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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
ca59b74cf5c49e6fe15f7f335c4a5f1e3853ccd3 | b2fe74b11b57d362c13326bc5651244f111fa6f4 | /src/algebra/ordered_ring.lean | b1c086b08be616a9e6233c63980d8a2157540a42 | [
"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 | 43,140 | 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
-/
import algebra.ordered_group
import data.set.intervals.basic
set_option old_structure_cmd true
universe u
variable {α : Type u}
/-... |
46219348216e48e8de64e9617f3fa439b98f9447 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/extra/slow1.lean | b0c462d9384f89b3fd096437044f3cb492d2928b | [
"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 | 398 | lean | open nat
definition f (a : nat) : nat := a
definition g (a : nat) : nat := zero
example (a b : nat) :
@eq nat
(g (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f a))))))))))))))))))))))
(g (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f b))))))))))))))))))))))
:=
@eq.refl nat (g (f (f (f ... |
e12a9860adf066498f9276df2e216a3999bebcca | 5d166a16ae129621cb54ca9dde86c275d7d2b483 | /tests/lean/cases_induction_fresh.lean | 169e73accc1dfcad7a40216c7365e15ca78627a0 | [
"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 | 334 | lean | example (p q r s: Prop): p ∧ q → r ∧ s → s ∧ q :=
begin
intros h1 h2,
cases h1,
cases h2,
trace_state,
constructor; assumption
end
#print "------------"
example (p q r s: Prop): p ∧ q → r ∧ s → s ∧ q :=
begin
intros h1 h2,
induction h1,
induction h2,
trace_state,
constructor; assumption
end
|
3c9fa5ef51f90f1801918285bb995fccf80cdf38 | 0e175f34f8dca5ea099671777e8d7446d7d74227 | /library/init/data/nat/lemmas.lean | f0ad95534582089dee82b096939c7f914ff2c760 | [
"Apache-2.0"
] | permissive | utensil-contrib/lean | b31266738071c654d96dac8b35d9ccffc8172fda | a28b9c8f78d982a4e82b1e4f7ce7988d87183ae8 | refs/heads/master | 1,670,045,564,075 | 1,597,397,599,000 | 1,597,397,599,000 | 287,528,503 | 0 | 0 | Apache-2.0 | 1,597,408,338,000 | 1,597,408,337,000 | null | UTF-8 | Lean | false | false | 50,218 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad
-/
prelude
import init.data.nat.basic init.data.nat.div init.meta init.algebra.functions
universes u
namespace nat
attribute [pre_smt] nat_zero... |
d83e150baf749ec8677de3b86e4b9dad0829e6c3 | 8c9f90127b78cbeb5bb17fd6b5db1db2ffa3cbc4 | /two_definitions_of_prime_numbers.lean | d6e7a2104297fd75b66624cc7c1ae501c4918083 | [] | 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 | 4,930 | lean | def is_divisible: nat → nat → Prop :=
λ n m : nat, ∃ k : nat, m * k = n
def is_prime1: nat → Prop :=
λ p, p > 1 ∧ ∀ (m : nat) (Pmdp : is_divisible p m), ((m = 1) ∨ (m = p))
def is_prime2: nat → Prop :=
λ p, p > 1 ∧ ∀ (k : nat), (∀ (b1 : k < p) (b2 : 1 < k), (¬ is_divisible p k))
def prime_equiv_left : ∀... |
4931d0423e60f1265cbb891902d0a02a313266a8 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/list/big_operators.lean | 293952ebd1164abe29be9d8b45ddec7d358885b9 | [
"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 | 16,203 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Floris van Doorn, Sébastien Gouëzel
-/
import data.list.basic
/-!
# Sums and products from lists
This file provides basic results about `list.prod` and `list.sum`, wh... |
bfbffb0b50ea8b53f2b506d9f0ca347e7380dddc | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/convex/combination.lean | 15443b1b1fa4f9648a44e57c88ce90734d8f6242 | [
"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 | 23,039 | lean | /-
Copyright (c) 2019 Yury Kudriashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudriashov
-/
import algebra.big_operators.order
import analysis.convex.hull
import linear_algebra.affine_space.basis
/-!
# Convex combinations
> THIS FILE IS SYNCHRONIZED WITH... |
bdaf043e61de10f8ba36b8aa91a14c48fed462da | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/order/iterate.lean | 69a9d6be42f9afbb0102401893d80ea9aa62261a | [] | 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 | 5,090 | lean | /-
Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Yury G. Kudryashov
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.order.basic
import Mathlib.logic.function.iterate
import Mathlib.data.nat.basic
impo... |
6883f96ccb37bc4d6271322f784dfd6c023f4dd0 | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/group_theory/perm/cycle_type.lean | a8467566c273b5df9412c527eefb2249ae41c068 | [
"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 | 26,329 | lean | /-
Copyright (c) 2020 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import algebra.gcd_monoid.multiset
import combinatorics.partition
import group_theory.perm.cycles
import ring_theory.int.basic
import tactic.linarith
/-!
# Cycle ... |
5726ee551354b8d8c19ee0741bc548e1a96bb79e | 5749d8999a76f3a8fddceca1f6941981e33aaa96 | /src/data/semiquot.lean | 0f133d3e984be0886455585bc534df8a2cab4b91 | [
"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 | 7,487 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
A data type for semiquotients, which are classically equivalent to
nonempty sets, but are useful for programming; the idea is that
a semiquotient set `S` represents som... |
542c10e8756b0a2dc2f3a2d81a4b588ce9987e2d | a4673261e60b025e2c8c825dfa4ab9108246c32e | /tests/lean/run/meta3.lean | 55ba4dec8a0caba9f2ed0f415e9a7f327a91accf | [
"Apache-2.0"
] | permissive | jcommelin/lean4 | c02dec0cc32c4bccab009285475f265f17d73228 | 2909313475588cc20ac0436e55548a4502050d0a | refs/heads/master | 1,674,129,550,893 | 1,606,415,348,000 | 1,606,415,348,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,847 | lean | import Lean.Meta
open Lean
open Lean.Meta
def dbgOpt : Options :=
let opt : Options := {};
let opt := opt.setBool `trace.Meta true;
-- let opt := opt.setBool `trace.Meta.check false;
opt
def print (msg : MessageData) : MetaM Unit :=
trace! `Meta.debug msg
def check (x : MetaM Bool) : MetaM Unit :=
unless (← x) do t... |
a8bf664f140832aa153854251b4c72cbfccf0eb0 | 8cd68b0e4eb405ef573e16a6d92dcbcdb92d1c29 | /tests/lean/revert_err.lean | 4b18ebbf3d30828d5f98913611b7480c83bf26c8 | [
"Apache-2.0"
] | permissive | ratmice/lean | 5d7a7bbaa652899941fe73dff2154ddc5ab2f20a | 139ac0d773dbf0f54cc682612bf8f02297c211dd | refs/heads/master | 1,590,259,859,627 | 1,557,951,491,000 | 1,558,099,319,000 | 186,896,142 | 0 | 0 | Apache-2.0 | 1,557,951,143,000 | 1,557,951,143,000 | null | UTF-8 | Lean | false | false | 81 | lean | open tactic
example (a b : Prop) : true :=
by do to_expr ```(a ∧ b) >>= revert
|
4698e81fef4a8bbf79cad0e479ab2f2e700f486c | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/data/list/defs.lean | e3e3c2930a1e6c5d822c001016851787a8f2fcd8 | [
"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 | 32,108 | lean | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
import data.option.defs
import logic.basic
import tactic.cache
/-!
