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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
7f1eb27c9295bc42b3b14038a498a56890b058c2 | 77c5b91fae1b966ddd1db969ba37b6f0e4901e88 | /src/data/nat/choose/basic.lean | 17a7051e63454fe5b0942153ddc4e2c09394f9af | [
"Apache-2.0"
] | permissive | dexmagic/mathlib | ff48eefc56e2412429b31d4fddd41a976eb287ce | 7a5d15a955a92a90e1d398b2281916b9c41270b2 | refs/heads/master | 1,693,481,322,046 | 1,633,360,193,000 | 1,633,360,193,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,496 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Bhavik Mehta
-/
import data.nat.factorial.basic
/-!
# Binomial coefficients
This file defines binomial coefficients and proves simple lemmas (i.e. those not
requiring mor... |
c8cbc2be2d3251c0170145d88290bf5910fb6a09 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/group_theory/congruence.lean | bf450ce3ba6aea600f39d7e68f685eec9dea9e3b | [
"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 | 44,950 | lean | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
import data.setoid.basic
import algebra.group.pi
import algebra.group.prod
import data.equiv.mul_add
import group_theory.submonoid.operations
/-!
# Congruence ... |
1417b6a2ead032b4670c53af25a6b4f9e531e5b7 | 8c95816d6379a6864848d68ce735a5700c1cbbc3 | /src/smt2/builder.lean | 35cf7eadbeb6334f5db46060f658bdc429e3975b | [
"Apache-2.0"
] | permissive | aqjune/smt2_interface | f00ed0a4317d7c9112deb0806c8e89e6512a901e | 598848a7a6fa47520fadcfe1b16891053a296084 | refs/heads/master | 1,631,518,664,718 | 1,524,489,340,000 | 1,524,489,340,000 | 115,204,811 | 0 | 0 | null | 1,514,043,428,000 | 1,514,043,427,000 | null | UTF-8 | Lean | false | false | 4,850 | lean | import .syntax
@[reducible] def smt2.builder :=
except_t string (state (list smt2.cmd))
instance smt2.builder.monad : monad smt2.builder :=
by apply_instance
meta def smt2.builder.to_format {α : Type} (build : smt2.builder α) : format :=
format.join $ list.intersperse "\n" $ (list.map to_fmt $ (build.run.run []).snd... |
8db321321ba66d834b3bdc9d9d28bb1430f3b73b | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/mv_polynomial/comap.lean | d7e2f2437108584231d8a239e1458b5481c81c00 | [] | 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 | 3,594 | 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.mv_polynomial.rename
import Mathlib.PostPort
universes u_1 u_2 u_4 u_3
namespace Ma... |
f0c3ef413abd1f2e6baa9b70d9e401768168e10b | b2fe74b11b57d362c13326bc5651244f111fa6f4 | /src/data/real/nnreal.lean | 827598b3225bf1a3f8ee89d44917133de238a90d | [
"Apache-2.0"
] | permissive | midfield/mathlib | c4db5fa898b5ac8f2f80ae0d00c95eb6f745f4c7 | 775edc615ecec631d65b6180dbcc7bc26c3abc26 | refs/heads/master | 1,675,330,551,921 | 1,608,304,514,000 | 1,608,304,514,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 29,177 | lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import algebra.linear_ordered_comm_group_with_zero
import algebra.big_operators.ring
import data.real.basic
import data.indicator_function
/-!
# Nonnegative real num... |
269b79f0b381fc0adaec0d93a6264faea8be24bc | ac2987d8c7832fb4a87edb6bee26141facbb6fa0 | /Mathlib/Algebra/Group/Basic.lean | 435990243a3d75111ef216c0f83864a32928770f | [
"Apache-2.0"
] | permissive | AurelienSaue/mathlib4 | 52204b9bd9d207c922fe0cf3397166728bb6c2e2 | 84271fe0875bafdaa88ac41f1b5a7c18151bd0d5 | refs/heads/master | 1,689,156,096,545 | 1,629,378,840,000 | 1,629,378,840,000 | 389,648,603 | 0 | 0 | Apache-2.0 | 1,627,307,284,000 | 1,627,307,284,000 | null | UTF-8 | Lean | false | false | 1,397 | lean | import Mathlib.Algebra.Group.Defs
import Mathlib.Logic.Basic
section AddCommSemigroup_lemmas
variable {A : Type u} [AddCommSemigroup A]
lemma add_left_comm (a b c : A) : a + (b + c) = b + (a + c) :=
by rw [← add_assoc, add_comm a, add_assoc]
lemma add_right_comm (a b c : A) : a + b + c = a + c + b :=
by rw [add_ass... |
00bc2c5713353dbee573747e55bc66db742e9705 | bd30ef9a38da5172e55165b5cf19d92706763afa | /src/array_perm_group.lean | ffbb8132ae9efbe31b7c0c550874bf1a0b15cc9a | [] | no_license | kendfrey/rubiks-cube-group | 8838ce34704d8d150e5feba6f1e536b3d228dd37 | 3baebd73972384294931c75d584a491eb0fbc15c | refs/heads/master | 1,671,557,772,358 | 1,601,554,362,000 | 1,601,554,362,000 | 285,715,961 | 21 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,549 | lean | import algebra.group
import data.equiv.basic
import array_group
open equiv
section perm_array
parameters {n : ℕ} {α : Type*}
@[simp] private lemma array.read_def {f : fin n → α} {i : fin n} : array.read { data := f } i = f i := rfl
def perm_array (a : array n α) (p : perm (fin n)) : array n α := ⟨a.read ∘ p.... |
97f1327d2a386b48e0dd81d8a55266ec6f790e72 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /tests/lean/run/1308.lean | 86f28e6f18505d767c6e92fc78d63a736c6b0a6e | [
"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 | 157 | lean | @[defaultInstance high] instance : HPow R Nat R where hPow a _ := a
example (x y : Nat) : (x + y) ^ 3 = x ^ 3 + y ^ 3 + 3 * (x * y ^ 2 + x ^ 2 * y) := sorry
|
bb02b3ad25e947a320d957dd98801c93e3e26d92 | 82b86ba2ae0d5aed0f01f49c46db5afec0eb2bd7 | /stage0/src/Std/ShareCommon.lean | bf35e1f5a9dafde73b708c53d07db4024c27f377 | [
"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 | 6,648 | 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 Std.Data.HashSet
import Std.Data.HashMap
import Std.Data.PersistentHashMap
import Std.Data.PersistentHashSet
namespace Std
universes u v
namespace S... |
9e7a6fa3fbade05f4b31c9f827e37800047239ce | acc85b4be2c618b11fc7cb3005521ae6858a8d07 | /data/seq/seq.lean | a46f0f982ec1b8f92f09c91ba5b6a4e6fdac8864 | [
"Apache-2.0"
] | permissive | linpingchuan/mathlib | d49990b236574df2a45d9919ba43c923f693d341 | 5ad8020f67eb13896a41cc7691d072c9331b1f76 | refs/heads/master | 1,626,019,377,808 | 1,508,048,784,000 | 1,508,048,784,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 21,998 | lean | import data.stream data.lazy_list data.seq.computation logic.basic
universes u v w
/-
coinductive seq (α : Type u) : Type u
| nil : seq α
| cons : α → seq α → seq α
-/
def seq (α : Type u) : Type u := { f : stream (option α) // ∀ {n}, f n = none → f (n+1) = none }
def seq1 (α) := α × seq α
namespace seq
variables {... |
5729d8b02408c250b1dda13484df9341a9a99ec6 | 958488bc7f3c2044206e0358e56d7690b6ae696c | /lean/tacticComb.lean | 4d6ceb81016d740ee2257038646db424d5074522 | [] | 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 | 2,326 | lean | lemma L1 : ∀ (p q:Prop), p → p ∨ q :=
begin intros p q H, left, assumption end
--#check L1
lemma L2 : ∀ (p q:Prop), p → p ∨ q :=
assume p q (H : p), by {left, assumption}
--#check L2
lemma L3 : ∀ (p q:Prop), p → q → p ∧ q :=
assume p q Hp Hq, by {split; assumption}
--#check L3
lemma L4 : ∀ (p q:Prop), p → p... |
17dbb7d4181b55bc9fba8e18a67fe7cdb1d54600 | 3ed5a65c1ab3ce5d1a094edce8fa3287980f197b | /src/herstein/ex1_1/Q_08.lean | 0d22421211c20a5a5f79afe57d10ff11470639a8 | [] | no_license | group-study-group/herstein | 35d32e77158efa2cc303c84e1ee5e3bc80831137 | f5a1a72eb56fa19c19ece0cb3ab6cf7ffd161f66 | refs/heads/master | 1,586,202,191,519 | 1,548,969,759,000 | 1,548,969,759,000 | 157,746,953 | 0 | 0 | null | 1,542,412,901,000 | 1,542,302,366,000 | Lean | UTF-8 | Lean | false | false | 565 | lean | import data.set.basic data.finset
variable α: Type*
variables A B C: set α
open set
-- requires classical logic?
