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87c50ef97afdb05e5732b0f790c22b76c3fe86b2 | 77c5b91fae1b966ddd1db969ba37b6f0e4901e88 | /src/topology/sheaves/sheaf_condition/opens_le_cover.lean | b5543d696aa94b271a46b82cfd28bd656e04b75a | [
"Apache-2.0"
] | permissive | dexmagic/mathlib | ff48eefc56e2412429b31d4fddd41a976eb287ce | 7a5d15a955a92a90e1d398b2281916b9c41270b2 | refs/heads/master | 1,693,481,322,046 | 1,633,360,193,000 | 1,633,360,193,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,617 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import topology.sheaves.presheaf
import category_theory.limits.final
import topology.sheaves.sheaf_condition.pairwise_intersections
/-!
# Another version of the shea... |
07988dfe31ab0b12dd8c80319af7eac3a70d85f2 | 097294e9b80f0d9893ac160b9c7219aa135b51b9 | /instructor/predicate_logic/intro_and_elim_rules/not_&_false.lean | 065960a0a3c7a6c72974a93715932be917a15303 | [] | no_license | AbigailCastro17/CS2102-Discrete-Math | cf296251be9418ce90206f5e66bde9163e21abf9 | d741e4d2d6a9b2e0c8380e51706218b8f608cee4 | refs/heads/main | 1,682,891,087,358 | 1,621,401,341,000 | 1,621,401,341,000 | 368,749,959 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,000 | lean | /-
If P is an arbitrary proposition, then the
negation introduction rule tells you how to
prove ¬P. You do it by showing that P → false.
In English, you do it by *assuming* that P is
true and then *showing* that that leads to a
contradiction from which a proof of false can
be obtained. Because there is no proof of
f... |
64daf14535fb839423325beab964a7243dd03373 | 95dcf8dea2baf2b4b0a60d438f27c35ae3dd3990 | /src/data/nat/basic.lean | 8b6068a5caa636dea42faa33813e70e9b2547ae1 | [
"Apache-2.0"
] | permissive | uniformity1/mathlib | 829341bad9dfa6d6be9adaacb8086a8a492e85a4 | dd0e9bd8f2e5ec267f68e72336f6973311909105 | refs/heads/master | 1,588,592,015,670 | 1,554,219,842,000 | 1,554,219,842,000 | 179,110,702 | 0 | 0 | Apache-2.0 | 1,554,220,076,000 | 1,554,220,076,000 | null | UTF-8 | Lean | false | false | 35,762 | lean | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
Basic operations on the natural numbers.
-/
import logic.basic algebra.ordered_ring data.option.basic
universes u... |
505098a67a860a59d6629e030b7c837114b4de37 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/convex/normed.lean | 91399a8f31073ac4f67c3cdd6357517ae85e6510 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 6,274 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, Yury Kudryashov
-/
import analysis.convex.jensen
import analysis.convex.topology
import analysis.normed.group.pointwise
import analysis.normed_space.ray
/-!
# Top... |
c64f4d41d14db80f0d692af6291c0331c6525b37 | 618003631150032a5676f229d13a079ac875ff77 | /src/data/sigma/basic.lean | cbbe23e98a75379c4903a3bcf485f5c41dc548c1 | [
"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 | 3,776 | 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 tactic.lint
section sigma
variables {α : Type*} {β : α → Type*}
instance [inhabited α] [inhabited (β (default α))] : inhabited (sigma β) :=
⟨⟨default α, defau... |
4ed9d0a8b8c33681622841593b59a9528d104e97 | 7cdf3413c097e5d36492d12cdd07030eb991d394 | /src/game/world4/level4.lean | ed66d04e4fd9ae813c810d8b919a9cf39fadff5c | [] | no_license | alreadydone/natural_number_game | 3135b9385a9f43e74cfbf79513fc37e69b99e0b3 | 1a39e693df4f4e871eb449890d3c7715a25c2ec9 | refs/heads/master | 1,599,387,390,105 | 1,573,200,587,000 | 1,573,200,691,000 | 220,397,084 | 0 | 0 | null | 1,573,192,734,000 | 1,573,192,733,000 | null | UTF-8 | Lean | false | false | 354 | lean | import game.world4.level3 -- hide
namespace mynat -- hide
/-
# World 4 : Power World
## Level 4: `one_pow`
-/
/- Lemma
For all naturals $m$, $1 ^ m = 1$.
-/
lemma one_pow (m : mynat) : (1 : mynat) ^ m = 1 :=
begin [less_leaky]
induction m with t ht,
rw pow_zero,
refl,
rw pow_succ,
rw ht,
rw mul_one... |
f483391cbd2302c683126daf3146f36a6dedd3dd | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/1495.lean | 790376963457af1c4465e9d3a3a220b95c23153e | [
"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 | 182 | lean | section
variables (r : ℕ → ℕ → Prop)
local infix `≼` : 50 := r
example {a b : ℕ} : a ≼ b → true :=
begin
show a ≼ b → true,
{intro x, tactic.triv}
end
end
|
f154b233ebdcd8d313c0727171a6acbe607dd463 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /test/free_algebra.lean | 9ede4d91548420641b8623de1bdbbb56977e6e6c | [
"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 | 1,175 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import linear_algebra.exterior_algebra
import linear_algebra.clifford_algebra
/-!
Tests that the ring instances for `free_algebra` and derived quotient types actually ... |
18202c50c976f71ae2e0f51ece120c5ec7744639 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/data/polynomial/ring_division.lean | be79fddd9e60a81e8d65d478402e9cbb466cd4c8 | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 31,105 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker, Johan Commelin
-/
import data.polynomial.algebra_map
import data.polynomial.degree.lemmas
import data.polynomial.div
/-!
# ... |
4812ab824b7c1c89d3968e439663bda1be966526 | 827a8a5c2041b1d7f55e128581f583dfbd65ecf6 | /id_embedding.hlean | ce8b97823c76555f5fc9caab0fdeaeefbd9569ab | [
"Apache-2.0"
] | permissive | fpvandoorn/leansnippets | 6af0499f6f3fd2c07e4b580734d77b67574e7c27 | 601bafbe07e9534af76f60994d6bdf741996ef93 | refs/heads/master | 1,590,063,910,882 | 1,545,093,878,000 | 1,545,093,878,000 | 36,044,957 | 2 | 2 | null | 1,442,619,708,000 | 1,432,256,875,000 | Lean | UTF-8 | Lean | false | false | 742 | hlean | import function
open is_equiv function eq equiv
exit
/- email from Martin Escardo, nov 25. Try to prove that `Id_X` for all X without assumptions. Seems to fail -/
definition eq_cast {X A : Type} {E : X → A → Type} {x x' : X} {a a' : A} (p : E x ~ E x') (b' : E x' a') :
begin note z := cast (p a')⁻¹ b' end = p a' :... |
1674e80ee8933850c08444d4e81422e046ddb52a | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /src/Init/SimpLemmas.lean | 53ca57959fb774856e6d1ea44811aa61c2e3aaae | [
"Apache-2.0"
] | permissive | collares/lean4 | 861a9269c4592bce49b71059e232ff0bfe4594cc | 52a4f535d853a2c7c7eea5fee8a4fa04c682c1ee | refs/heads/master | 1,691,419,031,324 | 1,618,678,138,000 | 1,618,678,138,000 | 358,989,750 | 0 | 0 | Apache-2.0 | 1,618,696,333,000 | 1,618,696,333,000 | null | UTF-8 | Lean | false | false | 6,170 | 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
notation, basic datatypes and type classes
-/
prelude
import Init.Core
@[simp] theorem eqSelf (a : α) : (a = a) = True :=
propext <| Iff.intro (fun _ => tr... |
f11e1698dc074574d88af92301754305a9b3b7dd | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/data/polynomial/monomial.lean | 7146c98bb55b588f09e506eef26090115f411841 | [
"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 | 3,030 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
-/
import data.polynomial.basic
/-!
