81cd0920ad569158c06a3fd5abb9e63301 | refs/heads/master | 1,669,546,404,255 | 1,595,254,668,000 | 1,595,254,668,000 | 281,173,504 | 0 | 0 | Apache-2.0 | 1,595,263,582,000 | 1,595,263,581,000 | null | UTF-8 | Lean | false | false | 15,325 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
-/
import data.fintype.basic
import algebra.big_operators
/-!
Results about "big operations" over a `fintype`, and consequent
results about cardinalities of certain type... |
0b112fc051d3bdd8f891898036b37c56bc0e998c | c31182a012eec69da0a1f6c05f42b0f0717d212d | /src/pseudo_normed_group/CLC.lean | ccdbf3d1d5ed7ee917a1dbd2a9f32ee9cae89414 | [] | no_license | Ja1941/lean-liquid | fbec3ffc7fc67df1b5ca95b7ee225685ab9ffbdc | 8e80ed0cbdf5145d6814e833a674eaf05a1495c1 | refs/heads/master | 1,689,437,983,362 | 1,628,362,719,000 | 1,628,362,719,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,666 | lean | import pseudo_normed_group.LC
import for_mathlib.normed_group_hom_completion
/-!
# V-hat(M_c^n)
One of the key players in the proof of the main theorem of this repo is
the normed group V-hat(M-bar_r'(S)_{≤c}^n). This file constructs
## Key defintions
- `CLCP V n`: the functor that sends a profinite set `S` to `V-ha... |
557f9eb2f05f488c64b0f40626f0d965c50d123b | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/induction_tac3.lean | 9b4d4c04582c6f9528152174d0237e9fa9d9d5f7 | [
"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 | 598 | lean | open tactic
example (p q : Prop) : p ∨ q → q ∨ p :=
by do
H ← intro `H,
induction_core semireducible H `or.rec [],
constructor_idx 2, assumption,
constructor_idx 1, assumption
open nat
example (n : ℕ) : n = 0 ∨ n = succ (pred n) :=
by do
n ← get_local `n,
induction_core semireducible n `nat.rec [],
cons... |
cfac9e481cb6c6dca237ff5a52c2c371106d5eb8 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/data/list/basic.lean | ba4da63e740094398a86420dd24c6f34aaf0f176 | [
"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 | 161,230 | lean | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
import algebra.order_functions
import control.monad.basic
import data.nat.basic
import order.r... |
f71d353dea330831cb6b256997126ee33f609ec2 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/group_theory/quotient_group.lean | 884a201a4aee7099b7557db1427677666313d7c2 | [
"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 | 17,846 | lean | /-
Copyright (c) 2018 Kevin Buzzard, 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 Hölzl.
-/
import group_theory.coset
import group_theory.congr... |
db1e0e12a00d31ff0e5ff26cea3fc56a55fb14b3 | 4fa161becb8ce7378a709f5992a594764699e268 | /src/ring_theory/subsemiring.lean | 5c81c83106460e975e595486e02d318f76d1fb36 | [
"Apache-2.0"
] | permissive | laughinggas/mathlib | e4aa4565ae34e46e834434284cb26bd9d67bc373 | 86dcd5cda7a5017c8b3c8876c89a510a19d49aad | refs/heads/master | 1,669,496,232,688 | 1,592,831,995,000 | 1,592,831,995,000 | 274,155,979 | 0 | 0 | Apache-2.0 | 1,592,835,190,000 | 1,592,835,189,000 | null | UTF-8 | Lean | false | false | 22,474 | lean | /-
Copyright (c) 2020 Yury Kudryashov All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import ring_theory.prod
import group_theory.submonoid
import data.equiv.ring
/-!
