blob_id stringlengths 40 40 | directory_id stringlengths 40 40 | path stringlengths 7 139 | content_id stringlengths 40 40 | detected_licenses listlengths 0 16 | license_type stringclasses 2
values | repo_name stringlengths 7 55 | snapshot_id stringlengths 40 40 | revision_id stringlengths 40 40 | branch_name stringclasses 6
values | visit_date int64 1,471B 1,694B | revision_date int64 1,378B 1,694B | committer_date int64 1,378B 1,694B | github_id float64 1.33M 604M ⌀ | star_events_count int64 0 43.5k | fork_events_count int64 0 1.5k | gha_license_id stringclasses 6
values | gha_event_created_at int64 1,402B 1,695B ⌀ | gha_created_at int64 1,359B 1,637B ⌀ | gha_language stringclasses 19
values | src_encoding stringclasses 2
values | language stringclasses 1
value | is_vendor bool 1
class | is_generated bool 1
class | length_bytes int64 3 6.4M | extension stringclasses 4
values | content stringlengths 3 6.12M |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
5114ebfaa4ec51c1f8b97abcf6a0460cf08ea3ff | 592ee40978ac7604005a4e0d35bbc4b467389241 | /Library/generated/mathscheme-lean/TwoPointed.lean | e2439f9476aec09aeabc13de776dfbae7ed2fc4a | [] | no_license | ysharoda/Deriving-Definitions | 3e149e6641fae440badd35ac110a0bd705a49ad2 | dfecb27572022de3d4aa702cae8db19957523a59 | refs/heads/master | 1,679,127,857,700 | 1,615,939,007,000 | 1,615,939,007,000 | 229,785,731 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,918 | lean | import init.data.nat.basic
import init.data.fin.basic
import data.vector
import .Prelude
open Staged
open nat
open fin
open vector
section TwoPointed
structure TwoPointed (A : Type) : Type :=
(e1 : A)
(e2 : A)
open TwoPointed
structure Sig (AS : Type) : Type :=
(e1S : AS)
(e... |
18c8fd300c90b2c83d14f83cba21495c5982233b | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/data/nat/basic_auto.lean | 1b13a21c7db73bc810e6f3a4c16823b3873cdf20 | [] | 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 | 5,388 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.logic
universes u
namespace Mathlib
namespace nat
notation:1024 "ℕ" => Mathlib.n... |
0d93b875e5cbf48cb8cd3d127c0bc816eb3b5b30 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/category_theory/abelian/basic.lean | 1d0d3e8df9ed45badaa8a48119ee47e9c92f1d21 | [
"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 | 30,104 | lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Johan Commelin, Scott Morrison
-/
import category_theory.limits.constructions.pullbacks
import category_theory.limits.shapes.biproducts
import category_theory.limits.sha... |
f0413cb0974c5bec11cd483e311000b57d0689f4 | 9b9a16fa2cb737daee6b2785474678b6fa91d6d4 | /src/order/order_iso.lean | 02544e436e616aceeb03841912f2d1835ab5c4bc | [
"Apache-2.0"
] | permissive | johoelzl/mathlib | 253f46daa30b644d011e8e119025b01ad69735c4 | 592e3c7a2dfbd5826919b4605559d35d4d75938f | refs/heads/master | 1,625,657,216,488 | 1,551,374,946,000 | 1,551,374,946,000 | 98,915,829 | 0 | 0 | Apache-2.0 | 1,522,917,267,000 | 1,501,524,499,000 | Lean | UTF-8 | Lean | false | false | 13,004 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import order.basic logic.embedding data.nat.basic
open function
universes u v w
variables {α : Type*} {β : Type*} {γ : Type*}
{r : α → α → Prop} {s : β → β → Prop... |
d50099e412136e296aa97c7b7c3df8c69f6b467d | 5df84495ec6c281df6d26411cc20aac5c941e745 | /src/formal_ml/ennreal.lean | f770bf50096e675ded4d84dafd962781b9251fb9 | [
"Apache-2.0"
] | permissive | eric-wieser/formal-ml | e278df5a8df78aa3947bc8376650419e1b2b0a14 | 630011d19fdd9539c8d6493a69fe70af5d193590 | refs/heads/master | 1,681,491,589,256 | 1,612,642,743,000 | 1,612,642,743,000 | 360,114,136 | 0 | 0 | Apache-2.0 | 1,618,998,189,000 | 1,618,998,188,000 | null | UTF-8 | Lean | false | false | 23,839 | lean | /-
Copyright 2020 Google LLC
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
di... |
82684af4104808f1a0d2a7e5e5af453df9233371 | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/ring_theory/fractional_ideal.lean | 82222fef50da7b360fa175e6f7380fb6f74c0923 | [
"Apache-2.0"
] | permissive | mcncm/mathlib | 8d25099344d9d2bee62822cb9ed43aa3e09fa05e | fde3d78cadeec5ef827b16ae55664ef115e66f57 | refs/heads/master | 1,672,743,316,277 | 1,602,618,514,000 | 1,602,618,514,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 27,490 | 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 ring_theory.localization
import ring_theory.principal_ideal_domain
/-!
# Fractional ideals
This file defines fractional ideals of an integral domain and proves bas... |
4bfb374e88d2cd8001516feab3695d1151d22f4d | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/as_pattern.lean | 3f45c846057a3b6a964c6a1e194d8275c9daec2d | [
"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 | 1,194 | lean | namespace as_pattern
inductive foo
| a | b | c
inductive bar : foo → Type
| a : bar foo.a
| b : bar foo.b
def basic : list foo → list foo
| x@([_]) := x -- `@[` starts an attribute
| x@_ := x
#print prefix as_pattern.basic.equations
def nested : list foo → list foo
| (x@foo.b :: _) := [x]
| x ... |
fb43c631210f1112c5e72cc889831f2de3e461d8 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/ring_theory/discrete_valuation_ring.lean | 96093bf8d466fd71b99a3e4e259b3bf7eef08037 | [
"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 | 17,295 | lean | /-
Copyright (c) 2020 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard
-/
import ring_theory.principal_ideal_domain
import order.conditionally_complete_lattice
import ring_theory.ideal.local_ring
import ring_theory.multiplicity
import ring_t... |
91ec8eed70aa2924320a77ba4ff681d2c75703a9 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/check_expr.lean | 67e0946f758bebb7c2a152cb001fd792e2528214 | [
"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 | 141 | lean | import data.list
open sigma list
theorem foo (A : Type) (l : list A): A → A → list A :=
begin
intros [a, b],
check_expr (a::l),
end
|
5991361e6214a800c30d7592164b7303617a6c4b | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /test/matrix.lean | d5006062da3e7abd82a31f9a4b489c06840773b1 | [
"Apache-2.0"
] | permissive | ilitzroth/mathlib | ea647e67f1fdfd19a0f7bdc5504e8acec6180011 | 5254ef14e3465f6504306132fe3ba9cec9ffff16 | refs/heads/master | 1,680,086,661,182 | 1,617,715,647,000 | 1,617,715,647,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,188 | lean | import data.matrix.notation
import linear_algebra.determinant
import group_theory.perm.fin
import tactic.norm_swap
variables {α β : Type} [semiring α] [ring β]
namespace matrix
open_locale matrix
example {a a' b b' c c' d d' : α} :
![![a, b], ![c, d]] + ![![a', b'], ![c', d']] = ![![a + a', b + b'], ![c + c', d +... |
ec480981f00d1fee61b942d7b1ab0b521e3033de | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /stage0/src/Lean/Meta/Match/MatchPatternAttr.lean | bd5367b4e3bdef67394f0d9fecc840a0306769af | [
"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 | 579 | 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.Attributes
namespace Lean
builtin_initialize matchPatternAttr : TagAttribute ←
registerTagAttribute `matchPattern "mark that a definition ca... |
a3a3d232392133ea30b751b957a6519538c61217 | 7056dcccc8ffc1e6f9f533f3fed8ef16ff9fcc1e | /src/Init/Lean/Parser/Parser.lean | 995cb7d1949edd7cde14bff4ca8975c0df849a29 | [
"Apache-2.0"
] | permissive | graydon/lean4 | d73f60d0aa60e64e8d15674538bb5921aad5a4d1 | ec9f4b579dc6b4a20407d2735f8ad91de29bfdb5 | refs/heads/master | 1,650,641,753,817 | 1,587,651,832,000 | 1,587,733,896,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 78,671 | 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.Data.Trie
import Init.Lean.Data.Position
import Init.Lean.Syntax
import Init.Lean.ToExpr
import Init.Lean.Enviro... |
ec81c339628e13f66c41ce612353555e27e4712f | 57fdc8de88f5ea3bfde4325e6ecd13f93a274ab5 | /analysis/measure_theory/lebesgue_measure.lean | 9e6f26f0980b686adfc6b46de99d2ede3be8290d | [
"Apache-2.0"
] | permissive | louisanu/mathlib | 11f56f2d40dc792bc05ee2f78ea37d73e98ecbfe | 2bd5e2159d20a8f20d04fc4d382e65eea775ed39 | refs/heads/master | 1,617,706,993,439 | 1,523,163,654,000 | 1,523,163,654,000 | 124,519,997 | 0 | 0 | Apache-2.0 | 1,520,588,283,000 | 1,520,588,283,000 | null | UTF-8 | Lean | false | false | 12,494 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Lebesgue measure on the real line
-/
import analysis.measure_theory.measure_space analysis.measure_theory.borel_space
noncomputable theory
open classical set lattice fi... |
449fcab72ddbc40f5bd8e95ba21af3b45ada9ac7 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/algebra/field.lean | 743511452107bf7a69f24eca06bcfd1d3e9c6d11 | [
"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 | 10,123 | 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 algebra.ring logic.basic
open set
universe u
variables {α : Type u}
/-- Core version `division_ring_has_div` erratically requires two instanc... |
d4b337ab5a3773803130986a2e9a6238d0f305f9 | 26ac254ecb57ffcb886ff709cf018390161a9225 | /src/measure_theory/bochner_integration.lean | 35e9f72d427eeabd1211bf41f55b734621df1e46 | [
"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 | 55,625 | lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
-/
import measure_theory.simple_func_dense
import analysis.normed_space.bounded_linear_maps
import topology.sequences
/-!