# Univariate monomials
Preparatory lemmas for degree_basic.
-/
noncomputable theory
o... |
a497157cb50f61ece29f73918224912e0807027d | a721fe7446524f18ba361625fc01033d9c8b7a78 | /src/principia/myring/ideal.lean | c9d3ebfc15db870a16e9ead5b864c59f72760230 | [] | no_license | Sterrs/leaning | 8fd80d1f0a6117a220bb2e57ece639b9a63deadc | 3901cc953694b33adda86cb88ca30ba99594db31 | refs/heads/master | 1,627,023,822,744 | 1,616,515,221,000 | 1,616,515,221,000 | 245,512,190 | 2 | 0 | null | 1,616,429,050,000 | 1,583,527,118,000 | Lean | UTF-8 | Lean | false | false | 2,193 | lean | import .basic
import ..myset.basic
namespace hidden
namespace myring
structure is_ideal {α : Type} [myring α] (I : myset α) : Prop :=
intro ::
(contains_zero: (0: α) ∈ I)
(add_closure (a b : α) : a ∈ I → b ∈ I → a + b ∈ I)
(mul_closure (r x : α) : x ∈ I → r * x ∈ I)
variables {α : Type} [myring α] (I J : myset α)
... |
bde5ba48820c3366a97592cfadb4306f0e51179e | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/tactic/linarith/preprocessing.lean | 647ce378b2e7c66dc33461fd4a3e71bca741c7fb | [
"Apache-2.0"
] | permissive | waynemunro/mathlib | e3fd4ff49f4cb43d4a8ded59d17be407bc5ee552 | 065a70810b5480d584033f7bbf8e0409480c2118 | refs/heads/master | 1,693,417,182,397 | 1,634,644,781,000 | 1,634,644,781,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 12,419 | lean | /-
Copyright (c) 2020 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
-/
import tactic.linarith.datatypes
import tactic.zify
import tactic.cancel_denoms
/-!
# Linarith preprocessing
This file contains methods used to preprocess inputs... |
1dfd8b956b30ce70fcb3b8bdbf4bd68b0dc5f774 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/model_theory/skolem.lean | 33d7de5234f3e5f78cce3afa24bc091ff8a85635 | [
"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 | 6,043 | 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 model_theory.elementary_maps
/-!
# Skolem Functions and Downward Löwenheim–Skolem
## Main Definitions
* `first_order.language.skolem₁` is a language consisti... |
32573510f22d7baeaa3327b90627740c5b1ed7bd | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /archive/examples/mersenne_primes.lean | 2c5a28bdbea00e04d5e5240d4c3d18b7facbcf58 | [
"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 | 2,040 | 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 number_theory.lucas_lehmer
/-!
# Explicit Mersenne primes
We run some Lucas-Lehmer tests to prove some Mersenne primes are prime.
See the discussion at the ... |
893d28488baf8f95a5fa71f13fb8e1e619ff1ac2 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/W/constructions.lean | 3e1698d34aa5e0386be8274cf1feb50581637fe4 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 4,979 | lean | /-
Copyright (c) 2015 Joseph Hua. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Hua
-/
import data.W.basic
/-!
# Examples of W-types
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
We take the vie... |
a88a229e2b13334b8219c8f67444f1704711c050 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/group_theory/specific_groups/alternating.lean | 0265a2d6adf688d78a29b5a5d00627d9993f9738 | [
"Apache-2.0"
] | permissive | waynemunro/mathlib | e3fd4ff49f4cb43d4a8ded59d17be407bc5ee552 | 065a70810b5480d584033f7bbf8e0409480c2118 | refs/heads/master | 1,693,417,182,397 | 1,634,644,781,000 | 1,634,644,781,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 15,092 | 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 group_theory.perm.fin
import tactic.interval_cases
/-!
# Alternating Groups
The alternating group on a finite type `α` is the subgroup of the permutation gr... |
d229474518237fcef0f2d5f778afb3b7aae8e10e | ee8cdbabf07f77e7be63a449b8483ce308d37218 | /lean/src/test/imo-2007-a6.lean | 082df24783c0701a08d2b016df3b30c5027ab86f | [
"MIT",
"Apache-2.0"
] | permissive | zeta1999/miniF2F | 6d66c75d1c18152e224d07d5eed57624f731d4b7 | c1ba9629559c5273c92ec226894baa0c1ce27861 | refs/heads/main | 1,681,897,460,642 | 1,620,646,361,000 | 1,620,646,361,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 455 | lean | /-
Copyright (c) 2021 OpenAI. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kunhao Zheng
-/
import data.real.nnreal
import data.real.basic
import algebra.big_operators.basic
open_locale big_operators
example (a : ℕ → nnreal) (h₀ : ∑ x in finset.range 100, (( a (x + 1... |
c901badc8b17465a28ce53486389ccee9ab3ec72 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/div_eqn.lean | 091f0768e3f44c46c22ae5ce179635d9acb5e086 | [
"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 | 218 | lean | def Div : nat → nat → nat
| x y :=
if h : 0 < y ∧ y ≤ x then
have x - y < x, from nat.sub_lt (nat.lt_of_lt_of_le h.left h.right) h.left,
Div (x - y) y + 1
else
0
#check Div.equations._eqn_1
|
b55d25b8f36ae1bee6ae5fa43a8ff41831ced5b4 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/group_power/basic.lean | bf6e45ad63f2980f5a9bcb8109985c7b2993fc55 | [
"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 | 15,804 | 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
-/
import data.nat.basic
import tactic.monotonicity.basic
import group_theory.group_action.defs
/-!
