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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
8b0b8de2cb7e6cd1542964697f83cf78b26f9450 | 843cffbd2a25fd01677509247a92e9e8b33bec48 | /(a + b)^3.lean | 870a9bf06b28a294dbed07748acd8349de9cf9ba | [] | no_license | AlexandruBosinta/MyLeanPlayground | 9a78eba4a5c7a2b82edf84e1794a966f53f06c4f | 5dc50a590d784bfc27e7fb37b6361a6dcc1b2790 | refs/heads/master | 1,586,230,010,351 | 1,542,487,422,000 | 1,542,487,422,000 | 158,016,626 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,920 | lean | import data.real.basic
variables (a b : ℝ)
include a b
example : (a + b) ^ 3 = a ^ 3 + 3 * (a ^ 2) * b + 3 * a * b ^ 2 + b ^ 3 :=
by calc
(a + b) ^ 3 = (a + b) ^ (2 + 1) : rfl
... = (a + b) ^ 2 * (a + b) : by rw pow_succ'
... = (a + b) * (a + b) * (a + b) : by rw pow_two
... = ((a + b) * a ... |
935e3ba43ffff698684788b7076d5751269919ea | 47c6e122a73eb61594f0426d74d9c1897ac5668e | /src/sylowtwo.lean | 4e0d55ca9d83d525245c9cd44d9e8ae313854b6a | [] | no_license | ineswright/Lean-Sylow | 19ec5d964be8a66e25e227621fbac79c88a83ddf | 74b99544ab1ca96dc28fbe152125f565763a893b | refs/heads/main | 1,688,108,643,799 | 1,627,664,383,000 | 1,627,664,383,000 | 382,315,172 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,550 | lean | import group_theory.group_action
import group_theory.quotient_group
import data.zmod.basic
import data.fintype.card
import group_theory.sylow
import tactic
-- import algebra.group.conj
open equiv fintype finset mul_action function nat sylow
open subgroup quotient_group
universe u
variables {G : Type u} [group G]
open... |
7806e59ebd54393f8a34025f4d8d187ea79812a4 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/data/real/cau_seq.lean | d5ddf07cc5541358e4d83ad4daa6238b11d13fad | [
"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 | 25,905 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import algebra.big_operators.order
/-!
# Cauchy sequences
A basic theory of Cauchy sequences, used in the construction of the reals and p-adic numbers. Where
applic... |
863df27844e4e7101bd5f7a5013290b091b22527 | 7d5ad87afb17e514aee234fcf0a24412eed6384f | /src/reflection.lean | 93ffc355068db7e6c6d2aa687cb904d4fa1a6473 | [] | no_license | digama0/flypitch | 764f849eaef59c045dfbeca142a0f827973e70c1 | 2ec14b8da6a3964f09521d17e51f363d255b030f | refs/heads/master | 1,586,980,069,651 | 1,547,078,141,000 | 1,547,078,283,000 | 164,965,135 | 1 | 0 | null | 1,547,082,858,000 | 1,547,082,857,000 | null | UTF-8 | Lean | false | false | 1,934 | lean | import .fol tactic.tidy .abel tactic.ring .completeness .zfc
open fol
local notation h :: t := dvector.cons h t
local notation `[]` := dvector.nil
local notation `[` l:(foldr `, ` (h t, dvector.cons h t) dvector.nil `]`) := l
namespace reflection
section
/- rephrasing of soundness -/
def by_reflection {L} (T : The... |
d03e11fa9b33cd8189acb1c119624a178a757b40 | ef4d3feecef33d1c1b4bd3a023b85e6a58f9e708 | /theorem-proving-in-lean/ch5/Exercises.lean | eef8948d01dc1da6e5f1da7f5326ad3538c8d842 | [] | no_license | MikeMKH/kata | 1b7da1b8d2cc115c912f2b06b583a8e675a449e1 | 305b054a37517dbe4d09545d41f024937f536c20 | refs/heads/master | 1,585,594,368,426 | 1,542,835,119,000 | 1,542,835,119,000 | 16,891,298 | 0 | 0 | null | 1,542,835,120,000 | 1,392,575,890,000 | Racket | UTF-8 | Lean | false | false | 2,860 | lean | -- https://leanprover.github.io/theorem_proving_in_lean/tactics.html#exercises
-- 1
section three
open classical
variables p q r s : Prop
-- commutativity of ∧ and ∨
example : p ∧ q ↔ q ∧ p := by simp
example : p ∨ q ↔ q ∨ p := by simp
-- associativity of ∧ and ∨
example : (p ∧ q) ∧ r ↔ p ∧ (q ... |
0f2373c2327d02a0ad6c15440efba6faf8aa784c | fd39fc7e47201556d5e53b9c37552ed9f5aa76cb | /data/leanlibrary/test.lean | ecda4b7c06b9d5a86b739768392e5b5a2c5a8640 | [
"MIT"
] | permissive | sundararajan-s/ProvingGround | 947a741d10d54a1c6d6f8a5f8664ed5aa31e4d77 | f111b791369a94a5b95d24f51e12bfa309f3a50b | refs/heads/master | 1,677,893,530,903 | 1,599,286,921,000 | 1,599,286,921,000 | 288,640,864 | 1 | 0 | MIT | 1,598,694,036,000 | 1,597,814,549,000 | Jupyter Notebook | UTF-8 | Lean | false | false | 160 | lean | prelude
inductive boolean : Type
| true : boolean
| false : boolean
definition not : boolean -> boolean := fun b, boolean.rec_on b boolean.false boolean.true
|
b76fce03eea8b4e0df8bbf3f3f90f8bb2de26a93 | 1fd908b06e3f9c1252cb2285ada1102623a67f72 | /types/arrow.lean | 29c8c3d53e0fbe15acea4696f5c43321e1c8ea83 | [
"Apache-2.0"
] | permissive | avigad/hott3 | 609a002849182721e7c7ae536d9f1e2956d6d4d3 | f64750cd2de7a81e87d4828246d1369d59f16f43 | refs/heads/master | 1,629,027,243,322 | 1,510,946,717,000 | 1,510,946,717,000 | 103,570,461 | 0 | 0 | null | 1,505,415,620,000 | 1,505,415,620,000 | null | UTF-8 | Lean | false | false | 5,883 | lean | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Floris van Doorn
Ported from Coq HoTT
Theorems about arrow types (function spaces)
-/
import types.pi
universe u
hott_theory
namespace hott
open eq equiv is_equiv funext pi is_tru... |
dc9ef8244bf2f61981f50af090b060dd791de5cc | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/refineOccursCheck.lean | f017c5bb2410c8b87a114c67288fa5340184d98e | [
"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 | 215 | lean | theorem ex1 : True := by
refine ?a
refine ?a
refine ?a
exact True.intro
axiom ax.{u} {α : Sort u} (a : α) : α
theorem ex2 : True := by
refine ?a
refine ax ?a -- Error trying to assign `?a := ax ?a`
|
cf5c46078bae6cb8e3d306f79f5c90cf64efa51b | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/logic/function/conjugate.lean | a3208e9d3d108553759db67d0c97e65cd5f2aec3 | [
"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 | 4,944 | 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 logic.function.basic
/-!
