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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
664da2f41cbb6887977b8fa72b51a5f0f21d4f36 | 367134ba5a65885e863bdc4507601606690974c1 | /src/algebra/group_with_zero/power.lean | 85991b81ad853044e6afdeabd9a82294632f20b3 | [
"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 | 9,335 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import algebra.group_power
/-!
# Powers of elements of groups with an adjoined zero element
In this file we define integer power functions for groups with an adjoin... |
fa016a2a6e7fb36748efaccf5e8ff8e6a53d655c | a9d59fc3316fcc8c227c3cbecb1202b6201ddd07 | /lean/Benchmark.lean | a3516b2378fe4246dd9d299b7414635a7abc0f27 | [] | no_license | PeterKementzey/lean-graph-benchmarking | 57db96d940c87cfe7906f1b49c8b81529b8cc905 | 00a1517cf22203f7fb89df5fb1598a2eff88bf54 | refs/heads/master | 1,686,192,971,424 | 1,625,278,683,000 | 1,625,278,683,000 | 374,718,875 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,475 | lean | import Graph.Graph
import Graph.Parser
import Graph.TopologicalSort
import Graph.Search
/-- This function ensures that the expression does not get dropped by compiler optimizations. -/
def evaluate [ToString α] (expression : α) : IO Unit := IO.FS.writeFile "/dev/null" (toString expression)
def benchmarkParsing (fileP... |
23e996b1555d14ec39667882663460aeb353748d | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/set_theory/game/winner.lean | 093107e7d31fa26f3c75793d2663ee9b7f0f07cc | [
"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 | 3,398 | lean | /-
Copyright (c) 2020 Fox Thomson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fox Thomson
-/
import set_theory.pgame
/-!
# Basic definitions about who has a winning stratergy
We define `G.first_loses`, `G.first_wins`, `G.left_wins` and `G.right_wins` for a pgame ... |
87000ed10df3d49ea5d3fab531f437729d194a5b | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/simp_inductive_compiler_issue.lean | 5e40fc5b26d97e7fcfb20f27e1b055429df45d72 | [
"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 | 236 | lean | structure box (α : Type) :=
(val : α)
def f1 (g h : ℕ → ℕ) (b : bool) : ℕ → ℕ :=
box.val (bool.cases_on b (box.mk g) (box.mk h))
def f2 (g h : box (ℕ → ℕ)) (b : bool) : ℕ → ℕ :=
box.val (bool.cases_on b g h)
|
05a8c279a686edd6fe167c73b9e60b93e6749924 | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /tests/lean/run/obtain.lean | b87338ac371f78182a68fee84cff12fa27cd1c2e | [
"Apache-2.0"
] | permissive | walterhu1015/lean4 | b2c71b688975177402758924eaa513475ed6ce72 | 2214d81e84646a905d0b20b032c89caf89c737ad | refs/heads/master | 1,671,342,096,906 | 1,599,695,985,000 | 1,599,695,985,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 709 | lean | new_frontend
macro "obtain " p:term " from " d:term "; " body:term : term =>
`(match $d:term with | $p:term => $body:term)
theorem tst1 {p q r} (h : p ∧ q ∧ r) : q ∧ p ∧ r :=
match h with
| ⟨h₁, ⟨h₂, h₃⟩⟩ => ⟨h₂, ⟨h₁, h₃⟩⟩
theorem tst2 {p q r} (h : p ∧ q ∧ r) : q ∧ p ∧ r :=
obtain ⟨h₁, ⟨h₂, h₃⟩⟩ from h;
⟨h₂, ⟨h₁, h₃... |
71ee50dd427febe38f570316637ecc9f907c58a1 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /library/data/string.lean | c5eed5186909d7dd7c043dafedaa3bf817416cd8 | [
"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 | 1,716 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
import data.bool
open bool
protected definition char.is_inhabited [instance] : inhabited char :=
inhabited.mk (char.mk ff ff ff ff ff ff ff ff)
protected d... |
0bfc2ccddd4431a8207c43d6de403108797ae050 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /test/linarith.lean | 9c609b7db1cc9eed56897bcef12dc66b8f721141 | [
"Apache-2.0"
] | permissive | Lix0120/mathlib | 0020745240315ed0e517cbf32e738d8f9811dd80 | e14c37827456fc6707f31b4d1d16f1f3a3205e91 | refs/heads/master | 1,673,102,855,024 | 1,604,151,044,000 | 1,604,151,044,000 | 308,930,245 | 0 | 0 | Apache-2.0 | 1,604,164,710,000 | 1,604,163,547,000 | null | UTF-8 | Lean | false | false | 10,367 | lean | import tactic.linarith
