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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
6c04fd6c38664a69bf1c6ed23821de0daf5d2315 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/hash_map.lean | 048ef0bdd822ff1a062cdb8f860db5db5a0eec80 | [
"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 | 29,571 | 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, Mario Carneiro
-/
import data.pnat.basic
import data.list.range
import data.array.lemmas
/-!
# Hash maps
Defines a hash map data structure, representing a f... |
c4fb66cbd33ce722506b326eb16e7a92b7bc73c0 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /test/tactics.lean | bf37e81f2112e0b495f38cf220dc656982939c1e | [
"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 | 12,762 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Scott Morrison
-/
import tactic.interactive tactic.finish tactic.ext tactic.lift tactic.apply
tactic.reassoc_axiom tactic.tfae tactic.elide tactic.ring_exp
example (... |
226af82ee33af2c8ab53900c285b9da3ee8de0cc | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/category_theory/preadditive/biproducts.lean | 431ef9e6be087163d52c3d1ddded0bb42d574985 | [
"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 | 11,601 | 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 tactic.abel
import category_theory.limits.shapes.biproducts
import category_theory.preadditive
/-!
# Basic facts about morphisms between biproducts in preaddi... |
30bf683f97aeef09f7e7ff7b57e5f016b9b28693 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/linear_algebra/basic.lean | 94c9ca5c8599084ad07b0a347f87eb63a2e830e4 | [
"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 | 84,479 | 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, Kevin Buzzard, Yury Kudryashov, Frédéric Dupuis,
Heather Macbeth
-/
import algebra.big_operators.pi
import algebra.module.hom
import algebra.module.pr... |
a4458193888c1b58016a6720aef6551ce9e2193a | f4bff2062c030df03d65e8b69c88f79b63a359d8 | /src/game/order/level07.lean | 2d51627571aa5de94e5481187e0ad416033bc82f | [
"Apache-2.0"
] | permissive | adastra7470/real-number-game | 776606961f52db0eb824555ed2f8e16f92216ea3 | f9dcb7d9255a79b57e62038228a23346c2dc301b | refs/heads/master | 1,669,221,575,893 | 1,594,669,800,000 | 1,594,669,800,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 932 | lean | import game.order.level06
import data.real.irrational
open real
namespace xena -- hide
/-
# Chapter 2 : Order
## Level 7
Prove by example that there exist pairs of real numbers
$a$ and $b$ such that $a \in \mathbb{R} \setminus \mathbb{Q}$,
$b \in \mathbb{R} \setminus \mathbb{Q}$,
but their sum $a + b$ is a ration... |
eb0b3387553825153b0d942a1eaf9b69655084aa | 42c01158c2730cc6ac3e058c1339c18cb90366e2 | /group_projects/Ellen_Arlt_solutions.lean | ac0dd2b0a912dc85ee9cf69146b901bd33c7a58a | [] | no_license | ChrisHughes24/xena | c80d94355d0c2ae8deddda9d01e6d31bc21c30ae | 337a0d7c9f0e255e08d6d0a383e303c080c6ec0c | refs/heads/master | 1,631,059,898,392 | 1,511,200,551,000 | 1,511,200,551,000 | 111,468,589 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,086 | lean | namespace xena
inductive xnat
| zero : xnat
| succ : xnat → xnat
open xnat
open classical
--#check @succ.inj
definition one := succ zero
definition two := succ one
definition add : xnat → xnat → xnat
| n zero := n
| n (succ p) := succ (add n p)
notation a + b := add a b
theorem one_add_one_equals... |
c114b5eef5b680bf2a2bca19340a24929becf2e4 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/order/partial_sups.lean | 8ca66aa100f0c05742c056d1fa1c9c1547681efb | [
"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 | 5,784 | 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.finset.lattice
import data.set.pairwise
import order.preorder_hom
/-!
# The monotone sequence of partial supremums of a sequence
We define `partial_sups... |
350f49cd24db6cd31c04245cf10433906c1e8925 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/set_theory/cardinal/finite.lean | 8014e39334561f10c0a02978737821b6cbe45816 | [
"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 | 2,913 | lean | /-
Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import set_theory.cardinal.basic
/-!
# Finite Cardinality Functions
## Main Definitions
* `nat.card α` is the cardinality of `α` as a natural number.
If `α` is i... |
2e52952fcf3b003dda218110a2a1877f46d5432d | ad0c7d243dc1bd563419e2767ed42fb323d7beea | /data/real/cau_seq.lean | d7d4310c112fce4b6e14c0128b39ed40b0b4487c | [
"Apache-2.0"
] | permissive | sebzim4500/mathlib | e0b5a63b1655f910dee30badf09bd7e191d3cf30 | 6997cafbd3a7325af5cb318561768c316ceb7757 | refs/heads/master | 1,585,549,958,618 | 1,538,221,723,000 | 1,538,221,723,000 | 150,869,076 | 0 | 0 | Apache-2.0 | 1,538,229,323,000 | 1,538,229,323,000 | null | UTF-8 | Lean | false | false | 22,353 | 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 basic theory of Cauchy sequences, used in the construction of the reals.
Where applicable, lemmas that will be reused in other contexts have
been stated in extra gene... |
16a34b31e304685f2d3d5b4b99f9dbccb86cb67c | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/sites/surjective.lean | 93c68c5866ca0c454bf59fcd8327210898dd7ef6 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 7,191 | lean | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import category_theory.sites.subsheaf
import category_theory.sites.compatible_sheafification
/-!
# Locally surjective morphisms
## Main definitions
- `is_locally_surjec... |
919aa39f17ade8cd3a09ad08903554ec9e3b2ceb | e37bb385769d6f4ac9931236fd07b708397e086b | /src/exercises/src_37_completeness_axiom.lean | 71951f963f6da6d9caeba3b93813a2b0b9d7742f | [] | no_license | gihanmarasingha/ems_reals | 5f5d5b9d9dfb5a10da465046336d74995132dff6 | 9df527742db69d0a389add44b506538fdb4d0800 | refs/heads/master | 1,675,327,747,064 | 1,608,036,820,000 | 1,608,036,820,000 | 315,825,726 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,622 | lean | import ..library.src_real_field
import ..library.src_ordered_field_lemmas
import data.set.basic
import tactic
namespace mth1001
namespace myreal
open myreal_field classical myordered_field
open_locale classical
variables {R : Type} [myreal_field R]
def has_upper_bound (S : set R) := ∃ u : R, upper_bound u S
lemm... |
e3cd956b760b44dd5601dfe561712ea77bcda0cf | 1446f520c1db37e157b631385707cc28a17a595e | /src/Init/Lean/Parser/Term.lean | 1c2cf0f467a421dfd13f5bdcec0c73876067a6c4 | [
"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 | 12,845 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
prelude
import Init.Lean.Parser.Parser
import Init.Lean.Parser.Level
namespace Lean
namespace Parser
@[init] def regBuiltinTacticParser... |
148984e762c2c9a42502bb00dfe49ca0c426c25e | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/tactic/tidy.lean | 0898314626bffa963933c58894030f9ae8308ed3 | [
"Apache-2.0"
] | permissive | gebner/mathlib | eab0150cc4f79ec45d2016a8c21750244a2e7ff0 | cc6a6edc397c55118df62831e23bfbd6e6c6b4ab | refs/heads/master | 1,625,574,853,976 | 1,586,712,827,000 | 1,586,712,827,000 | 99,101,412 | 1 | 0 | Apache-2.0 | 1,586,716,389,000 | 1,501,667,958,000 | Lean | UTF-8 | Lean | false | false | 4,435 | 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 tactic.ext
import tactic.auto_cases
import tactic.chain
import tactic.solve_by_elim
import tactic.norm_cast
import tactic.hint
import tactic.interactive
names... |
c07a90c7a1efbe3152c19475a1ba07a4dd477d56 | 90bd8c2a52dbaaba588bdab57b155a7ec1532de0 | /src/homotopy/lift.lean | 8baf95083c070e3d24a7877c5e852508d0b7bef2 | [
"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 | 345 | lean | import homotopy.basic
import covering_space.lift
variables {X X' Y : Type _} [topological_space X] [topological_space X'] [topological_space Y]
open_locale unit_interval
example (p : C(X', X)) (hp : is_covering_map p) (f₀ f₁ : C(Y, X)) (H : homotopy f₀ f₁) (f₀' : C(Y, X'))
(hf₀' : p.comp f₀' = f₀) : C(Y × I, X) :... |
78b923f076a2fc027e74034a2b7ab3d62b07a1ff | f68c8823d8ddc719de8a4513815174aa7408ac4a | /lean_resolutions/PUZ134_2.lean | 2eb8b5d6bf624606dfd5ff29eee7e8425d577b60 | [] | no_license | FredsoNerd/tptp-lean-puzzles | e7ea66a0de9aa3cb7cc7480299f01adf885440a6 | 43d4d77524e797a4ac7a62b2cfaf8df08b409815 | refs/heads/master | 1,606,359,611,765 | 1,576,824,274,000 | 1,576,824,274,000 | 228,945,807 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,217 | lean | ------------------------------------------------------------------------------
-- File : PUZ134_2 : TPTP v7.3.0. Released v5.1.0.