# Semiconjugate and commuting maps
We define the following predicates:
* `function.semiconj`: `f : α → β` semiconjugates `ga : α ... |
0dd0e89965724d51ae0c2cdcbe991fb492c9dbab | 00d2363f9655e2a7618f6b94dda7e2c4e5cf8d19 | /src/proof_recording_example.lean | 94fb8ac7b69b3bdd3426af8e4a1daa55d7470156 | [
"Apache-2.0"
] | permissive | devjuice1/lean_proof_recording | 927e276e2ab8fb1288f51d9146dcfbf0d6444a87 | bf7c527315deccd35363fa7ca89d97d7b9cb6ac1 | refs/heads/master | 1,692,914,925,585 | 1,633,018,872,000 | 1,633,018,872,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,858 | lean | -- co-opting pp.colors as a flag to turn the tracing on
-- can also be set from the command line with -D pp.colors=false
set_option pp.colors false
example : true := begin
skip, exact by trivial, done
end
example : true := by exact true.intro
example : true := by trivial
example (a b c : ℕ) (H1 : a = b + 1) (... |
2caa40b6627d1debdfe48cb5f740ac5a958ba520 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/data/char/default.lean | 9a39e92636d63586a3d5a913fa41e63d17e5a851 | [] | 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 | 347 | 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
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.data.char.basic
import Mathlib.Lean3Lib.init.data.char.lemmas
import Mathlib.Lean3Lib.init.data.char.cla... |
19ad87c872bfd6a2ec616e3be41ee1839a72794a | 6afa22d5eee6e9a56b6a2f1210eca8f7a1067466 | /tests/lean/widget/widget2.lean | 66f0437d92cc911c383df68c2eab73d21a23a7ea | [
"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 | 371 | lean |
open widget
/-- A simple counter that can be incremented or decremented with some buttons. -/
meta def counter_widget {π α : Type} : component π α :=
component.ignore_props $ component.mk_simple int int 0 (λ _ x y, (x + y, none)) (λ _ s,
h "div" [] [
button "+" (1 : int),
html.of_string $ to_string $ s,
... |
58fb3449fb7928b188e8f0f4d1844e88da4cfffb | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/idempotents/functor_extension.lean | 0307fbd5ed354441f559308e94cda2d1601cfb89 | [
"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 | 11,101 | lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import category_theory.idempotents.karoubi
/-!
# Extension of functors to the idempotent completion
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file req... |
60ff84160cfccff830df93f25616eedceea65223 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/linarith/lemmas_auto.lean | 248105fa5d490c3811f1a50f8d452bf5588f0cfe | [] | 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 | 3,637 | lean | /-
Copyright (c) 2020 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.ordered_ring
import Mathlib.data.int.basic
import Mathlib.tactic.norm_num
import ... |
62bc19a56251affcb6326f3f1683540ebf7c02bc | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/ring_theory/polynomial/basic.lean | f287919dda4e2682d27d4b8ff6b49c5af40c443e | [
"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 | 43,980 | 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.char_p.basic
import algebra.geom_sum
import data.mv_polynomial.comm_ring
import data.mv_polynomial.equiv
import ring_theory.polynomial.content
import ring_theor... |
69e59635ee729a349a0c3f8423d20eb8d8c854c9 | aa5a655c05e5359a70646b7154e7cac59f0b4132 | /tests/lean/PPRoundtrip.lean | 94ad4fefb727bc1d68fe5fecfb32ac212d796247 | [
"Apache-2.0"
] | permissive | lambdaxymox/lean4 | ae943c960a42247e06eff25c35338268d07454cb | 278d47c77270664ef29715faab467feac8a0f446 | refs/heads/master | 1,677,891,867,340 | 1,612,500,005,000 | 1,612,500,005,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,036 | lean | import Lean
open Lean
open Lean.Elab
open Lean.Elab.Term
open Lean.Elab.Command
open Std.Format open Std
open Lean.PrettyPrinter
open Lean.Meta
def checkM (stx : TermElabM Syntax) (optionsPerPos : OptionsPerPos := {}) : TermElabM Unit := do
let opts ← getOptions
let stx ← stx
let e ← elabTermAndSynthesize stx none <... |
1eb0ea1c31b4cdeb66d309908acff70c47acde88 | e5c11e5a7d990ce404047c2bd848eeafac3c0a85 | /src/dedekind_domain.lean | 6a9e1a3cbf909680f75610cf513dcb02c46d214b | [
"LPPL-1.3c"
] | permissive | lean-forward/class-number | 9ec63c24845e46efc8fa8b15324d0815918292c7 | 4fccf36d5e0e16accae84c16df77a3839ad964e4 | refs/heads/main | 1,686,927,014,542 | 1,624,886,724,000 | 1,624,886,724,000 | 327,319,245 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 41,587 | lean | /-
Copyright (c) 2020 Kenji Nakagawa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenji Nakagawa, Anne Baanen, Filippo A. E. Nuccio, Ashvni Narayanan
-/
import algebra.group_with_zero.basic
import field_theory.minpoly
import linear_algebra.finite_dimensional
import ... |
946babad6f07688fad9628c97c686ae8420b0447 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/ring_theory/unique_factorization_domain.lean | 268c6a5c17543a636f083aeb120a91d2a2c36d68 | [
"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 | 70,282 | 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 algebra.big_operators.associated
import algebra.gcd_monoid.basic
import data.finsupp.multiset
import ring_theory.noetherian
im... |
a755844a0b92a5cf2f9798d85b793e4ee93d2ccf | 9cb9db9d79fad57d80ca53543dc07efb7c4f3838 | /src/breen_deligne/universal.lean | 438b5d4d3b65017f4e4fc7881dfda02dccb81772 | [] | no_license | mr-infty/lean-liquid | 3ff89d1f66244b434654c59bdbd6b77cb7de0109 | a8db559073d2101173775ccbd85729d3a4f1ed4d | refs/heads/master | 1,678,465,145,334 | 1,614,565,310,000 | 1,614,565,310,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,498 | lean | -- n©
import breen_deligne.basic
/-!
# Universality of universal maps
A `universal_map m n` in this repo is a finite formal `ℤ`-linear combination
of `m × n` matrices (so-called `basic_universal_map`s). In this file we show that
to give a term of this type is to give a term of type `functorial_map m n`, which is
de... |
9398aee13811158fc55d9d3399149b542cba94b5 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/matrix2.lean | a6ffae2e72243f76dc1ec9208f198601d55498fd | [
"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 | 815 | lean | constant {u} matrix : Type u → Type u
constant same_dim {A : Type} : matrix A → matrix A → Prop
constant add1 {A : Type} (m1 m2 : matrix A) {H : same_dim m1 m2} : matrix A
open eq
theorem same_dim_eq_args {A : Type} {m1 m2 m1' m2' : matrix A} (H1 : m1 = m1') (H2 : m2 = m2') (H : same_dim m1 m2) : same_dim m1' m2' :=
su... |
4d2829e43867b066790712f2aa9ad3256879a4e5 | 649957717d58c43b5d8d200da34bf374293fe739 | /src/algebra/group/basic.lean | c65b4215f5571e6d571cec18f300ca73f84d0f08 | [
"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 | 7,867 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Simon Hudon, Mario Carneiro
Various multiplicative and additive structures.
-/
import algebra.group.to_additive
universe u
variable {α : Type u}
instance monoid_to_is_... |
d32830b8af0a3933a4d5709edeb1a9f2f91c46cb | 27a31d06bcfc7c5d379fd04a08a9f5ed3f5302d4 | /stage0/src/Lean/Data/Format.lean | d459a0edc525d098c018c993b0b2cc6c0fa692e2 | [
"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 | joehendrix/lean4 | 0d1486945f7ca9fe225070374338f4f7e74bab03 | 1221bdd3c7d5395baa451ce8fdd2c2f8a00cbc8f | refs/heads/master | 1,640,573,727,861 | 1,639,662,710,000 | 1,639,665,515,000 | 198,893,504 | 0 | 0 | Apache-2.0 | 1,564,084,645,000 | 1,564,084,644,000 | null | UTF-8 | Lean | false | false | 1,705 | lean | /-
Copyright (c) 2018 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
import Lean.Data.Options
universe u v
namespace Std
namespace Format
open Lean
def getWidth (o : Options) : Nat := o.get `format.width defWidth
def get... |
7725ae7c8874973ae703b8292b4dd4d9ffcd3c29 | 649957717d58c43b5d8d200da34bf374293fe739 | /src/topology/instances/real.lean | ea3e63a924d489e00a27b3f64f56edcc31fe4227 | [
"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 | 18,905 | 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
The real numbers ℝ.
They are constructed as the topological completion of ℚ. With the following steps:
(1) prove that ℚ forms a uniform space.