# Power operations on monoids and groups
The power o... |
fcd6a19e1f465843253963004d8f6cb05bb2cd72 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/linear_algebra/bilinear_form.lean | 2d9903fac10d6e85c7e984df4a705899e0872af7 | [
"Apache-2.0"
] | permissive | abentkamp/mathlib | d9a75d291ec09f4637b0f30cc3880ffb07549ee5 | 5360e476391508e092b5a1e5210bd0ed22dc0755 | refs/heads/master | 1,682,382,954,948 | 1,622,106,077,000 | 1,622,106,077,000 | 149,285,665 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 63,003 | lean | /-
Copyright (c) 2018 Andreas Swerdlow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andreas Swerdlow, Kexing Ying
-/
import linear_algebra.dual
import linear_algebra.matrix.nonsingular_inverse
import linear_algebra.matrix.to_lin
import linear_algebra.tensor_product... |
c7a8c38f815d6000ce2dfb59a0296a9352c69c49 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /test/solve_by_elim.lean | 17843c93777a89b0560b3f2c86a636602f4f5d0f | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 4,628 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Scott Morrison
-/
import tactic.solve_by_elim
import tactic.rcases
import tactic.interactive
example {a b : Prop} (h₀ : a → b) (h₁ : a) : b :=
begin
apply_assumption,
ap... |
2cfb6679a7f58d9ed0625f0b980b8a243174b3f8 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/group_theory/eckmann_hilton_auto.lean | 6612b06ba73fd0db9729249671fe6786c6a20a45 | [] | 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 | 4,392 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Kenny Lau, Robert Y. Lewis
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.group.basic
import Mathlib.PostPort
universes u l
namespa... |
633ced26c355512cf6f1a5fd240f09a5e7b39896 | b561a44b48979a98df50ade0789a21c79ee31288 | /stage0/src/Lean/Elab/Match.lean | 8f55846f96858a597b1a4eeb89eb5f08709622aa | [
"Apache-2.0"
] | permissive | 3401ijk/lean4 | 97659c475ebd33a034fed515cb83a85f75ccfb06 | a5b1b8de4f4b038ff752b9e607b721f15a9a4351 | refs/heads/master | 1,693,933,007,651 | 1,636,424,845,000 | 1,636,424,845,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 45,467 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Util.CollectFVars
import Lean.Meta.Match.MatchPatternAttr
import Lean.Meta.Match.Match
import Lean.Meta.SortLocalDecls
import Lean.Meta.Generali... |
7185f654c50000286c0d8d41b543592faada2b6d | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/PrettyPrinter/Delaborator/Builtins.lean | a7532394088200bba2417dd02b0eeb9f35a0a9e5 | [
"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 | 35,037 | lean | /-
Copyright (c) 2020 Sebastian Ullrich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
-/
import Lean.PrettyPrinter.Delaborator.Basic
import Lean.PrettyPrinter.Delaborator.SubExpr
import Lean.PrettyPrinter.Delaborator.TopDownAnalyze
import Lean.Pars... |
a6b2728c29da74ec92f42ff3000526517ee844b0 | 626e312b5c1cb2d88fca108f5933076012633192 | /src/analysis/calculus/fderiv.lean | 62d0af6190153b76154351451f83b91fac5b6da6 | [
"Apache-2.0"
] | permissive | Bioye97/mathlib | 9db2f9ee54418d29dd06996279ba9dc874fd6beb | 782a20a27ee83b523f801ff34efb1a9557085019 | refs/heads/master | 1,690,305,956,488 | 1,631,067,774,000 | 1,631,067,774,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 125,081 | lean | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Sébastien Gouëzel, Yury Kudryashov
-/
import analysis.analytic.basic
import analysis.asymptotics.asymptotic_equivalent
import analysis.calculus.tangent_cone
import analys... |
388377090dc16657ee97128b28ed73b80f82fd34 | 97c8e5d8aca4afeebb5b335f26a492c53680efc8 | /ground_zero/cubical/connection.lean | 2bdc2d4219da406d4dc94b20ab5f262cb6d017a9 | [] | 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 | 370 | lean | import ground_zero.cubical.path
open ground_zero.cubical ground_zero.HITs
/-
Connections as lines.
-/
namespace ground_zero.cubical.connection
universe u
def and {α : Sort u} {a b : α} (p : a ⇝ b) (i : I) : a ⇝ p # i :=
<j> p # i ∧ j
def or {α : Sort u} {a b : α} (p : a ⇝ b) (i : I) : p # i ⇝ b :=
<j> p # i ∨ j
... |
4a66958afe32caa1c47a4dd32aae3b4539b8d371 | a45212b1526d532e6e83c44ddca6a05795113ddc | /test/solve_by_elim.lean | fdb5f8751396ca3512d28db87b4ab4943023706d | [
"Apache-2.0"
] | permissive | fpvandoorn/mathlib | b21ab4068db079cbb8590b58fda9cc4bc1f35df4 | b3433a51ea8bc07c4159c1073838fc0ee9b8f227 | refs/heads/master | 1,624,791,089,608 | 1,556,715,231,000 | 1,556,715,231,000 | 165,722,980 | 5 | 0 | Apache-2.0 | 1,552,657,455,000 | 1,547,494,646,000 | Lean | UTF-8 | Lean | false | false | 2,525 | 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 data.set.lattice data.prod data.vector
tactic.rewrite data.stream.basic
example {a b : Prop} (h₀ : a → b) (h₁ : a) : b :=
begin
appl... |
9c776442202001c64d073784e95c47e7e722cc34 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /stage0/src/Lean/PrettyPrinter/Parenthesizer.lean | 77a89cb5cd61ab1af0c7a66a51cfd65d3eb56854 | [
"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 | 29,685 | lean | /-
Copyright (c) 2020 Sebastian Ullrich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
-/
import Lean.CoreM
import Lean.KeyedDeclsAttribute
import Lean.Parser.Extension
import Lean.ParserCompiler.Attribute
import Lean.PrettyPrinter.Basic
/-!
The pa... |
4baa44968391104e9ab3bc2d9551fc5fd7478018 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/tfae_auto.lean | 730b61a8f5bfd1589e929b294a4dc92e5e49f84d | [] | 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 | 1,164 | 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, Simon Hudon
"The Following Are Equivalent" (tfae) :
Tactic for proving the equivalence of a set of proposition
using various implications between them.
-/... |
3d0c99873e6c5b041f327fb251ab9799ef1fa88d | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/topology/homotopy/homotopy_group.lean | 929002c56e848fa2109ebc6f539f71fe14e7dd69 | [
"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 | 6,704 | lean | /-
Copyright (c) 2021 Roberto Alvarez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Roberto Alvarez
-/
import algebraic_topology.fundamental_groupoid.fundamental_group
/-!
# `n`th homotopy group
We define the `n`th homotopy group at `x`, `π n x`, as the equivalenc... |
709dc0ec0f37ddb4bb9d498e3886a335cc0722fc | a726f88081e44db9edfd14d32cfe9c4393ee56a4 | /src/game/world9/level3.lean | 7d2be5630d2b7be53fdf8edf06710a6224c9c66d | [] | no_license | b-mehta/natural_number_game | 80451bf10277adc89a55dbe8581692c36d822462 | 9faf799d0ab48ecbc89b3d70babb65ba64beee3b | refs/heads/master | 1,598,525,389,186 | 1,573,516,674,000 | 1,573,516,674,000 | 217,339,684 | 0 | 0 | null | 1,571,933,100,000 | 1,571,933,099,000 | null | UTF-8 | Lean | false | false | 609 | lean | import game.world9.level2 -- hide
namespace mynat -- hide
/-
# Advanced Multiplication World
## Level 3: `mul_eq_zero_iff`
Now you have `eq_zero_or_eq_zero_of_mul_eq_zero` this is pretty straightforward.
-/
/- Theorem
$a * b = 0$, if and only if at least one of $a$ or $b$ is equal to zero.