# Bochner integral
The Bochner integral extends... |
1c20cc65bcd168e16bef56b5bc68bdf61171ec9a | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/let3.lean | 1987d9cd5088cd6c2aac1a97c6c016c49acaa717 | [
"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 | 750 | lean |
definition p1 := (10, 20, 30)
definition v1 : nat :=
let (a, b, c) := p1 in
a + b + c
definition v2 : nat :=
let ⟨a, b, c⟩ := p1 in
a + b + c
example : v2 = 60 :=
rfl
/-
let with patterns is just syntax sugar for the match convoy pattern.
let (a, b, c) := p1 in
a + b + c
is encoded as
match p1 with
... |
8396792a7551d20005c842123409cf6805812848 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/natural_transformation_auto.lean | 73c10a7cda71b799d0f684c67fba605e43854459 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,626 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tim Baumann, Stephen Morgan, Scott Morrison, Floris van Doorn
Defines natural transformations between functors.
Introduces notations
`τ.app X` for the components of natural transfo... |
bec6fbddaf29f81102f9bfb4968cf3ce377e71d2 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/seq/computation_auto.lean | e4e6c340a8d7f15aee80cafb4349021d66cfaef5 | [] | 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 | 35,223 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
Coinductive formalization of unbounded computations.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.Lean3Lib.data.stream
import Mat... |
34c85480cb744f583154837544f92857cbc33e8b | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /tests/lean/run/CommandExtOverlap.lean | c93741b2a8c46aa63311e0d8723b42d8b05d6299 | [
"Apache-2.0"
] | permissive | mhuisi/lean4 | 28d35a4febc2e251c7f05492e13f3b05d6f9b7af | dda44bc47f3e5d024508060dac2bcb59fd12e4c0 | refs/heads/master | 1,621,225,489,283 | 1,585,142,689,000 | 1,585,142,689,000 | 250,590,438 | 0 | 2 | Apache-2.0 | 1,602,443,220,000 | 1,585,327,814,000 | C | UTF-8 | Lean | false | false | 335 | lean | new_frontend
syntax [mycheck] "#check" (sepBy term ",") : command
open Lean
macro_rules [mycheck]
| `(#check $es*) =>
let cmds := es.getSepElems.map $ fun e => Syntax.node `Lean.Parser.Command.check #[Syntax.atom none "#check", e];
pure $ mkNullNode cmds
#check true
#check true, true
#check true, 1, 3, fun (x :... |
e600182dd888717a2a04f546dbb93eba2f57d7f6 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebraic_geometry/morphisms/ring_hom_properties.lean | b9dfba0ca93c5632205d52dcb9ca358c43501f04 | [
"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 | 25,184 | 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 algebraic_geometry.morphisms.basic
import ring_theory.local_properties
/-!
# Properties of morphisms from properties of ring homs.
We provide the basic framework ... |
228378543971a2d4e3b5fdb70d9a7d4ca80ec28d | 01f6b345a06ece970e589d4bbc68ee8b9b2cf58a | /src/limsup.lean | 4b023cb132f039b601cfbb929e9f66bc9d5ed43c | [] | no_license | mariainesdff/norm_extensions_journal_submission | 6077acb98a7200de4553e653d81d54fb5d2314c8 | d396130660935464fbc683f9aaf37fff8a890baa | refs/heads/master | 1,686,685,693,347 | 1,684,065,115,000 | 1,684,065,115,000 | 603,823,641 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,057 | lean | /-
Copyright (c) 2023 María Inés de Frutos-Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: María Inés de Frutos-Fernández
-/
import order.liminf_limsup
import topology.instances.nnreal
/-!
# Limsup
We prove some auxiliary results about limsups, infis, and ... |
86bc68da9411c5ab2871a610d1fd6f8180667678 | ed27983dd289b3bcad416f0b1927105d6ef19db8 | /src/inClassNotes/predicate_logic/and.lean | ae06b4df9c832039ffbb7c4cb1a862735255dcfe | [] | no_license | liuxin-James/complogic-s21 | 0d55b76dbe25024473d31d98b5b83655c365f811 | 13e03e0114626643b44015c654151fb651603486 | refs/heads/master | 1,681,109,264,463 | 1,618,848,261,000 | 1,618,848,261,000 | 337,599,491 | 0 | 0 | null | 1,613,141,619,000 | 1,612,925,555,000 | null | UTF-8 | Lean | false | false | 2,141 | lean | /-
The connective, ∧, in predicate as in
propositional logic builds a proposition
that asserts that each of two propositions
is true. Given propositions P, Q, P ∧ Q
is also a proposition, and we judge it to
be true iff we judge P to be true and we
judge Q to be true. We judge P and Q to
be true iff we have evidence th... |
050af46c437502ae4671243923ed67fd6f736b9a | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/category/Group/colimits.lean | 7853b3466a1d93c927611492e42d1f259d9a88a4 | [
"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 | 9,772 | 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 algebra.category.Group.preadditive
import group_theory.quotient_group
import category_theory.limits.shapes.kernels
import category_theory.concrete_category.ele... |
226dfa22abaa0fbffb564ab7025baa83d0a15328 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/category_theory/limits/opposites.lean | e5db4a11ddf339d4f63b0a0cf6274c5648168d6a | [
"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 | 5,526 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Floris van Doorn
-/
import category_theory.limits.shapes.finite_products
import category_theory.limits.shapes.kernels
import category_theory.discrete_category
/-!