-- Domain : Puzzles
-- Problem : The Knowheyan Job Puzzle - Ages
-- Version : Especial.
-- English : Five Knowheyans, A, B, C, D, and E, work in Metropolisas Airfoil
-- T... |
51f01e33fdeeae1f81820b4e1ee4c6f8cc05224d | 8f209eb34c0c4b9b6be5e518ebfc767a38bed79c | /code/src/internal/result.lean | 2f50d6f6ce79b10ac80c02b59fb084cd719eee86 | [] | no_license | hediet/masters-thesis | 13e3bcacb6227f25f7ec4691fb78cb0363f2dfb5 | dc40c14cc4ed073673615412f36b4e386ee7aac9 | refs/heads/master | 1,680,591,056,302 | 1,617,710,887,000 | 1,617,710,887,000 | 311,762,038 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 730 | lean | import tactic
import data.bool
import ..definitions
import .internal_definitions
variable [GuardModule]
open GuardModule
@[simp]
lemma Result.is_match_tt_neq_no_match { α: Type } (r: Result α): r.is_match = tt ↔ r ≠ Result.no_match :=
by cases r; simp [Result.is_match]
@[simp]
lemma Result.is_match_ff_neq_no_match {... |
fa86b04f58f94509cec367ecd8637be80f3d680d | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/measure_theory/lattice.lean | 46576ba07dbdf39fd7ede6e896ca91850a0ddd30 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 7,878 | 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 measure_theory.measure.ae_measurable
/-!
# Typeclasses for measurability of lattice operations
In this file we define classes `has_measurable_sup` and `has_meas... |
1f6f35c34fdc5a3bfea2009f2ef2ae542ffcb56d | bb31430994044506fa42fd667e2d556327e18dfe | /src/data/finset/sups.lean | 97f93b29855e2f66491b1161fc50b3b51a8c412d | [
"Apache-2.0"
] | permissive | sgouezel/mathlib | 0cb4e5335a2ba189fa7af96d83a377f83270e503 | 00638177efd1b2534fc5269363ebf42a7871df9a | refs/heads/master | 1,674,527,483,042 | 1,673,665,568,000 | 1,673,665,568,000 | 119,598,202 | 0 | 0 | null | 1,517,348,647,000 | 1,517,348,646,000 | null | UTF-8 | Lean | false | false | 12,969 | 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 data.finset.n_ary
/-!
# Set family operations
This file defines a few binary operations on `finset α` for use in set family combinatorics.
## Main declarations
... |
4ad0a5459b0c816bbc3d75c7167e32e4e3acfaec | b328e8ebb2ba923140e5137c83f09fa59516b793 | /src/Lean/Meta/Tactic/Intro.lean | 36930ce3086034b74be3e83f42a7c9a9fa7ddaa9 | [
"Apache-2.0"
] | permissive | DrMaxis/lean4 | a781bcc095511687c56ab060e816fd948553e162 | 5a02c4facc0658aad627cfdcc3db203eac0cb544 | refs/heads/master | 1,677,051,517,055 | 1,611,876,226,000 | 1,611,876,226,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,581 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.Tactic.Util
namespace Lean.Meta
@[inline] private partial def introNImp {σ} (mvarId : MVarId) (n : Nat) (mkName : LocalContext → Name → σ... |
2667872c67d774c148cc3e99e139b573883a2bad | 367134ba5a65885e863bdc4507601606690974c1 | /src/order/directed.lean | 80f421af889084f5964cfa4a60e163b13dd7d099 | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 3,053 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
-/
import order.lattice
import data.set.basic
universes u v w
variables {α : Type u} {β : Type v} {ι : Sort w} (r : α → α → Prop)
local infix ` ≼ ` : 50 := r
/-- A fam... |
3c29f5580c6f7440ebe623e7454b092b2f198ab6 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /library/data/finset/card.lean | 78cff73e3b338975e46a33683007e3426e19967b | [
"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 | 10,450 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
Cardinality calculations for finite sets.
-/
import .to_set .bigops data.set.function data.nat.power data.nat.bigops
open nat nat.finset eq.ops
namespace finset
... |
ec8b93e4895b2e575abd140ed2673d2f62d3a087 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/analysis/ODE/gronwall.lean | a68f9966e0bf3407e8dbd918941295ee84d61f67 | [
"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 | 13,199 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import analysis.special_functions.exp_deriv
/-!
# Grönwall's inequality
The main technical result of this file is the Grönwall-like inequality
`norm_le_gronwall_b... |
76827ee8195eb481b99451469ffadd735f903d73 | 78630e908e9624a892e24ebdd21260720d29cf55 | /src/logic_propositional/prop_18.lean | 5a648ff3712cdfaf7a906754d5c535547c5416b9 | [
"CC0-1.0"
] | permissive | tomasz-lisowski/lean-logic-examples | 84e612466776be0a16c23a0439ff8ef6114ddbe1 | 2b2ccd467b49c3989bf6c92ec0358a8d6ee68c5d | refs/heads/master | 1,683,334,199,431 | 1,621,938,305,000 | 1,621,938,305,000 | 365,041,573 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 590 | lean | namespace prop_18
variables P Q : Prop
theorem prop_18 : ¬ (P ∧ Q) → ¬¬ (¬ P ∨ ¬ Q) :=
assume h1: ¬ (P ∧ Q),
assume h2: ¬(¬P ∨ ¬Q),
have h3: ¬ P ∨ ¬ Q, from or.elim
(classical.em P)
(assume h4: P,
have h5: Q, from (classical.by_contradiction
(assume h6: ¬ Q,
h2 (or.inr h6))),
have h... |
171e27c7ff6c1ba7c660095fe337fb550c801cab | f57570f33b51ef0271f8c366142363d5ae8fff45 | /src/analysis_course.lean | 50ed4f68987fc296ff5e92d0072d8b182d1c6c1b | [] | no_license | maxd13/lean-logic | 4083cb3fbb45b423befca7fda7268b8ba85ff3a6 | ddcab46b77adca91b120a5f37afbd48794da8b52 | refs/heads/master | 1,692,257,681,488 | 1,631,740,832,000 | 1,631,740,832,000 | 246,324,437 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 20,309 | lean | --Thu Aug 22 08:26:12 -03 2019
-- Luiz Carlos R. Viana
import data.set.basic algebra.big_operators
data.nat.basic data.real.basic
tactic.tidy
-- We formalize the curriculum of a basic analysis course from scratch in Lean
-- (even though this is already part of the standard library).