# Bundled subsemirings
We define bundled subsemirings and some standard construct... |
7a1ae3b188969e89d2b9b19f53059eee810e8578 | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/arith5.lean | 3fab16b9bed33c8b6c8c582851e423d490eee376 | [
"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 | 113 | lean | import specialfn.
variable x : Real
eval sinh(x)
eval cosh(x)
eval tanh(x)
eval coth(x)
eval sech(x)
eval csch(x) |
6a4786e2df53785208d59bae680df4d3a9a4d72b | f1dc39e1c68f71465c8bf79910c4664d03824751 | /library/init/algebra/ordered_ring.lean | edc3cb33dcb0ae1ed41d96bacf78f8f819bdabbd | [
"Apache-2.0"
] | permissive | kckennylau/lean-2 | 6504f45da07bc98b098d726b74130103be25885c | c9a9368bc0fd600d832bd56c5cb2124b8a523ef9 | refs/heads/master | 1,659,140,308,864 | 1,589,361,166,000 | 1,589,361,166,000 | 263,748,786 | 0 | 0 | null | 1,589,405,915,000 | 1,589,405,915,000 | null | UTF-8 | Lean | false | false | 17,045 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
-/
prelude
import init.algebra.ordered_group init.algebra.ring
/- Make sure instances defined in this file have lower priority than the ones
... |
d97c582d7fcfd54bf71d1a76d03cd1868d6ec0e4 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/sheaves/local_predicate.lean | 04659ff17fd1b963cebf252f92a5eef71119f7ae | [
"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 | 11,808 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Scott Morrison, Adam Topaz
-/
import topology.sheaves.sheaf_of_functions
import topology.sheaves.stalks
import topology.local_homeomorph
import topology.sheaves.sheaf_c... |
a32d918b847223b0235e95b26dd00b5456bc2175 | 46125763b4dbf50619e8846a1371029346f4c3db | /src/data/polynomial.lean | 24f9b5fdc6dd7d6147670dc374a865a662a9374a | [
"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 | 103,701 | 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, Jens Wagemaker
Theory of univariate polynomials, represented as `ℕ →₀ α`, where α is a commutative semiring.
-/
import data.finsupp algebra.gcd_domain ring... |
f7ba943259855e59a298338798a8c90f12bd026d | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/shift/basic.lean | fb22baa97b3b6b44f7c4108a81c02413108744e8 | [
"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 | 30,106 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Johan Commelin, Andrew Yang, Joël Riou
-/
import category_theory.limits.preserves.shapes.zero
import category_theory.monoidal.End
import category_theory.monoidal.discre... |
545416e5da5e129b83444b9298ed0768917c3660 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/topology/continuous_function/compact.lean | 85f7602caab899f7e21e9e9dfc24b3b767d05892 | [
"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 | 18,216 | 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 topology.continuous_function.bounded
import topology.uniform_space.compact
import topology.compact_open
import topology.sets.compacts
/-!
# Continuous functio... |
5d9380b7999ce8b1adbbd99c1ac428f46c1d07c1 | ea4aee6b11f86433e69bb5e50d0259e056d0ae61 | /src/tidy/its.lean | 86cef693ef7fef6618df8cf7efe2b6e617854af3 | [] | no_license | timjb/lean-tidy | e18feff0b7f0aad08c614fb4d34aaf527bf21e20 | e767e259bf76c69edfd4ab8af1b76e6f1ed67f48 | refs/heads/master | 1,624,861,693,182 | 1,504,411,006,000 | 1,504,411,006,000 | 103,740,824 | 0 | 0 | null | 1,505,553,968,000 | 1,505,553,968,000 | null | UTF-8 | Lean | false | false | 564 | lean | -- Copyright (c) 2017 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Scott Morrison
import .transport .tidy
namespace tactic
meta def its { α : Type } (e : expr) (discharger : tactic α): tactic α := (`[refine (transport %%e _)] <|> `[refine (cas... |
44218971beb9c7e95beadbf5ca4407b0df50f6ea | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Init/Data/Nat/Basic.lean | e3c81142029580e03bd51541a22986080ac71cc9 | [
"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 | 28,515 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura
-/
prelude
import Init.SimpLemmas
set_option linter.missingDocs true -- keep it documented
universe u
namespace Nat
/--
`Nat.fold` evaluate... |