-/
theorem mul_eq_zero_if... |
35f2c5435d95c7ef158fe83a3ca7d1c87b169a33 | e030b0259b777fedcdf73dd966f3f1556d392178 | /library/init/meta/expr.lean | 8bb2406f0050e9bf27d44d52d472356b763991ac | [
"Apache-2.0"
] | permissive | fgdorais/lean | 17b46a095b70b21fa0790ce74876658dc5faca06 | c3b7c54d7cca7aaa25328f0a5660b6b75fe26055 | refs/heads/master | 1,611,523,590,686 | 1,484,412,902,000 | 1,484,412,902,000 | 38,489,734 | 0 | 0 | null | 1,435,923,380,000 | 1,435,923,379,000 | null | UTF-8 | Lean | false | false | 8,061 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.meta.level
inductive binder_info
| default | implicit | strict_implicit | inst_implicit | other
meta constant macro_def : Type
/- Ref... |
410726cef6f46a473c7d1a7218acd1c78be726d2 | 32a2d1642d7519c99693bc1d3b24069e4853dd1f | /data/set/basic.lean | 317c2d1e6335b58733c1e978265221f9441843a5 | [
"Apache-2.0"
] | permissive | Cedric0099/mathlib | 7edb81d5d68e280b4d21f6c0377dad1f9b8c0d71 | a97101d2df5d186848075a2d0452f6a04d8a13eb | refs/heads/master | 1,584,201,847,599 | 1,524,979,632,000 | 1,524,979,632,000 | 131,690,350 | 0 | 0 | null | 1,525,162,341,000 | 1,525,162,341,000 | null | UTF-8 | Lean | false | false | 35,524 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad, Leonardo de Moura
-/
import tactic tactic.finish data.sigma
open function
namespace set
universes u v w x
variables {α : Type u} {β : Type v} {γ : Type w} {ι : Sort x} {a... |
74831a7a27d321950ab1fe8225608d3af908fd89 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/linear_algebra/matrix/pos_def.lean | 036ba42ff1c3c213859008f7c8724035d21e47f2 | [
"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 | 3,325 | lean | /-
Copyright (c) 2022 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp
-/
import linear_algebra.matrix.spectrum
import linear_algebra.quadratic_form.basic
/-! # Positive Definite Matrices
This file defines positive definite matric... |
3baba3d14e89ae07ce87d32d6e91b8779683df89 | 2a70b774d16dbdf5a533432ee0ebab6838df0948 | /_target/deps/mathlib/src/category_theory/limits/shapes/binary_products.lean | 98944c48952ad38bc9159c69625e234880607526 | [
"Apache-2.0"
] | permissive | hjvromen/lewis | 40b035973df7c77ebf927afab7878c76d05ff758 | 105b675f73630f028ad5d890897a51b3c1146fb0 | refs/heads/master | 1,677,944,636,343 | 1,676,555,301,000 | 1,676,555,301,000 | 327,553,599 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 34,032 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Bhavik Mehta
-/
import category_theory.limits.limits
import category_theory.limits.shapes.terminal
import category_theory.discrete_category
import category_theory.epi_m... |
ae935dbdbf4d38cfbd83688a20aadd93f257a597 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/erasureConfusion.lean | 051dd921af97c0c01425420e5ae30c6fd1e5d806 | [
"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 | 186 | lean | import Lean
structure S (α : Type u) (β : Type v) (f : α → β) where
a : α
b : β := f a
def f : S Nat Type (fun _ => Nat) :=
S.mk 0 Nat
#eval Lean.Compiler.compile #[``f]
|
2451b0601103f1d9f8631455aaffe16686913a26 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/algebra/lie/classical.lean | 90cf7ae9b6cab667ba0d84b23158b65635d3daaa | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 13,409 | lean | /-
Copyright (c) 2020 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import algebra.invertible
import data.matrix.basis
import data.matrix.dmatrix
import algebra.lie.abelian
import linear_algebra.matrix.trace
import algebra.lie.skew_adjoint
... |
4cb36a05a3d46bccc0db9c1ec07640373dbfb050 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/algebra/order.lean | 20eb31f06af577c1002f0ae8fbe52847699c91be | [] | 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 | 11,968 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.logic
import Mathlib.Lean3Lib.init.classical
import Mathlib.Lean3Lib.init.meta.name
import Mathlib.Lean3... |
b9bdfad78e89512b0e2865ae2274a900cad57243 | 43390109ab88557e6090f3245c47479c123ee500 | /src/xenalib/Keji_domains.lean | 12f95e2fb90c107ebbceddfb765213a7297f6c5b | [
"Apache-2.0"
] | permissive | Ja1941/xena-UROP-2018 | 41f0956519f94d56b8bf6834a8d39473f4923200 | b111fb87f343cf79eca3b886f99ee15c1dd9884b | refs/heads/master | 1,662,355,955,139 | 1,590,577,325,000 | 1,590,577,325,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,409 | lean | import algebra.euclidean_domain ring_theory.ideals
universes u v
variables {α : Type u} {β : Type v} [comm_ring α] {a b : α}
open set function
local attribute [instance] classical.prop_decidable
class is_principal_ideal {α : Type u} [comm_ring α] (S : set α) : Prop :=
(principal : ∃ a : α, S = {x | a ∣ x})
class pr... |
bc801aee2799812bb70b3278042b143f8cf6e0b0 | 43390109ab88557e6090f3245c47479c123ee500 | /src/Topology/Problem_Sheets/BASIC_ps_2_ex_4b(incomplete).lean | 545918c9ffeeb329a28f334f8d139bb83eecf145 | [
"Apache-2.0"
] | permissive | Ja1941/xena-UROP-2018 | 41f0956519f94d56b8bf6834a8d39473f4923200 | b111fb87f343cf79eca3b886f99ee15c1dd9884b | refs/heads/master | 1,662,355,955,139 | 1,590,577,325,000 | 1,590,577,325,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,669 | lean | import analysis.topology.continuity
import analysis.topology.topological_space
import analysis.topology.infinite_sum
import analysis.topology.topological_structures
import analysis.topology.uniform_space
universe u
open set filter lattice classical
#print definition set
#check empty
def empty_topology : topologic... |
cb0cccfeab00f54101c675d8dc96c4c726da32ad | 8b9f17008684d796c8022dab552e42f0cb6fb347 | /hott/algebra/category/constructions.hlean | d715644c92772037345290b1276d457a327996f5 | [
"Apache-2.0"
] | permissive | chubbymaggie/lean | 0d06ae25f9dd396306fb02190e89422ea94afd7b | d2c7b5c31928c98f545b16420d37842c43b4ae9a | refs/heads/master | 1,611,313,622,901 | 1,430,266,839,000 | 1,430,267,083,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,187 | hlean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.constructions
Authors: Floris van Doorn
-/
import .basic algebra.precategory.constructions types.equiv types.trunc
--open eq eq.ops equiv category.ops iso cat... |
b632787a9c4d4e6d1ff46124be563e0700bba48e | 6094e25ea0b7699e642463b48e51b2ead6ddc23f | /library/data/real/complete.lean | 15a1b6209c9f380b43eafc2512bb7cdb4b2298c8 | [
"Apache-2.0"
] | permissive | gbaz/lean | a7835c4e3006fbbb079e8f8ffe18aacc45adebfb | a501c308be3acaa50a2c0610ce2e0d71becf8032 | refs/heads/master | 1,611,198,791,433 | 1,451,339,111,000 | 1,451,339,111,000 | 48,713,797 | 0 | 0 | null | 1,451,338,939,000 | 1,451,338,939,000 | null | UTF-8 | Lean | false | false | 30,443 | lean | /-
Copyright (c) 2015 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Robert Y. Lewis
The real numbers, constructed as equivalence classes of Cauchy sequences of rationals.
This construction follows Bishop and Bridges (1985).
At this point, we no longer... |
c99cf9a3f668466cd7f24fa84d306bd35722e5ca | 38bf3fd2bb651ab70511408fcf70e2029e2ba310 | /src/category_theory/limits/over.lean | bfb7358b17c445fc0e613cb079d4af1010f19a59 | [
"Apache-2.0"
] | permissive | JaredCorduan/mathlib | 130392594844f15dad65a9308c242551bae6cd2e | d5de80376088954d592a59326c14404f538050a1 | refs/heads/master | 1,595,862,206,333 | 1,570,816,457,000 | 1,570,816,457,000 | 209,134,499 | 0 | 0 | Apache-2.0 | 1,568,746,811,000 | 1,568,746,811,000 | null | UTF-8 | Lean | false | false | 5,931 | 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
-/
import category_theory.comma
import category_theory.limits.preserves
universes v u -- declare the `v`'s first; see `category_theory.category` for an exp... |
4bbd798c27f195a5a2fb44aed5cd18495e97144f | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/data/polynomial/basic.lean | 73641d189a948a40201734de88cc05dc02bfecbb | [
"Apache-2.0"
] | permissive | abentkamp/mathlib | d9a75d291ec09f4637b0f30cc3880ffb07549ee5 | 5360e476391508e092b5a1e5210bd0ed22dc0755 | refs/heads/master | 1,682,382,954,948 | 1,622,106,077,000 | 1,622,106,077,000 | 149,285,665 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 23,907 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
-/
import tactic.ring_exp
import tactic.chain
import algebra.monoid_algebra
import data.finset.sort
import tactic.ring
/-!