theorem Q8: (A - B) ∪ (B - A) = (A ∪ B) - (A ∩ B) :=
ext $ λ x,
⟨λ hl,
⟨or.elim hl
(λ hab, or.inl hab.1)
(λ hba, or.inr hba.1),
λ ⟨ha, hb⟩, or.elim hl
(λ hab, hab.2 hb)
... |
6c2e248cfcb05f2a754e03ace11c1244d6c261b5 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/list/palindrome.lean | 74d22c24122dda21b5ae1458a7ec095abf1d97ca | [
"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 | 2,296 | lean | /-
Copyright (c) 2020 Google LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Wong
-/
import data.list.basic
/-!
# Palindromes
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
This module defines... |
3a81e6186d044b7a172e1ccde8f171f0729b5efd | 4727251e0cd73359b15b664c3170e5d754078599 | /src/control/fix.lean | 839187dc350dff95fd9e1243f2b00c9c24f6f360 | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 3,244 | lean | /-
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import data.stream.init
import data.part
import data.nat.upto
/-!
# Fixed point
This module defines a generic `fix` operator for defining recursive
computations that are... |
3ccc1564ab8429861a03a35e70b51e17bec3d59a | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/probability/martingale/upcrossing.lean | 473fa98d7aa0c2f73c8a1fbd7046e6599276a6e6 | [
"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 | 41,414 | lean | /-
Copyright (c) 2022 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import probability.hitting_time
import probability.martingale.basic
/-!
# Doob's upcrossing estimate
Given a discrete real-valued submartingale $(f_n)_{n \in \mathbb{N}}... |
79f4eeb00e25d0e91a27f79e864fb04ea703159e | 29cc89d6158dd3b90acbdbcab4d2c7eb9a7dbf0f | /Exercises week 6/23_homework_sheet.lean | 71063c69e9defa1d94c7a636b295a0245938c8c6 | [] | no_license | KjellZijlemaker/Logical_Verification_VU | ced0ba95316a30e3c94ba8eebd58ea004fa6f53b | 4578b93bf1615466996157bb333c84122b201d99 | refs/heads/master | 1,585,966,086,108 | 1,549,187,704,000 | 1,549,187,704,000 | 155,690,284 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,144 | lean | /- Homework 2.3: Functional Programming — Monads -/
namespace homework
/- Question 1: `map` for monads
Define `map` for monads. This is the generalization of `map` on lists. Use the monad operations to
define `map`. The _functorial properties_ (`map_id` and `map_map`) are derived from the monad laws.
This time, we... |
edb3d19734821c32495e2af707196f43cfbe1bfe | 6b45072eb2b3db3ecaace2a7a0241ce81f815787 | /data/num/lemmas.lean | 783cbd70f230df4006ffb62a9b8d9b336e13c3fe | [] | 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 | 20,204 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
Properties of the binary representation of integers.
-/
import .basic .bitwise pending
meta def unfold_coe : tactic unit :=
`[unfold coe lift_t has_lift_t.lift c... |
0aa4272510e9417c9cda3dcb187bce7db8074a0c | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/direct_sum/internal.lean | dc481b292617336b5cb809ccff3e378361fe40c7 | [
"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 | 14,309 | lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Kevin Buzzard, Jujian Zhang
-/
import algebra.algebra.operations
import algebra.algebra.subalgebra.basic
import algebra.direct_sum.algebra
/-!
# Internally graded rings and... |
656a760dd08676be6a091e826336239ec212eff1 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/measure_theory/measure/measure_space.lean | 800a0da32ee4a4b1373faef46e654d299a66b37f | [
"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 | 134,427 | 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.measure.measure_space_def
import measure_theory.measurable_space
/-!
# Measure spaces
The definition of a measure and a measur... |
063f796dfd65c58e37f1888b7b800fe04af2651b | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/blast_ematch_ss1.lean | 7bbd92380835f55db926632b4fa7e1776e8ebb14 | [
"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 | 329 | lean | constant q (a : Prop) (h : decidable a) : Prop
constant r : nat → Prop
constant rdec : ∀ a, decidable (r a)
constant s : nat → nat
axiom qax : ∀ a h, (: q (r (s a)) h :)
attribute qax [forward]
set_option blast.strategy "ematch"
definition ex1 (a : nat) (b : nat) : b = s a → q (r b) (rdec b) :=
by blast
print ex1
|
cf6dfadb6516364e5204f6b805454cca75534279 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/measure_theory/measure/with_density_vector_measure.lean | 0c3e962978718f4c4de5784d875636392d788284 | [
"Apache-2.0"
] | permissive | hikari0108/mathlib | b7ea2b7350497ab1a0b87a09d093ecc025a50dfa | a9e7d333b0cfd45f13a20f7b96b7d52e19fa2901 | refs/heads/master | 1,690,483,608,260 | 1,631,541,580,000 | 1,631,541,580,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,647 | lean | /-
Copyright (c) 2021 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import measure_theory.measure.vector_measure
import measure_theory.function.ae_eq_of_integral
/-!
# Vector measure defined by an integral
Given a measure `μ` and an inte... |
ff1257d472c82f5ee0b456f03baf4f208664b505 | 8aabfc0cb7ee877354be18461793fa0a16e8c624 | /src/first_proofs.lean | 78d3284ac04bc1d67b8a8413d4f323b505a90cc1 | [
"Apache-2.0"
] | permissive | dwrensha/tutorials | f2596cf6f4a408d553bb4947f37b7960f8141b29 | e6f872936c222b06bf13d4fb7e3a41d43da9c338 | refs/heads/master | 1,600,265,863,399 | 1,573,904,974,000 | 1,573,904,974,000 | 223,796,679 | 0 | 0 | null | 1,574,623,038,000 | 1,574,623,037,000 | null | UTF-8 | Lean | false | false | 17,965 | lean | /-
This file is intended for Lean beginners. The goal is to demonstrate what it feels like to prove
things using Lean and mathlib. Complicated definitions and theory building are not covered.
-/
-- We want real numbers and their basic properties
import data.real.basic
-- We want to be able to define functions using t... |
67a4b5f68eb524a5aba2dcf0dc05149d29e270dd | 02005f45e00c7ecf2c8ca5db60251bd1e9c860b5 | /src/data/fintype/card.lean | ab992f6a0af9fe4faf9a56ad38ee41760aa2226d | [
"Apache-2.0"
] | permissive | anthony2698/mathlib | 03cd69fe5c280b0916f6df2d07c614c8e1efe890 | 407615e05814e98b24b2ff322b14e8e3eb5e5d67 | refs/heads/master | 1,678,792,774,873 | 1,614,371,563,000 | 1,614,371,563,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 17,200 | 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.ring
/-!