## Definitions on lists
Th... |
aac2220d574107a34864ee2434c050e92a7e13d2 | 30b012bb72d640ec30c8fdd4c45fdfa67beb012c | /data/set/countable.lean | cb4bfbb4ae655af71d92504d70ef057def15c74e | [
"Apache-2.0"
] | permissive | kckennylau/mathlib | 21fb810b701b10d6606d9002a4004f7672262e83 | 47b3477e20ffb5a06588dd3abb01fe0fe3205646 | refs/heads/master | 1,634,976,409,281 | 1,542,042,832,000 | 1,542,319,733,000 | 109,560,458 | 0 | 0 | Apache-2.0 | 1,542,369,208,000 | 1,509,867,494,000 | Lean | UTF-8 | Lean | false | false | 5,342 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
Countable sets.
-/
import data.equiv.list data.set.finite logic.function data.set.function
noncomputable theory
open function set encodable
open classical (hiding som... |
a85f8acb0b89e2f0e068423cd4763949517d77a7 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/ring_theory/dedekind_domain/integral_closure.lean | 9c7c808642bfabd0f2c3e80e233a2e9fe2897548 | [
"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 | 10,273 | 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
-/
import ring_theory.dedekind_domain.basic
import ring_theory.trace
/-!
# Integral closure of Dedekind domains
This file shows the ... |
970d3be6eb1a7a8d6234c080e93537f031838dfd | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /tests/lean/439.lean | e31c43acb3cb802a19d36753764b55f977a17baf | [
"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 | 747 | lean | universe u
structure Fn (E I : Sort u) := (exp : E) (imp : I)
instance (E I : Sort u) : CoeFun (Fn E I) (fun _ => I) := {coe := fun K => K.imp}
class Bar.{w} (P : Sort u) :=
fn : P -> Sort w
variable {P : Sort u} (B : Bar P)
variable (fn : Fn ((p : P) -> B.fn p) ({p : P} -> B.fn p))
#check coeFun fn -- Result is ... |
ca806718e6b89be09e86b77d3e1774a9ab7b0c68 | 0845ae2ca02071debcfd4ac24be871236c01784f | /library/init/lean/parser/trie.lean | 121907d971b853ad1a00c81a0c52309809a33844 | [
"Apache-2.0"
] | permissive | GaloisInc/lean4 | 74c267eb0e900bfaa23df8de86039483ecbd60b7 | 228ddd5fdcd98dd4e9c009f425284e86917938aa | refs/heads/master | 1,643,131,356,301 | 1,562,715,572,000 | 1,562,715,572,000 | 192,390,898 | 0 | 0 | null | 1,560,792,750,000 | 1,560,792,749,000 | null | UTF-8 | Lean | false | false | 2,881 | lean | /-
Copyright (c) 2018 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Sebastian Ullrich, Leonardo de Moura
Trie for tokenizing the Lean language
-/
prelude
import init.data.rbmap
import init.lean.format
namespace Lean
namespace Parser
inductive ... |
33df33b10fe37a83b94b4cdc3ba3cc821531ee01 | 6fca17f8d5025f89be1b2d9d15c9e0c4b4900cbf | /src/game/world10/level8.lean | 8b3dc8b576ad84f9c2701a699768d8faf6a392dc | [
"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 | 375 | lean | import game.world10.level7 -- hide
namespace mynat -- hide
/-
# Inequality world.
## Level 8: `succ_le_succ`
Another straightforward one.
-/
/- Lemma
For all naturals $a$ and $b$, if $a\le b$, then $\operatorname{succ}(a)\le\operatorname{succ}(b)$.
-/
lemma succ_le_succ (a b : mynat) (h : a ≤ b) : succ a ≤ succ... |
16260d447793009a684b0be6b6bb1af5905b218b | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/rb_map1.lean | 9e2628217128475ac59c8b12b5583b9a20ed806b | [
"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 | 786 | lean | import system.io
open io
section
open native.nat_map
#eval size (insert (insert (mk nat) 10 20) 10 21)
meta definition m := (insert (insert (insert (mk nat) 10 20) 5 50) 10 21)
#eval find m 10
#eval find m 5
#eval find m 8
#eval contains m 5
#eval contains m 8
open list
meta definition m2 := of_list [((1:nat), "on... |
9303b8d1873c17e91fd23ec2e39fba306c6c8ef0 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/analysis/calculus/extend_deriv.lean | f29f87d24d725fbdb5b133ffc811b6909ad84ccc | [
"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 | 11,068 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import analysis.calculus.mean_value
import tactic.monotonicity
/-!
# Extending differentiability to the boundary
We investigate how differentiable functions i... |
de9436a1163f2259b5e7832d93355067618c0539 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /archive/imo/imo2011_q5.lean | 08d4e6a1b8da5518e47e1f9a4831452a285acfc6 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 2,103 | lean | /-
Copyright (c) 2021 Alain Verberkmoes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alain Verberkmoes
-/
import data.int.basic
/-!
# IMO 2011 Q5
Let `f` be a function from the set of integers to the set
of positive integers. Suppose that, for any two integers
`... |
b8a6be1faadf26284c03f8f72c6a002f45049886 | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /tests/lean/run/matchArrayLit.lean | d4a4b2eca36a24ba17a624c3e6a64493ee43cac9 | [
"Apache-2.0"
] | permissive | walterhu1015/lean4 | b2c71b688975177402758924eaa513475ed6ce72 | 2214d81e84646a905d0b20b032c89caf89c737ad | refs/heads/master | 1,671,342,096,906 | 1,599,695,985,000 | 1,599,695,985,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,084 | lean | universes u v
theorem eqLitOfSize0 {α : Type u} (a : Array α) (hsz : a.size = 0) : a = #[] :=
a.toArrayLitEq 0 hsz
theorem eqLitOfSize1 {α : Type u} (a : Array α) (hsz : a.size = 1) : a = #[a.getLit 0 hsz (ofDecideEqTrue rfl)] :=
a.toArrayLitEq 1 hsz
theorem eqLitOfSize2 {α : Type u} (a : Array α) (hsz : a.size = 2)... |
910284c55bbb137594469e540346de4f05c4760a | d1a52c3f208fa42c41df8278c3d280f075eb020c | /stage0/src/Lean/Util/ForEachExpr.lean | efd97b5947a2015f1851032605926661d1f870de | [
"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 | 1,476 | 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.Expr
import Lean.Util.MonadCache
namespace Lean
/-
Remark: we cannot use the caching trick used at `FindExpr` and `ReplaceExpr` because they
ma... |
d7ffca203ff24d5ba7200c81324ec4e8f05d3a3b | c777c32c8e484e195053731103c5e52af26a25d1 | /src/set_theory/ordinal/basic.lean | 2e146285a1f99141d6cbf105f682884dfc41ef39 | [
"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 | 49,626 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Floris van Doorn
-/
import data.sum.order
import order.initial_seg
import set_theory.cardinal.basic
/-!
# Ordinals
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any ch... |
499bf583da386e323cd74faab659a9e444e23ec7 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/recInfo1.lean | fa38cb19fc25b44a0ad74dcc501ae71762680f97 | [
"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 | 638 | lean | import Lean.Meta
open Lean
open Lean.Meta
def print (msg : MessageData) : MetaM Unit := do
trace[Meta.debug] msg
def showRecInfo (declName : Name) (majorPos? : Option Nat := none) : MetaM Unit := do
let info ← mkRecursorInfo declName majorPos?
print (toString info)
theorem Iff.elim {a b c} (h₁ : (a → b) → (b → a) →... |
70c5e773ece295a81d42db115046b0044dfa4d80 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/order/monoid/with_top.lean | 616d4148549cb0c9c5e30f2e929d155d64aeca27 | [
"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 | 21,428 | 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.hom.group
import algebra.order.monoid.order_dual
import algebra.order.monoid.with_zero.basic
import da... |
8cb77c10452c2f9f4d20160d04b1c0ff2baa1125 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/geometry/manifold/local_invariant_properties.lean | fedd470ff9b59ae342f6bde3163b2d06122d33d4 | [
"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 | 34,748 | lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Floris van Doorn
-/
import geometry.manifold.charted_space
/-!