(2) subt... |
e0b2c30d1424689ed83a7520f5dece66d902f0c5 | 958488bc7f3c2044206e0358e56d7690b6ae696c | /lean/first_order.lean | 294a9d70d6e328330a1a9185624123ede51e6a28 | [] | 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 | 320 | lean | lemma L1 : ∀ (α : Type) (p q : α → Prop),
(∀ (x:α), p x ∧ q x) → ∀ (y:α), p y :=
λ α p q H y, show p y, from (H y).left
--#check L1
lemma L2 : ∀ (α : Type) (p q : α → Prop),
(∀ (x:α), p x ∧ q x) → ∀ (y:α), p y :=
assume α p q H y, show p y, from
(H y).left
--#check L2
|
c73f001b886ca9d82cf48b698f73fccfb706eeed | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/uniform_space/uniform_convergence_topology.lean | b7309d6fb990ef7629ae5309e6901d4f21693edb | [
"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 | 46,950 | lean | /-
Copyright (c) 2022 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
import topology.uniform_space.uniform_convergence
import topology.uniform_space.pi
import topology.uniform_space.equiv
/-!
# Topology and uniform structure of un... |
6299180969517c1fb31daccf59c4c6cad7812cd9 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/category/Mon/colimits.lean | 3fd2f27ef898099d6660bb512ba11fea5fb37840 | [] | 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 | 8,307 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.category.Mon.basic
import Mathlib.category_theory.limits.limits
import Mathlib.cate... |
e1f8bf347f228c30c516197d35d8d6095d1d8a79 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/nat/dist_auto.lean | 4b6b3e8aaf794e9dfd17ef8aac431b7f8b30f701 | [] | 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 | 3,911 | lean | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Jeremy Avigad
Distance function on the natural numbers.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.nat.basic
import Mathlib... |
d82dfa265ae72b246bd4c6c503b51153a3aafe3e | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Data/RBMap.lean | 6b235c260ec7ca0d86b09538d4c25b5c1c60ac53 | [
"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 | 15,405 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
namespace Lean
universe u v w w'
inductive RBColor where
| red | black
inductive RBNode (α : Type u) (β : α → Type v) where
| leaf ... |
9cb99582ed1867616a82af56d108df6f1385b36e | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/check.lean | 451c69de5bc9ebb01d00ee258e7b209cb3bf2621 | [
"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 | 97 | lean | import logic
set_option pp.metavar_args true
check and.intro
check or.elim
check eq
check eq.rec
|
5d4c0c282571a007ca8c37cbdc2d8552cb9a5a53 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/category/Mon/filtered_colimits.lean | 93d263d8b09419f80ddbff3ec8c9f443a40ac943 | [
"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 | 14,515 | lean | /-
Copyright (c) 2021 Justus Springer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Justus Springer
-/
import algebra.category.Mon.basic
import category_theory.limits.preserves.filtered
import category_theory.concrete_category.elementwise
import category_theory.limit... |
34c1bd69d1d8108e487f59b587effb798c0ba15a | 0ed3609caf1962115b28aeb010d2bda5f67ddc4c | /src/set_theory/ordinal.lean | 2af3b90bf513a5db906f145e49c7f6c2ad4c17f0 | [
"Apache-2.0"
] | permissive | jonaslippert/mathlib | 82dba29632969e3ed1c153a6454306f6bc9d9037 | 1435a196db69a7886a11e310e8923f3dcf249b81 | refs/heads/master | 1,609,938,673,069 | 1,582,018,388,000 | 1,582,018,388,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 138,225 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
Ordinal arithmetic.
Ordinals are defined as equivalences of well-ordered sets by order isomorphism.
-/
import order.order_iso set_theory.cardinal data.sum
noncomputable... |
9d561a7a2271420ffa2a4f75f7af46cd5fc7e344 | ac49064e8a9a038e07cf5574b4fccd8a70d115c8 | /hott/algebra/default.hlean | c12af809b60b6561954e69ac318c9064eed5ffd8 | [
"Apache-2.0"
] | permissive | Bolt64/lean2 | 7c75016729569e04a3f403c7a4fc7c1de4377c9d | 75fd8162488214a959dbe3303a185cbbb83f60f9 | refs/heads/master | 1,611,290,445,156 | 1,493,763,922,000 | 1,493,763,922,000 | 81,566,307 | 0 | 0 | null | 1,486,732,167,000 | 1,486,732,167,000 | null | UTF-8 | Lean | false | false | 206 | hlean | /-
Copyright (c) 2016 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import .homotopy_group .ordered_field .lattice
|
27942cc1fea4e9b2fec33e3326b67cab609ffc99 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/matrix/notation.lean | a5b8ce8843f08475771ce299fdab25caf078f0b2 | [] | 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 | 20,260 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
Notation for vectors and matrices
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.fintype.card
import Mathlib.data.matrix.basic
import Math... |
d5f2e69d6ce46e7d712f21fc4bda89e82329f38a | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /archive/100-theorems-list/82_cubing_a_cube.lean | cbfd9936ff2aec2d9badf251b7efc828414329b9 | [
"Apache-2.0"
] | permissive | dupuisf/mathlib | 62de4ec6544bf3b79086afd27b6529acfaf2c1bb | 8582b06b0a5d06c33ee07d0bdf7c646cae22cf36 | refs/heads/master | 1,669,494,854,016 | 1,595,692,409,000 | 1,595,692,409,000 | 272,046,630 | 0 | 0 | Apache-2.0 | 1,592,066,143,000 | 1,592,066,142,000 | null | UTF-8 | Lean | false | false | 23,055 | lean | /-
Copyright (c) 2019 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Floris van Doorn
-/
import data.real.basic
import data.set.disjointed
import data.set.intervals
import set_theory.cardinal
/-!
Proof that a cube (in dimension n ≥ 3) cannot be cubed:
... |
9907166387e0cc15f62415c2816b2abf90493760 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/1132.lean | cc8c16ccccaf31691f2564d88a30d27df06529ee | [
"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 | 512 | lean | class FooClass (α : Type) where
mkFoo : {m : Type → Type} → [Monad m] → α → m Nat
inductive Baz where | a | b
instance : FooClass Baz where
mkFoo := fun
| .a => return 0
| .b => return 1
instance : FooClass Baz where
mkFoo {m} _ := fun
| .a => return 0
| .b => return 1
instance : FooClass Baz ... |
f3182f89b87066b460884d0e00ace8df506b3bf3 | 90bd8c2a52dbaaba588bdab57b155a7ec1532de0 | /src/simply_connected/basic.lean | 7c216ca553c53f6b7a44609356b7ca30151dbe01 | [
"Apache-2.0"
] | permissive | shingtaklam1324/alg-top | fd434f1478925a232af45f18f370ee3a22811c54 | 4c88e28df6f0a329f26eab32bae023789193990e | refs/heads/master | 1,689,447,024,947 | 1,630,073,400,000 | 1,630,073,400,000 | 381,528,689 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 815 | lean | import homotopy_group.basic
/-!
# Simply Connected Spaces
In this file, we define what it means for a path connected space to be simply connected.