Results about "big operations" over a `fintype`, and consequent
results about cardinalities of certain... |
1a0d4058278bc3d12de46bda30ae78166b23bfd5 | 8c9f90127b78cbeb5bb17fd6b5db1db2ffa3cbc4 | /succ_over_eq.lean | 162f73a007861aa03075a723eba3b82e619ec726 | [] | no_license | picrin/lean | 420f4d08bb3796b911d56d0938e4410e1da0e072 | 3d10c509c79704aa3a88ebfb24d08b30ce1137cc | refs/heads/master | 1,611,166,610,726 | 1,536,671,438,000 | 1,536,671,438,000 | 60,029,899 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 418 | lean | inductive natural : Type
| zero : natural
| succ : natural -> natural
lemma succ_over_equality (a b : natural) (H : a = b) : (natural.succ a) = (natural.succ b) :=
eq.rec_on H (eq.refl (natural.succ a))
--eq.rec_on H rfl
--eq.subst H rfl
--eq.subst H (eq.refl (natural.succ a))
--congr_arg (λ (n : ... |
6a8bad30c3fd139a052c0a4d732702f20fcceea9 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/algebra/associated.lean | 3d32871c7b471a1735d18d3c718146f1155e0124 | [
"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 | 25,440 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker
-/
import algebra.group.is_unit data.multiset
/-!
# Associated, prime, and irreducible elements.
-/
variables {α : Type*} {β : Type*} {γ : Type*} {δ : ... |
983427f055fa9bc69150d3e7d2d9c403c75e7a08 | 2bafba05c98c1107866b39609d15e849a4ca2bb8 | /src/week_8/ideas/Part_D_boundary_map.lean | 393368d1a95a52b6bfc8e41d0c019e498ac62be0 | [
"Apache-2.0"
] | permissive | ImperialCollegeLondon/formalising-mathematics | b54c83c94b5c315024ff09997fcd6b303892a749 | 7cf1d51c27e2038d2804561d63c74711924044a1 | refs/heads/master | 1,651,267,046,302 | 1,638,888,459,000 | 1,638,888,459,000 | 331,592,375 | 284 | 24 | Apache-2.0 | 1,669,593,705,000 | 1,611,224,849,000 | Lean | UTF-8 | Lean | false | false | 3,180 | lean | import week_8.ideas.Part_C_H1
/-
# Boundary maps
If 0 → A → B → C → 0 is exact, we want
a boundary map `H0 G C →+ H1 G A`
We're going to use the axiom of choice in our definition.
Whenever we invoke the axiom of choice we are using something
noncomputable, so it's important that we make a proper API
for the object w... |
a18f0c4baae2e916767741c1cc82c3f3c0f79fa4 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /counterexamples/cyclotomic_105.lean | 1bddc4c4f722470beee6db627355c3acbcbfbd4a | [
"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 | 3,956 | lean | /-
Copyright (c) 2021 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
import ring_theory.polynomial.cyclotomic
/-!
# Not all coefficients of cyclotomic polynomials are -1, 0, or 1
We show that not all coefficients of cyclotomic pol... |
530701fb81490a16b8b2637de3fb7bfd4a2cb1a7 | b3fced0f3ff82d577384fe81653e47df68bb2fa1 | /src/topology/algebra/open_subgroup.lean | acbb437fc2664bd6bbaa41db99d14849a5ae3de0 | [
"Apache-2.0"
] | permissive | ratmice/mathlib | 93b251ef5df08b6fd55074650ff47fdcc41a4c75 | 3a948a6a4cd5968d60e15ed914b1ad2f4423af8d | refs/heads/master | 1,599,240,104,318 | 1,572,981,183,000 | 1,572,981,183,000 | 219,830,178 | 0 | 0 | Apache-2.0 | 1,572,980,897,000 | 1,572,980,896,000 | null | UTF-8 | Lean | false | false | 5,928 | lean | import order.filter.lift
import linear_algebra.basic
import topology.opens topology.algebra.ring
section
open topological_space
variables (G : Type*) [group G] [topological_space G]
/-- The type of open subgroups of a topological group. -/
@[to_additive open_add_subgroup]
def open_subgroup := { U : set G // is_open U... |
1fa59f766b1fc066fbd043a19743b939328c08be | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/group_theory/perm/basic.lean | 02f99f3bce4249a4ebdb865d4b0645edd62ebdee | [
"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 | 15,762 | 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 algebra.group.pi
import algebra.group_power.lemmas
import logic.function.iterate
/-!
# The group of permutations (self-equivalences)... |
a9e8738357979e9c5136012e398e73da4e166fbd | 432d948a4d3d242fdfb44b81c9e1b1baacd58617 | /src/order/boolean_algebra.lean | 9dfb8e92afd8f92d2977b243715832f26b1da533 | [
"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 | 31,567 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Bryan Gin-ge Chen
-/
import order.bounded_lattice
/-!
# (Generalized) Boolean algebras
A Boolean algebra is a bounded distributive lattice with a complement operator. ... |
301e5c00855731e4ec1fb65678facc3ca0492bc5 | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/measure_theory/function/special_functions.lean | 2b27694345231fede6b3a415aace4d0ab9dc472c | [
"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 | 9,537 | 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 analysis.special_functions.pow
import analysis.special_functions.trigonometric.arctan
import analysis.inner_product_space.calculus
import measure_theory.con... |
6994482205c274ece97cd1bb88797f15815b8a0a | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/stackoverflow/tactic2.lean | c17fef84114579ea65e2dd28a9abc45a0f145b3b | [
"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 | 70 | lean | Theorem T (a : Bool) : a.
apply (** REPEAT(id_tac) **).
done.
|
d914029da59bb8b91ad33b1c2997ea4d1a56cc97 | f3a5af2927397cf346ec0e24312bfff077f00425 | /src/game/world3/level9.lean | d9bb2fdd23ea5e70086a907de24b82093f96da9b | [
"Apache-2.0"
] | permissive | ImperialCollegeLondon/natural_number_game | 05c39e1586408cfb563d1a12e1085a90726ab655 | f29b6c2884299fc63fdfc81ae5d7daaa3219f9fd | refs/heads/master | 1,688,570,964,990 | 1,636,908,242,000 | 1,636,908,242,000 | 195,403,790 | 277 | 84 | Apache-2.0 | 1,694,547,955,000 | 1,562,328,792,000 | Lean | UTF-8 | Lean | false | false | 1,219 | lean | import game.world3.level8 -- hide
import mynat.mul -- hide
namespace mynat -- hide
/-
# Multiplication World
## Level 9: `mul_left_comm`
You are equipped with
* `mul_assoc (a b c : mynat) : (a * b) * c = a * (b * c)`
* `mul_comm (a b : mynat) : a * b = b * a`
Re-read the docs for `rw` so you know all the tricks.
Y... |
b1298d660771cdc01b735f46ac31448da6b76713 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/tactic/transform_decl.lean | 8f1296bf7d948d18144fd332bb9105a92f6d69a3 | [
"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 | 7,910 | lean | /-
Copyright (c) 2017 Mario Carneiro All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Floris van Doorn
-/
import tactic.core
namespace tactic
/-- `copy_attribute' attr_name src tgt p d_name` copy (user) attribute `attr_name` from
`src` to `tgt` if it... |
fa349a208f85502897791cc17507e09904cbcaf8 | 4bcaca5dc83d49803f72b7b5920b75b6e7d9de2d | /stage0/src/Lean/Parser/Do.lean | 94c60efe3152ea7ee47c9be9db68afa7cef77464 | [
"Apache-2.0"
] | permissive | subfish-zhou/leanprover-zh_CN.github.io | 30b9fba9bd790720bd95764e61ae796697d2f603 | 8b2985d4a3d458ceda9361ac454c28168d920d3f | refs/heads/master | 1,689,709,967,820 | 1,632,503,056,000 | 1,632,503,056,000 | 409,962,097 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,260 | 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.Parser.Term
namespace Lean
namespace Parser
builtin_initialize registerBuiltinParserAttribute `builtinDoElemParser `doElem
builtin_initialize ... |
0b0d4eab2c719df07dfc429769d4057b69b44ec0 | 6fca17f8d5025f89be1b2d9d15c9e0c4b4900cbf | /src/game/world1/level1.lean | e9f9595f2248130bb62ffd878ae5ad0d5f489594 | [
"Apache-2.0"
] | permissive | arolihas/natural_number_game | 4f0c93feefec93b8824b2b96adff8b702b8b43ce | 8e4f7b4b42888a3b77429f90cce16292bd288138 | refs/heads/master | 1,621,872,426,808 | 1,586,270,467,000 | 1,586,270,467,000 | 253,648,466 | 0 | 0 | null | 1,586,219,694,000 | 1,586,219,694,000 | null | UTF-8 | Lean | false | false | 3,781 | lean | import mynat.definition -- imports the natural numbers {0,1,2,3,4,...}.