# Local properties invariant under a groupoid
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any ch... |
9396adefca6892e07fdfec82462278d3e60150c5 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/fold.lean | 8f83d0a4818699ab85ca2419a923fd0101b3389a | [
"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 | 991 | lean | prelude
definition Prop := Type.{0} inductive true : Prop := intro : true inductive false : Prop constant num : Type
inductive prod (A B : Type) := mk : A → B → prod A B infixl ` × `:30 := prod
variables a b c : num
section
local notation `(` t:(foldr `, ` (e r, prod.mk e r)) `)` := t
check (a, false, b, true, c)
... |
6f89ca8ecb92d234c68c70ba2f87d6a3df65dc52 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/probability/process/filtration.lean | 9bcf5a38d2a62a5e0893085d19e58a37b32f63ed | [
"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 | 13,183 | lean | /-
Copyright (c) 2021 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying, Rémy Degenne
-/
import measure_theory.function.conditional_expectation.real
/-!
# Filtrations
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require ... |
b8c3a4e0532f4cca3807349d8b102b052afca00e | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Util/PtrSet.lean | 38bc51ea7d05a516b1a3d2ce39a0bd116af9c04d | [
"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 | 876 | lean | /-
Copyright (c) 2023 Leonardo de Moura. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Data.HashSet
namespace Lean
structure Ptr (α : Type u) where
value : α
unsafe instance : Hashable (Ptr α) where
hash a := hash64 (ptrAddrUnsa... |
e5d4e5cb692bf4b24fdf2d5099f67e1586874d17 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/analysis/normed_space/indicator_function.lean | 42b01e95ff6e771806a2ddae84f9aa2af88952f8 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 1,340 | lean | /-
Copyright (c) 2020 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Yury Kudryashov
-/
import algebra.indicator_function
import analysis.normed_space.basic
/-!
# Indicator function and norm
This file contains a few simple lemmas about `... |
ece38db9e218692d1efe128e544ef2995c71b423 | df561f413cfe0a88b1056655515399c546ff32a5 | /5-advanced-proposition-world/l8.lean | 3f53aacf892ac9de9f23ac78550c03d6d5d59c8f | [] | no_license | nicholaspun/natural-number-game-solutions | 31d5158415c6f582694680044c5c6469032c2a06 | 1e2aed86d2e76a3f4a275c6d99e795ad30cf6df0 | refs/heads/main | 1,675,123,625,012 | 1,607,633,548,000 | 1,607,633,548,000 | 318,933,860 | 3 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 377 | lean | lemma and_or_distrib_left (P Q R : Prop) : P ∧ (Q ∨ R) ↔ (P ∧ Q) ∨ (P ∧ R) :=
begin
split,
intro paqor,
cases paqor with p qor,
cases qor with q r,
left,
split,
exact p,
exact q,
right,
split,
exact p,
exact r,
intro long,
split,
cases long with paq par,
exact paq.left,
exact par.left,
cases long with paq par,
left,
e... |
d6e184da76e9ceb9edb893532932da64a010e872 | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/algebra/char_zero.lean | 8484e6cbb8ea941f536235ba46cc127d6ec7276a | [
"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 | 3,118 | lean | /-
Copyright (c) 2014 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
Natural homomorphism from the natural numbers into a monoid with one.
-/
import data.nat.cast algebra.group algebra.field
/-- Typeclass for monoids with characteristic... |
514960990a2e16545e94ca8a59eed3eaf496234d | 94e33a31faa76775069b071adea97e86e218a8ee | /src/ring_theory/finiteness.lean | b90466397fd90bc5a5a4b8af831afe0f249ea468 | [
"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 | 38,574 | 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 group_theory.finiteness
import ring_theory.algebra_tower
import ring_theory.ideal.quotient
import ring_theory.noetherian
/-!
# Finiteness conditions in commu... |
2df3b613eb2260cd5a1eb3e2595bcbfe575a705b | 968e2f50b755d3048175f176376eff7139e9df70 | /examples/prop_logic_theory/unnamed_196.lean | 399eff0231f10a40e6fa6f185f9f5858e55ed8af | [] | no_license | gihanmarasingha/mth1001_sphinx | 190a003269ba5e54717b448302a27ca26e31d491 | 05126586cbf5786e521be1ea2ef5b4ba3c44e74a | refs/heads/master | 1,672,913,933,677 | 1,604,516,583,000 | 1,604,516,583,000 | 309,245,750 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 149 | lean | variables p q r : Prop
-- BEGIN
example (h : (p ∧ q) ∧ r ) : q :=
begin
have h₂ : p ∧ q, from h.left,
show q, from h₂.right,
end
-- END |
b562d90c0f2244dacb797a268b52564f070613bd | c777c32c8e484e195053731103c5e52af26a25d1 | /src/data/real/golden_ratio.lean | 4c0ef8fec16ca893766c659ecc1b740ae5a64dd1 | [
"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 | 5,678 | lean | /-
Copyright (c) 2020 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker, Alexey Soloyev, Junyan Xu
-/
import data.real.irrational
import data.nat.fib
import data.nat.prime_norm_num
import data.fin.vec_notation
import tactic.ring_exp
impo... |
22ce3b092cb6579dc097ab2b8b3fd6948b963d5c | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/order/lexicographic.lean | 7083507dfe515d5c413aa98ffaf9a2668ccc1db1 | [] | 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 | 5,145 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Scott Morrison, Minchao Wu
Lexicographic preorder / partial_order / linear_order / linear_order,
for pairs and dependent pairs.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.d... |
4c0b90cb8b840401298597dcdf1963d0a99d65a4 | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /library/hott/funext_from_ua.lean | 94cca2b3deff662eb38c9ad5976be97e870eefab | [
"Apache-2.0"
] | permissive | codyroux/lean | 7f8dff750722c5382bdd0a9a9275dc4bb2c58dd3 | 0cca265db19f7296531e339192e9b9bae4a31f8b | refs/heads/master | 1,610,909,964,159 | 1,407,084,399,000 | 1,416,857,075,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,353 | lean | -- Copyright (c) 2014 Jakob von Raumer. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Author: Jakob von Raumer
-- Ported from Coq HoTT
import hott.equiv hott.funext_varieties hott.axioms.ua hott.axioms.funext
import data.prod data.sigma data.unit
open path function prod... |
41df024e1b029254ff8ce73a6c932673300e6c1d | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/algebra/lie/weights.lean | 7556a23d2de0230d2f770c7264f25b2c84bb6da4 | [
"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 | 21,189 | lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import algebra.lie.nilpotent
import algebra.lie.tensor_product
import algebra.lie.character
import algebra.lie.cartan_subalgebra
import linear_algebra.eigenspace
import rin... |
e4f279011633999f5af40c5554fe7998dac65ccc | 98beff2e97d91a54bdcee52f922c4e1866a6c9b9 | /src/opens.lean | dd41d3a897882c8d85200ac6b8a40ff90afe5d1e | [] | no_license | b-mehta/topos | c3fc43fb04ba16bae1965ce5c26c6461172e5bc6 | c9032b11789e36038bc841a1e2b486972421b983 | refs/heads/master | 1,629,609,492,867 | 1,609,907,263,000 | 1,609,907,263,000 | 240,943,034 | 43 | 3 | null | 1,598,210,062,000 | 1,581,877,668,000 | Lean | UTF-8 | Lean | false | false | 4,169 | lean | import topology.category.Top.opens
import grothendieck
import tactic.equiv_rw
universes u
open category_theory topological_space category_theory.limits
namespace topological_space.opens
section
variables (X : Type u) [topological_space X]
section
variables {X} (U V : opens X)
@[derive partial_order]
def opens_sie... |
4af5988c417b0c73b2570f326e38b1ac0cd3ebd1 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/probability/independence.lean | 4adcf7ed67e6369fb3e44076d444158e822e2996 | [
"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 | 18,403 | lean | /-
Copyright (c) 2021 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import algebra.big_operators.intervals
import measure_theory.measure.measure_space
import measure_theory.pi_system
/-!