4124cfbe0443b8c4313bc97760e088830a21a006 | 59a4b050600ed7b3d5826a8478db0a9bdc190252 | /src/category_theory/products/associator.lean | 82a3286ef86b7bb1363ca1475510ac629060bf36 | [] | no_license | rwbarton/lean-category-theory | f720268d800b62a25d69842ca7b5d27822f00652 | 00df814d463406b7a13a56f5dcda67758ba1b419 | refs/heads/master | 1,585,366,296,767 | 1,536,151,349,000 | 1,536,151,349,000 | 147,652,096 | 0 | 0 | null | 1,536,226,960,000 | 1,536,226,960,000 | null | UTF-8 | Lean | false | false | 1,610 | lean | -- Copyright (c) 2017 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Stephen Morgan, Scott Morrison
import category_theory.products
import category_theory.equivalence
open category_theory
namespace category_theory.prod
universes u₁ v₁ u₂ v₂ u₃... |
ab77e88a5b02426692891c16593b7267b263a057 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /doc/examples/NFM2022/nfm10.lean | 6f1dba630fb2c2bb7b6a59fd7e422b72f6a67716 | [
"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 | 610 | lean | /- Dependent pattern matching -/
inductive Vector (α : Type u) : Nat → Type u
| nil : Vector α 0
| cons : α → Vector α n → Vector α (n+1)
infix:67 "::" => Vector.cons
def Vector.zip : Vector α n → Vector β n → Vector (α × β) n
| nil, nil => nil
| a::as, b::bs => (a, b) :: zip as bs
#print Vector.zip
/-
def ... |
831d42e678e9c06002c188ef3c07bd17ff4a8f45 | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /src/Lean/PrettyPrinter/Formatter.lean | 9f125eaab7c4e72166503cebed7e242f0aa0ad57 | [
"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 | 16,643 | lean | /-
Copyright (c) 2020 Sebastian Ullrich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
-/
/-!
The formatter turns a `Syntax` tree into a `Format` object, inserting both mandatory whitespace (to separate adjacent
tokens) as well as "pretty" optional ... |
dd87f65ad9f8c7c9da2fdd7b4c7fb358a5d46d01 | c31182a012eec69da0a1f6c05f42b0f0717d212d | /src/hacks_and_tricks/type_pow.lean | ab87ffec5177eda7a6527b216cd79137cfdbc8b2 | [] | no_license | Ja1941/lean-liquid | fbec3ffc7fc67df1b5ca95b7ee225685ab9ffbdc | 8e80ed0cbdf5145d6814e833a674eaf05a1495c1 | refs/heads/master | 1,689,437,983,362 | 1,628,362,719,000 | 1,628,362,719,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,371 | lean | import topology.constructions
/-
In this file, we define notation `X^n` to take powers of types.
By definition, `X^n` is modelled as functions from `fin n` to `X`.
-/
/-- A definition of powers of a type. -/
def type_pow : has_pow (Type*) ℕ := ⟨λ A n, fin n → A⟩
namespace type_pow_topology
local attribute [instanc... |
52ccdcb2fb0d5297799282a89a7b1a4366eaa247 | 9a0b1b3a653ea926b03d1495fef64da1d14b3174 | /tidy/rewrite_search/tracer/graph.lean | b479477836c05dbe90f2fab7b520bef47df06a12 | [
"Apache-2.0"
] | permissive | khoek/mathlib-tidy | 8623b27b4e04e7d598164e7eaf248610d58f768b | 866afa6ab597c47f1b72e8fe2b82b97fff5b980f | refs/heads/master | 1,585,598,975,772 | 1,538,659,544,000 | 1,538,659,544,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,265 | lean | import tidy.rewrite_search.core
import tidy.lib.utf8
import system.io
open tidy.rewrite_search
namespace tidy.rewrite_search.tracer.graph
open tactic
open io.process.stdio
def SUCCESS_CHAR : string := "S"
def ERROR_CHAR : string := "E"
def SEARCH_PATHS : list string := [
"_target/deps/lean-tidy/res/graph_trace... |
b2505653cc251aec532472690b588530f8857228 | 1446f520c1db37e157b631385707cc28a17a595e | /tests/compiler/closure_bug5.lean | 524a4554227a44fb90c2ea02869ad48388f8a3c6 | [
"Apache-2.0"
] | permissive | bdbabiak/lean4 | cab06b8a2606d99a168dd279efdd404edb4e825a | 3f4d0d78b2ce3ef541cb643bbe21496bd6b057ac | refs/heads/master | 1,615,045,275,530 | 1,583,793,696,000 | 1,583,793,696,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 538 | lean | def f (x : Nat) : Nat × (Nat → String) :=
let x1 := x + 1;
let x2 := x + 2;
let x3 := x + 3;
let x4 := x + 4;
let x5 := x + 5;
let x6 := x + 6;
let x7 := x + 7;
let x8 := x + 8;
let x9 := x + 9;
let x10 := x + 10;
let x11 := x + 11;
let x12 := x + 12;
let x13 := x + 13;
let x14 := x + 14;
let x15 := x + 15;
let x16 := ... |
8913ca73bdd334a3a66d71b784c4104d9f70c187 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/tactic/slim_check.lean | 90fea73ae418ceb146bd9ea69838c98a304e3f09 | [
"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 | 7,213 | 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 testing.slim_check.testable
/-!