import mynat.add -- imports definition of addition on the natural numbers.
import mynat.mul -- imports definition of multiplication on the natural numbers.
namespace mynat -- hide
-- World name : Tutorial world
/-
# Tutorial World
## Level 1: t... |
db712d3f9da79727971e4df09e3e83886d80a0e7 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/match_expr.lean | c86e784aea8f2702179bf47c711a48190a493c91 | [
"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 | 407 | lean | open tactic
axiom Sorry : ∀ {A:Type*}, A
example (a b c : nat) (h₀ : c > 0) (h₁ : a > 1) (h₂ : b > 0) : a + b + c = 0 :=
by do
[x, y] ← match_target_subexpr `(λ x y : nat, x + y) | failed,
trace "------ subterms -------",
trace x, trace y,
(h, [z]) ← match_hypothesis `(λ x : nat, x > 1) | failed,
trace "--- ... |
97064f172c52b29acf51336884f416090c026d30 | 36c7a18fd72e5b57229bd8ba36493daf536a19ce | /hott/types/univ.hlean | 720e37fada740d37d23e7bb87a5d3f802f088824 | [
"Apache-2.0"
] | permissive | YHVHvx/lean | 732bf0fb7a298cd7fe0f15d82f8e248c11db49e9 | 038369533e0136dd395dc252084d3c1853accbf2 | refs/heads/master | 1,610,701,080,210 | 1,449,128,595,000 | 1,449,128,595,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,894 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Floris van Doorn
Theorems about the universe
-/
-- see also init.ua
import .bool .trunc .lift .pullback
open is_trunc bool lift unit eq pi equiv equiv.ops sum sigma fiber prod pul... |
489b80d1b5ce77011b969ce0914c22423b4e3be1 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/algebra/category/Mon/limits.lean | d373283921bdea2f01e06eaff96c9a8facc84e3b | [
"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 | 6,594 | 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 algebra.group.pi
import algebra.category.Mon.basic
import category_theory.limits.types
import category_theory.limits.creates
/-!
# The category of (commutativ... |
945337e9d2722832121dbc2992c4e38ab835e605 | 9db059bff49b1090a86ec0050ac6c577eb16ac67 | /src/meetings/topology.lean | d8a2570f410fa01a83f282418c24b6c982671348 | [] | no_license | fpvandoorn/Harvard-tutoring | d64cd75c4c529009ee562c30e9cb245fe237e760 | a8846c08e32cdc7b91a7e28adfa5d9b2810088b0 | refs/heads/master | 1,680,870,428,641 | 1,617,022,194,000 | 1,617,022,194,000 | 330,297,467 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,938 | lean | import tactic
import analysis.special_functions.trigonometric
/-
# Topology in Lean
In this and the next meetings we will discuss how to do various areas of math in mathlib.
We will start with topology.
-/
noncomputable theory
open set topological_space filter
open_locale topological_space filter big_operators classi... |
9a05ebb9de36c14fedff903871173eb9ff16178a | 856e2e1615a12f95b551ed48fa5b03b245abba44 | /src/algebra/pointwise.lean | 996ff9a035279cb4e1f63daf06406adc6d6fa1b2 | [
"Apache-2.0"
] | permissive | pimsp/mathlib | 8b77e1ccfab21703ba8fbe65988c7de7765aa0e5 | 913318ca9d6979686996e8d9b5ebf7e74aae1c63 | refs/heads/master | 1,669,812,465,182 | 1,597,133,610,000 | 1,597,133,610,000 | 281,890,685 | 1 | 0 | null | 1,595,491,577,000 | 1,595,491,576,000 | null | UTF-8 | Lean | false | false | 13,538 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Floris van Doorn
-/
import algebra.module
import data.set.finite
/-!
# Pointwise addition, multiplication, and scalar multiplication of sets.
This file defines pointw... |
41ef53ac0fe603786715045fb521c8f44e6881cd | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/ring_theory/filtration.lean | b037c0da93ecb179629f5bbab546d1766e85b0e5 | [
"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 | 17,167 | lean | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import ring_theory.ideal.local_ring
import ring_theory.noetherian
import ring_theory.rees_algebra
import ring_theory.finiteness
import data.polynomial.module
import order.h... |
234f574d359effc224273e430a8ff0adfe080a7a | 50b3917f95cf9fe84639812ea0461b38f8f0dbe1 | /Examples/well_founded_lists.lean | 5733dec0d9cc7f747e4efe44625dde7129a2e284 | [] | no_license | roro47/xena | 6389bcd7dcf395656a2c85cfc90a4366e9b825bb | 237910190de38d6ff43694ffe3a9b68f79363e6c | refs/heads/master | 1,598,570,061,948 | 1,570,052,567,000 | 1,570,052,567,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 543 | lean | import data.equiv.basic
namespace xena
inductive W (L : Type) (A : L → Type) : Type
| Node : ∀ (lbl : L), (A lbl → W) → W
def nat := W bool (λ b, bool.rec empty unit b)
def list (L : Type) :=
W (option L) (λ l, option.rec_on l empty (λ _, unit))
end xena
example : equiv nat xena.nat :=
{ to_fun := λ n, nat.rec_on... |
5f5a345b4b66e88c1a86c7707b1f8c3bbb5faf16 | ac2987d8c7832fb4a87edb6bee26141facbb6fa0 | /Mathlib/Data/ByteArray.lean | d784e7c7c3a05127f79cb32d5ab881db24add9cc | [
"Apache-2.0"
] | permissive | AurelienSaue/mathlib4 | 52204b9bd9d207c922fe0cf3397166728bb6c2e2 | 84271fe0875bafdaa88ac41f1b5a7c18151bd0d5 | refs/heads/master | 1,689,156,096,545 | 1,629,378,840,000 | 1,629,378,840,000 | 389,648,603 | 0 | 0 | Apache-2.0 | 1,627,307,284,000 | 1,627,307,284,000 | null | UTF-8 | Lean | false | false | 4,165 | lean | import Mathlib.Data.Nat.Basic
import Mathlib.Data.Char
import Mathlib.Data.UInt
/-- A terminal byte slice, a suffix of a byte array. -/
structure ByteSliceT := (arr : ByteArray) (off : Nat)
namespace ByteSliceT
/-- The number of elements in the byte slice. -/
@[inline] def size (self : ByteSliceT) : Nat := self.arr.... |
4fc305e1d83674f8d02dac0d6abd67c785346578 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /tests/lean/warningAsError.lean | cd35d1f68806d8c53d7c5d7fb7e2dfd64da9cb4c | [
"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 | 217 | lean | def f (x : Nat) := x + 1
@[deprecated f]
def g (x : Nat) := x + 1
#eval g 0 -- warning
set_option warningAsError true
#eval g 0 -- error
set_option linter.unusedVariables true
def h (unused : Nat) := 0 -- error
|
babf2a4bd62ad11ce89dbdf1cb4517a1d8efaae1 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/ring_theory/int/basic.lean | c09fd91e8fc6727178c0a9e0f165360177fac971 | [
"Apache-2.0"
] | permissive | Lix0120/mathlib | 0020745240315ed0e517cbf32e738d8f9811dd80 | e14c37827456fc6707f31b4d1d16f1f3a3205e91 | refs/heads/master | 1,673,102,855,024 | 1,604,151,044,000 | 1,604,151,044,000 | 308,930,245 | 0 | 0 | Apache-2.0 | 1,604,164,710,000 | 1,604,163,547,000 | null | UTF-8 | Lean | false | false | 11,961 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker, Aaron Anderson
-/
import data.int.gcd
import ring_theory.multiplicity
import ring_theory.principal_ideal_domain
/-!