# Independence of sets of sets and measure spaces ... |
35209d323989fd054ee8e33c6eb1eaf7e2df5e81 | 572fb32b6f5b7c2bf26921ffa2abea054cce881a | /src/week_1/Part_D_relations.lean | 69c992e29e09c9762fc8c6f1e54091dd15648b01 | [
"Apache-2.0"
] | permissive | kgeorgiy/lean-formalising-mathematics | 2deb30756d5a54bee1cfa64873e86f641c59c7dc | 73429a8ded68f641c896b6ba9342450d4d3ae50f | refs/heads/master | 1,683,029,640,682 | 1,621,403,041,000 | 1,621,403,041,000 | 367,790,347 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,415 | lean | import tactic
/-!
# Equivalence relations are the same as partitions
In this file we prove that there's a bijection between
the equivalence relations on a type, and the partitions of a type.
Three sections:
1) partitions
2) equivalence classes
3) the proof
## Overview
Say `α` is a type, and `R : α → α → Prop` i... |
e2f55e50fcc8a2665f55d18ad00aacd39ef92744 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/ring_theory/dedekind_domain/dvr.lean | 4e4592bbdea2244824bdd77050987f3327ad0ebc | [
"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 | 7,444 | 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
-/
import ring_theory.localization.localization_localization
import ring_theory.localization.submodule
import ring_theory.discrete_val... |
88b78bfacea85638a5ee1e0025b53b432b183364 | d642a6b1261b2cbe691e53561ac777b924751b63 | /src/topology/uniform_space/complete_separated.lean | 64bb7ddb18d1821b8ab315a1049385e28dc1fcd2 | [
"Apache-2.0"
] | permissive | cipher1024/mathlib | fee56b9954e969721715e45fea8bcb95f9dc03fe | d077887141000fefa5a264e30fa57520e9f03522 | refs/heads/master | 1,651,806,490,504 | 1,573,508,694,000 | 1,573,508,694,000 | 107,216,176 | 0 | 0 | Apache-2.0 | 1,647,363,136,000 | 1,508,213,014,000 | Lean | UTF-8 | Lean | false | false | 1,327 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
Theory of complete separated uniform spaces.
This file is for elementary lemmas that depend on both Cauchy filters and separation.
-/
import topology.uniform_spa... |
fba405ec569245a86f6ba6f66d9bac808269a00b | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/ring_theory/polynomial/tower.lean | d781e40d379b3037d9bea5971756a7e39024d65a | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 2,681 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import algebra.algebra.tower
import data.polynomial.algebra_map
/-!
# Algebra towers for polynomial
This file defines the algebra tower structure for the type `polynomial R`... |
4172c3101a29b68d72462cdbf2255265bc4117f0 | 0845ae2ca02071debcfd4ac24be871236c01784f | /tests/bench/qsort.lean | 69ab3ca9da33ee827584fe438319d3c5205586db | [
"Apache-2.0"
] | permissive | GaloisInc/lean4 | 74c267eb0e900bfaa23df8de86039483ecbd60b7 | 228ddd5fdcd98dd4e9c009f425284e86917938aa | refs/heads/master | 1,643,131,356,301 | 1,562,715,572,000 | 1,562,715,572,000 | 192,390,898 | 0 | 0 | null | 1,560,792,750,000 | 1,560,792,749,000 | null | UTF-8 | Lean | false | false | 2,395 | lean | abbreviation Elem := UInt32
def badRand (seed : Elem) : Elem :=
seed * 1664525 + 1013904223
def mkRandomArray : Nat → Elem → Array Elem → Array Elem
| 0 seed as := as
| (i+1) seed as := mkRandomArray i (badRand seed) (as.push seed)
partial def checkSortedAux (a : Array Elem) : Nat → IO Unit
| i :=
if i < a.siz... |
ec7194b0b3188d23b17ae19061eb60ed27ffc91a | 8f0ea954c1cc4f4cda83826954d6186c68fc9536 | /hott/homotopy/connectedness.hlean | 975bb3f11a33477893b11a4fd37630b28aba970c | [
"Apache-2.0"
] | permissive | piyush-kurur/lean | fb3cbd339dfa8c70c49559fbea88ac0d3102b8ca | a8db8bc61a0b00379b3d0be8ecaf0d0858dc82ee | refs/heads/master | 1,594,387,140,961 | 1,457,548,608,000 | 1,457,909,538,000 | 53,615,930 | 0 | 0 | null | 1,457,642,939,000 | 1,457,642,939,000 | null | UTF-8 | Lean | false | false | 11,443 | hlean | /-
Copyright (c) 2015 Ulrik Buchholtz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ulrik Buchholtz, Floris van Doorn
-/
import types.trunc types.arrow_2 .sphere
open eq is_trunc is_equiv nat equiv trunc function fiber funext pi
namespace homotopy
definition is_... |
fd8db7d4a5ea4710c606d49acb7f2928bb7142f5 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/data/mv_polynomial/equiv.lean | 2ec5e18d0e10c5a6680ea3383cc480d809b8ea07 | [
"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 | 10,162 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
-/
import data.mv_polynomial.rename
import data.equiv.fin
/-!
# Equivalences between polynomial rings
This file establishes a number o... |
e7d5398e21dc1b0d5f0bf875b14a21b69a11555f | 6ae186a0c6ab366b39397ec9250541c9d5aeb023 | /src/category_theory/currying.lean | a7425040a16755cf173a0efdc8f08a0ad74ddf80 | [] | no_license | ThanhPhamPhuong/lean-category-theory | 0d5c4fe1137866b4fe29ec2753d99aa0d0667881 | 968a29fe7c0b20e10d8a27e120aca8ddc184e1ea | refs/heads/master | 1,587,206,682,489 | 1,544,045,056,000 | 1,544,045,056,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,864 | lean | -- Copyright (c) 2017 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Scott Morrison
import category_theory.products.bifunctors
import category_theory.equivalence
-- FIXME why do we need this here?