-- The goal here however is the ... |
e9a39d80ca03ce41d31b973fad8606a896cdc562 | b815abf92ce063fe0d1fabf5b42da483552aa3e8 | /library/init/data/nat/lemmas.lean | dcd8da0d05d6d293930d3666109054479f0ef206 | [
"Apache-2.0"
] | permissive | yodalee/lean | a368d842df12c63e9f79414ed7bbee805b9001ef | 317989bf9ef6ae1dec7488c2363dbfcdc16e0756 | refs/heads/master | 1,610,551,176,860 | 1,481,430,138,000 | 1,481,646,441,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 22,375 | 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.data.nat.basic init.meta init.algebra
namespace nat
protected lemma zero_add : ∀ n : ℕ, 0 + n = n
| 0 := rfl
| (n+1) := congr_arg ... |
0b37ba05d48e1d46716950030de555a13932146a | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /tests/lean/run/gcd.lean | 917626a10cd3adde8d44e4b54c34c28f7854ceaf | [
"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 | 1,663 | lean | import data.nat data.prod
open nat well_founded decidable prod eq.ops
namespace playground
-- Setup
definition pair_nat.lt := lex lt lt
definition pair_nat.lt.wf [instance] : well_founded pair_nat.lt :=
intro_k (prod.lex.wf lt.wf lt.wf) 20 -- the '20' is for being able to execute the examples... it means 20 recurs... |
84c26eb15e18c3389125d14c9dec8331c89e2f29 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/category/Group/basic.lean | 17a1980b15b3d6f3462683743ce074b500f7d318 | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 10,135 | lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import algebra.category.Mon.basic
import category_theory.endomorphism
/-!
# Category instances for group, add_group, comm_group, and add_comm_group.
We introduce th... |
fb7df9a2c506575beafa2f1e052aa07b93eadcc7 | 97c8e5d8aca4afeebb5b335f26a492c53680efc8 | /ground_zero/structures.lean | bc65ef6bbc26005507e7a6fe64eea6e3e90ad011 | [] | no_license | jfrancese/lean | cf32f0d8d5520b6f0e9d3987deb95841c553c53c | 06e7efaecce4093d97fb5ecc75479df2ef1dbbdb | refs/heads/master | 1,587,915,151,351 | 1,551,012,140,000 | 1,551,012,140,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,394 | lean | import ground_zero.types.unit ground_zero.types.coproduct
open ground_zero.types.unit
hott theory
namespace ground_zero
namespace structures
universes u v
def prop (α : Sort u) :=
Π (a b : α), a = b :> α
def hset (α : Sort u) :=
Π {a b : α} (p q : a = b :> α), p = q :> a = b :> α
structure contr (α : Sort u) :=
(... |
67ffafed0c3b53ee09916182a722d7d31f9d1ec0 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/group_theory/general_commutator.lean | 59cef90c874b1805a0c3978d728462a91f11071f | [
"Apache-2.0"
] | permissive | hikari0108/mathlib | b7ea2b7350497ab1a0b87a09d093ecc025a50dfa | a9e7d333b0cfd45f13a20f7b96b7d52e19fa2901 | refs/heads/master | 1,690,483,608,260 | 1,631,541,580,000 | 1,631,541,580,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,387 | lean | /-
Copyright (c) 2021 Jordan Brown, Thomas Browning, Patrick Lutz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jordan Brown, Thomas Browning, Patrick Lutz
-/
import data.bracket
import group_theory.subgroup
import tactic.group
/-!
# General commutators.
If `G` is... |
aeb2bffd296471d494d5d0b7763ae211b379e030 | 97f752b44fd85ec3f635078a2dd125ddae7a82b6 | /library/theories/analysis/real_limit.lean | 28fb9800d97f13d7a7f4fc8b652e5707ef8f34cb | [
"Apache-2.0"
] | permissive | tectronics/lean | ab977ba6be0fcd46047ddbb3c8e16e7c26710701 | f38af35e0616f89c6e9d7e3eb1d48e47ee666efe | refs/heads/master | 1,532,358,526,384 | 1,456,276,623,000 | 1,456,276,623,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 24,508 | 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
Instantiates the reals as a Banach space.
-/
import .metric_space data.real.complete data.set .normed_space
open real classical analysis nat
noncomputabl... |
3e0077fcfac7e3eee1fc84b73db8378729a0e4a1 | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /tests/lean/run/e18.lean | a9f55a97ac34d9b92560f852f4c3f72d92994e94 | [
"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 | 494 | lean | prelude
inductive nat : Type :=
zero : nat,
succ : nat → nat
inductive list (A : Type) : Type :=
nil {} : list A,
cons : A → list A → list A
inductive int : Type :=
of_nat : nat → int,
neg : nat → int
attribute int.of_nat [coercion]
constants n m : nat
constants i j : int
constant l : list nat
namespace list end ... |
d45a4d5224fd7ce1b8382189a936521c6fd5bc5c | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/diamond3.lean | 637cb84982f4c4abe5af1ffa16dea25e4d64f36e | [
"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 | 254 | lean | structure A where
x : Nat := 0
y : Nat := 0
f : Nat → Nat := (. + 10)
structure B extends A where
z : Nat
structure C extends A where
w : Nat
set_option structureDiamondWarning false
structure D extends B, C where
a : Nat
#print D.toC
|
a44f7fb462b800037a63c56d10a3d82778575be8 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/whiskering.lean | 60bed39c4592b7475c0d2e1e2023004fab64f4d4 | [
"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 | 8,699 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.isomorphism
import category_theory.functor.category
import category_theory.functor.fully_faithful
/-!
# Whiskering
> THIS FILE IS SYNCHRONIZE... |
55fd8d1f3dccd1c7dec271039ba196f42d36d39f | dce2ec26258c35f21c8a5318a7a2ed297ddba7c6 | /src/Problems/1_2.lean | 7022d8a6b6120a1934ac4fe005bd80438b358c1d | [] | no_license | nedsu/lean-category-theory-pr | c151c4f95d58a2d3b33e8f38ff7734d85d82e5ee | 8d72f4645d83c72d15afaee7a2df781b952417e9 | refs/heads/master | 1,625,444,569,743 | 1,597,056,476,000 | 1,597,056,476,000 | 145,738,350 | 0 | 0 | null | 1,534,957,201,000 | 1,534,957,201,000 | null | UTF-8 | Lean | false | false | 3,942 | lean | import ncategory_theory.CatGroups
import category_theory.natural_transformation
import data.equiv.basic
open category_theory category_theory.isomorphism category_theory.functor category_theory.CatGroup category_theory.nat_trans
--delaration of universes and variables
universes u v u₀ v₀ u₁ v₁ u₂ v₂
lemma t {C : Typ... |
91d04449a6d4e22a4ed608dbfb9216e334128170 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/algebra/archimedean.lean | 00f518fe2d943a1cc910a3484cdbdead896e8282 | [
"Apache-2.0"
] | permissive | lacker/mathlib | f2439c743c4f8eb413ec589430c82d0f73b2d539 | ddf7563ac69d42cfa4a1bfe41db1fed521bd795f | refs/heads/master | 1,671,948,326,773 | 1,601,479,268,000 | 1,601,479,268,000 | 298,686,743 | 0 | 0 | Apache-2.0 | 1,601,070,794,000 | 1,601,070,794,000 | null | UTF-8 | Lean | false | false | 10,315 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
Archimedean groups and fields.