# Divisibility over ℕ and ℤ
This ... |
3840ddcce19ff71c52506186ce464648ce5d6006 | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /stage0/src/Lean/Meta/SortLocalDecls.lean | df39bf5ede64a4329477ff6be00eff3c8e635f50 | [
"Apache-2.0"
] | permissive | WojciechKarpiel/lean4 | 7f89706b8e3c1f942b83a2c91a3a00b05da0e65b | f6e1314fa08293dea66a329e05b6c196a0189163 | refs/heads/master | 1,686,633,402,214 | 1,625,821,189,000 | 1,625,821,258,000 | 384,640,886 | 0 | 0 | Apache-2.0 | 1,625,903,617,000 | 1,625,903,026,000 | null | UTF-8 | Lean | false | false | 1,785 | 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.Basic
namespace Lean.Meta
namespace SortLocalDecls
structure Context where
localDecls : NameMap LocalDecl := {}
structure State where... |
8f5fb310d81fea46af6e194418871f46ceac55ae | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/measure_theory/giry_monad.lean | b20c52f9866cdc8576fcbe40f0b7e0cd089a606c | [
"Apache-2.0"
] | permissive | Lix0120/mathlib | 0020745240315ed0e517cbf32e738d8f9811dd80 | e14c37827456fc6707f31b4d1d16f1f3a3205e91 | refs/heads/master | 1,673,102,855,024 | 1,604,151,044,000 | 1,604,151,044,000 | 308,930,245 | 0 | 0 | Apache-2.0 | 1,604,164,710,000 | 1,604,163,547,000 | null | UTF-8 | Lean | false | false | 8,188 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import measure_theory.integration
/-!
# The Giry monad
Let X be a measurable space. The collection of all measures on X again
forms a measurable space. This constru... |
69dc3b034aa55a67b1f78b53aa35b6da702a01ec | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/algebra/infinite_sum/real.lean | 3db37b9ec67705c975185ae8a483721576ce46c9 | [
"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 | 4,256 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Yury Kudryashov
-/
import algebra.big_operators.intervals
import topology.algebra.infinite_sum.order
import topology.instances.real
/-!
# Infinite sum in the rea... |
20285250856b6758c0eb2a892f9062f486cb80fe | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/int/order/lemmas.lean | 658dd4abab57b1f3c50d3dac536e280bea47d2c8 | [
"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 | 2,044 | 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 algebra.group_with_zero.divisibility
import algebra.order.ring.abs
/-!
# Further lemmas about the integers
The distinction between t... |
0495ed8f5038793cb318eb0b85853c7b8d6712bf | 4fa118f6209450d4e8d058790e2967337811b2b5 | /src/sheaves/opens.lean | f0be9ad22acbdbec08ec8a5ba00859a59fd35432 | [
"Apache-2.0"
] | permissive | leanprover-community/lean-perfectoid-spaces | 16ab697a220ed3669bf76311daa8c466382207f7 | 95a6520ce578b30a80b4c36e36ab2d559a842690 | refs/heads/master | 1,639,557,829,139 | 1,638,797,866,000 | 1,638,797,866,000 | 135,769,296 | 96 | 10 | Apache-2.0 | 1,638,797,866,000 | 1,527,892,754,000 | Lean | UTF-8 | Lean | false | false | 1,936 | lean | /-
Basic definitions and lemmas about opens.
TODO : Not use opens as sets when possible.
Author: Ramon Fernandez Mir
-/
import topology.basic
import topology.opens
universes u v
open topological_space lattice lattice.lattice
section opens
variables {α : Type u} [topological_space α]
-- A couple of useful ... |
2ac716820e79ba15b03f5d855cb58ac43e0a66c1 | 432d948a4d3d242fdfb44b81c9e1b1baacd58617 | /src/algebra/group_ring_action.lean | d1cdf3676f663b064e122a81205525768b3c691f | [
"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 | 5,544 | 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 group_theory.group_action.group
import data.equiv.ring
import deprecated.subring
/-!
# Group action on rings
This file defines the typeclass of monoid acting on semir... |
70b4083e55110c9395e30febd61b80ce16e43c82 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/analysis/analytic/inverse.lean | 91a9a365f5f3a0dbdf1b7ff79db9ad94d4fce07c | [
"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 | 27,270 | lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import analysis.analytic.composition
import tactic.congrm
/-!
# Inverse of analytic functions
We construct the left and right inverse of a formal multilinear ... |
8609d80d28c0cb0ec128bcc1439ea0e6fe62d492 | 432d948a4d3d242fdfb44b81c9e1b1baacd58617 | /src/tactic/aesop/default.lean | 930f687b7fb4d579929ddf4dad16d77f1d535418 | [
"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 | 436 | lean | /-
Copyright (c) 2021 Jannis Limperg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jannis Limperg
-/
import tactic.aesop.search
/-!
# Aesop, a general-purpose proof search tactic
-/
namespace tactic
export aesop (aesop)
namespace interactive
open interactive (p... |
d8be4faa7ad448694fea535b390e17ee96645ef0 | 36c7a18fd72e5b57229bd8ba36493daf536a19ce | /tests/lean/run/blast_simp1.lean | cb290d523fd1fdc8c9ecee7599c20f893aca00db | [
"Apache-2.0"
] | permissive | YHVHvx/lean | 732bf0fb7a298cd7fe0f15d82f8e248c11db49e9 | 038369533e0136dd395dc252084d3c1853accbf2 | refs/heads/master | 1,610,701,080,210 | 1,449,128,595,000 | 1,449,128,595,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 416 | lean | example (a b c : Prop) : a ∧ b ∧ c ↔ c ∧ b ∧ a :=
by blast
example (a b c : Prop) : a ∧ false ∧ c ↔ false :=
by blast
example (a b c : Prop) : a ∨ false ∨ b ↔ b ∨ a :=
by blast
example (a b c : Prop) : ¬ true ∨ false ∨ b ↔ b :=
by blast
example (a b c : Prop) : if true then a else b ↔ if false then b else a :=
by b... |
a38b1de91cec37a315cc3d957f669332bf27015e | 4f065978c49388d188224610d9984673079f7d91 | /zorn.lean | 988ae425d3e5e108f7e0b4fad4672e4e40160474 | [] | 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 | 8,343 | lean | -- https://proofwiki.org/wiki/Axiom_of_Choice_Implies_Zorn%27s_Lemma/Proof_1
universe u
instance set.partial_order {α} : partial_order (set α) :=
{ le := (⊆),
le_refl := λ A z, id,
le_trans := λ A B C hab hbc z hz, hbc (hab hz),
le_antisymm := λ A B hab hba, funext $ λ z, propext ⟨@hab z, @hba z⟩ }
local attri... |
10cdad3babf399d27be4b3909cd7b8b0584a5531 | 92b50235facfbc08dfe7f334827d47281471333b | /library/algebra/field.lean | 64a130ca5ae0b8e23b828b34bcfe1ef1d7d7da35 | [
"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 | 18,926 | lean | /-
Copyright (c) 2014 Robert Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Lewis
Structures with multiplicative and additive components, including division rings and fields.
The development is modeled after Isabelle's library.
-/
-----------------------... |
9f7265761f9ba22d0de28ddc095bbbff103d5cac | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/haveDestruct.lean | bef657029eee5ca497b546e42c3e1445c3ac3b47 | [
"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 | 316 | lean | def f (x : Nat) :=
have y := x+1
y+y
def g (x : Nat × Nat) :=
have (y, z) := x
y + y
theorem ex1 (h : p ∧ q ∧ r) : p := by
have ⟨h', _, _⟩ := h
exact h'
theorem ex2 (h : p ∧ q ∧ r) : p :=
have ⟨h, _, _⟩ := h
h
theorem ex3 (h : p ∧ q ∧ r) : r :=
have ⟨_, _, h⟩ := h
h
|
bd0ccaa5a3cbd0ca943942aea44df0ad7f23dc5a | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/algebraic_geometry/presheafed_space.lean | 2a922611555fe8e6f9af29aeec6d3b6dcf725c75 | [
"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 | 10,845 | 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.sheaves.presheaf
/-!