-- @[obviously] meta def obviously_2 := tactic.t... |
787f616f72cca14cdde50771e884d316ac0e3086 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/770.lean | 7c7b41a87cba9cf91a83750a0d29d64625a22a80 | [
"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 | 86 | lean | def u (x : Nat) : Nat := do
let y := x + x
y * (if y > 100 then 1 else (5 : Nat))
|
d8b6b8f95875fdd0a3b6a742abaa121dcb012aa2 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/hott/noc.hlean | 50eaa5fa9dc9f74eca46a59e97038d8f3e96b647 | [
"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 | 446 | hlean | set_option pp.beta true
structure foo :=
mk :: (A : Type) (B : A → Type) (a : A) (b : B a)
namespace foo
definition foo.inj₁
{A₁ : Type} {B₁ : A₁ → Type} {a₁ : A₁} {b₁ : B₁ a₁}
{A₂ : Type} {B₂ : A₂ → Type} {a₂ : A₂} {b₂ : B₂ a₂}
(H : foo.mk A₁ B₁ a₁ b₁ = foo.mk A₂ B₂ a₂ b₂)
: A₁ = A₂
:= lift.... |
f7e42914b23759fa6044ad1cae7e8a01408f13b0 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/group_with_zero/defs_auto.lean | cab0827dab4644503f23b3c5a499589d6d565fe6 | [] | 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 | 4,445 | 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.algebra.group.defs
import Mathlib.logic.nontrivial
import Mathlib.PostPort
universes u_4 l... |
b52e0c8437fef09f83da04f509634cc35c9ad440 | d0f9af2b0ace5ce352570d61b09019c8ef4a3b96 | /hw3/dm_prod_test.lean | 4e47f07fdaf540e087138338e40d19ee8652d8a1 | [] | no_license | jngo13/Discrete-Mathematics | 8671540ef2da7c75915d32332dd20c02f001474e | bf674a866e61f60e6e6d128df85fa73819091787 | refs/heads/master | 1,675,615,657,924 | 1,609,142,011,000 | 1,609,142,011,000 | 267,190,341 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,229 | lean | -- Justin Ngo
-- jmn4fms
-- 2/3/20
-- Sullivan 2102-001
/-Then, in a second file called dm_prod_test.lean,
write test cases for your implementation. You
will have to import your dm_prod.lean file into
this test file so that it has access to your
dm_prod definitions.
Your test cases should include (1) the definitions ... |
e6d9eb5e8c4cd9c8728dc59c9ae02f70feaba116 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/dynamics/omega_limit.lean | 8a9c50a52a212bcd8e361791e46cf91ba1cd6a69 | [
"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 | 16,560 | lean | /-
Copyright (c) 2020 Jean Lo. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean Lo
-/
import dynamics.flow
/-!
# ω-limits
For a function `ϕ : τ → α → β` where `β` is a topological space, we
define the ω-limit under `ϕ` of a set `s` in `α` with respect to
filter `f... |
0d0a6e7a75291a6ee3cd7beb41bd8b010068a3ad | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /hott/hit/two_quotient.hlean | 25111b9b6ab08a1fde70062c94526c25fad6861d | [
"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 | 22,956 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import homotopy.circle eq2 algebra.e_closure cubical.squareover cubical.cube cubical.square2
open quotient eq circle sum sigma equiv function relation e_closur... |
02d034d1384c5538bdb3b5d69c184db7089dea42 | 82b86ba2ae0d5aed0f01f49c46db5afec0eb2bd7 | /tests/lean/run/fun.lean | b4af8c6be4d05193b449234a4998175a7fbecd1c | [
"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 | 295 | lean | open Function Bool
constant f : Nat → Bool := arbitrary _
constant g : Nat → Nat := arbitrary _
#check f ∘ g ∘ g
#check (id : Nat → Nat)
constant h : Nat → Bool → Nat := arbitrary _
constant f1 : Nat → Nat → Bool := arbitrary _
constant f2 : Bool → Nat := arbitrary _
|
4763a9d202199128433ba50f202f7945de5ec82f | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/nat/units.lean | 5b2818a4c7816734acfa9de92456eceec170c685 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 1,109 | lean | /-
Copyright (c) 2014 Floris van Doorn (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
import data.nat.basic
import algebra.group.units
/-! # The units of the natural ... |
062f250fa720e6e4d709a1ee89aa99e5518fde13 | 1446f520c1db37e157b631385707cc28a17a595e | /stage0/src/Init/Data/String/Basic.lean | c5309c9aa14697d67f13e0366db14643150906f3 | [
"Apache-2.0"
] | permissive | bdbabiak/lean4 | cab06b8a2606d99a168dd279efdd404edb4e825a | 3f4d0d78b2ce3ef541cb643bbe21496bd6b057ac | refs/heads/master | 1,615,045,275,530 | 1,583,793,696,000 | 1,583,793,696,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 15,507 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import Init.Data.List.Basic
import Init.Data.Char.Basic
import Init.Data.Option.Basic
universes u
structure String :=
(data : List Char)
abbrev Str... |
1512354448a4b5daf25309929fce92a50ba52858 | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/category_theory/functor_category.lean | faa4f6b1515660ddf8ebf355ebf1a627cdb0d2e3 | [
"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 | 4,228 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tim Baumann, Stephen Morgan, Scott Morrison, Floris van Doorn
-/
import category_theory.natural_transformation
namespace category_theory
universes v₁ v₂ v₃ u₁ u₂ u₃ -- declare the `v... |
055628b1e8d654817bbca3ed9db64d8dbf9f78b5 | d642a6b1261b2cbe691e53561ac777b924751b63 | /src/algebra/pi_instances.lean | 6fd375338c3b23fab8a2c805f965bd1ed79f7a19 | [
"Apache-2.0"
] | permissive | cipher1024/mathlib | fee56b9954e969721715e45fea8bcb95f9dc03fe | d077887141000fefa5a264e30fa57520e9f03522 | refs/heads/master | 1,651,806,490,504 | 1,573,508,694,000 | 1,573,508,694,000 | 107,216,176 | 0 | 0 | Apache-2.0 | 1,647,363,136,000 | 1,508,213,014,000 | Lean | UTF-8 | Lean | false | false | 18,362 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot
Pi instances for algebraic structures.
-/
import order.basic
import algebra.module algebra.group
import data.finset
import ring_theory.subring
import tactic.p... |
cd840493d3c917e32db555e712dbef6bdee53188 | d7189ea2ef694124821b033e533f18905b5e87ef | /galois/network/action.lean | f7d0b44f10c4b207832c383b8a5f43b1de8812f0 | [
"Apache-2.0"
] | permissive | digama0/lean-protocol-support | eaa7e6f8b8e0d5bbfff1f7f52bfb79a3b11b0f59 | cabfa3abedbdd6fdca6e2da6fbbf91a13ed48dda | refs/heads/master | 1,625,421,450,627 | 1,506,035,462,000 | 1,506,035,462,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,317 | lean | import galois.map.fmap_func
galois.network.labels
universes u v
namespace network
inductive act (A : Type u) : Type u
-- return a poll result and the amount of time elapsed
| poll : Π (ports : list port) (sockets : list socket) (bound : time),
(poll_result ports sockets bound → (list (socket × message_... |
f971148d1df41a9f3de13ea0f6a7d1bb5ccb16a5 | b00eb947a9c4141624aa8919e94ce6dcd249ed70 | /stage0/src/Init/Data/List/Basic.lean | f3a78bb2214d2ab400c20e890d9c483e966cf73c | [
"Apache-2.0"
] | permissive | gebner/lean4-old | a4129a041af2d4d12afb3a8d4deedabde727719b | ee51cdfaf63ee313c914d83264f91f414a0e3b6e | refs/heads/master | 1,683,628,606,745 | 1,622,651,300,000 | 1,622,654,405,000 | 142,608,821 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,382 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import Init.SimpLemmas
import Init.Data.Nat.Basic
open Decidable List
universes u v w
variable {α : Type u} {β : Type v} {γ : Type w}
namespace Li... |
908d5b235e04327b2890f3542c3c5f21d621db2e | de91c42b87530c3bdcc2b138ef1a3c3d9bee0d41 | /old/expressions/language_expressions.lean | 435587f0a602d9db906f80cbd5d0c0d4ffd2b295 | [] | no_license | kevinsullivan/lang | d3e526ba363dc1ddf5ff1c2f36607d7f891806a7 | e9d869bff94fb13ad9262222a6f3c4aafba82d5e | refs/heads/master | 1,687,840,064,795 | 1,628,047,969,000 | 1,628,047,969,000 | 282,210,749 | 0 | 1 | null | 1,608,153,830,000 | 1,595,592,637,000 | Lean | UTF-8 | Lean | false | false | 20 | lean | import .expression
|
7c0f3d9603b5c1306a782dd3f2b7e138698067b3 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/equiv/basic.lean | 67f841b00ddaa60d0f97bcafbfde75b06082db4f | [] | 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 | 97,090 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.set.function
import Mathlib.PostPort
universes u_1 u_2 l u ... |
2532971833d5cb7ddacff2b49416b0d9b2c641cb | 02005f45e00c7ecf2c8ca5db60251bd1e9c860b5 | /src/algebra/continued_fractions/computation/approximations.lean | f30a6481d8655ea8560c54450d227318d2f368a9 | [
"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 | 14,571 | lean | /-
Copyright (c) 2020 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import algebra.continued_fractions.computation.translations
import algebra.continued_fractions.continuants_recurrence
import algebra.continued_fractions.terminate... |
e41210aba95d3cd639e1eb5b2df46cd6da07aa62 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Elab/Tactic/Conv/Basic.lean | bc4bb3ce7632261390ac8d03349e2ebf7aa44def | [
"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 | 7,405 | 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.Reduce
import Lean.Meta.Tactic.Apply
import Lean.Meta.Tactic.Replace
import Lean.Elab.Tactic.Basic
import Lean.Elab.Tactic.BuiltinTactic
n... |
9660c184c249f9cf118fe1a6ee42e7650e4ef4ef | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/topology/uniform_space/uniform_embedding.lean | c2871bd762278a35367f882e381f71d6eec99df4 | [
"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 | 26,239 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Sébastien Gouëzel, Patrick Massot
-/
import topology.uniform_space.cauchy
import topology.uniform_space.separation
import topology.dense_embedding
/-!