# Li... |
4bc74fb5408357f475e6e37a4af4bd8195b2afe3 | bb31430994044506fa42fd667e2d556327e18dfe | /src/topology/locally_constant/basic.lean | ffae47b95d1ede28eb7ab44d3425aeb974a2a1d0 | [
"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 | 19,436 | lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import topology.subset_properties
import topology.connected
import topology.continuous_function.basic
import algebra.indicator_function
import tactic.tfae
import tact... |
695c7efc8358c2228bc476b1279511212adec0dd | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/set_theory/cardinal_ordinal.lean | 3b4e1176c6d97f3f10f078388227ff343ef7dc2f | [
"Apache-2.0"
] | permissive | jumpy4/mathlib | d3829e75173012833e9f15ac16e481e17596de0f | af36f1a35f279f0e5b3c2a77647c6bf2cfd51a13 | refs/heads/master | 1,693,508,842,818 | 1,636,203,271,000 | 1,636,203,271,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 38,740 | 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, Floris van Doorn
-/
import set_theory.ordinal_arithmetic
import tactic.linarith
import logic.small
/-!
# Cardinals and ordinals
Relationships between... |
eaf5779c62173d48414c65c1804237f6c2ae676b | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/def9.lean | 5a9652d8324cbb2b7ef51dcb4b888cb5f9f496a5 | [
"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 | 93 | lean | lemma ex4 (A : Type) : ∀ (a b : A) (H : a = b), b = a
| .(z) z (eq.refl .(z)) := eq.refl z
|
438ab44adb86f056c260b5e077b29212bd1484c4 | 95dcf8dea2baf2b4b0a60d438f27c35ae3dd3990 | /src/algebra/direct_sum.lean | a17a92343818dcfcf8ecaf43641f147a335cabdc | [
"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 | 6,060 | lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
Direct sum of abelian groups, indexed by a discrete type.
-/
import data.dfinsupp
universes u v w u₁
variables (ι : Type v) [decidable_eq ι] (β : ι → Type w) [Π i, add_comm_gr... |
ec7db65283160b35f7213fd04e777498a4ad7606 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Elab/BuiltinCommand.lean | 482a45bec8fa090861175262173923dabc8d7c4b | [
"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 | 20,013 | 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.Util.CollectLevelParams
import Lean.Meta.Reduce
import Lean.Elab.DeclarationRange
import Lean.Elab.Eval
import Lean.Elab.Command
import Lean.Ela... |
802e403d852b4ab84482107feba2f6530d2b9d3f | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/data/bool.lean | 72253feec3c3939e4802b2c5991bf1dc1878b4eb | [
"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 | 7,832 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad
-/
/-!
# booleans
This file proves various trivial lemmas about booleans and their
relation to decidable propositions.
## Notations
This fil... |
dbb3dbafa64cf63a106263ffd73a5708c1f05286 | dd4e652c749fea9ac77e404005cb3470e5f75469 | /src/vector.lean | eed2bca7c5ff7f85deecea93344388483fc6bfbc | [] | no_license | skbaek/cvx | e32822ad5943541539966a37dee162b0a5495f55 | c50c790c9116f9fac8dfe742903a62bdd7292c15 | refs/heads/master | 1,623,803,010,339 | 1,618,058,958,000 | 1,618,058,958,000 | 176,293,135 | 3 | 2 | null | null | null | null | UTF-8 | Lean | false | false | 4,060 | lean | import data.vector .list
variables {α : Type} {k m n : nat}
open tactic
namespace vector
def zero [has_zero α] (m) : vector α m :=
vector.repeat 0 m
instance has_zero [has_zero α] : has_zero (vector α m) := ⟨zero m⟩
lemma zero_succ [has_zero α] {m} :
(0 : vector α (m+1)) = (0 : α)::(0 : vector α m) := rfl
... |
64c46219a31c972d8c047f24dd871556a61e0b7b | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/order/complete_boolean_algebra.lean | f57bcd8473ed8fd5255a7ec9929685d5455fc8e3 | [
"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 | 5,892 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Theory of complete Boolean algebras.
-/
import order.complete_lattice
set_option old_structure_cmd true
universes u v w
variables {α : Type u} {β : Type v} {ι : Sort ... |
c319c64cdfa27174d0432533ce8708d16f1a184a | 471bedbd023d35c9d078c2f936dd577ace7f5813 | /library/init/algebra/functions.lean | 58e69f4a475aba1dd73e9fe926846dd2470bdb56 | [
"Apache-2.0"
] | permissive | lambdaxymox/lean | e06f0fa503666df827edd9867d7f49ca017aae64 | fc13c8c72a15dab71a2c2b31410c2cadc3526bd7 | refs/heads/master | 1,666,785,407,985 | 1,666,153,673,000 | 1,666,153,673,000 | 310,165,986 | 0 | 0 | Apache-2.0 | 1,604,542,096,000 | 1,604,542,095,000 | null | UTF-8 | Lean | false | false | 4,527 | 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.algebra.order init.meta
universe u
export linear_order (min max)
section
open decidable tactic
variables {α : Type u}... |
072aa15b0023e49c46d1f074b266bd8d9d0c3929 | a45212b1526d532e6e83c44ddca6a05795113ddc | /test/ring.lean | 6eb3de57bcd52666d595a8e58ae20e01703679fa | [
"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 | 594 | lean | import tactic.ring data.real.basic
example (x y : ℕ) : x + y = y + x := by ring
example (x y : ℕ) : x + y + y = 2 * y + x := by ring
example (x y : ℕ) : x + id y = y + id x := by ring
example {α} [comm_ring α] (x y : α) : x + y + y - x = 2 * y := by ring
example (x y : ℚ) : x / 2 + x / 2 = x := by ring
example (x y : ... |
45f985db82f462eac82fe140942f5823cc1d20c7 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/probability/martingale/borel_cantelli.lean | cd5664dcbcf35f4b164cdb1bcec32a54679f9084 | [
"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 | 18,830 | lean | /-
Copyright (c) 2022 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import probability.martingale.convergence
import probability.martingale.optional_stopping
import probability.martingale.centering
import probability.conditional_expectation... |
136738e9ebc79de40f329c6bb8f7ebeb50c44959 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/equiv/option.lean | fdd45996bf22febafe4678f5eb78464368a7acc1 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 3,226 | lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import data.equiv.basic
import control.equiv_functor
/-!
# Equivalences for `option α`
We define `remove_none` which acts to provide a `e : α ≃ β` if given a `f : option ... |
57387215b9069da1b041bb3df23720757604db49 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/linear_algebra/ray.lean | 9d9a2801a262fe7c7108bd2ccb5b9470ef044982 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 26,395 | lean | /-
Copyright (c) 2021 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import linear_algebra.linear_independent
/-!
# Rays in modules
This file defines rays in modules.
## Main definitions
* `same_ray`: two vectors belong to the same ray... |
325807d95e2c754db8b8bd76d7931ab91dec313e | 2bafba05c98c1107866b39609d15e849a4ca2bb8 | /src/week_8/ideas/distrub_mul_action_hom/Z1.lean | 70a256c39e0b76dcd19b3153fa33b88d15dd1b4e | [
"Apache-2.0"
] | permissive | ImperialCollegeLondon/formalising-mathematics | b54c83c94b5c315024ff09997fcd6b303892a749 | 7cf1d51c27e2038d2804561d63c74711924044a1 | refs/heads/master | 1,651,267,046,302 | 1,638,888,459,000 | 1,638,888,459,000 | 331,592,375 | 284 | 24 | Apache-2.0 | 1,669,593,705,000 | 1,611,224,849,000 | Lean | UTF-8 | Lean | false | false | 3,370 | lean | import week_8.ideas.Z1
/-
## The map `φ.Z1 : Z1 G M →+ Z1 G N`.
Let `G` be a group. Or a monoid.
`Z1` is not just the construction of the group of cocycles
associated to a `G`-module `M`. `Z1` is a functor, which
means that we well as sending G-modules to abelian groups,
it also sends morphisms of `G`-modules to mo... |
8556b55383664f13cc86907c8ddef4e80e30aba8 | ccb7cdf8ebc2d015a000e8e7904952a36b910425 | /src/prop/classes.lean | 20b319328ace06c8306cb3055583424ad0a58bc3 | [] | no_license | cipher1024/lean-pl | f7258bda55606b75e3e39deaf7ce8928ed177d66 | 829680605ac17e91038d793c0188e9614353ca25 | refs/heads/master | 1,592,558,951,987 | 1,565,043,356,000 | 1,565,043,531,000 | 196,661,367 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,741 | lean |
import order.bounded_lattice
import order.complete_lattice
import prop
open lattice
class has_impl (α : Type*) :=
(impl : α → α → α)
-- infixr ` ⇒ `:60 := has_impl.impl
infixr ` ⇒ ` := has_impl.impl
set_option old_structure_cmd true
class heyting_algebra (α : Type*) extends bounded_lattice α, has_impl α :=
(le_im... |
bfdf24e446b2fa59b3f0f3d499803b6277e2deef | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/logic/unique.lean | 53df3e35e7f4cfa2912f576ba2d8997391af3d8e | [
"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 | 5,561 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import tactic.basic
import logic.is_empty
/-!