## Finding counterexamples automatically using `slim_check`
A proposition can be tested by writing it out as:
```lean
example (xs ... |
dd90f309aa7298ef6d0908df73a38a5e87dae759 | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /tests/lean/run/group4.lean | 9ac8b8271bdea045c25b5f401686f64710d3c6ad | [
"Apache-2.0"
] | permissive | tjiaqi/lean | 4634d729795c164664d10d093f3545287c76628f | d0ce4cf62f4246b0600c07e074d86e51f2195e30 | refs/heads/master | 1,622,323,796,480 | 1,422,643,069,000 | 1,422,643,069,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,054 | 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
-- algebra.group
-- =============
-- Various structures with 1, *, inv, including groups.
import logic.eq
import data.unit data.sigma data.prod... |
0fc1d44512880716604e9f827d203c3e7442ef13 | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /tests/lean/doSeqRightIssue.lean | 999c456ec8e5c42c3caf82c142da24c8f49a6ec1 | [
"Apache-2.0"
] | permissive | collares/lean4 | 861a9269c4592bce49b71059e232ff0bfe4594cc | 52a4f535d853a2c7c7eea5fee8a4fa04c682c1ee | refs/heads/master | 1,691,419,031,324 | 1,618,678,138,000 | 1,618,678,138,000 | 358,989,750 | 0 | 0 | Apache-2.0 | 1,618,696,333,000 | 1,618,696,333,000 | null | UTF-8 | Lean | false | false | 302 | lean | --
set_option autoBoundImplicitLocal false
universes u
variable {α : Type u}
variable {β : α → Type v}
theorem ex {p₁ p₂ : Sigma (fun a => β a)} (h₁ : p₁.1 = p₂.1) (h : p₁.2 ≅ p₂.2) : p₁ = p₂ :=
match p₁, p₂, h₁, h with
| ⟨_, _⟩, ⟨_, _⟩, rfl, HEq.refl _ => rfl
|
b87089db39322977dac8e078022bfde250f4f6ab | fe25de614feb5587799621c41487aaee0d083b08 | /stage0/src/Lean/Environment.lean | be2dfc68fe3b992df5027034b26de9a2fd50b237 | [
"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 | 34,074 | 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 Std.Data.HashMap
import Lean.ImportingFlag
import Lean.Data.SMap
import Lean.Declaration
import Lean.LocalContext
import Lean.Util.Path
import Lean.U... |
a0191c22c5ebfadd4cbf7041dfd0f20021b01ed3 | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/ring_theory/subsemiring.lean | df933db4679522c81a6eeb9d9f3299fb93df2b21 | [
"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 | 25,021 | lean | /-
Copyright (c) 2020 Yury Kudryashov All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import algebra.ring.prod
import group_theory.submonoid
import data.equiv.ring
/-!
# Bundled subsemirings
We define bundled subsemirings and some standard construc... |
6349edf5bb4729bb8ead129aad10e38241929249 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/data/pi/lex.lean | ef90361179189aa9dc11e6d54daa8e5119221a52 | [
"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 | 5,192 | lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import order.well_founded
import algebra.group.pi
import order.min_max
/-!
# Lexicographic order on Pi types
This file defines the lexicographic order for Pi types. `a`... |
fb7a84113ed4f9388cbd0d5e0e624774db40fcd9 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/data/rat/cast.lean | c1ee9080a2723c89662edab919974611c5f8d36d | [
"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 | 11,950 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import data.rat.order
import data.int.char_zero
/-!