# Uniform embedd... |
93300036abc73c465ac97ac965b1f5a4000cebdf | c31182a012eec69da0a1f6c05f42b0f0717d212d | /src/hacks_and_tricks/by_exactI_hack.lean | 106285ac889c097cc93e97fff5a07bf7c54d290f | [] | no_license | Ja1941/lean-liquid | fbec3ffc7fc67df1b5ca95b7ee225685ab9ffbdc | 8e80ed0cbdf5145d6814e833a674eaf05a1495c1 | refs/heads/master | 1,689,437,983,362 | 1,628,362,719,000 | 1,628,362,719,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 556 | lean | -- brilliant hack by Gabriel Ebner
-- thanks!!
-- files that import this file can use the zero-width space char
-- to reset the TC instance cache, and avoid `by exactI` kludges
open tactic expr
open lean
open lean.parser
open interactive
open tactic
reserve prefix ` `:100 -- zero-width space Unicode char
@[user_no... |
ddf38d166b2aed45bcc1dd7165746d6b461d3b95 | 87fd6b43d22688237c02b87c30d2a524f53bab24 | /src/game/sets/sets_level06.lean | 814810c313bf26ebab376da4df8eb5364986a02c | [
"Apache-2.0"
] | permissive | grthomson/real-number-game | 66142fedf0987db90f66daed52f9c8b42b70f909 | 8ddc15fdddc241c246653f7bb341df36e4e880a8 | refs/heads/master | 1,668,059,330,605 | 1,592,873,454,000 | 1,592,873,454,000 | 262,025,764 | 0 | 0 | null | 1,588,849,107,000 | 1,588,849,106,000 | null | UTF-8 | Lean | false | false | 1,106 | lean | import game.sets.sets_level05 -- hide
import tactic -- hide
namespace xena -- hide
variable X : Type
open_locale classical -- hide
/-
# Chapter 1 : Sets
## Level 6 : `sdiff` and `neg`
-/
/-
The set-theoretic difference `A \ B` satisfies the following property:
```
lemma mem_sdiff_iff : x ∈ A \ B ↔ x ∈ A ∧ x ∉ ... |
bae72e7c7a3077b303754633048d87288b9b9964 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/topology/continuous_function/cocompact_map.lean | 53042c5114a234e9adc89018073825d314dbf328 | [
"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 | 6,164 | lean | /-
Copyright (c) 2022 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import topology.continuous_function.basic
/-!
# Cocompact continuous maps
The type of *cocompact continuous maps* are those which tend to the cocompact filter on the
... |
94067fce517a111f0c094bd9d4a714fc8db5a4a4 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/e4.lean | b378203fe6306b029a9fc5a2066c924d5ab8c5e4 | [
"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 | 665 | lean | prelude
definition Prop := Type.{0}
definition false : Prop := ∀x : Prop, x
check false
theorem false.elim (C : Prop) (H : false) : C
:= H C
definition eq {A : Type} (a b : A)
:= ∀ P : A → Prop, P a → P b
check eq
infix `=`:50 := eq
theorem refl {A : Type} (a : A) : a = a
:= λ P H, H
definition true : Prop
:= fa... |
f39b3918cbf5403ba55616b03128eece33d24ddf | 09b3e1beaeff2641ac75019c9f735d79d508071d | /Mathlib/Data/Array/Basic.lean | f9ffddc1716ddd937cae8d967a96457683846fc6 | [
"Apache-2.0"
] | permissive | abentkamp/mathlib4 | b819079cc46426b3c5c77413504b07541afacc19 | f8294a67548f8f3d1f5913677b070a2ef5bcf120 | refs/heads/master | 1,685,309,252,764 | 1,623,232,534,000 | 1,623,232,534,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,044 | lean | import Mathlib.Data.List.Basic
@[simp] theorem List.toArrayAux_data : ∀ (l : List α) a, (l.toArrayAux a).data = a.data ++ l
| [], r => (append_nil _).symm
| a::as, r => (toArrayAux_data as (r.push a)).trans $
by simp [Array.push, append_assoc, List.concat_eq_append]
@[simp] theorem List.toArray_data (l : List α) : ... |
5fed0e49deaf52466e4b9679a2e5bbb489da078e | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /tests/lean/zipper.lean | c150919bafd262944064ef12a1479abee2a9b1f3 | [
"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 | 1,384 | lean | structure ListZipper (α : Type) :=
(xs : List α) (bs : List α)
-- set_option trace.compiler.ir.rc true
variables {α : Type}
namespace ListZipper
def goForward : ListZipper α → ListZipper α
| ⟨[], bs⟩ => ⟨[], bs⟩
| ⟨x::xs, bs⟩ => ⟨xs, x::bs⟩
def goBackward : ListZipper α → ListZipper α
| ⟨xs, []⟩ => ⟨xs, []⟩
... |
4350d9e25d3675a87cb5cddad425e2c8b0faa6a6 | d6124c8dbe5661dcc5b8c9da0a56fbf1f0480ad6 | /test/out/script/program.lean | ffe4fa09880cf72524766060b4bd99d08a6da533 | [
"Apache-2.0"
] | permissive | xubaiw/lean4-papyrus | c3fbbf8ba162eb5f210155ae4e20feb2d32c8182 | 02e82973a5badda26fc0f9fd15b3d37e2eb309e0 | refs/heads/master | 1,691,425,756,824 | 1,632,122,825,000 | 1,632,123,075,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,841 | lean | import Papyrus
open Papyrus Script
llvm module lean_hello do
declare %lean_object* @lean_mk_string(i8*)
declare %lean_object* @l_IO_println___at_Lean_instEval___spec__1(%lean_object*, %lean_object*)
define i32 @main() do
%hello = call @lean_mk_string("Hello World!"*)
call @l_IO_println___at_Lean_instEval_... |
605a81708e48210b1f997ad2be6b7e67fa52b7cc | 54d7e71c3616d331b2ec3845d31deb08f3ff1dea | /tests/lean/run/dep_coe_to_fn3.lean | 0b2b320eab0c7a5da0a1e8aca3761012b4e536c0 | [
"Apache-2.0"
] | permissive | pachugupta/lean | 6f3305c4292288311cc4ab4550060b17d49ffb1d | 0d02136a09ac4cf27b5c88361750e38e1f485a1a | refs/heads/master | 1,611,110,653,606 | 1,493,130,117,000 | 1,493,167,649,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 654 | lean | universe variables u v
structure Func :=
(A : Type u) (B : A → Type v) (fn : Π a, B a → B a)
instance F_to_fn : has_coe_to_fun Func :=
{ F := λ f, Π a, f^.B a → f^.B a,
coe := λ f a b, f^.fn a (f^.fn a b) }
variables (f : Func) (a : f^.A) (b : f^.B a)
#check (f a b)
def f1 : Func :=