-/
import algebra.field_power
import data.rat
variables {α : Type*}
/-- An ordered additive commutative monoid is called `archimedean` ... |
6a7571f7501d91e9eb3c6e46bff9f4cb8b89842e | f0f12a5b81106a798deda31dca238c11997a605e | /Playlean4/Order.lean | 45aa4689899f2f3509579b0131795db4f9104a91 | [
"MIT"
] | permissive | thejohncrafter/playlean4 | fe7119d492aab07048f78333eeda9862f6471740 | 81df180a71b8d84d0f45bc98db367aad203cf5df | refs/heads/master | 1,683,152,783,765 | 1,621,879,382,000 | 1,621,879,382,000 | 366,563,501 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 216 | lean |
class Order {α : Type} where
rel : α → α → Prop
reflexivity : ∀ x : α, rel x x
transitivity : ∀ x y z : α, rel x y → rel y z → rel x z
antisymettricity : ∀ x y : α, rel x y → ¬rel y x
|
71a932024eeae2eb8a8e38ed12cc3d605602bd0f | aa101d73b1a3173c7ec56de02b96baa8ca64c42e | /src/my_exercises/02_iff_if_and.lean | 8e21ace515eaaa538e4b2897284c1a5e6ab3332f | [
"Apache-2.0"
] | permissive | gihanmarasingha/tutorials | b554d4d53866c493c4341dc13e914b01444e95a6 | 56617114ef0f9f7b808476faffd11e22e4380918 | refs/heads/master | 1,671,141,758,153 | 1,599,173,318,000 | 1,599,173,318,000 | 282,405,870 | 0 | 0 | Apache-2.0 | 1,595,666,751,000 | 1,595,666,750,000 | null | UTF-8 | Lean | false | false | 15,473 | lean | import data.real.basic
/-
In the previous file, we saw how to rewrite using equalities.
The analogue operation with mathematical statements is rewriting using
equivalences. This is also done using the `rw` tactic.
Lean uses ↔ to denote equivalence instead of ⇔.
In the following exercises we will use the lemma:
su... |
974805070464d92d897dbc145fa2b3e2369e0915 | de4548698671d50981659ecc9f4910de15969d3d | /lakefile.lean | 7e027c93acb7f899011f4ae9c539854757eb9449 | [] | no_license | digama0/mm-lean4 | 7ad17c81853816c6cd4bb97b8abe4bea0fd35ff6 | 6a427edecb851cec04818848a755c0145a5f2e98 | refs/heads/master | 1,688,934,520,262 | 1,687,937,043,000 | 1,687,937,043,000 | 365,257,017 | 15 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 346 | lean | import Lake
open Lake DSL
package «mm-lean4»
require std from git "https://github.com/leanprover/std4" @ "main"
@[default_target]
lean_lib Metamath where
roots := #[`Metamath.Verify]
@[default_target]
lean_lib MetamathExperimental where
roots := #[`Metamath.Translate]
@[default_target]
lean_exe «mm-lean4» wher... |
659267277fae9ba59669aa308503a53923d91cfd | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/measure_theory/constructions/pi.lean | fcd29e3840ae41c5358e7be6bb621597bcde32af | [
"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 | 32,287 | lean | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import measure_theory.constructions.prod
/-!
# Product measures
In this file we define and prove properties about finite products of measures
(and at some point... |
a95baf9a8085d74d8312c681d18f1c15f6332386 | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /src/Lean/Meta/Check.lean | a10e0d7ff558ffc23e1a193ba8c779d3a94ef11d | [
"Apache-2.0"
] | permissive | dupuisf/lean4 | d082d13b01243e1de29ae680eefb476961221eef | 6a39c65bd28eb0e28c3870188f348c8914502718 | refs/heads/master | 1,676,948,755,391 | 1,610,665,114,000 | 1,610,665,114,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,191 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.InferType
import Lean.Meta.LevelDefEq
/-
This is not the Kernel type checker, but an auxiliary method for checking
whether terms produced ... |
367d9204128223024882970fb374b1e42a46cf21 | f083c4ed5d443659f3ed9b43b1ca5bb037ddeb58 | /data/int/gcd.lean | 40e2aa81d5171e3e338615a6b345ca01b5c04b0c | [
"Apache-2.0"
] | permissive | semorrison/mathlib | 1be6f11086e0d24180fec4b9696d3ec58b439d10 | 20b4143976dad48e664c4847b75a85237dca0a89 | refs/heads/master | 1,583,799,212,170 | 1,535,634,130,000 | 1,535,730,505,000 | 129,076,205 | 0 | 0 | Apache-2.0 | 1,551,697,998,000 | 1,523,442,265,000 | Lean | UTF-8 | Lean | false | false | 11,961 | lean | /-
Copyright (c) 2018 Guy Leroy. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sangwoo Jo (aka Jason), Guy Leroy, Johannes Hölzl
Greatest common divisor (gcd) and least common multiple (lcm) for integers.
This sets up ℤ to be a GCD domain, and introduces rules about... |
7ec7827afee9995f0baf00e384dccfd58aafaaa7 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/complex/locally_uniform_limit.lean | cc91ebd185d1fb1fec84a3dd01dcb04f296ea787 | [
"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 | 10,428 | lean | /-
Copyright (c) 2022 Vincent Beffara. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Vincent Beffara
-/
import analysis.complex.removable_singularity
import analysis.calculus.series
/-!
# Locally uniform limits of holomorphic functions
> THIS FILE IS SYNCHRONIZED WI... |
9a36cd4dea925a0df06e5e17434acaa4164d1b29 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/data/int/order_auto.lean | 6c1df57e5b8a8ee9ce7e60e276f9745448e75351 | [] | 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 | 35,793 | 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 order relation on the integers.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.data.int.basic
import Mathlib.Lean3Lib.init.data.ordering.basic
namespace Math... |
99a2b4a4621ead32503f08ff69a75d3df80f4574 | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/tactic/squeeze.lean | 12b05b94eb7e44f2c463be32e67659186ae5de76 | [
"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 | 12,110 | lean | /-
Copyright (c) 2019 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Simon Hudon
-/
import category.traversable.basic
import tactic.simpa
open interactive interactive.types lean.parser
private meta def loc.to_string_aux : option name → string
| none := "⊢... |
dc6592d08489b0dcf320d8c0cc9d2649af79c9ba | 29cc89d6158dd3b90acbdbcab4d2c7eb9a7dbf0f | /3.3/33_exercise_sheet.lean | 9ff136ee17c842bfc2e9514807df38aa52c90c00 | [] | no_license | KjellZijlemaker/Logical_Verification_VU | ced0ba95316a30e3c94ba8eebd58ea004fa6f53b | 4578b93bf1615466996157bb333c84122b201d99 | refs/heads/master | 1,585,966,086,108 | 1,549,187,704,000 | 1,549,187,704,000 | 155,690,284 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,209 | lean | /- Exercise 3.3: Programming Semantics — Denotational Semantics -/
/- First we repeat some material from the lecture. -/
import .x33_library
set_option pp.beta true
class complete_lattice (α : Type) extends partial_order α :=
(Inf : set α → α)
(Inf_le : ∀{s a}, a ∈ s → Inf s ≤ a)
(le_Inf : ∀{s a}, (∀a', a' ∈ s →... |
69c5c7e0d677633dd7ab79e91659ea632bfe92d8 | 9e90bb7eb4d1bde1805f9eb6187c333fdf09588a | /src/stump/algorithm_measurable.lean | 645f26a84e87864a3487b644112a0d9494a27c3b | [
"Apache-2.0"
] | permissive | alexjbest/stump-learnable | 6311d0c3a1a1a0e65ce83edcbb3b4b7cecabb851 | f8fd812fc646d2ece312ff6ffc2a19848ac76032 | refs/heads/master | 1,659,486,805,691 | 1,590,454,024,000 | 1,590,454,024,000 | 266,173,720 | 0 | 0 | Apache-2.0 | 1,590,169,884,000 | 1,590,169,883,000 | null | UTF-8 | Lean | false | false | 3,673 | lean | /-
Copyright © 2019, Oracle and/or its affiliates. All rights reserved.