-/
variables {X : Type _} [topological_space X] [path_connected_space X]
/--
A path connected space `X` is simply connected if there is a `x₀` such that `π₁ x₀` is trivi... |
f5f2f437fa72c64102c619db442c30e5b0e55443 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /src/Lean/Meta/Tactic/Apply.lean | 81acd807e7a83b3dc082d1b74265e4f4bb84b010 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | EdAyers/lean4 | 57ac632d6b0789cb91fab2170e8c9e40441221bd | 37ba0df5841bde51dbc2329da81ac23d4f6a4de4 | refs/heads/master | 1,676,463,245,298 | 1,660,619,433,000 | 1,660,619,433,000 | 183,433,437 | 1 | 0 | Apache-2.0 | 1,657,612,672,000 | 1,556,196,574,000 | Lean | UTF-8 | Lean | false | false | 6,889 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Util.FindMVar
import Lean.Meta.SynthInstance
import Lean.Meta.CollectMVars
import Lean.Meta.Tactic.Util
namespace Lean.Meta
/--
Compute the ... |
a66c87d367a6b9549d1756ec1d6a0d31030c86e7 | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /tests/lean/run/match4.lean | 4aa55c10da67be655c533fd7f41cd9f64afe6b1a | [
"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 | 518 | lean | open nat bool inhabited prod
definition diag (a b c : bool) : nat :=
match (a, b, c) with
(_, tt, ff) := 1,
(ff, _, tt) := 2,
(tt, ff, _) := 3,
(_, _, _) := arbitrary nat
end
theorem diag1 (a : bool) : diag a tt ff = 1 :=
bool.cases_on a rfl rfl
theorem diag2 (a : bool) : diag ff a tt = 2 :=
bool.cases... |
170ec621279f6fb0f38c275fd79c0e4b8cffc996 | 54c9ed381c63410c9b6af3b0a1722c41152f037f | /Binport/ParseExport.lean | 56d91d1ab9f9f50812789fd6ca48d499a4dd611c | [
"Apache-2.0"
] | permissive | dselsam/binport | 0233f1aa961a77c4fc96f0dccc780d958c5efc6c | aef374df0e169e2c3f1dc911de240c076315805c | refs/heads/master | 1,687,453,448,108 | 1,627,483,296,000 | 1,627,483,296,000 | 333,825,622 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,756 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Selsam, Gabriel Ebner
-/
import Binport.Util
import Binport.Basic
import Binport.ActionItem
import Lean
import Std.Data.HashSet
import Std.Data.HashMap
namespace Binport... |
bd4485b1298bac92de8a55f55f7c5818d8350c92 | efce24474b28579aba3272fdb77177dc2b11d7aa | /src/homotopy_theory/topological_spaces/closed_t1_inclusion.lean | 87a2d4aff6bfaa49670ef8ac87c029bae69a2e72 | [
"Apache-2.0"
] | permissive | rwbarton/lean-homotopy-theory | cff499f24268d60e1c546e7c86c33f58c62888ed | 39e1b4ea1ed1b0eca2f68bc64162dde6a6396dee | refs/heads/lean-3.4.2 | 1,622,711,883,224 | 1,598,550,958,000 | 1,598,550,958,000 | 136,023,667 | 12 | 6 | Apache-2.0 | 1,573,187,573,000 | 1,528,116,262,000 | Lean | UTF-8 | Lean | false | false | 3,037 | lean | import .pushout_lemmas
local attribute [instance] classical.prop_decidable
universe u
open category_theory set
namespace homotopy_theory.topological_spaces
open homotopy_theory.topological_spaces.Top
local notation `Top` := Top.{u}
def closed_t1_inclusion {A X : Top} (i : A ⟶ X) : Prop :=
embedding i ∧ is_closed (... |
3603e58b26cf12b15325101fe679cab29fc7a81e | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/algebra/group_with_zero/basic.lean | 9d7c48dd57d3a5770b620cfd1fe2445cd492284f | [
"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 | 46,586 | 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 logic.nontrivial
import algebra.group.units_hom
import algebra.group.inj_surj
import algebra.group_with_zero.defs
/-!
# Groups with an adjoined zero element
... |
b1890fe41be7cdbb2fbabc6d3fd2bd347b02cd65 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/group_theory/transfer.lean | db47f440cf7487ad4148310e439cf619613e80b7 | [
"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 | 2,994 | lean | /-
Copyright (c) 2022 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import group_theory.complement
import group_theory.group_action.basic
import group_theory.index
/-!
# The Transfer Homomorphism
In this file we construct the tra... |
05e3fc3a359872acafda839f590db14f3fa7ea5a | 5d166a16ae129621cb54ca9dde86c275d7d2b483 | /tests/lean/run/and_rec_code_gen_issue.lean | fa0f9b99a6b2e3df1f837c8d991e8f5d4e025afe | [
"Apache-2.0"
] | permissive | jcarlson23/lean | b00098763291397e0ac76b37a2dd96bc013bd247 | 8de88701247f54d325edd46c0eed57aeacb64baf | refs/heads/master | 1,611,571,813,719 | 1,497,020,963,000 | 1,497,021,515,000 | 93,882,536 | 1 | 0 | null | 1,497,029,896,000 | 1,497,029,896,000 | null | UTF-8 | Lean | false | false | 3,219 | lean | import data.buffer
structure hoare_state (σ : Type) (α : Type) :=
(pre : σ → Prop)
(post : σ → α → σ → Prop)
(action : ∀ s : {s // pre s}, {as' : α × σ // post s.val as'.1 as'.2})
namespace hoare_state
protected def return (σ : Type) {α : Type} (a : α) : hoare_state σ α :=
{pre := λ s, true,
post := λ s a... |
1c4875165275e644056fd7e1e1d3ea4eefde1e52 | 969dbdfed67fda40a6f5a2b4f8c4a3c7dc01e0fb | /src/linear_algebra/quadratic_form.lean | 0d78495eb220c77b1884a52c23274d5d2cb809b4 | [
"Apache-2.0"
] | permissive | SAAluthwela/mathlib | 62044349d72dd63983a8500214736aa7779634d3 | 83a4b8b990907291421de54a78988c024dc8a552 | refs/heads/master | 1,679,433,873,417 | 1,615,998,031,000 | 1,615,998,031,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 30,397 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Anne Baanen
-/
import algebra.invertible
import linear_algebra.bilinear_form
import linear_algebra.determinant
import linear_algebra.special_linear_group
/-!
# Quadratic forms
This file... |
a13037897ee20784851f32d36760669a9a6fc568 | 367134ba5a65885e863bdc4507601606690974c1 | /src/algebra/ordered_monoid.lean | 42d29f05fa292eeb852ac1c5aa890ba81ee45f49 | [
"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 | 47,585 | 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.group.with_one
import algebra.group.type_tags
import algebra.group.prod
import algebra.order_functions... |
3122b8638223bf42e70a801f217c095c276f4555 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/run/cpdt.lean | 38f55ace1a482589562fef63941095af8ebad1d8 | [
"Apache-2.0"
] | permissive | GaloisInc/lean | aa1e64d604051e602fcf4610061314b9a37ab8cd | f1ec117a24459b59c6ff9e56a1d09d9e9e60a6c0 | refs/heads/master | 1,592,202,909,807 | 1,504,624,387,000 | 1,504,624,387,000 | 75,319,626 | 2 | 1 | Apache-2.0 | 1,539,290,164,000 | 1,480,616,104,000 | C++ | UTF-8 | Lean | false | false | 1,081 | lean | /- "Proving in the Large" chapter of CPDT -/
inductive exp : Type
| Const (n : nat) : exp
| Plus (e1 e2 : exp) : exp
| Mult (e1 e2 : exp) : exp
open exp
def eeval : exp → nat
| (Const n) := n
| (Plus e1 e2) := eeval e1 + eeval e2
| (Mult e1 e2) := eeval e1 * eeval e2
def times (k : nat) : exp → exp
| (Const n) ... |
9b9847fdd6786eb6ea66b1421cbde6469f2cbf67 | f3a5af2927397cf346ec0e24312bfff077f00425 | /src/game/world10/level11.lean | 359ddc842be9db7a23637d1b1c21faddbc60330a | [
"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 | 571 | lean | import game.world10.level10 -- hide
namespace mynat -- hide
/-
# Inequality world.
## Level 11: `add_le_add_right`
If you're faced with a goal of the form `forall t, ...`, then the next
line is "so let $t$ be arbitrary". The way to do this in Lean is `intro t`.
-/
/- Lemma
For all naturals $a$ and $b$, $a\le b$ i... |
ebdf08f4b60b09038269304ea1cd3baeb6d0e12b | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/nat/dist.lean | c6eacfc7255103a3dc91bcaf2bd58a52c616f7fe | [
"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 | 4,135 | lean | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Jeremy Avigad
-/
import data.nat.basic
/-!