{ A := nat,
B := λ a, na... |
4a763bf8ddf45af1fe99ebf92fdc45749d1e34d6 | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/tactic/core.lean | fc2d0a48164ae188f3530d7a2228910c4e1bf64c | [
"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 | 95,678 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Simon Hudon, Scott Morrison, Keeley Hoek
-/
import data.dlist.basic
import logic.function.basic
import control.basic
import meta.expr
import meta.rb_map
import data.boo... |
1fb455beb8933c91df42cc783a1f6d0036972e49 | 4e3bf8e2b29061457a887ac8889e88fa5aa0e34c | /lean/love05_inductive_predicates_homework_solution.lean | 65584a498f9441173e10c82da637167f91e6f78d | [] | 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 | 1,638 | lean | /- LoVe Homework 5: Inductive Predicates -/
import .lovelib
namespace LoVe
/- Question 2: Transitive Closure -/
/- In mathematics, the transitive closure `R+` of a binary relation `R` over a
set `A` can be defined as the smallest solution satisfying the following rules:
(base) for all a, b ∈ A, if a R b, then... |
c85198193e1521c74a117d66e804bc2475165c15 | d7b899533a520b46d705c8f4eaab26bb8571c153 | /basic.lean | 3c8705c78e54d888cfc3424c8e6d4acb8ee7ae6b | [
"MIT"
] | permissive | fgdorais/old_birkhoff | d043467859476eb412cc612f4daa9933dd031090 | c528743f6ebe65633cee5e9fef83a5794d2350c6 | refs/heads/master | 1,631,920,649,967 | 1,530,902,154,000 | 1,530,902,154,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,029 | lean | -- birkhoff/basic.lean --
-- Copyright Ⓒ 2015 François G. Dorais. All rights reserved.
-- Relesed under the MIT License as described in the file LICENSE.
import data
open nat
structure SIG [class] :=
(index : Type)
(arity : index → nat)
attribute SIG.index [coercion]
definition func.arity [sig : SIG] : sig → na... |
607f6fb882822987cc96548ea27c36cbe1fc0cd0 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/linear_algebra/dfinsupp.lean | 5772a005ceae4fe30e8e3669d2a37e969f5c1e3c | [
"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 | 18,458 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau
-/
import data.finsupp.to_dfinsupp
import linear_algebra.basis
/-!
# Properties of the module `Π₀ i, M i`
Given an indexed collection of `R`-modules `M i`, the `... |
6e02530ea963b382bb937b7c441be5ad2075b535 | 0408d6ea582e97d5cc55ac8a0980d26df896ce66 | /src/padics/padic_norm.lean | 4854a09546b22c30049a996fdba01c4168403f23 | [] | no_license | lean-forward/coe_tactic | bba94535c7fb6ef65fcd81bedc28062b238a1594 | d5c30df244c3402de6323a538e99b5324779a2cb | refs/heads/master | 1,588,474,971,049 | 1,557,135,293,000 | 1,557,135,293,000 | 178,387,237 | 1 | 0 | null | 1,556,542,286,000 | 1,553,856,413,000 | Lean | UTF-8 | Lean | false | false | 13,477 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
Define the p-adic valuation on ℤ and ℚ, and the p-adic norm on ℚ
-/
import data.rat algebra.gcd_domain algebra.field_power
import ring_theory.multiplicity tactic.rin... |
aa052727fd13624267fc627d7d8d6c0638edd2ca | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/1569.lean | ea18364db88f365e8acb09c9cda3884a9bc3e3f7 | [
"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 | 93 | lean | def foo (x : Nat) (_ : x = 0) : Nat := x
example : foo 0 (by simp [typo]; done) = 0 := sorry
|
258d09e8066085dbd24ffa099d2c03b6a4872d8b | 4727251e0cd73359b15b664c3170e5d754078599 | /src/analysis/normed_space/enorm.lean | 54c986e82aed4f163da1c25472a9a6fce3a6a23b | [
"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 | 7,795 | lean | /-
Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import analysis.normed_space.basic
/-!
# Extended norm
In this file we define a structure `enorm 𝕜 V` representing an extended norm (i.e., a norm that can
... |
408723b70a56a6e9da37aa374baac1b93c3e62e7 | ac2987d8c7832fb4a87edb6bee26141facbb6fa0 | /Mathlib/Data/List/Card.lean | 68acf299c6bf192877a5353817c5ac598b61a31d | [
"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 | 7,279 | lean | /-
Author: Jeremy Avigad
This is a makeshift theory of the cardinality of a list. Any list can be taken to represent the
finite set of its elements. Cardinality counts the number of distinct elements. Cardinality
respects equivalence and is preserved by any mapping that is injective on its elements.
It might make sen... |
174494b1c415d1e4c36dffea72cd34b41d0d3382 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/topology/uniform_space/complete_separated.lean | f5a81543b009d730baf60e7b58712fc1b0f3231e | [
"Apache-2.0"
] | permissive | rmitta/mathlib | 8d90aee30b4db2b013e01f62c33f297d7e64a43d | 883d974b608845bad30ae19e27e33c285200bf84 | refs/heads/master | 1,585,776,832,544 | 1,576,874,096,000 | 1,576,874,096,000 | 153,663,165 | 0 | 2 | Apache-2.0 | 1,544,806,490,000 | 1,539,884,365,000 | Lean | UTF-8 | Lean | false | false | 1,358 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
Theory of complete separated uniform spaces.
This file is for elementary lemmas that depend on both Cauchy filters and separation.
-/
import topology.uniform_spa... |
38711e3534792865cc64ac9b3feff69a6cda80d8 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/linear_algebra/sesquilinear_form.lean | 6515c4dcc34e53540debd45facfa37e2b346e984 | [
"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 | 12,012 | lean | /-
Copyright (c) 2018 Andreas Swerdlow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andreas Swerdlow
-/
import ring_theory.ring_invo
import algebra.module.linear_map
/-!