# Presheafed spaces
Introduces the category of topological spaces equipped with a presheaf (taking values in an
arbitrary targe... |
f1f3bcc8fcc8cba95d84f55338ab3cc666d0cbe4 | bf532e3e865883a676110e756f800e0ddeb465be | /data/real/basic.lean | d224b69ef770f0ea10f79eed55ee820b2b666a39 | [
"Apache-2.0"
] | permissive | aqjune/mathlib | da42a97d9e6670d2efaa7d2aa53ed3585dafc289 | f7977ff5a6bcf7e5c54eec908364ceb40dafc795 | refs/heads/master | 1,631,213,225,595 | 1,521,089,840,000 | 1,521,089,840,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 24,458 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
The (classical) real numbers ℝ. This is a direct construction
from Cauchy sequences.
-/
import order.conditionally_complete_lattice data.real.cau_seq algebra.big_operat... |
e3597c9b3119a44dfec806f62aa48b8acf925ce2 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/interactive/completionIStr.lean | 49c205940cba3cbd7b20a422e15fe61472b711fa | [
"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 | 153 | lean | structure C where
f1 : Nat
f2 : Bool
b1 : String
#check fun c : C => s!"testing {c. "
--^ textDocument/completion
|
f81b86d1d70f2f66d890f0547c729945343c79a9 | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/set/intervals/surj_on.lean | 926a9847064a757a8ccd1ca8c0bcc05b60df217d | [
"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 | 3,984 | lean | /-
Copyright (c) 2020 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Heather Macbeth
-/
import data.set.intervals.basic
import data.set.function
/-!
# Monotone surjective functions are surjective on intervals
A monotone surjective function sends any i... |
4715a457eec41383db7f9fea34370a90579e588c | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/polynomial/hasse_deriv.lean | 5f3aa05c42f83a2aa9642dad03da396ce1b855e8 | [
"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 | 10,395 | 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 algebra.polynomial.big_operators
import data.nat.choose.cast
import data.nat.choose.vandermonde
import data.polynomial.degree.lemmas
import data.polynomial.de... |
cc8073cddc007f37ccd6f72ecca8c8640650fc0c | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/topology/sheaves/sheaf_condition/opens_le_cover.lean | 2a982b84618e885d4e3481c35d97305cb41e3272 | [
"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 | 9,602 | 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.presheaf
import category_theory.limits.cofinal
import topology.sheaves.sheaf_condition.pairwise_intersections
/-!
# Another version of the sh... |
6d6b13086467737fbad7321549ab19b2a76aff00 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/red.lean | db62a23c8845da5d04d1c4510ed5115e938c151c | [
"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 | 486 | lean | constant g : nat → nat
noncomputable definition f := g
example : f = g := rfl
attribute [irreducible] f
example : f = g := rfl -- Error
example (a : nat) (H : a = g a) : f a = a :=
eq.subst H rfl -- Error
attribute [semireducible] f
example (a : nat) (H : a = g a) : f a = a :=
eq.subst H rfl -- Error
example :... |
3f2523a98587749e2fd90efb3b63f5f2edf3646f | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /tests/lean/shadow.lean | dc54137f3e93a2be851a1f230d508c26280b9202 | [
"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 | 202 | lean | open nat
variable a : nat
-- The variable 'a' in the following definition is not the variable 'a' above
definition tadd : nat → nat → nat,
tadd zero b := b,
tadd (succ a) b := succ (tadd a b)
|
f664d6573a772cca96e34cf9c02ebc4fa6b5462f | 95dcf8dea2baf2b4b0a60d438f27c35ae3dd3990 | /src/category_theory/opposites.lean | c09fadbca9c0e073585f9e411b4ae67a16769c04 | [
"Apache-2.0"
] | permissive | uniformity1/mathlib | 829341bad9dfa6d6be9adaacb8086a8a492e85a4 | dd0e9bd8f2e5ec267f68e72336f6973311909105 | refs/heads/master | 1,588,592,015,670 | 1,554,219,842,000 | 1,554,219,842,000 | 179,110,702 | 0 | 0 | Apache-2.0 | 1,554,220,076,000 | 1,554,220,076,000 | null | UTF-8 | Lean | false | false | 7,369 | 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.types
namespace category_theory
universes v₁ v₂ u₁ u₂ -- declare the `v`'s first; see `ca... |
075af6f67a1d2adfb0e175da7eb771a6940be8b8 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/field_theory/intermediate_field.lean | 37afbfec245a71d74f99ca7792009bf8166c5b8d | [
"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 | 21,913 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import field_theory.minpoly
import field_theory.subfield
import field_theory.tower
/-!
# Intermediate fields
Let `L / K` be a field extension, given as an instance `alge... |
78cc2564f1e0b020cbca58577be1d952457470d1 | 6f1049e897f569e5c47237de40321e62f0181948 | /src/solutions/07_first_negations.lean | 1caf59291b61283f9edc93c37fa0964a4b3127b2 | [
"Apache-2.0"
] | permissive | anrddh/tutorials | f654a0807b9523608544836d9a81939f8e1dceb8 | 3ba43804e7b632201c494cdaa8da5406f1a255f9 | refs/heads/master | 1,655,542,921,827 | 1,588,846,595,000 | 1,588,846,595,000 | 262,330,134 | 0 | 0 | null | 1,588,944,346,000 | 1,588,944,345,000 | null | UTF-8 | Lean | false | false | 8,309 | lean | import tuto_lib
import data.int.parity
/-
Negations, proof by contradiction and contraposition
This file introduces the logical rules and tactics related to negation:
exfalso, by_contradiction, contrapose, by_cases and push_neg.
There is a special statement denoted by false which, by definition,
has no proof.
So fal... |
d31e1792390668ca80e958026e80f60c0f07159d | 2eab05920d6eeb06665e1a6df77b3157354316ad | /test/simp_command.lean | 8fd6f17401bd0018c34d22d83e327aaf8f74a17f | [
"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 | 2,489 | lean | import tactic.simp_command
import analysis.special_functions.trigonometric.basic
/- Turn off trace messages only if the statements are simplified to true: -/
set_option trace.silence_simp_if_true true
/-!
Tests for the #simp command.
-/
#simp 5 - 5 = 0
section arith
def f (x : ℤ) := x + (x - x)
#simp [f] f 3 = 3
... |
c8e0d5e66f772c85cc01d0b26c66c22af79897e3 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Compiler/ClosedTermCache.lean | 69f5b9b30271f5186ddb4afcfdbb74f668d2fda0 | [
"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 | 959 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Environment
namespace Lean
structure ClosedTermCache where
map : PHashMap Expr Name := {}
constNames : NameSet := {}
deriving Inh... |
c3f82163e8fc524c1e21659a4e0f75e101b8afe3 | 618003631150032a5676f229d13a079ac875ff77 | /src/linear_algebra/dimension.lean | 4aaf452f2bc396254258a97967eb11e02b975268 | [
"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 | 16,677 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro, Johannes Hölzl, Sander Dahmen
-/
import linear_algebra.basis
import set_theory.ordinal
/-!