# Distance function on ℕ
This file defines a simple distance function on naturals from truncated substraction.
-/
nam... |
fefdd194dd07f730bb26870e86575f98bbe4ef24 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/algebra/triv_sq_zero_ext.lean | eba81416ae1c79019bd8cc8e895b04336162f1a6 | [
"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 | 16,678 | 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.basic
import linear_algebra.prod
/-!
# Trivial Square-Zero Extension
Given a module `M` over a ring `R`, the trivial square-zero extension of `M` over... |
c515e30dd622c05893a62494a01e0096e408d0af | 5749d8999a76f3a8fddceca1f6941981e33aaa96 | /src/data/zsqrtd/basic.lean | bb72887cc9e98fa0aadd0fa8ad0826f2b27736ab | [
"Apache-2.0"
] | permissive | jdsalchow/mathlib | 13ab43ef0d0515a17e550b16d09bd14b76125276 | 497e692b946d93906900bb33a51fd243e7649406 | refs/heads/master | 1,585,819,143,348 | 1,580,072,892,000 | 1,580,072,892,000 | 154,287,128 | 0 | 0 | Apache-2.0 | 1,540,281,610,000 | 1,540,281,609,000 | null | UTF-8 | Lean | false | false | 26,811 | 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.int.basic algebra.associated data.nat.gcd
/-- The ring of integers adjoined with a square root of `d`.
These have the form `a + b √d` where `a b : ℤ`. ... |
ac664e7cbe674fcc4c9bedf685880c7aa1f03152 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /10_Structures_and_Records.org.6.lean | e94c6fb62deb999a0a80d6ef0a6ad768eaf2fdcb | [] | no_license | cjmazey/lean-tutorial | ba559a49f82aa6c5848b9bf17b7389bf7f4ba645 | 381f61c9fcac56d01d959ae0fa6e376f2c4e3b34 | refs/heads/master | 1,610,286,098,832 | 1,447,124,923,000 | 1,447,124,923,000 | 43,082,433 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 65 | lean | import standard
record point (A : Type) :=
mk :: (x : A) (y : A)
|
800a5222014475a2bcae33658d54d57e60937840 | 367134ba5a65885e863bdc4507601606690974c1 | /src/linear_algebra/finsupp_vector_space.lean | 15e0e9b36c5e90f0e83025d1d3132c720c9fe48f | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 7,091 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
-/
import data.mv_polynomial
import linear_algebra.dimension
import linear_algebra.direct_sum.finsupp
import linear_algebra.finite_dimensional
/-!
# Linear structures o... |
c2b9d9b9836e721ab2c4983f2fccfd42e8c857d2 | 08bd4ba4ca87dba1f09d2c96a26f5d65da81f4b4 | /src/Lean/MetavarContext.lean | e1040c1af21e9a266483761f4bb76f267563cbc9 | [
"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",
"Apache-2.0",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | gebner/lean4 | d51c4922640a52a6f7426536ea669ef18a1d9af5 | 8cd9ce06843c9d42d6d6dc43d3e81e3b49dfc20f | refs/heads/master | 1,685,732,780,391 | 1,672,962,627,000 | 1,673,459,398,000 | 373,307,283 | 0 | 0 | Apache-2.0 | 1,691,316,730,000 | 1,622,669,271,000 | Lean | UTF-8 | Lean | false | false | 64,085 | 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.Util.MonadCache
import Lean.LocalContext
namespace Lean
/-!
The metavariable context stores metavariable declarations and their
assignments. I... |
5306a6fb268fac3a6482f89dbfd79aceffe5989e | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /tests/lean/run/500_lean3.lean | 39de9ca088c99e041d39f40a4a56c3a59efaed6a | [
"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 | 124 | lean | example (foo bar : OptionM Nat) : False := by
have do { let x ← bar; foo } = bar >>= fun x => foo := rfl
admit
done
|
7d762ba3fb4eef58684d538f11809d6e5c4284ff | abd85493667895c57a7507870867b28124b3998f | /src/group_theory/order_of_element.lean | 186fa205ab6bf0432aca30c7febc02cf8e14f8c6 | [
"Apache-2.0"
] | permissive | pechersky/mathlib | d56eef16bddb0bfc8bc552b05b7270aff5944393 | f1df14c2214ee114c9738e733efd5de174deb95d | refs/heads/master | 1,666,714,392,571 | 1,591,747,567,000 | 1,591,747,567,000 | 270,557,274 | 0 | 0 | Apache-2.0 | 1,591,597,975,000 | 1,591,597,974,000 | null | UTF-8 | Lean | false | false | 24,259 | 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 group_theory.coset
import data.nat.totient
import data.set.finite
open function
variables {α : Type*} {s : set α} {a a₁ a₂ b c: α}
-- TODO this lemma isn't u... |
e4828122c75a5c1d6be64c94bc6e432da880e104 | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/data/pnat/basic.lean | 89f01acb723e1fdc7d3c9c56fdbf316f746cd8bd | [
"Apache-2.0"
] | permissive | jumpy4/mathlib | d3829e75173012833e9f15ac16e481e17596de0f | af36f1a35f279f0e5b3c2a77647c6bf2cfd51a13 | refs/heads/master | 1,693,508,842,818 | 1,636,203,271,000 | 1,636,203,271,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 15,067 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Neil Strickland
-/
import algebra.group_power.basic
/-!
# The positive natural numbers
This file defines the type `ℕ+` or `pnat`, the subtype of natural number... |
0ad672fec854258c65d099192173d0afce5cf59c | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /stage0/src/Lean/Elab/Tactic/Conv/Rewrite.lean | 39861871c2d22503c6fd099cad9467a21a939134 | [
"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 | 781 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.Tactic.Rewrite
import Lean.Elab.Tactic.Rewrite
import Lean.Elab.Tactic.Conv.Basic
namespace Lean.Elab.Tactic.Conv
open Meta
@[builtinTact... |
bca5213117119db568e355c1cbac1eb96e654c59 | acc85b4be2c618b11fc7cb3005521ae6858a8d07 | /logic/basic.lean | ca0415ed48c7c3d47a20665f9d8235c085b5ddff | [
"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 | 18,343 | 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
Theorems that require decidability hypotheses are in the namespace "decidable".
Classical versions are in the namespace "classical".
Note: in the pres... |
f476a1008a2d2b57d11ec5d32301c745fa274116 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/order/filter/filter_product.lean | 97249ae6faafea570b95430dcad6dca13c44721b | [
"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 | 4,897 | 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, Yury Kudryashov
-/
import order.filter.ultrafilter
import order.filter.germ
/-!
# Ultraproducts
If `φ` is an ultrafilter, then the space of germs ... |
aa35af3c00c991b7cd2a00a3dc6e4287c6d32000 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/linear_algebra/alternating.lean | 14d0b96d0024b48bc6d57bac38fc7002dc2a84d4 | [
"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 | 42,986 | lean | /-
Copyright (c) 2020 Zhangir Azerbayev. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Zhangir Azerbayev
-/
import group_theory.group_action.quotient
import group_theory.perm.sign
import group_theory.perm.subgroup
import linear_algebra.linear_independent... |
b427a944ffc01b343c18257783252eb717e0dffc | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/continued_fractions/continuants_recurrence.lean | e3a6f7bf026d53a63f18560583dc8275933c1db5 | [
"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 | 3,761 | lean | /-
Copyright (c) 2019 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import algebra.continued_fractions.translations
/-!