-/
import .algorithm_definition
import .setup_measurable
open set
namespace stump
variables (μ: probability_measure ℍ) (target: ℍ) (n: ℕ)
@[simp]
lemma label_sample_measurable: ∀ n: ℕ, measurable (label_sample target n) :=
begin
intro,
... |
f4151ad8c04610458e5a7b4462ca910c8e89cc9b | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/inv_bug.lean | be3cd1f496bd1263833ed521fbfb60e2de9db9c1 | [
"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 | 462 | lean | open nat
open eq.ops
inductive even : nat → Prop :=
| even_zero : even zero
| even_succ_of_odd : ∀ {a}, odd a → even (succ a)
with odd : nat → Prop :=
| odd_succ_of_even : ∀ {a}, even a → odd (succ a)
example : even 1 → false :=
begin
intro He1,
cases He1 with [a, Ho0],
cases Ho0
end
example : even 3 →... |
bae140e3c7d8549f713f07bb487633152b139fb6 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /src/Lean/Util/MonadBacktrack.lean | 77b54c8d0fd52c95efccb7d47051f28ccfd6111d | [
"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 | 1,782 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
namespace Lean
/-- Similar to `MonadState`, but it retrieves/restores only the "backtrackable" part of the state -/
class MonadBacktrack (s : outParam Typ... |
647c666ead55189a7be1279301fb08d5663eeaa4 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/linear_algebra/vandermonde.lean | 4702d0b28eee6ce85ea933dc6d30bdb9a1519c23 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 6,526 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import algebra.big_operators.fin
import algebra.geom_sum
import group_theory.perm.fin
import linear_algebra.matrix.determinant
import linear_algebra.matrix.nondegenerate
/... |
4a65ef483e4ddbb1ad47e15713e558e7a1429bdd | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/algebra/indicator_function.lean | 08f80f48aabd828eb082613b1ae70ed021fae31f | [
"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 | 25,351 | lean | /-
Copyright (c) 2020 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
-/
import algebra.support
/-!
# Indicator function
- `indicator (s : set α) (f : α → β) (a : α)` is `f a` if `a ∈ s` and is `0` otherwise.
- `mul_indicator (s : set α) (... |
35c55b000baaa19e430b4276c1cea4d389a18bfb | 37da0369b6c03e380e057bf680d81e6c9fdf9219 | /hott/types/int/hott.hlean | 3a965c8c1011d6c522c5f292a8ba7494e51555b5 | [
"Apache-2.0"
] | permissive | kodyvajjha/lean2 | 72b120d95c3a1d77f54433fa90c9810e14a931a4 | 227fcad22ab2bc27bb7471be7911075d101ba3f9 | refs/heads/master | 1,627,157,512,295 | 1,501,855,676,000 | 1,504,809,427,000 | 109,317,326 | 0 | 0 | null | 1,509,839,253,000 | 1,509,655,713,000 | C++ | UTF-8 | Lean | false | false | 6,698 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Floris van Doorn
Theorems about the integers specific to HoTT
-/
import .order types.eq arity algebra.bundled
open core eq is_equiv equiv algebra is_trunc
open nat (hiding pred)
na... |
38fad0359617b1c6593cc8e3c741128f7b47a71d | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Init/Data/Nat/Gcd.lean | 7654c3a4abf859aabb8485914650d394a157cf77 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 1,116 | 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
-/
prelude
import Init.Data.Nat.Div
namespace Nat
private def gcdF (x : Nat) : (∀ x₁, x₁ < x → Nat → Nat) → Nat → Nat :=
match x with
| 0 => fun _ y... |
41526436cc15b0c1cc0fab0b8d26c8f56a274b5a | 8fe7510bd7f4eb87049ac0423b0476c841df8fe6 | /src/gen_graph.lean | 11671992f92d096ea962c0244affbccba71cecfc | [] | no_license | robertylewis/import-graph | 26201690ec3221b7923f8141f69023196536e6b1 | 8b82a030dab9b1247c968288e021d960eafa82a0 | refs/heads/master | 1,671,038,042,246 | 1,598,982,544,000 | 1,598,982,544,000 | 292,068,181 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,480 | lean | import meta.rb_map
import meta.expr
import system.io
import data.list.sort
import data.real.basic
import all
/-!
Usage:
```
leanproject get robertylewis/import-graph
cd import-graph
lean --run src/gen_graph.lean
```
-/
@[inline]
meta def expr.get_constants (e : expr) : name_set :=
e.fold mk_name_set $ λ e' _ ... |
a6cd8f7e5add5bf72a87d749afbd90bb95f7b1cf | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/erased.lean | 7ccca5b054b772e529c9004f463dceac5468cb4f | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 3,755 | 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 logic.equiv.basic
/-!
# A type for VM-erased data
This file defines a type `erased α` which is classically isomorphic to `α`,
but erased in the VM. That is, ... |
fa4f415e240b4bef43206fdffc9b5cf755040589 | d436468d80b739ba7e06843c4d0d2070e43448e5 | /src/set_theory/cardinal.lean | fa57a95c76ee4ea5241c2d0fd770ae2e15f2cc4e | [
"Apache-2.0"
] | permissive | roro47/mathlib | 761fdc002aef92f77818f3fef06bf6ec6fc1a28e | 80aa7d52537571a2ca62a3fdf71c9533a09422cf | refs/heads/master | 1,599,656,410,625 | 1,573,649,488,000 | 1,573,649,488,000 | 221,452,951 | 0 | 0 | Apache-2.0 | 1,573,647,693,000 | 1,573,647,692,000 | null | UTF-8 | Lean | false | false | 44,826 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl, Mario Carneiro
-/
import data.set.countable data.quot logic.function set_theory.schroeder_bernstein
/-!
# Cardinal Numbers
We define cardinal numbers as a quotient of... |
784df897d139e7e8ccca11c043664cc3b5628afa | 5fbbd711f9bfc21ee168f46a4be146603ece8835 | /lean/natural_number_game/advanced_multiplication/2.lean | d545313e7e24eb2139b97528132bd8edbe534d0a | [
"LicenseRef-scancode-warranty-disclaimer"
] | no_license | goedel-gang/maths | 22596f71e3fde9c088e59931f128a3b5efb73a2c | a20a6f6a8ce800427afd595c598a5ad43da1408d | refs/heads/master | 1,623,055,941,960 | 1,621,599,441,000 | 1,621,599,441,000 | 169,335,840 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 266 | lean | theorem eq_zero_or_eq_zero_of_mul_eq_zero (a b : mynat) (h : a * b = 0) :
a = 0 ∨ b = 0 :=
begin
cases a with n hn,
left,
cc,
cases b with m hm,
right,
cc,
have g := mul_pos (succ n) (succ m) (succ_ne_zero n) (succ_ne_zero m),
exfalso,
cc,
end
|
8098430ea85fc9af8334bb226b14e2f7e36107f0 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Elab/PatternVar.lean | 29854a4ed43be321c3410bbf346a48e9352cc9a1 | [
"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 | 13,717 | 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.Match.MatchPatternAttr
import Lean.Elab.Arg
import Lean.Elab.MatchAltView
namespace Lean.Elab.Term
open Meta
abbrev PatternVar := Syntax... |
2b1708ce570d1d74f647f91016b55f33a3fe5055 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/limits/constructions/over/products_auto.lean | bc698438d78bb8cdab9f3efc12ebca911efaa324 | [] | 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 | 5,920 | lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Reid Barton, Bhavik Mehta
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.over
import Mathlib.category_theory.limits.shape... |
6670ec162a75de9f41eda9d49b00945b3d360c0e | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/data/polynomial/expand.lean | 85f7d0a63c6a959fb0efd656b3a0295c0fb69e92 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 9,954 | 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 ring_theory.polynomial.basic
import ring_theory.ideal.local_ring
import tactic.ring_exp
/-!