# Types with a unique term
In this file we define a typeclass `unique`,
which expresses that a type has a unique term.... |
dcdd46eed82c9d0d73b22c5d185e44b2c7c74afb | ce6917c5bacabee346655160b74a307b4a5ab620 | /src/ch2/ex0309.lean | 24075016fda95fee707168ac00d2056ad273d091 | [] | no_license | Ailrun/Theorem_Proving_in_Lean | ae6a23f3c54d62d401314d6a771e8ff8b4132db2 | 2eb1b5caf93c6a5a555c79e9097cf2ba5a66cf68 | refs/heads/master | 1,609,838,270,467 | 1,586,846,743,000 | 1,586,846,743,000 | 240,967,761 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 21 | lean | #eval 12345 * 54321
|
f4cd1f9a6be18c67f53a9036343f2de8c49e49df | 94e33a31faa76775069b071adea97e86e218a8ee | /src/data/polynomial/unit_trinomial.lean | 48f117061837cf2d3e19a2db6f07dd4c3dd328a7 | [
"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 | 16,190 | lean | /-
Copyright (c) 2022 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import analysis.complex.polynomial
import data.polynomial.mirror
/-!
# Unit Trinomials
This file defines irreducible trinomials and proves an irreducibility crit... |
65d1f6e6742cc407032b98540af2f8380888cb9c | e514e8b939af519a1d5e9b30a850769d058df4e9 | /test/rewrite_search_optimal.lean | 92a8c5e332cee637699f53e4ce611f6fb531acaa | [] | no_license | semorrison/lean-rewrite-search | dca317c5a52e170fb6ffc87c5ab767afb5e3e51a | e804b8f2753366b8957be839908230ee73f9e89f | refs/heads/master | 1,624,051,754,485 | 1,614,160,817,000 | 1,614,160,817,000 | 162,660,605 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 831 | lean | import tactic.rewrite_search
axiom foo : [0] = [1]
axiom bar1 : [1] = [2]
axiom bar2 : [2] = [3]
axiom bar3 : [3] = [4]
axiom bar4 : [4] = [5]
axiom bar5 : [5] = [6]
axiom bar6 : [6] = [7]
axiom baz : [4] = [0]
-- Obviously sub-optimal
example : [0] = [7] :=
begin
-- erw [foo, bar1, bar2, bar3, bar4, bar5, bar6],
... |
5324f7bf84bf35c570dba45ceb915fd13ba78259 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/ftree.lean | 1a3b861b8ebf857fc82070892a302dac3fd4a705 | [
"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 | 717 | lean | inductive List (T : Type*) : Type* | nil {} : List | cons : T → List → List
namespace explicit
inductive {u₁ u₂} ftree (A : Type u₁) (B : Type u₂) : Type (max 1 u₁ u₂)
| leafa : A → ftree
| leafb : B → ftree
| node : (A → ftree) → (B → ftree) → ftree
end explicit
namespace implicit
inductive ftree (A : Type) (B... |
067d4bfcbaa298c8687642b2a9964d6311e6ba97 | 97f752b44fd85ec3f635078a2dd125ddae7a82b6 | /hott/algebra/category/category.hlean | dc0a85f8d4b30db287806df05b18fc7659a50e45 | [
"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 | 4,796 | hlean | /-
Copyright (c) 2014 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jakob von Raumer
-/
import .iso
open iso is_equiv equiv eq is_trunc sigma equiv.ops
/-
A category is a precategory extended by a witness
that the function from paths to isomorp... |
a79010d2e501d6c1e77446afee799853c7650a65 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/group_theory/index.lean | 2d9fde97d06a97eaec6aba9b46b2f8b274bfbedd | [
"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 | 9,113 | lean | /-
Copyright (c) 2021 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import group_theory.quotient_group
import set_theory.fincard
/-!
# Index of a Subgroup
In this file we define the index of a subgroup, and prove several divisibi... |
8a9bbc4b100221c2d587c2c1131beacbe6c2ef21 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /test/compute_degree.lean | 495ed2537c49ed6ebc8f0260bc43f22be50384ef | [
"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 | 2,647 | lean | import tactic.compute_degree
open polynomial
open_locale polynomial
variables {R : Type*} [semiring R] {a b c d e : R}
example {p : R[X]} {n : ℕ} {p0 : p.nat_degree = 0} :
(p ^ n).nat_degree ≤ 0 :=
by compute_degree_le
example {p : R[X]} {n : ℕ} {p0 : p.nat_degree = 0} :
(p ^ n).nat_degree ≤ 0 :=
by cases n; comp... |
e5e6630b8b97539c429ea680fe2d19b5853d5ea2 | 0179bcdbf094a112437450a02dc2bdc8b2f921d4 | /meta_data.lean | a20ad29db3286ab74b32e9af17d2ef530c0073f1 | [
"CC-BY-4.0"
] | permissive | haselwarter/formalabstracts | cf0c129fc086526cef1bd65d95c6f95a9a7ec5c8 | eab6d94850308df9f09d23f3a9a2f7b5ac5c6c7a | refs/heads/master | 1,609,515,992,248 | 1,500,418,815,000 | 1,500,418,815,000 | 97,696,544 | 0 | 0 | null | 1,500,455,350,000 | 1,500,455,350,000 | null | UTF-8 | Lean | false | false | 5,346 | lean | /- Each fabstract contains a list of results. The following type lists the
various kinds of results. You may read the values as follows:
* `Proof p` -- the paper contains the proof `p`
* `Construction c` -- the paper contains the construction `c`
* `Conjecture C` -- the paper contains the conjecture `C`
... |
c29552703a09d2425d0896cf018d1bc529f33178 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/quadratic_discriminant.lean | 8b13bcb92b84687f8cc10695154ddf113358973a | [
"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 | 5,771 | lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
-/
import algebra.char_p.invertible
import order.filter.at_top_bot
import tactic.linarith
import tactic.field_simp
import tactic.linear_combination
/-!
# Quadratic discri... |
183e75160717a00e3f75dfb406dd26a18342d981 | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/topology/metric_space/basic.lean | f0b72b504d8241d9a15636a471f58651ee93ccfc | [
"Apache-2.0"
] | permissive | jumpy4/mathlib | d3829e75173012833e9f15ac16e481e17596de0f | af36f1a35f279f0e5b3c2a77647c6bf2cfd51a13 | refs/heads/master | 1,693,508,842,818 | 1,636,203,271,000 | 1,636,203,271,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 103,835 | 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.int.interval
import topology.algebra.ordered.compact
import topology.metric_space... |
c9f6f41fdd7fca310f0c0ff2625a203e2b9605f2 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/data/pfunctor/univariate/M.lean | 7f0b29b916e580151e597f1243bbb8c2674c5cdf | [
"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 | 22,015 | lean | /-
Copyright (c) 2017 Simon Hudon All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import data.pfunctor.univariate.basic
/-!
# M-types
M types are potentially infinite tree-like structures. They are defined
as the greatest fixpoint of a polynomial functo... |
4714be908dacd7967a1aaa5c76b790a698abe6b2 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/field_theory/adjoin.lean | fe37d48fabe22941bc56d842dad4e2ca0de4abcd | [
"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 | 37,060 | lean | /-
Copyright (c) 2020 Thomas Browning, Patrick Lutz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning, Patrick Lutz
-/
import field_theory.intermediate_field
import field_theory.separable
import ring_theory.tensor_product
/-!