# Dimension of modules and vector spaces
## Main definitions
* The dimension... |
20d36df6ce7c6cdd59d0bfdcf2469bc76e8b91eb | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /stage0/src/Init/Data/Nat/Bitwise.lean | 52a89b7a89ccaab3e7af58a16ee009063ae40615 | [
"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 | 752 | 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.Data.Nat.Basic
import Init.Data.Nat.Div
import Init.Coe
namespace Nat
partial def bitwise (f : Bool → Bool → Bool) : Nat → Nat → Nat |... |
a7e1b85c5bb092f1868d3fe09a0853ee16af9048 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/abelian/injective_resolution.lean | b72be7a1ac788dc387caa7922cc9e3291e3abfa5 | [
"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 | 12,728 | lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Scott Morrison
-/
import algebra.homology.quasi_iso
import category_theory.preadditive.injective_resolution
import category_theory.abelian.homology
import algebra.homology.... |
39533bc58d96fa050007cf11bda60e82c327074a | 297c4ceafbbaed2a59b6215504d09e6bf201a2ee | /theorem.lean | aec17ccd4cdb0949f968d177c29445253dfd7992 | [] | no_license | minchaowu/Kruskal.lean3 | 559c91b82033ce44ea61593adcec9cfff725c88d | a14516f47b21e636e9df914fc6ebe64cbe5cd38d | refs/heads/master | 1,611,010,001,429 | 1,497,935,421,000 | 1,497,935,421,000 | 82,000,982 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 20,857 | lean | import .kruskal .higman data.list
open classical fin set nat subtype finite_tree kruskal function prod
noncomputable theory
theorem dne {p : Prop} (H : ¬¬p) : p := or.elim (em p) (assume Hp : p, Hp) (assume Hnp : ¬p, absurd Hnp H)
lemma tag_eq_of_eq {A : Type} {P : A → Prop} {a b : subtype P} (H : a = b) :a.1 = b.1 ... |
3dac7c6c80da661ec5e33c575b260e4e06671dd5 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/category/fgModule/limits.lean | f4c114b7dccdb066fe35070e086343d8fa03d47f | [
"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 | 2,920 | 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.category.fgModule.basic
import algebra.category.Module.limits
import algebra.category.Module.products
import algebra.category.Module.epi_mono
import ca... |
735f476f8520def11fdffcb342a66344f63bcb81 | 4e3bf8e2b29061457a887ac8889e88fa5aa0e34c | /lean/love10_denotational_semantics_demo.lean | 1fbe2d2741771ef212344a3257bbc45d7515d1ab | [] | no_license | mukeshtiwari/logical_verification_2019 | 9f964c067a71f65eb8884743273fbeef99e6503d | 16f62717f55ed5b7b87e03ae0134791a9bef9b9a | refs/heads/master | 1,619,158,844,208 | 1,585,139,500,000 | 1,585,139,500,000 | 249,906,380 | 0 | 0 | null | 1,585,118,728,000 | 1,585,118,727,000 | null | UTF-8 | Lean | false | false | 6,470 | lean | /- LoVe Demo 10: Denotational Semantics -/
import .love08_operational_semantics_demo
namespace LoVe
/- Complete Lattices -/
class complete_lattice (α : Type)
extends partial_order α :=
(Inf : set α → α)
(Inf_le : ∀s a, a ∈ s → Inf s ≤ a)
(le_Inf : ∀s a, (∀a', a' ∈ s → a ≤ a') → a ≤ Inf s)
/- Instance for Co... |
4a4be09636cbe608c1b5137a3da82ed7990097b6 | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /library/logic/subsingleton.lean | 0fe2e0ddc13761c6c1afd67d734d3e2ac0300d29 | [
"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 | 1,419 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: logic.subsingleton
Author: Floris van Doorn
-/
import logic.eq
inductive subsingleton [class] (A : Type) : Prop :=
intro : (∀ a b : A, a = b) → subsingleton A
namespace subsi... |
32436da9ce9ad3fb2bf268dd093ecac3d55fb089 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/data/squash.lean | 33370c5ff1c73ec015d169bf19c5d1b4a2784253 | [
"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 | 1,839 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
Define squash type (aka propositional truncation) using quotients.
This definition is slightly better than defining the squash type ∥A∥ as (nonempty A).
If we ... |
8200378868ceed05fb3990c97bf29080b3c39c83 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/ring_theory/polynomial/chebyshev.lean | eaeb9496d582e171eeba989a92e11d707e31fa4c | [
"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 | 11,066 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Julian Kuelshammer, Heather Macbeth
-/
import data.polynomial.derivative
import tactic.ring
/-!
# Chebyshev polynomials
The Chebyshev polynomials are two families of ... |
5f8e06107de4666b0a5957d0a83972f404aa4853 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/qpf/multivariate/constructions/cofix.lean | b82c606ffc2319f9930e4fd2dc9b74e58aa26616 | [
"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 | 19,004 | lean | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Simon Hudon
-/
import control.functor.multivariate
import data.pfunctor.multivariate.basic
import data.pfunctor.multivariate.M
import data.qpf.multivariate.basic
/-!
# ... |
94fd7112dfe6de366795fa4ad24486c878defbe7 | 2d34dfb0a1cc250584282618dc10ea03d3fa858e | /src/for_mathlib/discrete_topology.lean | 82b93fa3e94a706755e14eac9e40cbc42f1d7372 | [] | no_license | zeta1999/lean-liquid | 61e294ec5adae959d8ee1b65d015775484ff58c2 | 96bb0fa3afc3b451bcd1fb7d974348de2f290541 | refs/heads/master | 1,676,579,150,248 | 1,610,771,445,000 | 1,610,771,445,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 552 | lean | import topology.subset_properties
variables {ι : Type*} (X : ι → Type*)
variables [fintype ι] [∀ i, topological_space (X i)] [∀ i, discrete_topology (X i)]
instance Pi.discrete_topology : discrete_topology (Π i, X i) :=
begin
rw ← singletons_open_iff_discrete,
intro x,
rw show {x} = ⋂ i, {y : Π i, X i | y i = x... |
b24e7606e4ab47eb72f2e256d8259d47340db290 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebraic_geometry/structure_sheaf_auto.lean | 9b682e7043727cc84ffd34d71638cd0e21e09239 | [] | 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 | 4,120 | 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
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebraic_geometry.prime_spectrum
import Mathlib.algebra.category.CommRing.... |
4ee8ef63660b8594a96851ad285af07a3ccfbe05 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/set_theory/game/pgame.lean | 60714d56fe29591246ecfead47ca8b35ee20e04d | [
"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 | 58,114 | lean | /-
Copyright (c) 2019 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Mario Carneiro, Isabel Longbottom, Scott Morrison
-/
import data.fin.basic
import data.list.basic
import logic.relation
/-!
# Combinatorial (pre-)games.
The basic theory... |
c251269f193dc22eb0e98183d84cbb33911361d2 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/category_theory/monoidal/Mod_.lean | e88e0ba3371710ca6023365bb7c7b3be15b382fa | [
"Apache-2.0"
] | permissive | kbuzzard/mathlib | 2ff9e85dfe2a46f4b291927f983afec17e946eb8 | 58537299e922f9c77df76cb613910914a479c1f7 | refs/heads/master | 1,685,313,702,744 | 1,683,974,212,000 | 1,683,974,212,000 | 128,185,277 | 1 | 0 | null | 1,522,920,600,000 | 1,522,920,600,000 | null | UTF-8 | Lean | false | false | 3,646 | 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.Mon_
/-!
# The category of module objects over a monoid object.
-/
universes v₁ v₂ u₁ u₂
open category_theory
open category_theory.... |
a8c6b76ddf4e06757cf437a28ec84321098fc46e | ba4794a0deca1d2aaa68914cd285d77880907b5c | /src/game/world2/level2.lean | 0dcc6217e0c3be1e26ac3b7056292d9d99a1bb5d | [
"Apache-2.0"
] | permissive | ChrisHughes24/natural_number_game | c7c00aa1f6a95004286fd456ed13cf6e113159ce | 9d09925424da9f6275e6cfe427c8bcf12bb0944f | refs/heads/master | 1,600,715,773,528 | 1,573,910,462,000 | 1,573,910,462,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,797 | lean | import mynat.definition -- hide
import mynat.add -- hide
import game.world2.level1 -- hide
namespace mynat -- hide
/-
# Addition world
Don't forget to use the drop down boxes on the left to see your tactics and
what you have proved so far.