# Expand a polynomial by a factor of p, so `∑ aₙ xⁿ` becomes `∑ aₙ xⁿᵖ`.
##... |
140de226f2a40a707cbd0f914dc48ddd15e055dd | 9dd3f3912f7321eb58ee9aa8f21778ad6221f87c | /tests/lean/run/list_notation.lean | 53994023f7562db5b8b26bc68e36cb0891b912fe | [
"Apache-2.0"
] | permissive | bre7k30/lean | de893411bcfa7b3c5572e61b9e1c52951b310aa4 | 5a924699d076dab1bd5af23a8f910b433e598d7a | refs/heads/master | 1,610,900,145,817 | 1,488,006,845,000 | 1,488,006,845,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 406 | lean | open nat
vm_eval [1, 2, 3]
vm_eval to_bool $ 1 ∈ [1, 2, 3]
vm_eval to_bool $ 4 ∈ [1, 2, 3]
vm_eval [1, 2, 3] ++ [3, 4]
vm_eval 2 :: [3, 4]
vm_eval ([] : list nat)
vm_eval (∅ : list nat)
vm_eval ({1, 3, 2, 2, 3, 1} : list nat)
vm_eval [1, 2, 3] ∪ [3, 4, 1, 5]
vm_eval [1, 2, 3] ∩ [3, 4, 1, 5]
vm_eval (mul 10) ... |
470fff1e97951c86febe8e7b5993d3b751c1729d | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/fintype/sort_auto.lean | ee22486d01e708d75461742f84e62d26dce02c7e | [] | 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 | 985 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.fintype.basic
import Mathlib.data.finset.sort
import Mathlib.PostPort
universes u_1
... |
61856c68ae43777f1fcd764ca7e6aa78bdfefd83 | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/linear_algebra/finsupp.lean | b83d1ca86318c400f97c29fcb0d6920b51a1aa66 | [
"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 | 17,175 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
Linear structures on function with finite support `α →₀ M`.
-/
import data.monoid_algebra linear_algebra.basic
noncomputable theory
open set linear_map submodule
open... |
0f947b4f9c141bc7a506549d81518328e38f44ca | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/topology/metric_space/emetric_space.lean | a1e8643c8967b1291a034f6462ead639f6028329 | [
"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 | 50,787 | lean | /-
Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
-/
import data.nat.interval
import data.real.ennreal
import topology.uniform_space.pi
import topo... |
44a4190eac4e180e967184e1906e1d06c0a6740f | 974acfb39e2c67da7ef1a06bb8e25c4bb2c8b44b | /src/Sample.lean | 649d5d9f597c538582132a1cdc5179913f19e6e3 | [
"LicenseRef-scancode-mit-taylor-variant",
"LicenseRef-scancode-warranty-disclaimer"
] | permissive | o89/sample-nitro | 76bce8f46945cebc6c8d9a0b9c46aa3feecbd133 | 81db2099e42de1a0d4af00ff98ca74c95a531546 | refs/heads/master | 1,658,491,011,767 | 1,655,472,656,000 | 1,655,472,656,000 | 204,481,412 | 1 | 3 | null | 1,567,435,234,000 | 1,566,826,033,000 | HTML | UTF-8 | Lean | false | false | 1,169 | lean | import N2O.Default
import NITRO.Default
inductive Example
| send
instance : BERT Example :=
{ toTerm := λ x => match x with
| Example.send => Term.atom "send",
fromTerm := λ x => match x with
| Term.atom "send" => Sum.ok Example.send
| _ => Sum.fail "invalid Example term" }
def index : Nitro Example → Result... |
04b9ea4550cd5ae2740588eda2eeaf5fff6c0e6a | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/topology/instances/nnreal.lean | ff0cd9279ce0ed52ca2a17aad3ad89e125e9bbf7 | [
"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 | 9,243 | lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import topology.algebra.infinite_sum
import topology.algebra.group_with_zero
/-!
# Topology on `ℝ≥0`
The natural topology on `ℝ≥0` (the one induced from `ℝ`), and a... |
345f22266d1848f336ee446c0e19d9c056dfdb58 | 129628888508a22919f176e3ba2033c3b52fa859 | /src/embedding.lean | 716e94786bc5586704d5267af064d97e0a251bf9 | [
"Apache-2.0"
] | permissive | ImperialCollegeLondon/P11-Galois-Theory | 1aa35b6aa71c08aec6da3296ba404bf246db8df3 | ced2caa52300feb633316b3120c40ca957c8e8ff | refs/heads/master | 1,671,253,848,362 | 1,600,080,687,000 | 1,600,080,687,000 | 160,926,153 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,455 | lean | import field_theory.minimal_polynomial
import ring_theory.algebra
import field_theory.subfield
import ring_theory.adjoin_root
import linear_algebra.basic
universes u v w
noncomputable theory
open_locale classical
def galois_conjugates (α : Type u) {β : Type v} {γ : Type w}
[field α] [field β] [field γ] [algebra α β... |
956e7c6f5beb7790618f46d459789150e71ff7dc | 1446f520c1db37e157b631385707cc28a17a595e | /tests/compiler/closure_bug8.lean | 5e53b8b36e2f0baf66b4e30ad79464e641409016 | [
"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 | 501 | lean | def f (x : Nat) : Nat × (Nat → String) :=
let x1 := x + 1;
let x2 := x + 2;
let x3 := x + 3;
let x4 := x + 4;
let x5 := x + 5;
let x6 := x + 6;
let x7 := x + 7;
let x8 := x + 8;
let x9 := x + 9;
let x10 := x + 10;
let x11 := x + 11;
let x12 := x + 12;
let x13 := x + 13;
let x14 := x + 14;
let x15 := x + 15;
let x16 := ... |
7ea82c10ff87da53ba56e5895499edaabb5acf46 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/analysis/normed_space/ordered.lean | 92612591ab467b1a419bd652773d69179d614c06 | [
"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 | 1,958 | lean | /-
Copyright (c) 2020 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
import analysis.normed_space.basic
/-!
# Ordered normed spaces
In this file, we define classes for fields and groups that are both normed and ordered.
These are... |
d2c98b2e3d799cc44e1eed58570bfc1cd82df185 | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /tests/lean/bad_notation.lean | acb2ed317a5e4d445c5530d66db870e636b1bb09 | [
"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 | 120 | lean | import logic data.nat.basic
open nat
section
variable a : nat
notation `a1`:max := a + 1
end
definition foo := a1
|
44a25f632358cd8b1085d3d28f87c4a312948eb8 | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/algebraic_geometry/locally_ringed_space.lean | 4c1c6871c84d2c0a83873f4cc151cbc39e1994a7 | [
"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 | 7,604 | 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 algebraic_geometry.ringed_space
import data.equiv.transfer_instance
/-!
# The category of locally ringed spaces
We define (bundled) locally ringed spaces (a... |
bdc69a4354eea252cd84550a53d9a8d7c896f7f6 | efce24474b28579aba3272fdb77177dc2b11d7aa | /src/homotopy_theory/formal/cofibrations/cofibration_category.lean | 54efefca93d2edd7bed75716a2128fba6f9ee4f4 | [
"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 | 2,529 | lean | import homotopy_theory.formal.weak_equivalences.definitions
import .precofibration_category
universes v u
open category_theory
local notation f ` ∘ `:80 g:80 := g ≫ f
namespace homotopy_theory.cofibrations
open homotopy_theory.weak_equivalences
variables {C : Type u} [category.{v} C]
/-
[Baues, Algebraic homotopy... |
f0c2aef5ded31d850c9caa4adb29048c0f9c0271 | f083c4ed5d443659f3ed9b43b1ca5bb037ddeb58 | /category_theory/category.lean | ee8f7cfb107c10592a551a7abb2b50c291bf3109 | [
"Apache-2.0"
] | permissive | semorrison/mathlib | 1be6f11086e0d24180fec4b9696d3ec58b439d10 | 20b4143976dad48e664c4847b75a85237dca0a89 | refs/heads/master | 1,583,799,212,170 | 1,535,634,130,000 | 1,535,730,505,000 | 129,076,205 | 0 | 0 | Apache-2.0 | 1,551,697,998,000 | 1,523,442,265,000 | Lean | UTF-8 | Lean | false | false | 2,860 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stephen Morgan, Scott Morrison
Defines a category, as a typeclass parametrised by the type of objects.