# Sesquilinear form
This file defines a sesquilinear form over a module. The definition requir... |
26cdc1737653f2bf292293d092074345d764d308 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/semiquot.lean | d0f35d73ca8288fa91d6717e342a384d4d687495 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 7,947 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.set.lattice
/-! # Semiquotients
A data type for semiquotients, which are classically equivalent to
nonempty sets, but are useful for programming; the id... |
c1a95c899cdcd295a436472a204d80ac9cbc8db8 | a1179fa077c09acc49e4fbc8d67084ba89ac4f4c | /tutorials/src/exercises/05_sequence_limits.lean | 487e9005b369ebcabc8acb2e4e321b00f1482130 | [] | no_license | Seeram/Lean-proof-assistant | 11ca0ca0e0446bacdd1773c4c481a3653b2f1074 | e672d46e0e5f39d8de2933ad4f4cac095ca6094f | refs/heads/master | 1,682,754,224,366 | 1,620,959,431,000 | 1,620,959,431,000 | 299,000,950 | 0 | 1 | null | 1,620,680,462,000 | 1,601,200,258,000 | Lean | UTF-8 | Lean | false | false | 5,889 | lean | import data.real.basic
import algebra.group.pi
import tuto_lib
notation `|`x`|` := abs x
/-
In this file we manipulate the elementary definition of limits of
sequences of real numbers.
mathlib has a much more general definition of limits, but here
we want to practice using the logical operators and relations
covered... |
91d5c8dc34fb4efa5b6ecc994a3292d3d622ce0f | d1a52c3f208fa42c41df8278c3d280f075eb020c | /src/Init/WF.lean | ab339d377b80e8316c5ec8192e98b617d025b956 | [
"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 | 10,932 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import Init.SizeOf
import Init.Data.Nat.Basic
universe u v
set_option codegen false
inductive Acc {α : Sort u} (r : α → α → Prop) : α → Prop where... |
116cf2c023b4e1031850a75ab31cec256a5eb021 | 947b78d97130d56365ae2ec264df196ce769371a | /stage0/src/Lean/Elab/Do.lean | de956aee2bad01c318f1fc7483d0a0655b241355 | [
"Apache-2.0"
] | permissive | shyamalschandra/lean4 | 27044812be8698f0c79147615b1d5090b9f4b037 | 6e7a883b21eaf62831e8111b251dc9b18f40e604 | refs/heads/master | 1,671,417,126,371 | 1,601,859,995,000 | 1,601,860,020,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 30,643 | 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.Elab.Term
import Lean.Elab.Binders
import Lean.Elab.Quotation
import Lean.Elab.Match
namespace Lean
namespace Elab
namespace Term
open Meta
@[... |
e5a94201faf6ce57213930c8a2edd5653759fb9e | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/ring_theory/free_comm_ring.lean | 31b6112224ef68d8d054bdf6cdb2748c686c3871 | [
"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 | 14,067 | lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Johan Commelin
-/
import data.mv_polynomial.equiv
import data.mv_polynomial.comm_ring
import logic.equiv.functor
import ring_theory.free_ring
/-!
# Free commutative rings
The t... |
7d6a3a8355fca899ef65cd9150abbd289e5631ae | a047a4718edfa935d17231e9e6ecec8c7b701e05 | /src/algebra/big_operators.lean | b2a66b2886cd268542103b72e290869b3f222717 | [
"Apache-2.0"
] | permissive | utensil-contrib/mathlib | bae0c9fafe5e2bdb516efc89d6f8c1502ecc9767 | b91909e77e219098a2f8cc031f89d595fe274bd2 | refs/heads/master | 1,668,048,976,965 | 1,592,442,701,000 | 1,592,442,701,000 | 273,197,855 | 0 | 0 | null | 1,592,472,812,000 | 1,592,472,811,000 | null | UTF-8 | Lean | false | false | 56,608 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import data.finset
import data.nat.enat
import tactic.omega
/-!
# Big operators
In this file we define products and sums indexed by finite sets (specifically, `fin... |
cd549149541f947c61026f3d4b5e14d61b1ef22c | 4727251e0cd73359b15b664c3170e5d754078599 | /src/model_theory/elementary_maps.lean | 3a32fae56b587951dd784e47bed664dd9cc73c2b | [
"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 | 13,432 | lean | /-
Copyright (c) 2022 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import data.fintype.basic
import model_theory.substructures
/-!
# Elementary Maps Between First-Order Structures
## Main Definitions
* A `first_order.language.eleme... |
42786bf809993a6502fb91a3def540e78282155b | e19b506b59d98b1469dd0023680087d321d0293d | /src/command/where/default.lean | 9f48a57496d72e31fd3a39d2fe29b1a4f2d71ef0 | [] | no_license | khoek/lean-where | ea28c2a63b0c28159f9363ee5f3101348b2b4744 | d2550de8655ece1cafbb9bf1beafe4d1c4481913 | refs/heads/master | 1,586,277,232,465 | 1,542,797,636,000 | 1,542,797,636,000 | 158,533,733 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 16 | lean | import .command
|
dc18827af56b8e3a1f389b74053efbde0d35c293 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/linear_algebra/affine_space/combination.lean | e58d5cd4e5ae4ecab234c254e6ecf1f0489d6fb3 | [
"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 | 42,858 | lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import algebra.invertible
import algebra.indicator_function
import linear_algebra.affine_space.affine_map
import linear_algebra.affine_space.affine_subspace
import linear... |
8ad1d7215c1764968e2e0aced03ec245189b9596 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /library/init/data/set.lean | fd664192de72292ebb7e4241a162705d5fdc3d3b | [
"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 | 2,307 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.meta.interactive
universes u v
def set (α : Type u) := α → Prop
def set_of {α : Type u} (p : α → Prop) : set α :=
p
namespace set
var... |
0551ecfd9514761c339b6a9e820d31bb629c7aa2 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /src/tests/shell/file1.lean | 4c2183f59c4cc0678bda525374a433eb89950d1b | [
"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 | 121 | lean | import data.nat
check nat
check nat.add_zero
check nat.zero_add
-- check finset
inductive foo : Type :=
mk : foo → foo
|
9b4ce8004bcb143b6f9cba1091e3fb008bcc1767 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/complex/module_auto.lean | 141c0e8a31d11a0b23696f80aa3c8b01c2f203d5 | [] | 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 | 3,675 | lean | /-
Copyright (c) 2020 Alexander Bentkamp, Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, Sébastien Gouëzel
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.complex.basic
import Mathlib.data.matrix... |
c705c8073784332c445241a95b1a2caaa245a2c7 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/class2.lean | 11c764d7b5c61f68ce0aa6fb1f17ce155daeccdf | [
"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 | 132 | lean | open tactic
theorem H {A B : Type} (H1 : inhabited A) : inhabited (Prop × A × (B → num))
:= by apply_instance
reveal H
print H
|
29e32f2937f6921058b7a69e20181bc40d096794 | 618003631150032a5676f229d13a079ac875ff77 | /src/data/nat/totient.lean | e1b4639f72ddbe54534f62af9ab4ad5fe5a81edb | [
"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 | 3,558 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import algebra.big_operators
open finset
namespace nat
def totient (n : ℕ) : ℕ := ((range n).filter (nat.coprime n)).card
localized "notation `φ` := nat.totient" in ... |
37fa553e6c2f6fa2f95050c0fef642687a3e8d86 | ebbdcbd7ddc89a9ef7c3b397b301d5f5272a918f | /qp/p1_categories/c4_topoi/s1_subobjects.lean | 09578d64cc7726fa877b69e401d5667f4dfe7f6d | [] | no_license | intoverflow/qvr | 34b9ef23604738381ca20b7d622fd0399d88f2dd | 0cfcd33fe4bf8d93851a00cec5bfd21e77105d74 | refs/heads/master | 1,616,591,570,371 | 1,492,575,772,000 | 1,492,575,772,000 | 80,061,627 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,819 | lean | /- -----------------------------------------------------------------------
Subobject classifiers.
----------------------------------------------------------------------- -/
import ..c2_limits
namespace qp
open stdaux
universe variables ℓ ℓobj ℓhom ℓobj₁ ℓhom₁ ℓobj₂ ℓhom₂
/-! #brief A subobject classifier.
-/
class... |
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