# Adjoining Elements to Fie... |
3ddce242554c728b53788140531f39af9f67d184 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/monad/limits.lean | 37d516fef5dc968edd75b1da593c2c76cc3f9f8c | [
"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 | 15,228 | 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.monad.adjunction
import category_theory.adjunction.limits
import category_theory.limits.shapes.terminal
/-!
# Limits and colimit... |
d797c12761aac259565f7808b22a168cf57b46e2 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/order/complete_lattice.lean | 89bb6e5baaa1f4b4baf49fea0f9ecd1f17e56e1c | [
"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 | 40,972 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import order.bounds
/-!
# Theory of complete lattices
## Main definitions
* `Sup` and `Inf` are the supremum and the infimum of a set;
* `supr (f : ι → α)` and `in... |
00e47d49120e1b6c1d97071a53df9f705651189b | 36938939954e91f23dec66a02728db08a7acfcf9 | /lean4/deps/galois_stdlib/src/Galois/Init/Int.lean | b72e089748177c1221ee580deb5519a0ed8fa840 | [] | no_license | pnwamk/reopt-vcg | f8b56dd0279392a5e1c6aee721be8138e6b558d3 | c9f9f185fbefc25c36c4b506bbc85fd1a03c3b6d | refs/heads/master | 1,631,145,017,772 | 1,593,549,019,000 | 1,593,549,143,000 | 254,191,418 | 0 | 0 | null | 1,586,377,077,000 | 1,586,377,077,000 | null | UTF-8 | Lean | false | false | 312 | lean | import Galois.Init.Nat
namespace Int
protected
def pow (v : Int) (n : Nat) : Int
:= (if Nat.bodd n ∧ v < 0 then (-1) else 1) * (Int.ofNat (v.natAbs ^ n))
instance intPow : HasPow Int Nat := ⟨Int.pow⟩
def shiftl (v : Int) (n : Nat) := v * 2 ^ n
def shiftr (v : Int) (n : Nat) := v / 2 ^ n
end Int
|
94c4dbad67b180e3a13734e6a2d2b00beca018d6 | 7d5ad87afb17e514aee234fcf0a24412eed6384f | /src/peano.lean | 4c722f12d68d68032bc0d52087c3d458e680b4e7 | [] | no_license | digama0/flypitch | 764f849eaef59c045dfbeca142a0f827973e70c1 | 2ec14b8da6a3964f09521d17e51f363d255b030f | refs/heads/master | 1,586,980,069,651 | 1,547,078,141,000 | 1,547,078,283,000 | 164,965,135 | 1 | 0 | null | 1,547,082,858,000 | 1,547,082,857,000 | null | UTF-8 | Lean | false | false | 23,482 | lean | import .fol tactic.tidy
open fol
local attribute [instance, priority 0] classical.prop_decidable
--local attribute [instance] classical.prop_decidable
local notation h :: t := dvector.cons h t
local notation `[]` := dvector.nil
local notation `[` l:(foldr `, ` (h t, dvector.cons h t) dvector.nil `]`) := l
namespac... |
b4a244ce351580c9e98a26acf6392c223cd4806c | aa2345b30d710f7e75f13157a35845ee6d48c017 | /category_theory/natural_transformation.lean | ba14d425d2172435980521d3d18b06177b0f1916 | [
"Apache-2.0"
] | permissive | CohenCyril/mathlib | 5241b20a3fd0ac0133e48e618a5fb7761ca7dcbe | a12d5a192f5923016752f638d19fc1a51610f163 | refs/heads/master | 1,586,031,957,957 | 1,541,432,824,000 | 1,541,432,824,000 | 156,246,337 | 0 | 0 | Apache-2.0 | 1,541,434,514,000 | 1,541,434,513,000 | null | UTF-8 | Lean | false | false | 4,718 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tim Baumann, Stephen Morgan, Scott Morrison
Defines natural transformations between functors.
Introduces notations
`F ⟹ G` for the type of natural transformations between functors ... |
2271f9c20947440016e675996dd9acb35e0cc406 | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/topology/constructions.lean | 4377c298ec830b6aeca8d77b2deda90bbeac5a4f | [
"Apache-2.0"
] | permissive | ChrisHughes24/mathlib | 98322577c460bc6b1fe5c21f42ce33ad1c3e5558 | a2a867e827c2a6702beb9efc2b9282bd801d5f9a | refs/heads/master | 1,583,848,251,477 | 1,565,164,247,000 | 1,565,164,247,000 | 129,409,993 | 0 | 1 | Apache-2.0 | 1,565,164,817,000 | 1,523,628,059,000 | Lean | UTF-8 | Lean | false | false | 49,816 | 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, Patrick Massot
Constructions of new topological spaces from old ones: product, sum, subtype, quotient, list, vector
-/
import topology.maps topology.su... |
9dcf65afc943965c0c1d0ba9e532788b60ed3eeb | 4727251e0cd73359b15b664c3170e5d754078599 | /src/group_theory/specific_groups/alternating.lean | 8e21bef327ee740de71f2c7f8c759691b4f79fca | [
"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 | 15,061 | 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... |
88dd9c0282e94da76bbf1719c68f3ecf36e72830 | 6b2a480f27775cba4f3ae191b1c1387a29de586e | /group_rep1/morphism/Reynold_operator.lean | bc617228f967b8cb1971c4c0c084c01d7aab23d6 | [] | no_license | Or7ando/group_representation | a681de2e19d1930a1e1be573d6735a2f0b8356cb | 9b576984f17764ebf26c8caa2a542d248f1b50d2 | refs/heads/master | 1,662,413,107,324 | 1,590,302,389,000 | 1,590,302,389,000 | 258,130,829 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 4,509 | lean | import group_representation
import morphism
import Tools.to_sum
import Tools.sum_group
/-!
* Let `ρ and π` two representations on `M` and `M'`. Let `f : M →ₗ[R] M'` a `linear_map`.
* Let `ℒ f := Σ_{g ∈ G} π g⁻¹ ∘ f ∘ ρ g`, then `ℒ f` is a morphism `ρ ⟶ π`.
* Proof : `∀ t ∈ G, ρ t ∘ ℒ f ∘ π t⁻¹ := ... |
777d83188f74616751d4029ae83f24e1ba2ad79d | 618003631150032a5676f229d13a079ac875ff77 | /src/topology/algebra/ring.lean | 4f5d14fbc83b55d5ee829a1840f4bbe4428353bb | [
"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 | 4,000 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
Theory of topological rings.
-/
import topology.algebra.group
import ring_theory.ideals
open classical set filter topological_space
open_locale classic... |
d30bf41f447aadbfe5edf6dd1f0e12fcd99b0594 | fecda8e6b848337561d6467a1e30cf23176d6ad0 | /src/category_theory/opposites.lean | f2182f2dae62c1562565929edc781e4bb73293ef | [
"Apache-2.0"
] | permissive | spolu/mathlib | bacf18c3d2a561d00ecdc9413187729dd1f705ed | 480c92cdfe1cf3c2d083abded87e82162e8814f4 | refs/heads/master | 1,671,684,094,325 | 1,600,736,045,000 | 1,600,736,045,000 | 297,564,749 | 1 | 0 | null | 1,600,758,368,000 | 1,600,758,367,000 | null | UTF-8 | Lean | false | false | 9,728 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stephen Morgan, Scott Morrison
-/
import category_theory.types
import category_theory.equivalence
import data.opposite
universes v₁ v₂ u₁ u₂ -- declare the `v`'s first; see `category_... |
29edbf5db72279860d8bd99a32853ceafce68f8a | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/data/set.lean | 5802358f52df8310a6ad8c37910776a051b6da3d | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,622 | 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.meta.interactive
import Mathlib.Lean3Lib.init.control.lawful
universes u v u_1
namespace Mathlib
d... |
1daefdf3d4b44f1fe1908c5a1e3de0dfbcd7928f | a7602958ab456501ff85db8cf5553f7bcab201d7 | /Notes/Theorem_Proving_in_Lean/Chapter2/2.2.lean | 4ea1cca51b5f82cb9b933306fdd7ba95224de781 | [] | no_license | enlauren/math-logic | 081e2e737c8afb28dbb337968df95ead47321ba0 | 086b6935543d1841f1db92d0e49add1124054c37 | refs/heads/master | 1,594,506,621,950 | 1,558,634,976,000 | 1,558,634,976,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,670 | lean | -- 2.2 Types as Objects
-- In Lean, types such as ℕ and bool are first-class objects as well,
-- meaning they must have a type.