Introduces notations
`X ⟶ Y` for the morphism spaces,
`f ≫ g` for compositio... |
0dd316ca6cb652f917eb9c7103de37f9d671516e | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/ring_theory/witt_vector/is_poly.lean | f4e53d386b559b0d7e58587decf2c2b22fd4d2cc | [
"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 | 23,404 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-/
import algebra.ring.ulift
import ring_theory.witt_vector.basic
import data.mv_polynomial.funext
/-!
# The `is_poly` predicate
`witt_vector.is_poly... |
244215e5949e010afa2b742aa0d56a7d7cad19e1 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/ring_theory/localization/inv_submonoid.lean | bbab92af6e54b6046b7b835c015fb373e4064004 | [
"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 | 3,966 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen
-/
import group_theory.submonoid.inverses
import ring_theory.finiteness
import ring_theory.localization.basic
impor... |
19e2d761ba3819f439964c3be38d05e911feb6d0 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/analysis/normed_space/complemented.lean | 288761a0350d489f2b18827b3b1cabd236890023 | [
"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 | 5,822 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import analysis.normed_space.banach
import analysis.normed_space.finite_dimension
/-!
# Complemented subspaces of normed vector spaces
A submodule `p` of a topolo... |
9032f5175d6a5ae9886e360bfc9eadf728045f55 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/1649a.lean | 555d30b1145f0f8b2058a3bdb6d4a47152418f94 | [
"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 | 131 | lean | section
def {u} typer (α : Type u) := α
parameter n : ℕ
meta def blah (n : typer ℕ) : ℕ := n
#check blah
end
#check blah
|
a38a10939e325fd125aadc38959ce72a9f08bef7 | 367134ba5a65885e863bdc4507601606690974c1 | /src/category_theory/limits/preserves/basic.lean | 18761bcd3f1164463a42d695505d4535810bbdca | [
"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 | 27,419 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Reid Barton, Bhavik Mehta
-/
import category_theory.limits.limits
/-!
# Preservation and reflection of (co)limits.
There are various distinct notions of "preserving l... |
6d8dfb780ebfacad3653b31e7acdfa8f2256b2b9 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/theories/analysis/normed_space.lean | 40eccfb6beb98b87c3413ea83ecfdef2f279d399 | [
"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 | 9,467 | lean | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
Normed spaces.
-/
import algebra.module .metric_space
open real nat classical
noncomputable theory
structure has_norm [class] (M : Type) : Type :=
(norm : M → ℝ)
namespa... |
0ea2e56215d24a2815913eeeac0b932bcb035acd | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/linear_algebra/matrix/reindex.lean | ee034d336aad5ea27d01a78b7b21630522b6bdc0 | [
"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 | 5,493 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-/
import linear_algebra.matrix.determinant
/-!
# Changing the index type of a matrix
This file concerns the map `matrix.rei... |
03016477febddbba501d3fbc55915e2d82fcd942 | 86f6f4f8d827a196a32bfc646234b73328aeb306 | /examples/logic/unnamed_1952.lean | f309b96b62308087581190563895bcef56817b63 | [] | no_license | jamescheuk91/mathematics_in_lean | 09f1f87d2b0dce53464ff0cbe592c568ff59cf5e | 4452499264e2975bca2f42565c0925506ba5dda3 | refs/heads/master | 1,679,716,410,967 | 1,613,957,947,000 | 1,613,957,947,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 242 | lean | import data.real.basic
variables {x y : ℝ}
namespace my_abs
-- BEGIN
theorem le_abs_self : x ≤ abs x :=
sorry
theorem neg_le_abs_self : -x ≤ abs x :=
sorry
theorem abs_add : abs (x + y) ≤ abs x + abs y :=
sorry
-- END
end my_abs |
66cc1736d76d68682f1d9b73a132ff025703c6db | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Util/RecDepth.lean | c74972e99b52b88dfc703221be16a86124fa61d9 | [
"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 | 363 | 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.Data.Options
namespace Lean
register_builtin_option maxRecDepth : Nat := {
defValue := defaultMaxRecDepth
descr := "maximum recursion d... |
4cede20564045a427c409f0f4aff2d5d12dbe6c5 | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/geometry/manifold/instances/real.lean | adede1bbdb5e70ea501d44667b005b1c74b1ae20 | [
"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 | 13,580 | 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 geometry.manifold.algebra.smooth_functions
import linear_algebra.finite_dimensional
import analysis.inner_product_space.pi_L2
/-!
# Constructing example... |
b2983ce26f80e1d545e5a5de584019017d7ced21 | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /tests/lean/run/ppbeta.lean | a387bf73189c457cd7da30ffdde262d9d187209f | [
"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 | 278 | lean | import data.int
open [coercions] int
open [coercions] nat
definition lt (a b : int) := int.le (int.add a 1) b
infix `<` := lt
infixl `+` := int.add
theorem lt_add_succ2 (a : int) (n : nat) : a < a + nat.succ n :=
int.le_intro (show a + 1 + n = a + nat.succ n, from sorry)
|
677b2c3fdcd5c72891c584241fb12a8bd8eb6410 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/smt/array.lean | 05f2e83c4f6e6d8411c70561733fc945174ab91b | [
"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 | 935 | 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
-/
namespace smt
definition array (A B : Type) := A → B
variables {A B : Type}
open tactic
definition select (a : array A B) (i : A) : B :=
a i
theorem array... |
188cbd0c4d59172c294cae9531c17bea6e125025 | 8e381650eb2c1c5361be64ff97e47d956bf2ab9f | /src/sheaves/presheaf_of_rings_maps.lean | 82a49a819ba0ca5f4fe67afcfc95cf2b986345ec | [] | no_license | alreadydone/lean-scheme | 04c51ab08eca7ccf6c21344d45d202780fa667af | 52d7624f57415eea27ed4dfa916cd94189221a1c | refs/heads/master | 1,599,418,221,423 | 1,562,248,559,000 | 1,562,248,559,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,820 | lean | /-
Continuous maps and presheaves of rings.