## Level 2: `add_assoc` -- associativity of addition.
It's well-known that ... |
f53b98e47cb022458976db7432d9494240e4973c | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/algebra/group/inj_surj.lean | d7b787ceb5faa438a846e071ccb1f589179aa02c | [
"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 | 12,702 | 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 algebra.group.defs
import logic.function.basic
/-!
# Lifting algebraic data classes along injective/surjective maps
This file provides definitions that are m... |
a8a252459f74f95f873a0f3c6664d423aaf791a6 | 737dc4b96c97368cb66b925eeea3ab633ec3d702 | /stage0/src/Lean/Parser/Extra.lean | 52d76fd089a6fe3a91dd0e33fb5d276d174c7fa2 | [
"Apache-2.0"
] | permissive | Bioye97/lean4 | 1ace34638efd9913dc5991443777b01a08983289 | bc3900cbb9adda83eed7e6affeaade7cfd07716d | refs/heads/master | 1,690,589,820,211 | 1,631,051,000,000 | 1,631,067,598,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,116 | 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, Sebastian Ullrich
-/
import Lean.Parser.Extension
-- necessary for auto-generation
import Lean.PrettyPrinter.Parenthesizer
import Lean.PrettyPrinter.Formatter... |
39c2e7ceb3c24a0a8e61f84352d1cf4a87539727 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/topology/tactic.lean | 4af4fea8429af2af40d1a8644b5b7fa80d1accf8 | [
"Apache-2.0"
] | permissive | AntoineChambert-Loir/mathlib | 64aabb896129885f12296a799818061bc90da1ff | 07be904260ab6e36a5769680b6012f03a4727134 | refs/heads/master | 1,693,187,631,771 | 1,636,719,886,000 | 1,636,719,886,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,068 | lean | /-
Copyright (c) 2020 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton
-/
import tactic.auto_cases
import tactic.tidy
import tactic.with_local_reducibility
import tactic.show_term
import topology.basic
/-!
# Tactics for topology
Currently we hav... |
e48b42654dbb06c553dff37c0b551a51c8759380 | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/coercion1.lean | e03ca901412d6fad21bb4505c5776a801af18095 | [
"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 | 283 | lean | variable T : Type
variable R : Type
variable f : T -> R
coercion f
print environment 2
variable g : T -> R
coercion g
variable h : forall (x : Type), x
coercion h
definition T2 : Type := T
definition R2 : Type := R
variable f2 : T2 -> R2
coercion f2
variable id : T -> T
coercion id
|
c0ba7acf9d4a829f45727073b2118c3a41ccb69e | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/order/monoid/basic.lean | f2a9adb01108a805128a58b37e38254956de244b | [
"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 | 3,190 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl
-/
import algebra.order.monoid.defs
import algebra.group.inj_surj
import order.hom.basic
/-!
# Ordered monoids
> THIS ... |
c87739b8dbb6ae123b3ab7d4150a4693140382f2 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/topology/separation.lean | a73d404eee26b28219bc893831b9b1f60641b7ee | [] | 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 | 21,788 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.topology.subset_properties
im... |
a95f90db55c5d0e867a99d617a4fbe8cd1870117 | 4fa161becb8ce7378a709f5992a594764699e268 | /src/linear_algebra/nonsingular_inverse.lean | 0f72630729ff29e7f8b55e3a80eb7afad1fa6f7b | [
"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 | 15,486 | lean | /-
Copyright (c) 2019 Tim Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Tim Baanen.
-/
import algebra.associated
import linear_algebra.determinant
import tactic.linarith
import tactic.ring_exp
/-!
# Nonsingular inverses
In this file, we define an inverse for ... |
e3f77bf62e5f65dae1335b3e57c67f5ed4535616 | 7565ffb53cc64430691ce89265da0f944ee43051 | /hott/init/funext.hlean | 64e7b0d3555a7db5b1a455ca4dfbac141c1fb373 | [
"Apache-2.0"
] | permissive | EgbertRijke/lean2 | cacddba3d150f8b38688e044960a208bf851f90e | 519dcee739fbca5a4ab77d66db7652097b4604cd | refs/heads/master | 1,606,936,954,854 | 1,498,836,083,000 | 1,498,910,882,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 12,041 | hlean | /-
Copyright (c) 2014 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer, Floris van Doorn
Ported from Coq HoTT
-/
prelude
import .trunc .equiv .ua
open eq is_trunc sigma function is_equiv equiv prod unit prod.ops lift
/-
We now pro... |
75fdec59ccb64ff9a20160688352f4b3f115f236 | 6b45072eb2b3db3ecaace2a7a0241ce81f815787 | /pending/default.lean | b2dc55c88a8ba710a2f780e918d800cd8b435ef5 | [] | 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 | 529 | lean | /- Temporary space for definitions pending merges to the lean repository -/
open tactic
-- PR #1761
meta def transport_multiplicative_to_additive' (ls : list (name × name)) : command :=
let dict := rb_map.of_list ls in
ls.foldl (λ t ⟨src, tgt⟩, do
env ← get_env,
if (env.get tgt).to_bool = ff
then t >> transport... |
25ab559afc2d1bd513d4769fa41224761e534d09 | 0942a74cc0b397d09bcd1059762fa076b1a5d308 | /src/lean5.lean | 15b5cff927a41af9f6e86bb4e96a7f8f44abd4bb | [
"Unlicense"
] | permissive | sguzman/lean-examples | 81df2010e204be1a9fde6ae18295e299e69cebca | c7428b2982d0468d0adb4453766a27e1550a72e8 | refs/heads/master | 1,668,438,655,034 | 1,594,156,605,000 | 1,594,156,605,000 | 277,626,098 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 304 | lean | theorem and_swap (p q : Prop) : p ∧ q → q ∧ p :=
begin
assume h : (p ∧ q), -- assume p ∧ q is true
cases h, -- extract the individual propositions from the conjunction
split, -- split the goal conjunction into two cases: prove p and prove q separately
repeat { assumption }
end |
2cb689a0b109b899388deb4e47986988fffe8aa6 | 8b0adce7bd4e8e06a22dbf65d3ef29169133227b | /inClassNotes/04_type_library/list.lean | 6f967778e5848568c16bdb7025d3e3719c2502a7 | [] | no_license | parvahujauva/complogic-s21 | 5420bce9c456cd9dafcb4965719d2e45fb53437a | ba8d38bfb9000420e0051bc07195026b0e39a29c | refs/heads/master | 1,677,682,663,658 | 1,613,232,309,000 | 1,613,232,309,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,242 | lean | #print nat
namespace hidden
/-
The list α type represents the
set of lists of values of type
α. So "list nat", for example, is
the type of lists that contain
natural numbers. It explains that
such a list is either empty (nil)
or is constructed (cons) from a
single element of type α and a
smaller list (possibly emp... |
86f1a659aac96d73bc781789f83401d1a694f056 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/finset/sym.lean | 9b6246c51e858b8a4360e8192603b6068635dac8 | [
"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 | 7,221 | lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import data.finset.lattice
import data.fintype.prod
import data.fintype.vector
import data.sym.sym2
/-!
# Symmetric powers of a finset
> THIS FILE IS SYNCHRONIZED WITH ... |
c4a32599b638be8ff275b9572cc435ff9304a645 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/heuristic_name_field_anonymous.lean | dc7b79a7d68e8a872c8c47cd138a73b33d215f82 | [
"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 | 236 | lean | class A {α : Type*} (x : α)
instance {α : Type*} {p : α → Prop} (x : subtype p) : A x.1 := A.mk
example := @subtype.field_1.A
instance {α : Type*} {p : α → Prop} (x : subtype p) : A x.val := A.mk
example := @subtype.val.A
|
d10e005b6840f69d0575995f51dbc1cea6fabb5f | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /src/Std/Data/RBTree.lean | e2bd9a4dc8c73c76af1d8b2bc6223c9f6c0a2313 | [
"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 | 3,216 | 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 Std.Data.RBMap
namespace Std
universes u v w
def RBTree (α : Type u) (lt : α → α → Bool) : Type u :=
RBMap α Unit lt
instance : Inhabited (RBTree... |
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