#check ℕ -- Its type is: |Type|.
-- Therefore we can create our own types:
constant α: Type
constant f: Type → Type
constant g: Type → Type → Type
#check α
#check f α
#check f ℕ
#check g ... |
171e448b6a5cce2c16b50d38750e8140e2310977 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/tactic/localized.lean | 9567958e8adba0f004713a33b0859f445e5a2239 | [
"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 | 4,530 | lean | /-
Copyright (c) 2019 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import tactic.core
/-!
# Localized notation
This consists of two user-commands which allow you to declare notation and commands localized to a
locale.
See the ... |
d95fbb5d4760b454f1b3767dff46a39f7a6d279f | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/data/nat/sqrt.lean | 98b405ff80774c64be0689743ef8b9f1016f6ab9 | [
"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 | 9,605 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Johannes Hölzl, Mario Carneiro
-/
import data.int.basic
/-!
# Square root of natural numbers
This file defines an efficient binary implementation of the squ... |
020d5d144d54cd0e46ab00bae08fe7d76be8ad21 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/cody2.lean | c4a984daf5e801c2d4cb9bd9bacd416b14813eb1 | [
"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 | 439 | lean | definition subsets (P : Type) := P → Prop.
section
parameter A : Type.
parameter r : A → subsets A.
parameter i : subsets A → A.
parameter retract {P : subsets A} {a : A} : r (i P) a = P a.
definition delta (a:A) : Prop := ¬ (r a a).
local notation `δ` := delta.
theorem delta_aux : ¬ (δ (i delta))
:= a... |
5f28915751796d29cbdeb16c74536286111fc695 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/init/meta/simp_tactic.lean | 42c9686cb53d7856a0f656e25dc5c01a33f18b37 | [
"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 | 4,330 | 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.tactic
namespace tactic
open list nat
meta_constant simp_lemmas : Type
/- Create a data-structure containing a simp lemma for ev... |
51b1e16b2a5d19f76b4aad060ef2360c71edd931 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/meta/float.lean | 21e3ed2ac476e1b168f387fbd224db8adbed84f9 | [] | 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 | 149 | lean | /- Authors: E.W.Ayers -/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.data.default
namespace Mathlib
namespace native
namespace float
|
0ee6919b9fab2f14500022cff4905319658c627c | e5af0662f9ce01ee71f473a50929b138e7f9ef33 | /even_and_odd.lean | cdca5fa45d9f5231c2603e730a299c6a9e6cbec9 | [] | no_license | cygnusx251/Computers-and-Mathematics | 3a5182ac3b7efa5cd110b74473f5953f9d4ff24e | de8a7b92ac99c7d506ccab87fc913e577be69ff5 | refs/heads/main | 1,676,401,846,067 | 1,610,164,573,000 | 1,610,164,573,000 | 327,054,950 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,726 | lean | import tactic
/-
The theory of even and odd numbers
-/
def even (n : ℕ) : Prop := ∃ d, n = 2 * d
def odd (n : ℕ) : Prop := ∃ d, n = 2 * d + 1
/-
see https://www.codewars.com/kata/5e998b42dcf07b0001581def/lean
for a completely different approach (inductive definitions)
-/
/- ## interaction with 0 -/
lemma even_zero :... |
f6274161e45104fe25c67ea9aac95d51818bf55b | a959f48a0621edea632487cf2130bbf70d301e05 | /src/tactic/refine.lean | a966f3ffc7f96909aca16107b661973094181cd9 | [] | no_license | cipher1024/lean-differential-topology | cf441b36af9fdb022f10afff6a2fdc5aa4afa379 | 1938b0a5d9e89faff89dac4bc51598698cae6dbb | refs/heads/master | 1,619,477,568,536 | 1,527,790,354,000 | 1,527,790,354,000 | 124,159,851 | 0 | 0 | null | 1,520,385,485,000 | 1,520,385,485,000 | null | UTF-8 | Lean | false | false | 3,389 | lean |
import data.dlist
section util
universes u v
def dlist.join {α} : list (dlist α) → dlist α
| [] := dlist.empty
| (x :: xs) := x ++ dlist.join xs
variables {m : Type u → Type v} [applicative m]
def mmap₂
{α₁ α₂ φ : Type u}
(f : α₁ → α₂ → m φ)
: Π (ma₁ : list α₁) (ma₂: list α₂), m (list φ)
| (x :: xs) (y :: ... |
c6e7203a2b2e2bcdf5283f368d32dddda4d9530b | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/order/filter/pointwise.lean | 0759bcb0ef67f925c533ed9344aeb4e853e00022 | [
"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 | 35,610 | lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Yaël Dillies
-/
import data.set.pointwise.smul
import order.filter.n_ary
import order.filter.ultrafilter
/-!
# Pointwise operations on filters
This file defines pointwi... |
f2cef9ba78fc5dda1a0d0149d1a7a64142cb98bd | b561a44b48979a98df50ade0789a21c79ee31288 | /stage0/src/Lean/Elab/Do.lean | 32a46ecf739e59d4bd77228b5b95da212d85e866 | [
"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 | 70,567 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Elab.Term
import Lean.Elab.BindersUtil
import Lean.Elab.PatternVar
import Lean.Elab.Quotation.Util
import Lean.Parser.Do
-- HACK: avoid code ex... |
e514c4ecaa40a475e81062e314c421b9bd774b87 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /tests/lean/macroscopes.lean | 7361395c346efc040ee7cbeee45ae4554e15b3ee | [
"Apache-2.0"
] | permissive | mhuisi/lean4 | 28d35a4febc2e251c7f05492e13f3b05d6f9b7af | dda44bc47f3e5d024508060dac2bcb59fd12e4c0 | refs/heads/master | 1,621,225,489,283 | 1,585,142,689,000 | 1,585,142,689,000 | 250,590,438 | 0 | 2 | Apache-2.0 | 1,602,443,220,000 | 1,585,327,814,000 | C | UTF-8 | Lean | false | false | 1,114 | lean | open Lean
def check (b : Bool) : IO Unit :=
unless b $ throw $ IO.userError "check failed"
def test1 : IO Unit := do
let x := `x;
let x := addMacroScope `main x 1;
IO.println $ x;
let v := extractMacroScopes x;
let x := { name := `y, .. v }.review;
IO.println $ x;
let v := extractMacroScopes x;
let x := { name := `x,... |
1afb111bffb9722fec72da616111d33536dc6d8e | 205f0fc16279a69ea36e9fd158e3a97b06834ce2 | /EXAMS/exam2-key.lean | 8adef334bd33ba81aa69d80f8f55f0763bab8766 | [] | no_license | kevinsullivan/cs-dm-lean | b21d3ca1a9b2a0751ba13fcb4e7b258010a5d124 | a06a94e98be77170ca1df486c8189338b16cf6c6 | refs/heads/master | 1,585,948,743,595 | 1,544,339,346,000 | 1,544,339,346,000 | 155,570,767 | 1 | 3 | null | 1,541,540,372,000 | 1,540,995,993,000 | Lean | UTF-8 | Lean | false | false | 5,077 | lean | /-
EXAM 2 ANSWER KEY AND GRADING RUBRIC
This is the answer key and grading
rubric for CS2102 Fall 2018 Exam 2.
There are acceptable ways to have
answered some of the questions on
the exam, so correct answers need
not literally match those provided
here.
#1. 5 points each, no partial credit
#2. 10 points for the pr... |
f0d11c49b9bcbbf5c80c7521d4ab0df848934909 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/nat/multiplicity.lean | ba4717738eae5c4967b06a12b9f8f6d92a03e772 | [
"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 | 11,044 | 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 algebra.big_operators.intervals
import algebra.geom_sum
import data.nat.bitwise
import data.nat.log
import data.nat.parity
import ring_theory.multiplicity
/-!