#... |
3ded86a4289dedee2cc5b8cd9ed0ecf907e3454a | a51edd9a1700339fa6dc7dc428eb5dfa3994b8bc | /src/fol/syntax.lean | 68f8885dc84657d89957b1398b11cb8888e1d540 | [] | no_license | avigad/formal_logic | 83f5c0534b3e9e7da53eff01bb82289daad65555 | 59d7fe7cb7a7927fb72d89d4fd40965bcd769349 | refs/heads/master | 1,585,302,642,116 | 1,541,000,469,000 | 1,541,000,469,000 | 146,376,915 | 1 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 14,237 | lean | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
We isolate the first-order fragment of hol over some basic sorts. Assume sorts are numbered
0, 1, ..., n-1 for some n. (We should change that later.)
-/
/-
This will be ... |
9da6d4020e90a360a235a160b6a25813ed22bd44 | 86f6f4f8d827a196a32bfc646234b73328aeb306 | /examples/introduction/unnamed_129.lean | 2d5e07db262e6dbe6425deafcb5a382830c54584 | [] | 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 | 238 | lean | import data.nat.basic
def fermat_last_theorem :=
∀ x y z n : ℕ, n > 2 ∧ x * y * z ≠ 0 → x^n + y^n ≠ z^n
-- BEGIN
theorem easy : 2 + 2 = 4 := rfl
#check easy
theorem hard : fermat_last_theorem := sorry
#check hard
-- END |
ddff6edb3f2d2efba9afb1162ac8f7108afdd492 | df561f413cfe0a88b1056655515399c546ff32a5 | /4-proposition-world/l7.lean | 4995d2583c63052e7e2e9f86fb7901df1e315fa5 | [] | 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 | 134 | lean | lemma imp_trans (P Q R : Prop) : (P → Q) → ((Q → R) → (P → R)) :=
begin
intros hpq hqr p,
apply hqr,
apply hpq,
exact p,
end |
b53c864607b488f52a5d6fb4b1e7d45630bb9536 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/number_theory/class_number/finite.lean | 5801e33d2ea96eebf323e2ca4612fe2bba361eba | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 17,843 | lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import analysis.special_functions.pow
import ring_theory.class_group
import ring_theory.norm
import linear_algebra.free_module.pid
import linear_algebra.matrix.absolute_va... |
fca544e12ae33616539ffb120bc020337c8495e6 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/algebra/covariant_and_contravariant.lean | 4950767b54fc850d7043566b9f3585b9c495493b | [
"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 | 11,515 | lean | /-
Copyright (c) 2021 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import algebra.group.defs
/-!
# Covariants and contravariants
This file contains general lemmas and instances to work with the interactions between a relation and
a... |
53003312bd30a37cf00864dc4264f400ae52c648 | 968e2f50b755d3048175f176376eff7139e9df70 | /examples/prop_logic_theory/unnamed_146.lean | 1a043bfcc1d0e1960f459b0e9075de92923b937f | [] | 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 | 126 | lean | variables p q r : Prop
example (h : (p ∧ q) ∧ r ) : q :=
begin
have h₂ : p ∧ q, from h.left,
exact h₂.right
end |
7f6184e0bdc63ed1b0d0a6d812c8477199c84505 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/field_theory/normal.lean | 213fe175445157754cc471540e3cf959d3243919 | [
"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 | 21,824 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Thomas Browning, Patrick Lutz
-/
import field_theory.adjoin
import field_theory.tower
import group_theory.solvable
import ring_theory.power_basis
/-!
# Normal field extensions
... |
20b581e04596c1fd95bb68bd13c35b672ed09364 | 26bff4ed296b8373c92b6b025f5d60cdf02104b9 | /hott/types/equiv.hlean | 1dc62f7747566093610946b3e40fa0be8b92787f | [
"Apache-2.0"
] | permissive | guiquanz/lean | b8a878ea24f237b84b0e6f6be2f300e8bf028229 | 242f8ba0486860e53e257c443e965a82ee342db3 | refs/heads/master | 1,526,680,092,098 | 1,427,492,833,000 | 1,427,493,281,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,105 | hlean | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: types.equiv
Author: Floris van Doorn
Ported from Coq HoTT
Theorems about the types equiv and is_equiv
-/
import types.fiber types.arrow arity
open eq is_trunc sigma sigma.ops arro... |
c13cde0058be847d1d1d9f8bfa97c1a016934502 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/category_theory/preadditive/projective.lean | 5fb7122a8b5224d761217f9b3c6ce2f510a777ff | [
"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 | 6,970 | lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Scott Morrison
-/
import algebra.homology.exact
import category_theory.types
import category_theory.limits.shapes.biproducts
/-!
# Projective objects and categories with... |
d51fa670be36e11f2c9c3289956203986c91392a | dc253be9829b840f15d96d986e0c13520b085033 | /algebra/direct_sum.hlean | 4156ed1cadf3a62fa239f0006d608be4d5f171ad | [
"Apache-2.0"
] | permissive | cmu-phil/Spectral | 4ce68e5c1ef2a812ffda5260e9f09f41b85ae0ea | 3b078f5f1de251637decf04bd3fc8aa01930a6b3 | refs/heads/master | 1,685,119,195,535 | 1,684,169,772,000 | 1,684,169,772,000 | 46,450,197 | 42 | 13 | null | 1,505,516,767,000 | 1,447,883,921,000 | Lean | UTF-8 | Lean | false | false | 9,506 | hlean | /-
Copyright (c) 2015 Floris van Doorn, Egbert Rijke, Favonia. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Egbert Rijke, Favonia
Constructions with groups
-/
import .quotient_group .free_abelian_group .product_group
open eq is_equiv algebra is_t... |
df764b0cea8669d285300c33c288162739ea4fdc | cbb817439c51008d66b37ce6b1964fea61434d35 | /theorem-proving-in-lean/src/chap_9.lean | f13629075b0c8f838a31ba4d0d5f5179a50b47f8 | [] | no_license | tomhoule/theorem-proving-in-lean-exercises | a07f99d4f6b41ce003e8a0274c7bc46359fa62b2 | 60ccc71b8a6df6924e7cc90aab713b804f78da9f | refs/heads/master | 1,663,582,321,828 | 1,590,352,467,000 | 1,590,352,476,000 | 257,107,936 | 3 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 765 | lean |
namespace hidden
instance inhabited_sum (α : Type) (β : Type) [inhabited α] : inhabited (α ⊕ β) :=
⟨@sum.inl α β (default α)⟩
instance inhabited_nonempty (α : Type) [inhabited α] : inhabited (list α) :=
⟨list.cons (default α) list.nil⟩
def add_lists (α : Type) [has_add α] : list α → list α → lis... |
a741a4e82b8e564b26bd5158b8597a8b39860c55 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/order/group/with_top.lean | f0fc8553bcfbf20f82df2dd5cb796015b77a9e6d | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 1,080 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl
-/
import algebra.order.group.instances
import algebra.order.monoid.with_top
/-!
# Adjoining a top element to a `linear... |
57930566da97c82a1eff67a449963c888dfa45c6 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/field_theory/finiteness.lean | a4a25d8a491b9ca426531a6144bb073ff6055eda | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 4,161 | lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import ring_theory.finiteness
import linear_algebra.dimension
/-!