# Casts for Rational Numbers
## Summary
We define the canonical injection from ℚ into an arbitr... |
4c8a43bd5c0f40f99ea95d8249a398c76dbc8b65 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /test/solve_by_elim.lean | 85ce7a1ec07daf38e9d258b4984f38656c7a1cba | [
"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 | 2,700 | 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.solve_by_elim
example {a b : Prop} (h₀ : a → b) (h₁ : a) : b :=
begin
apply_assumption,
apply_assumption,
end
example {X : Type} (x : X)... |
485534f1e3faf9cf51342330c5f6b3b8ce48d559 | fd3506535396cef3d1bdcf4ae5b87c8ed9ff2c2e | /group_theory/hom.lean | 1b13cc000f278133c67d36b300043130f479b3d1 | [
"Apache-2.0"
] | permissive | williamdemeo/leanproved | 77933dbcb8bfbae61a753ae31fa669b3ed8cda9d | d8c2e2ca0002b252fce049c4ff9be0e9e83a6374 | refs/heads/master | 1,598,674,802,432 | 1,437,528,488,000 | 1,437,528,488,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,185 | lean | /-
Copyright (c) 2015 Haitao Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author : Haitao Zhang
-/
import algebra.group data.set .subgroup
namespace group
open algebra
-- ⁻¹ in eq.ops conflicts with group ⁻¹
-- open eq.ops
notation H1 ▸ H2 := eq.subst H1 H2
open set... |
c33c3d41bc3da4770a3709649a372d02ce685679 | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/category_theory/limits/shapes/binary_products.lean | 4bc7e9e1aa16d1b9b27d9c660d359d7cbb2e3498 | [
"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 | 1,116 | 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 category_theory.limits.cones
import category_theory.discrete_category
universes v u
open category_theory
namespace category_theory.limits
@[derive decidabl... |
2c65cab9474dd0d86ce747a38eb313ac25107fd9 | 5f83eb0c32f15aeed5993a3ad5ededb6f31fe7aa | /lean/attic/bitvec-ind/bvaxioms.lean | 3b27d918a3427ee36a2fa87c19532e9e7ca6fc7c | [] | no_license | uw-unsat/jitterbug | 45b54979b156c0f5330012313052f8594abd6f14 | 78d1e75ad506498b585fbac66985ff9d9d05952d | refs/heads/master | 1,689,066,921,433 | 1,687,061,448,000 | 1,688,415,161,000 | 244,440,882 | 46 | 5 | null | null | null | null | UTF-8 | Lean | false | false | 3,518 | lean | -- Theorems for axiomatization:
-- mulhu_comm, mul_decomp, urem_of_sub_mul_udiv
import bv.lemmas
open nat
open bv
open bv.helper
-- mulhu represents the upper bits of the result of a 2n-bit multiplication,
-- by zero-extending two n-bit operands. For example, it can be used to model
-- the behavior of RISC-V's mul... |
65dbae5f67ada28d9424ca1e400422d6c20106a0 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/category/Module/biproducts.lean | ee08a2841074a3bad835466fd7acf7706ff9a17e | [
"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 | 4,447 | lean | /-
Copyright (c) 2022 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import algebra.group.pi
import category_theory.limits.shapes.biproducts
import algebra.category.Module.limits
/-!
# The category of `R`-modules has finite biproducts... |
65a979ff9a82ab0c13da3623b88cf9e7a040c9f4 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/analysis/specific_limits/normed.lean | b03be7f829169a7a22caff1514e0b547427408a1 | [
"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 | 30,250 | lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker, Sébastien Gouëzel, Yury G. Kudryashov, Dylan MacKenzie, Patrick Massot
-/
import analysis.asymptotics.asymptotics
import analysis.specific_limits.basic
/-!
# A co... |
e7fb0331f775188f4b6ff89f804a2ca86c4116a3 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/topology/uniform_space/basic.lean | 1477f9b7b8e96460e907c9d8222b6f0403c99cf8 | [
"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 | 68,585 | 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
-/
import order.filter.lift
import topology.separation
/-!