# N... |
81c0e5fed918aff82428b7f30570c01a914ffaa2 | 3dd1b66af77106badae6edb1c4dea91a146ead30 | /tests/lean/run/have2.lean | 71ca1ed2d53f51d01d9cca65c0981f53187109db | [
"Apache-2.0"
] | permissive | silky/lean | 79c20c15c93feef47bb659a2cc139b26f3614642 | df8b88dca2f8da1a422cb618cd476ef5be730546 | refs/heads/master | 1,610,737,587,697 | 1,406,574,534,000 | 1,406,574,534,000 | 22,362,176 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 174 | lean | abbreviation Prop : Type.{1} := Type.{0}
variables a b c : Prop
axiom Ha : a
axiom Hb : b
axiom Hc : c
check have H1 [fact] : a, from Ha,
have H2 : a, from H1,
H2 |
666bb88249eca58e2955db9452b382ecbd19769c | 3dd1b66af77106badae6edb1c4dea91a146ead30 | /tests/lean/run/e12.lean | 1be243c38c21b2b2121ceed95a11bf1178ad8af9 | [
"Apache-2.0"
] | permissive | silky/lean | 79c20c15c93feef47bb659a2cc139b26f3614642 | df8b88dca2f8da1a422cb618cd476ef5be730546 | refs/heads/master | 1,610,737,587,697 | 1,406,574,534,000 | 1,406,574,534,000 | 22,362,176 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 956 | lean | precedence `+`:65
namespace nat
variable nat : Type.{1}
variable add : nat → nat → nat
infixl + := add
end
namespace int
using nat (nat)
variable int : Type.{1}
variable add : int → int → int
infixl + := add
variable of_nat : nat → int
coercion of_nat
end
variables n m : nat.nat
variables i j : int... |
b42e34951323e15dd329dedca8a865c758e5c8e4 | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/data/part.lean | 1504168230125bf2014f9435b0ff13ef6bbc497e | [
"Apache-2.0"
] | permissive | jumpy4/mathlib | d3829e75173012833e9f15ac16e481e17596de0f | af36f1a35f279f0e5b3c2a77647c6bf2cfd51a13 | refs/heads/master | 1,693,508,842,818 | 1,636,203,271,000 | 1,636,203,271,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 16,843 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Jeremy Avigad, Simon Hudon
-/
import data.equiv.basic
import data.set.basic
/-!
# Partial values of a type
This file defines `part α`, the partial values of a type.
... |
d9b9b6231be8c6ca4c5b7b542dd6710a3c9b6a54 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /stage0/src/Lean/Elab/PreDefinition/Structural/Eqns.lean | 707814cbe836273a264c10ea5c8a974243f3ec77 | [
"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 | 3,912 | 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.Eqns
import Lean.Meta.Tactic.Split
import Lean.Meta.Tactic.Simp.Main
import Lean.Meta.Tactic.Apply
import Lean.Elab.PreDefinition.Basic
imp... |
e66daa17437b84802bdde6c1f6e3e620dc0f728d | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/236c.lean | 217bc8bba8813ebd4315686ae4b09c110f94a78e | [
"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 | 273 | lean | constant foo_rec (n : ℕ) (k : Type) [has_one k] : Prop
lemma stupid (k : Type) [has_one k] (n : ℕ) :
foo_rec nat.zero k ↔ foo_rec nat.zero k :=
by simp only [nat.nat_zero_eq_zero]
open tactic
#eval do
cgr ← mk_congr_lemma_simp `(foo_rec),
type_check cgr.proof
|
eb2d07818fcd2c1dec1f3457c15d01aa712a23e6 | 36c7a18fd72e5b57229bd8ba36493daf536a19ce | /library/data/matrix.lean | d8910f0dbdf88c47489652912999d847434d2e99 | [
"Apache-2.0"
] | permissive | YHVHvx/lean | 732bf0fb7a298cd7fe0f15d82f8e248c11db49e9 | 038369533e0136dd395dc252084d3c1853accbf2 | refs/heads/master | 1,610,701,080,210 | 1,449,128,595,000 | 1,449,128,595,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,284 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
Matrices
-/
import algebra.ring data.fin data.fintype
open algebra fin nat
definition matrix [reducible] (A : Type) (m n : nat) := fin m → fin n → A
namespac... |
4d3382f172ce5c81d0658b5b595f7ad3a91b0853 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/category_theory/monad/basic.lean | 6553049eaac8d9e184103219e995b6708a2b1e1c | [
"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 | 952 | 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 category_theory.functor_category
namespace category_theory
open category
universes v₁ u₁ -- declare the `v`'s first; see `category_theory.category` for an ex... |
d2cae3ec32272893c3bf6fb443d053975ca1e7c8 | 6e9cd8d58e550c481a3b45806bd34a3514c6b3e0 | /src/ring_theory/localization.lean | 7fa6709f56cab537ba3b5b2784d2370dd1290bfe | [
"Apache-2.0"
] | permissive | sflicht/mathlib | 220fd16e463928110e7b0a50bbed7b731979407f | 1b2048d7195314a7e34e06770948ee00f0ac3545 | refs/heads/master | 1,665,934,056,043 | 1,591,373,803,000 | 1,591,373,803,000 | 269,815,267 | 0 | 0 | Apache-2.0 | 1,591,402,068,000 | 1,591,402,067,000 | null | UTF-8 | Lean | false | false | 28,713 | 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
-/
import data.equiv.ring
import tactic.ring_exp
import ring_theory.ideal_operations
import group_theory.monoid_localization
/... |
2818a241de2835c43985af5ea03a818ce8e48f08 | c062f1c97fdef9ac746f08754e7d766fd6789aa9 | /tools/super/intuit.lean | 2bd1205cedf3f843605dc6bdf8a82f4287539baf | [] | no_license | emberian/library_dev | 00c7a985b21bdebe912f4127a363f2874e1e7555 | f3abd7db0238edc18a397540e361a1da2f51503c | refs/heads/master | 1,624,153,474,804 | 1,490,147,180,000 | 1,490,147,180,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,587 | lean | import tools.super.clausifier tools.super.cdcl tools.super.trim
open tactic super expr monad
-- Intuitionistic propositional prover based on
-- SAT Modulo Intuitionistic Implications, Claessen and Rosen, LPAR 2015
namespace intuit
meta def check_model (intuit : tactic unit) : cdcl.solver (option cdcl.proof_term) :=
... |
17d2464f0cbc1a7b0f1f5c17e812b502fd6b03bc | 947b78d97130d56365ae2ec264df196ce769371a | /tests/lean/mvar3.lean | 448f85ed4dea8f949a9738dbba3e98a1e5fc708f | [
"Apache-2.0"
] | permissive | shyamalschandra/lean4 | 27044812be8698f0c79147615b1d5090b9f4b037 | 6e7a883b21eaf62831e8111b251dc9b18f40e604 | refs/heads/master | 1,671,417,126,371 | 1,601,859,995,000 | 1,601,860,020,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,864 | lean | import Lean.MetavarContext
new_frontend
open Lean
def mkLambdaTest (mctx : MetavarContext) (ngen : NameGenerator) (lctx : LocalContext) (xs : Array Expr) (e : Expr)
: Except MetavarContext.MkBinding.Exception (MetavarContext × NameGenerator × Expr) :=
match MetavarContext.mkLambda xs e lctx { mctx := mctx, ngen :=... |
3237a261559cb06b84b3103773731d7eff41e84c | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/run_tactic1.lean | 08d1820e7c1fbb3b783422ba1a688a93c348770e | [
"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 | 727 | lean | open tactic
run_command tactic.trace "hello world"
run_command do
N ← to_expr `(nat),
v ← to_expr `(10),
add_decl (declaration.defn `val10 [] N v reducibility_hints.opaque tt)
vm_eval val10
example : val10 = 10 := rfl
meta_definition mk_defs : nat → command
| 0 := skip
| (n+1) := do
N ← to_expr `(nat),
... |
654ecb1e973698064d621add31649a1d8a9b9108 | 2f2aa789c57653a0a047d209e0401875a9427cfc | /src/homework/practice_2.lean | 590d76fe155f1c5af0dd48592418db8127243f86 | [] | no_license | AlexFetea/cs2120f21 | dc288aa4a907b116555758b7f63c37aa14f952ae | a2cf406a33e66aac2287341b1c3e9954db9b36ab | refs/heads/main | 1,693,910,053,038 | 1,636,678,382,000 | 1,636,678,382,000 | 399,946,831 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,362 | lean | /-
Prove the following simple logical conjectures.