https://stacks.math.columbia.edu/tag/008C
-/
import to_mathlib.opens
import sheaves.presheaf_of_rings
import sheaves.presheaf_maps
universes u v w
open topological_space
variables {α : Type u} [topological_space α]
variables {β : Type v} [topological_space β]
namesp... |
ee0514893665a5471b52b0c234d82552426d32ad | 74caf7451c921a8d5ab9c6e2b828c9d0a35aae95 | /library/init/algebra/group.lean | 39922a7b164c8a9adca9ce0da7154738fc8c9151 | [
"Apache-2.0"
] | permissive | sakas--/lean | f37b6fad4fd4206f2891b89f0f8135f57921fc3f | 570d9052820be1d6442a5cc58ece37397f8a9e4c | refs/heads/master | 1,586,127,145,194 | 1,480,960,018,000 | 1,480,960,635,000 | 40,137,176 | 0 | 0 | null | 1,438,621,351,000 | 1,438,621,351,000 | null | UTF-8 | Lean | false | false | 15,260 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
-/
prelude
import init.logic init.meta.interactive init.meta.decl_cmds
/- Make sure instances defined in this file have lower priority than the... |
9a52a6316bba504f308b82af50ce78c00e10237b | 0c1546a496eccfb56620165cad015f88d56190c5 | /library/init/meta/rewrite_tactic.lean | 4cc49f71d323859c0006497b2c6fb875297df567 | [
"Apache-2.0"
] | permissive | Solertis/lean | 491e0939957486f664498fbfb02546e042699958 | 84188c5aa1673fdf37a082b2de8562dddf53df3f | refs/heads/master | 1,610,174,257,606 | 1,486,263,620,000 | 1,486,263,620,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 903 | 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.relation_tactics init.meta.occurrences
namespace tactic
/- (rewrite_core m approx use_instances occs symm H) -/
meta constant rewr... |
087afc90014908e21630f95b22a0f492e4355a9c | c31182a012eec69da0a1f6c05f42b0f0717d212d | /src/for_mathlib/Profinite/clopen_limit.lean | 04ad99adfba9a495c4b418d54c65787ed2f1366c | [] | 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 | 4,033 | lean | import topology.category.Profinite.cofiltered_limit
import topology.discrete_quotient
import for_mathlib.order
noncomputable theory
open_locale classical
namespace Profinite
open category_theory
open category_theory.limits
universe u
variables {J : Type u} [semilattice_inf J] (F : J ⥤ Profinite.{u}) (C : cone F)... |
7cf7ae3e8e129bba2cd9466d45adfefddd19ef09 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/analysis/normed_space/star/mul.lean | 46e1f84950911bdb07e50210d8f44b9270a4c904 | [
"Apache-2.0"
] | permissive | kbuzzard/mathlib | 2ff9e85dfe2a46f4b291927f983afec17e946eb8 | 58537299e922f9c77df76cb613910914a479c1f7 | refs/heads/master | 1,685,313,702,744 | 1,683,974,212,000 | 1,683,974,212,000 | 128,185,277 | 1 | 0 | null | 1,522,920,600,000 | 1,522,920,600,000 | null | UTF-8 | Lean | false | false | 3,002 | 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 analysis.normed_space.star.basic
import analysis.normed_space.operator_norm
/-! # The left-regular representation is an isometry for C⋆-algebras -/
open contin... |
64e2bd58042977d5b6c8d84f0ef47f73b19c5ca2 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/linear_algebra/determinant.lean | 4c8000e69219d7f0a68f781740046171ceec7359 | [
"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 | 13,629 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Chris Hughes, Tim Baanen
-/
import data.matrix.pequiv
import data.fintype.card
import group_theory.perm.sign
import algebra.algebra.basic
import tactic.ring
universes u v w z
op... |
ac6f628a40f6041bc81e5b78cc0628793dbf6ebb | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/algebra/lie/weights.lean | 77086d8ea0f065cb78aa7ac28c56edab15eebfd2 | [
"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 | 23,993 | 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.engel
import algebra.lie.cartan_subalgebra
import linear_alge... |
45aebfb356b9492d3fc23c97d9d4c8663b473bfb | cf39355caa609c0f33405126beee2739aa3cb77e | /library/init/control/functor.lean | 9e41319e3de6fbe4ee9263772be988745425212c | [
"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 | 755 | lean | /-
Copyright (c) Luke Nelson and Jared Roesch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Luke Nelson, Jared Roesch, Sebastian Ullrich, Leonardo de Moura
-/
prelude
import init.core init.function init.meta.name
open function
universes u v
class functor (f : Type u... |
7e8e5b7d80b5369e5c375ffb5fbce3b440a0b1a1 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/generator.lean | 5f79ceb63f136d54724ee171342c19462ebe04a6 | [
"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 | 27,464 | lean | /-
Copyright (c) 2022 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import category_theory.balanced
import category_theory.limits.essentially_small
import category_theory.limits.opposites
import category_theory.limits.shapes.zero_morphi... |
bc688af34f1f48cbb894da054646376829214fd5 | bdc27058d2df65f1c05b3dd4ff23a30af9332a2b | /src/euclid.lean | be8778e783a57f47834867a2e7a2f43c36f1c673 | [] | no_license | bakerjd99/leanteach2020 | 19e3dda4167f7bb8785fe0e2fe762a9c53a9214d | 2160909674f3aec475eabb51df73af7fa1d91c65 | refs/heads/master | 1,668,724,511,289 | 1,594,407,424,000 | 1,594,407,424,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,748 | lean | /- Formalizing Euclid's Axioms.-/
import tactic
import data.real.basic -- imports ℝ
noncomputable theory
open_locale classical
-- # Postulated types and relations
----------------------------------
constant Point : Type
constant Line : Type
constant lies_on : Point → Line → Prop
constant between : Point → Point → Po... |
472b34c829ea94b2cb6c56c32215793de36be819 | 9a0b1b3a653ea926b03d1495fef64da1d14b3174 | /tidy/rewrite_search/tactic.lean | cb96c92b4de888b4c45d534c2f62376edbb6ddd2 | [
"Apache-2.0"
] | permissive | khoek/mathlib-tidy | 8623b27b4e04e7d598164e7eaf248610d58f768b | 866afa6ab597c47f1b72e8fe2b82b97fff5b980f | refs/heads/master | 1,585,598,975,772 | 1,538,659,544,000 | 1,538,659,544,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,073 | lean | -- Copyright (c) 2018 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Keeley Hoek, Scott Morrison
import .init
import .discovery
import tidy.lib.list
import tidy.lib.expr
open tactic
variables {α β γ δ : Type}
namespace tidy.rewrite_search
me... |
27bc7669c0f6631a21f61aac9bcbd58eca823db3 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/analysis/calculus/inverse.lean | 1ac8f0ab6c3bdc595e52237de8b192ea4276ded6 | [
"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 | 32,293 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Heather Macbeth, Sébastien Gouëzel
-/
import analysis.calculus.times_cont_diff
import analysis.normed_space.banach
import topology.local_homeomorph
import topology.me... |
da2e0c5189132eb596889d8fb31f7ae95608a91e | 618003631150032a5676f229d13a079ac875ff77 | /test/differentiable.lean | eeff8b757a967eccc9f88495381dfdd30eaf0a0c | [
"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 | 1,922 | lean | import analysis.special_functions.trigonometric
namespace real
example : differentiable ℝ (λ (x : ℝ), exp x) :=
by simp
example : differentiable ℝ (λ (x : ℝ), exp ((sin x)^2) - exp (exp (cos (x - 3)))) :=
by simp
example (x : ℝ) : deriv (λ (x : ℝ), (cos x)^2 + (sin x)^2) x = 0 :=
by { simp, ring }
example (x : ℝ) ... |
4a6e03b2f6ca80c38d110e86af3bd0c7a4a3c1c3 | 8d65764a9e5f0923a67fc435eb1a5a1d02fd80e3 | /src/logic/basic.lean | aed809947fffa438d733996a5b388ae9578f05db | [
"Apache-2.0"
] | permissive | troyjlee/mathlib | e18d4b8026e32062ab9e89bc3b003a5d1cfec3f5 | 45e7eb8447555247246e3fe91c87066506c14875 | refs/heads/master | 1,689,248,035,046 | 1,629,470,528,000 | 1,629,470,528,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 59,309 | 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
import tactic.reserved_notation
/-!
# Basic logic properties
This file is one of the earliest imports in mathlib.
## Im... |
e7167d224ef41ce2056be7f88adaf2ea27f485ef | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/category_theory/limits/types.lean | 75a202782b4bbce0fd01ec362eaa27233f6426e2 | [
"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 | 5,815 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Reid Barton
-/
import category_theory.limits.shapes.images
universes v u -- declare the `v`'s first; see `category_theory.category` for an explanation
open category_t... |
6e7490481b92160af47081d1822bbe40d71c86ea | 8e6cad62ec62c6c348e5faaa3c3f2079012bdd69 | /src/topology/connected.lean | 422bd2588e4b90a57af7575157725c46300d4784 | [
"Apache-2.0"
] | permissive | benjamindavidson/mathlib | 8cc81c865aa8e7cf4462245f58d35ae9a56b150d | fad44b9f670670d87c8e25ff9cdf63af87ad731e | refs/heads/master | 1,679,545,578,362 | 1,615,343,014,000 | 1,615,343,014,000 | 312,926,983 | 0 | 0 | Apache-2.0 | 1,615,360,301,000 | 1,605,399,418,000 | Lean | UTF-8 | Lean | false | false | 39,692 | 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, Yury Kudryashov
-/
import topology.subset_properties
/-!
# Connected subsets of topological spaces
In this file we define connected subsets of a topol... |
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