# A module over a division ring is noetherian if and only if it is finite.
-/
universes u v
open_loc... |
9cad14152f91a6d728b2799ce692339562d0f18a | 41ebf3cb010344adfa84907b3304db00e02db0a6 | /uexp/src/uexp/meta/generator_generator.lean | a258d187584f72cedc99d5ea30e6a636b8e83a52 | [
"BSD-2-Clause"
] | permissive | ReinierKoops/Cosette | e061b2ba58b26f4eddf4cd052dcf7abd16dfe8fb | eb8dadd06ee05fe7b6b99de431dd7c4faef5cb29 | refs/heads/master | 1,686,483,953,198 | 1,624,293,498,000 | 1,624,293,498,000 | 378,997,885 | 0 | 0 | BSD-2-Clause | 1,624,293,485,000 | 1,624,293,484,000 | null | UTF-8 | Lean | false | false | 255 | lean | import .u_semiring_AST
meta def generator (transform : ast → ast)
(transform_eq : tactic unit)
(get_expr : tactic expr)
: tactic unit := do
eq ← get_expr,
|
5c03ee86a80f577cf5027f591be2577887a5af6e | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/analysis/normed_space/conformal_linear_map.lean | f0849441bc6ccd2d3486199c2912caf78c431c8f | [
"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 | 5,409 | lean | /-
Copyright (c) 2021 Yourong Zang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yourong Zang
-/
import geometry.euclidean.basic
import analysis.normed_space.inner_product
/-!
# Conformal Linear Maps
A continuous linear map between `R`-normed spaces `X` and `Y` `is... |
b868204be153b5a838b8ab95cd002e9a4af14cb4 | 618003631150032a5676f229d13a079ac875ff77 | /src/order/boolean_algebra.lean | 51439e374d7bdb524d192672a0f45f869b089990 | [
"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 | 3,269 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Type class hierarchy for Boolean algebras.
-/
import order.bounded_lattice
import logic.function.basic
set_option old_structure_cmd true
universes u
variables {α : Typ... |
316603e23048a346ba9b3af5afbc759e7b85b71e | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/mv_polynomial/polynomial.lean | bbe843c6ba862eb70ea766e36287e867f7eb485b | [
"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 | 1,531 | lean | /-
Copyright (c) 2023 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import data.mv_polynomial.equiv
import data.polynomial.eval
/-!
# Some lemmas relating polynomials and multivariable polynomials.
> THIS FILE IS SYNCHRONIZED WITH M... |
22f253618b5ab03b99de3fd6a7e868d0dba8e8cf | b2fe74b11b57d362c13326bc5651244f111fa6f4 | /src/number_theory/arithmetic_function.lean | 4a83586ba39b709f4b0bf51c8d3e45425c4aca99 | [
"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 | 32,192 | lean | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import algebra.big_operators.ring
import number_theory.divisors
import algebra.squarefree
import algebra.invertible
/-!
# Arithmetic Functions and Dirichlet Convolut... |
e46eeff5e07cd74f955984905e94b8132313889d | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/logic/embedding/set.lean | 92c99975923c5666df09b778babdf282c712de33 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 4,062 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import logic.embedding.basic
import data.set.basic
/-!
# Interactions between embeddings and sets.
-/
universes u v w x
section equiv
variables {... |
d9f5cefdb424d9aa167851f507409d95f6084c93 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebraic_geometry/stalks.lean | 63dad4e5f3b40f9a50b1fe249b85082ba2bafe4a | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 8,529 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import algebraic_geometry.presheafed_space
import category_theory.limits.final
import topology.sheaves.stalks
/-!
# Stalks for presheaved spaces
This file lifts con... |
6907b1ace216356ab47b781e63b3122742d2add2 | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/category_theory/shift.lean | fb2216328101af3ffd42ba730854b97f615b77ae | [
"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 | 1,444 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.limits.shapes.zero
/-! #Shift
A `shift` on a category is nothing more than an automorphism of the category. An example to
keep in mind might ... |
e8df552f6533ccf538d4af2893e5a7addbd9d974 | 26ac254ecb57ffcb886ff709cf018390161a9225 | /src/data/polynomial/degree/basic.lean | 6c4eadcc825383bfea1120272fe9b39ec2e3f626 | [
"Apache-2.0"
] | permissive | eric-wieser/mathlib | 42842584f584359bbe1fc8b88b3ff937c8acd72d | d0df6b81cd0920ad569158c06a3fd5abb9e63301 | refs/heads/master | 1,669,546,404,255 | 1,595,254,668,000 | 1,595,254,668,000 | 281,173,504 | 0 | 0 | Apache-2.0 | 1,595,263,582,000 | 1,595,263,581,000 | null | UTF-8 | Lean | false | false | 10,213 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
-/
import data.polynomial.coeff
/-!
# Theory of univariate polynomials
The definitions include
`degree`, `monic`, `leading_... |
3bdad2e28dbc8c118d3f1745f52fea0699189479 | 54f4ad05b219d444b709f56c2f619dd87d14ec29 | /my_project/src/love11_logical_foundations_of_mathematics_demo.lean | b91f2815af54e7f9554dc60ffa259fda7073cd83 | [] | no_license | yizhou7/learning-lean | 8efcf838c7276e235a81bd291f467fa43ce56e0a | 91fb366c624df6e56e19555b2e482ce767cd8224 | refs/heads/master | 1,675,649,087,737 | 1,609,022,281,000 | 1,609,022,281,000 | 272,072,779 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,889 | lean | import .love05_inductive_predicates_demo
/-! # LoVe Demo 11: Logical Foundations of Mathematics
We dive deeper into the logical foundations of Lean. Most of the features
described here are especially relevant for defining mathematical objects and
proving theorems about them. -/
set_option pp.beta true
namespace L... |
ae983cb0775da36acef8cf9ab645409daaafd85c | 4727251e0cd73359b15b664c3170e5d754078599 | /src/ring_theory/polynomial_algebra.lean | f3be80b053384051a91dd3530f50b2e49c80a456 | [
"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 | 10,561 | 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 ring_theory.matrix_algebra
import data.polynomial.algebra_map
import data.matrix.basis
import data.matrix.dmatrix
/-!
# Algebra isomorphism between matrices o... |
396a067a06af5f45e8efb8a38a4f5a523e42773c | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /src/Init/System/Platform.lean | ec53df8e03b6048ef7195a6bc46b60c649ff14f0 | [
"Apache-2.0"
] | permissive | collares/lean4 | 861a9269c4592bce49b71059e232ff0bfe4594cc | 52a4f535d853a2c7c7eea5fee8a4fa04c682c1ee | refs/heads/master | 1,691,419,031,324 | 1,618,678,138,000 | 1,618,678,138,000 | 358,989,750 | 0 | 0 | Apache-2.0 | 1,618,696,333,000 | 1,618,696,333,000 | null | UTF-8 | Lean | false | false | 485 | lean | /-
Copyright (c) 2018 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
namespace System
namespace Platform
@[extern "lean_system_platform_windows"] constant getIsWindows : Unit → Bool
@[exte... |
c5493be6f1d36eb67ea91d814699b03de5c7eef9 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /doc/examples/interp.lean | c87c27ef928134c32ae1a0b5a07a2704f32d4773 | [
"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 | 6,299 | lean | /-!
# The Well-Typed Interpreter
In this example, we build an interpreter for a simple functional programming language,
with variables, function application, binary operators and an `if...then...else` construct.
We will use the dependent type system to ensure that any programs which can be represented are well-typed.
... |
3cdd929f3110d0b859559b0524ed9a1f4650892b | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/meta/smt/smt_tactic_auto.lean | 92a60391d466d25b90289128739747bb8aa50211 | [] | 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 | 1,187 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.control.default
import Mathlib.Lean3Lib.init.meta.simp_tactic
import Mathlib.Lean3Lib.init.meta.smt.cong... |
9ac70e5108b22f2cf5ed5f33a48a113428425a83 | 969dbdfed67fda40a6f5a2b4f8c4a3c7dc01e0fb | /src/ring_theory/hahn_series.lean | ec44c671746348b559551443f9c12f0bfe3fc1b6 | [
"Apache-2.0"
] | permissive | SAAluthwela/mathlib | 62044349d72dd63983a8500214736aa7779634d3 | 83a4b8b990907291421de54a78988c024dc8a552 | refs/heads/master | 1,679,433,873,417 | 1,615,998,031,000 | 1,615,998,031,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 26,309 | 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 order.well_founded_set
import algebra.big_operators
import ring_theory.valuation.basic
import algebra.module.pi
import ring_theory.power_series.basic
/-!