Give a formal and an English proof of each one.
Your English language proofs should be complete
in the sense that they identify all the axioms
and/or theorems that you use.
-/
example : true := true.intro
example : false := _ -- trick question? why?
example : ∀ (... |
6502e3cb851dac6f074e601177f85b1f4e6e77eb | 02005f45e00c7ecf2c8ca5db60251bd1e9c860b5 | /src/linear_algebra/finsupp.lean | cdb53e5b3bffad21354d4e9941cb0944487eaf0d | [
"Apache-2.0"
] | permissive | anthony2698/mathlib | 03cd69fe5c280b0916f6df2d07c614c8e1efe890 | 407615e05814e98b24b2ff322b14e8e3eb5e5d67 | refs/heads/master | 1,678,792,774,873 | 1,614,371,563,000 | 1,614,371,563,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 25,611 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
-/
import data.finsupp.basic
import linear_algebra.basic
/-!
# Properties of the semimodule `α →₀ M`
Given an `R`-semimodule `M`, the `R`-semimodule structure on `α →₀ ... |
fdfc3e6f5e5ecc08329535e7272ed20a8645c96a | 75bd9c50a345718d735a7533c007cf45f9da9a83 | /src/ring_theory/polynomial/basic.lean | df2aa3d49b801cf9bfa62a31433803afc33955d1 | [
"Apache-2.0"
] | permissive | jtbarker/mathlib | a1a3b1ddc16179826260578410746756ef18032c | 392d3e376b44265ef2dedbd92231d3177acc1fd0 | refs/heads/master | 1,671,246,411,096 | 1,600,801,712,000 | 1,600,801,712,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 23,567 | lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
Ring-theoretic supplement of data.polynomial.
Main result: Hilbert basis theorem, that if a ring is noetherian then so is its polynomial ring.
-/
import algebra.char_p
import da... |
9899c843a16b04b99835dfcb7ad069c6806c729a | 367134ba5a65885e863bdc4507601606690974c1 | /src/meta/rb_map.lean | f243c764744ffce68b547a4874b34dfa5b4ff416 | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 7,704 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Robert Y. Lewis
-/
import data.option.defs
import data.list.defs
/-!
# rb_map
This file defines additional operations on native rb_maps and rb_sets.
These structures are defined in c... |
bab24d489a848c38208c2b4be7e023cf3cf08b05 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/matrix/notation.lean | f82cd6f7c1009750e77aa611246e5de35c9368ad | [
"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 | 15,839 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Eric Wieser
-/
import data.matrix.basic
import data.fin.vec_notation
import tactic.fin_cases
import algebra.big_operators.fin
/-!
# Matrix and vector notation
> THIS FILE I... |
cdc46d85266212e0dabb6f4d041d8ee6dd6fcb95 | e953c38599905267210b87fb5d82dcc3e52a4214 | /hott/types/sum.hlean | f35f21793682c1f19f1315d3c918243a39c14bfa | [
"Apache-2.0"
] | permissive | c-cube/lean | 563c1020bff98441c4f8ba60111fef6f6b46e31b | 0fb52a9a139f720be418dafac35104468e293b66 | refs/heads/master | 1,610,753,294,113 | 1,440,451,356,000 | 1,440,499,588,000 | 41,748,334 | 0 | 0 | null | 1,441,122,656,000 | 1,441,122,656,000 | null | UTF-8 | Lean | false | false | 6,139 | 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 sums/coproducts/disjoint unions
-/
open lift eq is_equiv equiv equiv.ops prod prod.ops is_trunc sigma bool
namespace sum
universe variables u v
... |
7435700db3519ef68e48d399ddcc140eb60ac644 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/order/pilex_auto.lean | 34a4ff44c83745c606880599fa438e3bd3c405d0 | [] | 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 | 2,548 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.ordered_pi
import Mathlib.order.well_founded
import Mathlib.algebra.order_functions
imp... |
c3f57c0708d31331c79bb7f3f1a68a541ffa933f | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/polynomial/monic.lean | fcc459d3a46e57c47fe885c658a2a1975052173f | [] | 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 | 5,698 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.polynomial.reverse
import Mathlib.algebra.... |
537b4f5ff917043bd3ae24dd592f4d4fb1130474 | ee8cdbabf07f77e7be63a449b8483ce308d37218 | /lean/src/valid/mathd-algebra-51.lean | 940be87a4865cf68f49f922f9d540fb9e547eb73 | [
"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 | 295 | 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.basic
example (a b : ℝ) (h₀ : 0 < a ∧ 0 < b) (h₁ : a + b = 35) (h₂ : a = (2/5) * b) : b - a = 15 :=
begin
linarith,
end
|
302d46f4e95f0c90eafbf560baf4620cce3d1164 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/algebra/add_torsor.lean | baf94974eb81f4f8d2134dac533f46f253b348c8 | [
"Apache-2.0"
] | permissive | agjftucker/mathlib | d634cd0d5256b6325e3c55bb7fb2403548371707 | 87fe50de17b00af533f72a102d0adefe4a2285e8 | refs/heads/master | 1,625,378,131,941 | 1,599,166,526,000 | 1,599,166,526,000 | 160,748,509 | 0 | 0 | Apache-2.0 | 1,544,141,789,000 | 1,544,141,789,000 | null | UTF-8 | Lean | false | false | 14,885 | lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Yury Kudryashov.
-/
import algebra.group.prod
import algebra.group.type_tags
import algebra.group.pi
import data.equiv.basic
import data.set.finite
/-!
# Torsors of additi... |
f2fbd9597c131336dad83da700fc138a14fe129e | 432d948a4d3d242fdfb44b81c9e1b1baacd58617 | /src/ring_theory/integral_closure.lean | e5a626879033ab088f42f354d1771867dd579b26 | [
"Apache-2.0"
] | permissive | JLimperg/aesop3 | 306cc6570c556568897ed2e508c8869667252e8a | a4a116f650cc7403428e72bd2e2c4cda300fe03f | refs/heads/master | 1,682,884,916,368 | 1,620,320,033,000 | 1,620,320,033,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 25,888 | 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.scale_roots
import ring_theory.polynomial.tower
/-!
# Integral closure of a subring.
If A is an R-algebra then `... |
78f4391e89dbde4140223fffc48ae7b186971cbf | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/order/positive/ring.lean | 32bb2e3103b14903e21df71331953e6ae47cc66d | [
"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 | 4,735 | lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import algebra.order.ring.defs
import algebra.ring.inj_surj
/-!
# Algebraic structures on the set of positive numbers
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
>... |
35bcc29ab5b0c0d23f5dd2486813b9b9f25cbcba | 1b8f093752ba748c5ca0083afef2959aaa7dace5 | /src/category_theory/adjunctions/comparisons.lean | b9882860332ecd78d7b841264a752d594cdb52cf | [] | no_license | khoek/lean-category-theory | 7ec4cda9cc64a5a4ffeb84712ac7d020dbbba386 | 63dcb598e9270a3e8b56d1769eb4f825a177cd95 | refs/heads/master | 1,585,251,725,759 | 1,539,344,445,000 | 1,539,344,445,000 | 145,281,070 | 0 | 0 | null | 1,534,662,376,000 | 1,534,662,376,000 | null | UTF-8 | Lean | false | false | 4,971 | lean | -- Copyright (c) 2017 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Stephen Morgan, Scott Morrison
import category_theory.adjunctions
import category_theory.adjunctions.hom_adjunction
-- FIXME why do we need this here?
@[obviously] meta def obv... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.