# Uniform spaces
Uniform spaces are a generalization of metric spaces and top... |
1ea1d59583aec97bbf591947b24930877c49887a | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/topology/locally_constant/basic.lean | 74fb16f7b772e44c757bf3a85bac07d8198b6717 | [
"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 | 15,484 | 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 topology.subset_properties
import topology.connected
import topology.algebra.monoid
import tactic.tfae
import tactic.fin_cases
/-!
# Locally constant function... |
95371b445a0e31ca4ca02a2e7a9d20b020d52602 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/algebraic_card.lean | 1d88761edeca9aea12ec60ad67502385d84091cb | [
"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 | 3,684 | lean | /-
Copyright (c) 2022 Violeta Hernández Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Violeta Hernández Palacios
-/
import data.polynomial.cardinal
import ring_theory.algebraic
/-!
### Cardinality of algebraic numbers
> THIS FILE IS SYNCHRONIZED WITH MATH... |
abaf27668deb0a0451fe249d56937ae6d7028014 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/finset/pi.lean | 84c7a174884e3bdcf2191f958005dfd2a74a53a6 | [
"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 | 4,350 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import data.finset.basic
import data.multiset.pi
/-!
# The cartesian product of finsets
-/
namespace finset
open multiset
/-! ### pi -/
section pi
variables {α : T... |
45cafd541958102ceabd35b7ed43495ac0d7ffb9 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/topology/metric_space/baire.lean | 00d7e92f91d6466d4e0a8ef82efb00fdbe3fc07c | [
"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 | 17,615 | 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.specific_limits.basic
import order.filter.countable_Inter
import topology.G_delta
/-!
# Baire theorem
In a complete metric space, a countable ... |
0ac49200c36bc80f6ab3bd575d9f3a7b9219a749 | d840a2fd78ca0ee1e172fe2cf3751030229b56f3 | /lean_demo/src/solutions/propositons.lean | 6ecb75cb2908da211f13d1d89251bdb330353a92 | [] | no_license | stormymcstorm/VFRust_Presentation | 6e1d3964ce58d97320b36314ae83021bfb55f12d | 90142be25fa032464b3c4e68bc9f152213146254 | refs/heads/main | 1,673,178,849,384 | 1,605,289,504,000 | 1,605,289,504,000 | 312,644,751 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,875 | lean |
-- Shows that logical and is commutative
theorem my_and_comm : ∀ p q, p ∧ q ↔ q ∧ p :=
(
assume p q,
iff.intro
(
assume h: p ∧ q,
show q ∧ p, from and.intro (and.right h) (and.left h)
)
(
assume h: q ∧ p,
show p ∧ q, from and... |
38b509efca5d2217cee7cec3ecdb73e126519692 | 86f6f4f8d827a196a32bfc646234b73328aeb306 | /examples/sets_functions_and_relations/unnamed_1422.lean | 6e377203aca06933be1f240bbf4f8c9f83cfeedb | [] | 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 | 418 | lean | import data.set.basic
open function
variable {α : Type*}
-- BEGIN
theorem Cantor : ∀ f : α → set α, ¬ surjective f :=
begin
intros f surjf,
let S := { i | i ∉ f i},
rcases surjf S with ⟨j, h⟩,
have h₁ : j ∉ f j,
{ intro h',
have : j ∉ f j,
{ by rwa h at h' },
contradiction },
have h₂ : j ∈ ... |
848d20ae26fe517f6fe55789215e368c0339c184 | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /src/builtin/quotient.lean | 7d516229789156b1b3e4f8c54d4d56482df09995 | [
"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 | 5,131 | 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 macros
import subtype
definition reflexive {A : Type} (r : A → A → Bool) := ∀ a, r a a
definition symmetric {A : Type} (r : A → A → Bool) := ∀... |
6a1a422ec49500567d9858eb5c0c2c4dcb830e00 | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /archive/imo/imo2008_q2.lean | 4e86f033aff4b4697e08870da29eb15ac49cb433 | [
"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 | 6,313 | lean | /-
Copyright (c) 2021 Manuel Candales. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Manuel Candales
-/
import data.real.basic
import data.set.basic
import data.set.finite
/-!
# IMO 2008 Q2
(a) Prove that
```
x^2 / (x-1)^2 + y^2 / (y-1)^2 + z^2 / ... |
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