# Recurrence Lemmas for the `continuants` Function of Continued Fractions.
> THIS FILE IS SYNCHRONIZED WITH M... |
9e8bc2860416d415c47e2f11ecd73dfb52ebbc2c | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/implicitApplyIssue.lean | f6a03865900b1fd930b083e05dda7cd2bb9268ba | [
"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 | 848 | lean | def Set α := α → Prop
class HasMem (α : outParam $ Type u) (β : Type v) where
mem : α → β → Prop
infix:50 " ∈ " => HasMem.mem
instance {α : Type u} : HasMem α (Set α) := ⟨λ a s => s a⟩
instance {α : Type u} : LE (Set α) := ⟨λ s t => ∀ {x : α}, x ∈ s → x ∈ t⟩
class HasInf (P : Type u) where
inf : P → P → P
i... |
29e69d48d988c057ac3415fd668e89a5c715e571 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/field_theory/polynomial_galois_group.lean | ae71bd2348ebe5da46b1ae78086e878b626af98e | [
"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 | 21,463 | lean | /-
Copyright (c) 2020 Thomas Browning, Patrick Lutz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning, Patrick Lutz
-/
import analysis.complex.polynomial
import field_theory.galois
import group_theory.perm.cycle_type
import ring_theory.eisenstein_criteri... |
2f5cb89428fd02c2f654f2e38119dd41536bb789 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/data/int/basic_auto.lean | f7957cacdcb629f9f058c53529db357ec2b191fa | [] | 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 | 13,527 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
The integers, with addition, multiplication, and subtraction.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.data.nat.lemmas
import Mathlib.Lean3Lib.init.data.nat... |
d212b81f892ba12387f10410aa70d2677c794e05 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/assoc_flat.lean | c10c5aa4c7ec877f9dfd854697481f3d0598cabb | [
"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 | 2,369 | lean | open tactic expr
constant nat.add_assoc (a b c : nat) : (a + b) + c = a + (b + c)
meta_definition is_op_app (op : expr) (e : expr) : option (expr × expr) :=
match e with
| (app (app fn a1) a2) := if op = fn then some (a1, a2) else none
| e := none
end
meta_definition flat_with : expr → expr → expr... |
6ddb23e8710cdc1c4ab2cb6d0664da7575cdf3e0 | 90bd8c2a52dbaaba588bdab57b155a7ec1532de0 | /src/path/defs.lean | bd53b57b9a7b33846a274f1408d45175f0cbc641 | [
"Apache-2.0"
] | permissive | shingtaklam1324/alg-top | fd434f1478925a232af45f18f370ee3a22811c54 | 4c88e28df6f0a329f26eab32bae023789193990e | refs/heads/master | 1,689,447,024,947 | 1,630,073,400,000 | 1,630,073,400,000 | 381,528,689 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,874 | lean | import topology.continuous_function.basic
import topology.instances.real
import topology.path_connected
/-!
# Paths
Given a topological space `X`, and points `x₀ x₁ : X`, we define a `path' x₀ x₁` to be a continuous
function `to_fun : C(ℝ, X)` where `to_fun 0 = x₀` and `to_fun 1 = x₁`.
We define an API for a differe... |
7fa13a6a926c0254fabfb73f162b2018fc27e2e1 | 37683ecbb27d7c2037bfd9ad7e06d662f460a005 | /pointed_pi.hlean | 446f3247b678666416b1ecec6884b1d687494ddf | [
"Apache-2.0"
] | permissive | GRSEB9S/Spectral-1 | b2443b09cae7aac1247b1f88c846c532ac802b8e | dd14277e0bfc6270a488eb3b9ec231484065b9d8 | refs/heads/master | 1,631,315,269,407 | 1,522,048,315,000 | 1,522,799,803,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 45,544 | hlean | /-
Copyright (c) 2016 Ulrik Buchholtz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ulrik Buchholtz, Floris van Doorn
-/
import homotopy.connectedness types.pointed2 .move_to_lib .pointed
open eq pointed equiv sigma is_equiv trunc option pi function fiber
/-
In ... |
748254a05617e1792cec35a4196eeca5de811ce4 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/measure_theory/function/lp_space.lean | c4ecc2d2109e2c30b608fff95d648a05b5fd8980 | [
"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 | 122,273 | lean | /-
Copyright (c) 2020 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Sébastien Gouëzel
-/
import analysis.normed_space.indicator_function
import analysis.normed.group.hom
import measure_theory.function.ess_sup
import measure_theory.function.... |
9b323fa06bde3ff6c4b4a88bd085f08b6fde4f50 | 75db7e3219bba2fbf41bf5b905f34fcb3c6ca3f2 | /library/data/real/order.lean | 837f0ff6b5de7888bf1a0e52966bb0de5035a3be | [
"Apache-2.0"
] | permissive | jroesch/lean | 30ef0860fa905d35b9ad6f76de1a4f65c9af6871 | 3de4ec1a6ce9a960feb2a48eeea8b53246fa34f2 | refs/heads/master | 1,586,090,835,348 | 1,455,142,203,000 | 1,455,142,277,000 | 51,536,958 | 1 | 0 | null | 1,455,215,811,000 | 1,455,215,811,000 | null | UTF-8 | Lean | false | false | 38,741 | lean | /-
Copyright (c) 2015 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Robert Y. Lewis
The real numbers, constructed as equivalence classes of Cauchy sequences of rationals.
This construction follows Bishop and Bridges (1985).
To do:
o Rename things and... |
007382cd553501f93ffae61389f8af47bc977e1d | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/eval_constant.lean | f5dd5f289e3bb9b7efbb691e79455640e2447897 | [
"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 | 244 | lean | open tactic
run_cmd do
e ← to_expr ``(nat.add),
fn ← eval_expr (nat → nat → nat) e,
trace (fn 10 20)
run_cmd do
e ← to_expr ``(λ x y : nat, x + x + y),
fn ← eval_expr (nat → nat → nat) e,
trace (fn 10 20)
|
07e58140197e844f0a9d9e6f86151b911a8e4cc9 | 3dd1b66af77106badae6edb1c4dea91a146ead30 | /tests/lean/run/group2.lean | 5d1b2b6f23dd6775d1a4a7b20590dce9be1b38ec | [
"Apache-2.0"
] | permissive | silky/lean | 79c20c15c93feef47bb659a2cc139b26f3614642 | df8b88dca2f8da1a422cb618cd476ef5be730546 | refs/heads/master | 1,610,737,587,697 | 1,406,574,534,000 | 1,406,574,534,000 | 22,362,176 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,725 | lean | import standard
using num
section
parameter {A : Type}
parameter f : A → A → A
parameter one : A
parameter inv : A → A
infixl `*`:75 := f
postfix `^-1`:100 := inv
definition is_assoc := ∀ a b c, (a*b)*c = a*b*c
definition is_id := ∀ a, a*one = a
definition is_inv := ∀ a, a*a^-1 = one
end
... |
e246f9faa31cdc189d77168b01d7f1cd943c2bd4 | 36c7a18fd72e5b57229bd8ba36493daf536a19ce | /library/theories/group_theory/finsubg.lean | 67dff7079268eb7d8c041c39bb6e401b542e6271 | [
"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 | 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... |
d7aab8964464cccf6342abd06fdb7eba40a4b6a9 | 7c216aab58e7d519f010545575b6a843da4aa0ac | /metamath/lean/main.lean | e1b2bdec5d3a90656de7306d76c319f7ac0359aa | [] | no_license | digama0/twitchcoq | 82a301baf97eb5e0ec855ee7f45d5b2735c12601 | 2f3d63289b93456040491e8b50140a49f34d8b61 | refs/heads/master | 1,606,509,387,393 | 1,577,030,121,000 | 1,577,030,121,000 | 229,592,726 | 2 | 0 | null | 1,577,030,158,000 | 1,577,030,157,000 | null | UTF-8 | Lean | false | false | 3,542 | lean | import system.io
import init.data.string.ops
inductive stmt : Type
| constant_stmt : list string -> stmt
| variable_stmt : list string -> stmt
| disjoint_stmt : list string -> stmt
| floating_stmt : string -> string -> string -> stmt
| essential_stmt : string -> string -> (list string) -> stmt
| axiom_stmt : string ->... |
657f1baf3ffd03048af1c0c6c39b433d102efb41 | f7315930643edc12e76c229a742d5446dad77097 | /tests/lean/run/tactic22.lean | 9400e037838896393678bd10921fe53180e74582 | [
"Apache-2.0"
] | permissive | bmalehorn/lean | 8f77b762a76c59afff7b7403f9eb5fc2c3ce70c1 | 53653c352643751c4b62ff63ec5e555f11dae8eb | refs/heads/master | 1,610,945,684,489 | 1,429,681,220,000 | 1,429,681,449,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 177 | lean | import logic
open tactic
theorem T (a b c d : Prop) (Ha : a) (Hb : b) (Hc : c) (Hd : d) : a ∧ b ∧ c ∧ d
:= by fixpoint (λ f, (apply @and.intro; f | assumption; f | id))
|
7b978c084df301bb042991006e5ef81fe6fd8428 | b522075d31b564daeb3347a10eb9bb777ee93943 | /equiv.lean | 24ab6e143943bdfe3e21fd383b900ea91a89446a | [] | no_license | truonghoangle/manifolds | e6c2534dd46579f56ba99a48e2eb7ce51640e7c0 | 9c0d731a480e88758180b31ce7c3b371771d426b | refs/heads/master | 1,638,501,090,139 | 1,557,991,948,000 | 1,557,991,948,000 | 185,779,631 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,076 | lean | /-
Copyright (c) 2019 Joe Cool. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Hoang Le Truong.