# Ha... |
d9cf2143e5ae8bd73fb268b26fcd6f2212df4b5c | 618003631150032a5676f229d13a079ac875ff77 | /src/topology/continuous_on.lean | 9a9cbe252ec9f3392d61f57b7c2ebd006500e058 | [
"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 | 24,184 | lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import topology.constructions
/-!
# Neighborhoods and continuity relative to a subset
This file defines relative versions
`nhds_within` of `nhds`
`contin... |
18a347ca5f8d82a816b4340715a24f2c534488cb | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/limits/shapes/kernels.lean | 9fd70734c7124f6aca03a8b3aa2b1d83567ccd35 | [] | 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 | 33,898 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Markus Himmel
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.limits.shapes.zero
import Mathlib.PostPort
universes v u u'... |
b24b5b12220f259189c6eb6b9221f51ec2796198 | 6950a6e5cebf75da9b91f42789baf52514655111 | /leanhammer.lean | 8b471a2e5854f93e1ab88d5af514fdd90f8194d5 | [] | no_license | phlippe/Lean_hammer | a6d0a1af09fbce0c58b801032099b9b91d49ecf0 | 2116279b9c6b334f5b661e4abf4561368cca2391 | refs/heads/master | 1,587,486,769,513 | 1,561,466,931,000 | 1,561,466,931,000 | 169,705,506 | 0 | 1 | null | 1,550,228,564,000 | 1,549,614,939,000 | Lean | UTF-8 | Lean | false | false | 5,293 | lean | import system.io
-- import .tptp.tptp
import .premise_selection
-- import .tptp.simplification_tptp
-- import .tptp.translation_tptp
import .problem_translation
--#################
--## System test ##
--#################
-- def sum_two (x: ℕ) (y: ℕ) : ℕ := x+y
-- Inductive declaration because the simple version abov... |
2a880edf5c47f213800a82df725a48df31ccbba3 | 367134ba5a65885e863bdc4507601606690974c1 | /src/topology/sheaves/sheaf_condition/opens_le_cover.lean | f27c51f9948d4e4850df44a0eeb0d336cdd6c45d | [
"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 | 9,860 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import topology.sheaves.presheaf
import category_theory.limits.cofinal
import topology.sheaves.sheaf_condition.pairwise_intersections
/-!
# Another version of the sh... |
bd2dedf5bca859b4621c18ab12a387067ea3065f | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/run/back4.lean | 3d7708fa460072d84c956c048db33809a8104a94 | [
"Apache-2.0"
] | permissive | GaloisInc/lean | aa1e64d604051e602fcf4610061314b9a37ab8cd | f1ec117a24459b59c6ff9e56a1d09d9e9e60a6c0 | refs/heads/master | 1,592,202,909,807 | 1,504,624,387,000 | 1,504,624,387,000 | 75,319,626 | 2 | 1 | Apache-2.0 | 1,539,290,164,000 | 1,480,616,104,000 | C++ | UTF-8 | Lean | false | false | 1,591 | lean | /- Lean also support E-matching: a heuristic lemma instantiation procedure
that is available in many SMT solvers.
Goals such as mk_mem_list can also be discharged using heuristic instantiation. -/
open list tactic
universe variable u
lemma in_tail {α : Type u} {a : α} (b : α) {l : list α} : a ∈ l → a ∈ b... |
bb5afd1abf4fff215bcda4d47ae43da32b923bbd | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/data/buffer/basic.lean | 30f6ae67919368e7ac939626f2e88a56f7ee8f4b | [
"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 | 1,854 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
Traversable instance for buffers.
-/
import data.buffer data.array.lemmas
import category.traversable.instances data.equiv.basic
tactic.ext
namespace buffer
open fu... |
86f72ff61fd3ae2e1a5644d609f668602ccf2999 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/using_new_ref_interactive.lean | 215601dbfb520878723f1af620718be02820aa66 | [
"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 | 55 | lean | run_cmd tactic.using_new_ref (0 : ℕ) $ λ _, `[skip]
|
ddbab008c71e6de416ff177fdd06ef014eee5421 | ebb7367fa8ab324601b5abf705720fd4cc0e8598 | /pointed_pi.hlean | e0e3585db189eefd65e149a94568a5badf5d6841 | [
"Apache-2.0"
] | permissive | radams78/Spectral | 3e34916d9bbd0939ee6a629e36744827ff27bfc2 | c8145341046cfa2b4960ef3cc5a1117d12c43f63 | refs/heads/master | 1,610,421,583,830 | 1,481,232,014,000 | 1,481,232,014,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,371 | hlean | /-
Copyright (c) 2016 Ulrik Buchholtz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ulrik Buchholtz
-/
import move_to_lib
open eq pointed equiv sigma
/-
The goal of this file is to give the truncation level
of the type of pointed maps, giving the connectivity ... |
9d17e6593262f09e906da18cdb0c5adf2353aeb1 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/analysis/special_functions/exp.lean | 11de0b639b95545be1538dbaae3ee383a05dc086 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 15,126 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne
-/
import analysis.complex.basic
import data.complex.exponential
import analysis.asymptotics.theta
/-!
# Complex and real ex... |
d89cc1be4808dc2f6c7e7fdce1d7f605fa3bd7c0 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/set/constructions.lean | b8a794e3c683cfa6da14ae5c78e876925ecb477a | [
"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 | 2,822 | lean | /-
Copyright (c) 2020 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import data.finset.basic
/-!
# Constructions involving sets of sets.
## Finite Intersections
We define a structure `has_finite_inter` which asserts that a set `S` of subse... |
9c862233b31df732d6b9bdbcbb2d84ba3dcbb54c | bb31430994044506fa42fd667e2d556327e18dfe | /src/algebra/order/sub/with_top.lean | 5e755488d2801f7586ac226b50b3a5114a7763a0 | [
"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 | 1,763 | lean | /-
Copyright (c) 2021 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import algebra.order.sub.defs
import algebra.order.monoid.with_top
/-!
# Lemma about subtraction in ordered monoids with a top element adjoined.
> THIS FILE IS ... |
f67639a0da458494e7207ea093cb62c98dbe6e3c | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Init/System/IO.lean | fedc48dcd0d3f101819fa8c9940da445ea56934e | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 28,026 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Luke Nelson, Jared Roesch, Leonardo de Moura, Sebastian Ullrich, Mac Malone
-/
prelude
import Init.Control.EState
import Init.Control.Reader
import Init.Data.String
import Init.... |
e69b68d26a7b98c03807704a755b31dfb9350720 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/topology/sheaves/functors.lean | c8c0de8e47d4653bf6bd016220eb593e1423b935 | [
"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 | 2,433 | lean | /-
Copyright (c) 2021 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu
-/
import topology.sheaves.sheaf_condition.pairwise_intersections
/-!
# functors between categories of sheaves
Show that the pushforward of a sheaf is a sheaf, and define
the p... |
f1bd23fd4bf4f1bb0da87e27d2b3608056cd8ee7 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/ring_theory/integral_closure.lean | cda2988b052158136496a95ea8135d76e906426f | [
"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 | 17,192 | lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
Integral closure of a subring.
-/
import ring_theory.adjoin linear_algebra.finsupp
universes u v
open_locale classical
open polynomial submodule
section
variables (R : Type u... |
ebbf6205d4405176d36399c1422c0861539417ae | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/data/mv_polynomial/basic.lean | 4b3b818dc190fab17284be01e73c51fd238257aa | [
"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 | 35,760 | 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.polynomial.eval
/-!