-/
import data.equiv.algebra algebra.module data.pfun
universes u v w
variables {α : Type u} {β : Type v} {γ : Type w}
local attribute [instance] classical.prop_deci... |
24604991a081868e07abcf4646ad010bd537c40f | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/analysis/normed_space/bounded_linear_maps.lean | 243e941a68b29e594cad2c98ec16a02d1494e40f | [
"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 | 13,374 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
Continuous linear functions -- functions between normed vector spaces which are bounded and linear.
-/
import algebra.field
import analysis.normed_space... |
0d3f4e2e4b20d43fb07cc11983c5325ca296697f | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /06_Inductive_Types.org.35.lean | 8a17305c0d296d098d1800fafdfb3308ff2261d9 | [] | no_license | cjmazey/lean-tutorial | ba559a49f82aa6c5848b9bf17b7389bf7f4ba645 | 381f61c9fcac56d01d959ae0fa6e376f2c4e3b34 | refs/heads/master | 1,610,286,098,832 | 1,447,124,923,000 | 1,447,124,923,000 | 43,082,433 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 322 | lean | /- page 89 -/
import standard
namespace hide
-- BEGIN
inductive list (A : Type) : Type :=
| nil {} : list A
| cons : A → list A → list A
namespace list
notation `[` l:(foldr `,` (h t, cons h t) nil) `]` := l
section
open nat
check [1, 2, 3, 4, 5]
check ([1, 2, 3, 4, 5] : list ℕ)
end
end list
-- END
end hide
|
e6de58ff331db089a3adafb358bc919fa3590b98 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Meta/SizeOf.lean | be337143d0c62591d10636a241a45fbbe745023f | [
"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 | 23,640 | 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.AppBuilder
import Lean.Meta.Instances
namespace Lean.Meta
/-- Create `SizeOf` local instances for applicable parameters, and execute `k` ... |
f40f1df70efa79a53ef6408cda3cb8b94162c022 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/measure_theory/integration.lean | 5282b30bd407989c941b4a957a90938fe3218f95 | [] | 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 | 70,067 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.measure_theory.measure_space
import Mathlib.measure_theory.borel_space
impo... |
0b031e4d708ea638eda19aa6fdfc115f93df59dc | 35b83be3126daae10419b573c55e1fed009d3ae8 | /_target/deps/mathlib/algebra/group_power.lean | f266e95c9c0e771a97be6f3026678108c6820482 | [] | no_license | AHassan1024/Lean_Playground | ccb25b72029d199c0d23d002db2d32a9f2689ebc | a00b004c3a2eb9e3e863c361aa2b115260472414 | refs/heads/master | 1,586,221,905,125 | 1,544,951,310,000 | 1,544,951,310,000 | 157,934,290 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 23,082 | lean | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis
The power operation on monoids and groups. We separate this from group, because it depends on
nat, which in turn depends on other parts of algebra.
We h... |
646aa2c4b047b871d261d63d098c0acf76ab5713 | 4950bf76e5ae40ba9f8491647d0b6f228ddce173 | /src/logic/basic.lean | 73ba7bca130d208b2a6bf63293495e07efe2ccbc | [
"Apache-2.0"
] | permissive | ntzwq/mathlib | ca50b21079b0a7c6781c34b62199a396dd00cee2 | 36eec1a98f22df82eaccd354a758ef8576af2a7f | refs/heads/master | 1,675,193,391,478 | 1,607,822,996,000 | 1,607,822,996,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 51,272 | 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
-/
import tactic.doc_commands
/-!
# Basic logic properties
This file is one of the earliest imports in mathlib.
## Implementation notes
Theorems tha... |
12a1dba013476a6f3b2ab758fcf5d0ca47abbb9e | b66feea4001b6bd591938498243cbb311bef715f | /test.lean | 94ac7ebe706341749cb16354415abdf6de83e76a | [
"CC-BY-4.0"
] | permissive | vutuananh1210/formalabstracts | e19c27eded6272515db2293f5670d93c3f6cb2ab | 58400178f7b1996afc0d34a141ebaf1db6744eec | refs/heads/master | 1,584,645,359,178 | 1,529,492,486,000 | 1,529,492,486,000 | 136,415,832 | 0 | 0 | null | 1,528,341,384,000 | 1,528,341,384,000 | null | UTF-8 | Lean | false | false | 580 | lean | import
analysis.real
data.set.finite
analysis.topology.topological_structures
data.nat.prime
structure homeo (α β : Type* )[topological_space α ][topological_space β ] extends α ≃ β :=
(to_fun_cont: continuous to_fun)
(inv_fun_cont: continuous inv_fun )
variable (n:ℕ )
#check fin n
#check (by apply_instance:
topo... |
8fa9b2dbddd3e73cead2efadd55dc779d4d123a1 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/order/category/HeytAlg.lean | 5e3c7af5b84b4090a150b7ad78a9afb5c2a66569 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 1,789 | lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import order.category.BoundedDistribLattice
import order.heyting.hom
/-!
# The category of Heyting algebras
This file defines `HeytAlg`, the category of Heyting algebra... |
a8eb9339ac4ed722fa3bd062ee8802d480199bef | 618003631150032a5676f229d13a079ac875ff77 | /test/push_neg.lean | a0a36ae2aede160d3be94558ef418863e862ebb4 | [
"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 | 2,070 | lean | import tactic.push_neg
import init_.data.int.order
import data.nat.basic
example (h : ∃ p: ℕ, ¬ ∀ n : ℕ, n > p) (h' : ∃ p: ℕ, ¬ ∃ n : ℕ, n < p) : ¬ ∀ n : ℕ, n = 0 :=
begin
push_neg at *,
guard_target_strict ∃ (n : ℕ), n ≠ 0,
guard_hyp_strict h := ∃ (p n : ℕ), n ≤ p,
guard_hyp_strict h' := ∃ (p : ℕ), ∀ (n : ℕ),... |
897099c73835b30e32a25eed4def314cec0a0cc6 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/geom_sum.lean | d129841e1be0e4ac23cdfa1616357c485e0a991c | [
"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 | 21,695 | lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Neil Strickland
-/
import algebra.big_operators.order
import algebra.big_operators.ring
import algebra.big_operators.intervals
import tactic.abel
import data.nat.parity
/-!
# Partia... |
7159b0657b1f0081a9f56c581cea0b343d2ce6de | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/finsupp/lex.lean | 09fdd2c4fc9ef030b0535de8e5f297d12540c24f | [
"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 | 4,782 | lean | /-
Copyright (c) 2022 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import data.finsupp.order
import data.dfinsupp.lex
import data.finsupp.to_dfinsupp
/-!
# Lexicographic order on finitely supported functions
> THIS FILE IS SYNCHRONIZ... |
c879cc7676841f26167c4aefeb75659d091cb56f | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/equiv/encodable/small.lean | 0f645241bad783faba9a95a5c0af30768a934c04 | [
"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 | 473 | 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 data.equiv.encodable.basic
import logic.small
/-!
# All encodable types are small.
That is, any encodable type is equivalent to a type in any universe.
-/
u... |
9abc499744f63ee66dba000d027976ff54117f80 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /library/data/finset/equiv.lean | 2de7a0bf6c5d51dd964a9a680d29667bd28f7aef | [
"Apache-2.0"
] | permissive | davidmueller13/lean | 65a3ed141b4088cd0a268e4de80eb6778b21a0e9 | c626e2e3c6f3771e07c32e82ee5b9e030de5b050 | refs/heads/master | 1,611,278,313,401 | 1,444,021,177,000 | 1,444,021,177,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,880 | 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
-/
import data.finset.card
open nat nat.finset decidable
namespace finset
variable {A : Type}
protected definition to_nat (s : finset nat) : nat :=
nat.finset... |
d8a8ded43eece2c8724519c639772028f6722652 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/nat/dist.lean | 256b6f41b482c153feb6e09f167982a5c3fa18e1 | [
"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 | 4,141 | lean | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Jeremy Avigad
-/
import data.nat.order.basic
/-!
# Distance function on ℕ
This file defines a simple distance function on naturals from truncated substraction.
-... |
d04665a02bbc2aa4f5256481935dac19f6a3db1e | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/category_theory/single_obj.lean | 9275e9546200eb02eb6e4aac38bcc201c46bfa9d | [
"Apache-2.0"
] | permissive | agjftucker/mathlib | d634cd0d5256b6325e3c55bb7fb2403548371707 | 87fe50de17b00af533f72a102d0adefe4a2285e8 | refs/heads/master | 1,625,378,131,941 | 1,599,166,526,000 | 1,599,166,526,000 | 160,748,509 | 0 | 0 | Apache-2.0 | 1,544,141,789,000 | 1,544,141,789,000 | null | UTF-8 | Lean | false | false | 5,389 | lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import category_theory.endomorphism
import category_theory.category.Cat
import algebra.category.Mon.basic
/-!
# Single-object category
Single object category with... |
f6cb7a05ca51d4a4ed33253691a1c576bafd7eb9 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/probability/probability_mass_function/basic.lean | b849e214b150b9dbe5f6774bf6a11927ac7685e5 | [
"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 | 14,532 | 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 topology.instances.ennreal
import measure_theory.measure.measure_space
/-!
# Probability mass functions
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4... |
be73c1eb783b4405cb9351d0ebbdb8e80e3b89d9 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /library/theories/group_theory/cyclic.lean | 6b80cc44c3baf7f5a9a4e2583ae24796e65776c9 | [
"Apache-2.0"
] | permissive | davidmueller13/lean | 65a3ed141b4088cd0a268e4de80eb6778b21a0e9 | c626e2e3c6f3771e07c32e82ee5b9e030de5b050 | refs/heads/master | 1,611,278,313,401 | 1,444,021,177,000 | 1,444,021,177,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 15,737 | 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 data algebra.group algebra.group_power .finsubg .hom .perm
open function algebra finset
open eq.ops
namespace group
section cyclic
open nat fin list
local att... |
fddbf538f8b42dd238650df35f4a1af9aa6242aa | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/582.hlean | f540a022ff48d8ebc63aa994e58b47a285217d12 | [
"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 | 173 | hlean | open prod
variables {A B C : Type} (f : A → B → C) (a : A) (b b' : B)
example (p : b = b') : prod.cases_on (a, b) f = f a b' :=
begin
esimp,
state,
rewrite p
end
|
53bdfbd42c7a16e45722c5dd3e74608f53b10a90 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/1389.lean | e93994dc6eb3284c6636f6fd9c180247e6bce4dd | [
"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 | 181 | lean | inductive Bit where
| zero
| one
instance inst0 : OfNat Bit 0 where
ofNat := Bit.zero
instance : OfNat Bit 1 where
ofNat := Bit.one
example : Bit := 0
example : Bit := 1
|
115dd89234925bf6f3361743460deb93f2665004 | 626e312b5c1cb2d88fca108f5933076012633192 | /src/ring_theory/fractional_ideal.lean | 34f7fdb119dc378eca6a8df0adafec9911fe382b | [
"Apache-2.0"
] | permissive | Bioye97/mathlib | 9db2f9ee54418d29dd06996279ba9dc874fd6beb | 782a20a27ee83b523f801ff34efb1a9557085019 | refs/heads/master | 1,690,305,956,488 | 1,631,067,774,000 | 1,631,067,774,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 49,394 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Filippo A. E. Nuccio
-/
import ring_theory.localization
import ring_theory.noetherian
import ring_theory.principal_ideal_domain
import tactic.field_simp
/-!
# Fractional ide... |
19aae68208446bc719ffc200970e1ed0565a60af | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/ring_theory/algebra_tower.lean | a1934918f7194fca9b5604304928d86d07183a46 | [
"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 | 12,623 | 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 algebra.invertible
import linear_algebra.basis
import ring_theory.adjoin.basic
import ring_theory.polynomial.tower
/-!
# Towers of algebra... |
77972c32e28e4e7bbd6dd1fe245e191adbf63b3a | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/category_theory/limits/pi.lean | 780e1b0e3c5f785c52bf4b6ae8e38d2ad3dbfa5f | [
"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 | 4,499 | 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.pi.basic
import category_theory.limits.limits
/-!
# Limits in the category of indexed families of objects.
Given a functor `F : J ⥤ Π i, C i`... |
73b6da58bde25f3a39f64739b30a252323854d2d | 32da3d0f92cab08875472ef6cacc1931c2b3eafa | /src/category_theory/limits/shapes/binary_products.lean | 30ba1f56242c3721f14aaa300190d223c12eaa5f | [
"Apache-2.0"
] | permissive | karthiknadig/mathlib | b6073c3748860bfc9a3e55da86afcddba62dc913 | 33a86cfff12d7f200d0010cd03b95e9b69a6c1a5 | refs/heads/master | 1,676,389,371,851 | 1,610,061,127,000 | 1,610,061,127,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 34,014 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Bhavik Mehta
-/
import category_theory.limits.limits
import category_theory.limits.shapes.terminal
import category_theory.discrete_category
import category_theory.epi_m... |
f62c47d06e0f49942f743a78fedd2ffb27eadf02 | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/topology/metric_space/antilipschitz.lean | a3ae855ab0025a7e64090f346d82861a680c5402 | [
"Apache-2.0"
] | permissive | vaibhavkarve/mathlib | a574aaf68c0a431a47fa82ce0637f0f769826bfe | 17f8340912468f49bdc30acdb9a9fa02eeb0473a | refs/heads/master | 1,621,263,802,637 | 1,585,399,588,000 | 1,585,399,588,000 | 250,833,447 | 0 | 0 | Apache-2.0 | 1,585,410,341,000 | 1,585,410,341,000 | null | UTF-8 | Lean | false | false | 5,184 | 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 topology.metric_space.lipschitz
/-!
# Antilipschitz functions
We say that a map `f : α → β` between two (extended) metric spaces is
`antilipschitz_with K`,... |
2c1b1d854a0ec966d10c0f93d4a24582510f857b | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/diamond1.lean | 54d93ea796c725b3ad7cd2cfa774bf20f6dc523d | [
"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 | 635 | lean | structure Bar (α : Type) where
a : α
b : Nat → α
structure Baz (α : Type) where
a : α → α
c : Bool → α
d : Nat
set_option structureDiamondWarning false in
structure Foo (α : Type) extends Bar α, Baz α -- Error: parent field type mismatch
set_option structureDiamondWarning false in
structure Foo (α : Type) ... |
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