# Multivariate polynomials
This file defines polynomial rings over a base ring (or even semiring),
... |
13b560d0870997c7438344b7b7a09e069d46b9ec | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/combinatorics/quiver/connected_component.lean | 6ce1276737e98ff8b6a4cd6e39abfca544c7312f | [
"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 | 3,384 | lean | /-
Copyright (c) 2021 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
import combinatorics.quiver.subquiver
import combinatorics.quiver.path
/-!
## Weakly connected components
For a quiver `V`, we build a quiver `symmetrify V` by adding a rev... |
02ed6b7e0bce2b8a5b27f337d5cba0c47b69dbf6 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /test/abel.lean | 891727582444e48d2a701ca08e785a78f9eb9cff | [
"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 | 615 | lean | import tactic.abel
variables {α : Type*} {a b : α}
example [add_comm_monoid α] : a + (b + a) = a + a + b := by abel
example [add_comm_group α] : (a + b) - ((b + a) + a) = -a := by abel
example [add_comm_group α] (x : α) : x - 0 = x := by abel
example [add_comm_monoid α] (x : α) : (3 : ℕ) • a = a + (2 : ℕ) • a := by ab... |
fc4a9f919bd6cae594788060826aaf369b276cdb | 08bd4ba4ca87dba1f09d2c96a26f5d65da81f4b4 | /src/Lean/Compiler/IR/LiveVars.lean | 64ce289551aedc04759bc59c39aabbe5466ca0b5 | [
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"Apache-2.0",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | gebner/lean4 | d51c4922640a52a6f7426536ea669ef18a1d9af5 | 8cd9ce06843c9d42d6d6dc43d3e81e3b49dfc20f | refs/heads/master | 1,685,732,780,391 | 1,672,962,627,000 | 1,673,459,398,000 | 373,307,283 | 0 | 0 | Apache-2.0 | 1,691,316,730,000 | 1,622,669,271,000 | Lean | UTF-8 | Lean | false | false | 6,945 | 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.Compiler.IR.Basic
import Lean.Compiler.IR.FreeVars
namespace Lean.IR
/-! Remark: in the paper "Counting Immutable Beans" the concepts of
fr... |
7b98f78ffe238bd4091a9f41c210b91b4adf64e1 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/ring_theory/adjoin/polynomial.lean | e9dfc0b9e64d0edae9c108540e5f1dbf4139782d | [
"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 | 2,856 | lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import ring_theory.adjoin.basic
import ring_theory.polynomial.basic
/-!
# Adjoining elements to form subalgebras: relation to polynomials
In this file we prove a few results ... |
d6713bf150aee3abe9c68caf19f01a6009718000 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/algebraic_topology/cech_nerve.lean | f1e13ba9f41bef07c451231df7c8a473cc4e2ae8 | [
"Apache-2.0"
] | permissive | abentkamp/mathlib | d9a75d291ec09f4637b0f30cc3880ffb07549ee5 | 5360e476391508e092b5a1e5210bd0ed22dc0755 | refs/heads/master | 1,682,382,954,948 | 1,622,106,077,000 | 1,622,106,077,000 | 149,285,665 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,795 | lean | /-
Copyright (c) 2021 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import algebraic_topology.simplicial_object
import category_theory.limits.shapes.wide_pullbacks
import category_theory.arrow
/-!
# The Čech Nerve
This file provides a def... |
a45f3abbcf51b040859fbd2c6386253fbe9b5d01 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/ring_theory/unique_factorization_domain.lean | c811e2321981d07f84075fcde7f22e0bfcb04c7c | [
"Apache-2.0"
] | permissive | dupuisf/mathlib | 62de4ec6544bf3b79086afd27b6529acfaf2c1bb | 8582b06b0a5d06c33ee07d0bdf7c646cae22cf36 | refs/heads/master | 1,669,494,854,016 | 1,595,692,409,000 | 1,595,692,409,000 | 272,046,630 | 0 | 0 | Apache-2.0 | 1,592,066,143,000 | 1,592,066,142,000 | null | UTF-8 | Lean | false | false | 23,090 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker
Theory of unique factorization domains.
@TODO: setup the complete lattice structure on `factor_set`.
-/
import algebra.gcd_domain
import ring_theory.in... |
e1ee37b468cd9d7eb15a17cfd4a896217e437f5a | 7617a8700fc3eebd9200f1e620ee65b3565d2eff | /src/tests/cell.lean | 8b8eed5415a03e35f6ac567d87df07e29cedb8d1 | [] | no_license | digama0/vc0 | 9747eee791c5c2f58eb53264ca6263ee53de0f87 | b8b192c8c139e0b5a25a7284b93ed53cdf7fd7a5 | refs/heads/master | 1,626,186,940,436 | 1,592,385,972,000 | 1,592,385,972,000 | 158,556,766 | 5 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,346 | lean | import c0.ast
open c0 c0.ast c0.ast.gdecl c0.ast.type c0.ast.exp c0.ast.lval c0.ast.stmt
def cell : ast := list.reverse [
sdecl "CA" $ some [
("rule", (arr int))],
sdecl "config" $ some [
("size", int),
("vals", (arr int))],
fdecl ff "init_CA" [("f", int)] (some (ref (struct "CA"))) $ some $
dec... |
1d39bccbcff9f8b4e7a05c78798ae83acabdeb34 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/induction_naming.lean | 653a72f74e5e953d2ab4354f6cfd87644238c134 | [
"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 | 501 | lean | example (a b : nat) : a + b = b + a :=
begin
cases a,
trace_state, /- `a` was used to name constructor field -/
repeat { admit }
end
example (a b : nat) : a + b = b + a :=
begin
induction a,
trace_state, /- `a_n` and `a_ih` were used to name constructor fields -/
repeat { admit }
end
set_option tactic.ind... |
e05da3dfe38a9de5dedbb5dfe98b56faa98509da | d436468d80b739ba7e06843c4d0d2070e43448e5 | /src/topology/instances/ennreal.lean | db54a533378cf702e86c001906d03ab9b6e0aa6e | [
"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 | 33,456 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
Extended non-negative reals
-/
import topology.instances.nnreal data.real.ennreal
noncomputable theory
open classical set lattice filter metric
open_locale classical
ope... |
7659d8c6d469189f049528c76883a14e6a209e90 | 316671bfe98dfae2abac483407a5ae2daca54b1b | /03_Conjunction/00_and.lean | fc7835a09b653b0901f926c29f4a6a4c31bd448d | [] | no_license | chasedawson/cs-dm | 9b38bd7b0bd411a9f7713f5d613b8a0b2fdcd28b | ac3cca3eadc56a6355c8e9a56a39ed7eb1db55cb | refs/heads/master | 1,585,360,471,246 | 1,536,097,455,000 | 1,536,097,455,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,809 | lean | /-
Intuitively, if a proposition P is true and a
second proposition Q is true, then the more
complex proposition, "P and Q" is also true.
This proposition is written symbolically as
P ∧ Q. In mathematical logic, we say that
the proposition, P ∧ Q, is the conjunction
of the individual propositions, P and Q.
To give ... |
6bd0d43fd40a3b1b4d6fc1f93b5df2ad4cae0b2a | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/analysis/normed_space/operator_norm.lean | c18ec3e774e379a416804f21f894e5b255eeacad | [
"Apache-2.0"
] | permissive | hamdysalah1/mathlib | b915f86b2503feeae268de369f1b16932321f097 | 95454452f6b3569bf967d35aab8d852b1ddf8017 | refs/heads/master | 1,677,154,116,545 | 1,611,797,994,000 | 1,611,797,994,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 44,252 | lean | /-
Copyright (c) 2019 Jan-David Salchow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo
-/
import linear_algebra.finite_dimensional
import analysis.normed_space.linear_isometry
import analysis.normed_space.riesz_lemma
impor... |
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