import algebra.field_power
example {α : Type} (_inst : Π (a : Prop), decidable a)
[linear_ordered_field α]
{a b c : α}
(ha : a < 0)
(hb : ¬b = 0)
(hc' : c = 0)
(h : (1 - a) * (b * b) ≤ 0)
(hc : 0 ≤ 0)
(this : -(a * -b * -b + b * -b + 0) = (1 - a) * (b * b))
(h : (1 - a) * (b * ... |
ead01fa24fe759d29282622ce084977e19a2ec54 | 4e3bf8e2b29061457a887ac8889e88fa5aa0e34c | /lean/love13_rational_and_real_numbers_exercise_sheet.lean | f27b257ee76ff527672c3a162c9e57c816f0b801 | [] | no_license | mukeshtiwari/logical_verification_2019 | 9f964c067a71f65eb8884743273fbeef99e6503d | 16f62717f55ed5b7b87e03ae0134791a9bef9b9a | refs/heads/master | 1,619,158,844,208 | 1,585,139,500,000 | 1,585,139,500,000 | 249,906,380 | 0 | 0 | null | 1,585,118,728,000 | 1,585,118,727,000 | null | UTF-8 | Lean | false | false | 3,809 | lean | /- LoVe Exercise 13: Rational and Real Numbers -/
import .love05_inductive_predicates_demo
import .love13_rational_and_real_numbers_demo
namespace LoVe
set_option pp.beta true
/- Question 1: Rationals -/
/- 1.1. Prove the following lemma.
Hint: The lemma `fraction.mk.inj_eq` might be useful. -/
#check fraction.... |
5fc43142fde7a230a28e24db6b03617e0cee63de | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/topology/compact_open.lean | 4aa530e886677c0e9b6935d11400ff2f0f5d3f69 | [
"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 | 3,802 | lean | /-
Copyright (c) 2018 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton
Type of continuous maps and the compact-open topology on them.
-/
import topology.subset_properties
import topology.continuous_map
import tactic.tidy
open set
open_locale to... |
a5521c67ea1d7ef5ce168fe43af199022dc3238f | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/lake/test/102/lakefile.lean | 998c16955e7966fc7cce0421f40c0bb980af098a | [
"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 | 175 | lean | import Lake
open Lake DSL
package tba {
-- add package configuration options here
}
@[default_target]
lean_lib TBA := {
name := `TBA
globs := #[.andSubmodules `TBA]
}
|
2996285d2d04f3cdf102900968d0e80011b6d05c | 46125763b4dbf50619e8846a1371029346f4c3db | /src/order/bounds.lean | 2d064f8716d8d6772fe006e5c9e2403f94b8cf77 | [
"Apache-2.0"
] | permissive | thjread/mathlib | a9d97612cedc2c3101060737233df15abcdb9eb1 | 7cffe2520a5518bba19227a107078d83fa725ddc | refs/heads/master | 1,615,637,696,376 | 1,583,953,063,000 | 1,583,953,063,000 | 246,680,271 | 0 | 0 | Apache-2.0 | 1,583,960,875,000 | 1,583,960,875,000 | null | UTF-8 | Lean | false | false | 24,582 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov
-/
import algebra.order_functions data.set.intervals.basic
/-!
# Upper / lower bounds
In this file we define:
* `upper_bounds`, `lower_bounds` : the ... |
916711ab7d7f703a80d79e0a16f6331a3f348481 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/category_theory/eq_to_hom.lean | a3bd236b32a8c2748443641591cc8e59ed2b0ab2 | [
"Apache-2.0"
] | permissive | gebner/mathlib | eab0150cc4f79ec45d2016a8c21750244a2e7ff0 | cc6a6edc397c55118df62831e23bfbd6e6c6b4ab | refs/heads/master | 1,625,574,853,976 | 1,586,712,827,000 | 1,586,712,827,000 | 99,101,412 | 1 | 0 | Apache-2.0 | 1,586,716,389,000 | 1,501,667,958,000 | Lean | UTF-8 | Lean | false | false | 2,675 | lean | /-
Copyright (c) 2018 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Scott Morrison
-/
import category_theory.isomorphism
import category_theory.functor_category
import category_theory.opposites
import tactic.reassoc_axiom
universes v v' u u'... |
a300a089a3b08ce154cabb44eb843d97fc8a77be | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/group_theory/group_action.lean | 128ab00b6ca3597dbac76d66e6db2f5ad41a9c4c | [
"Apache-2.0"
] | permissive | gebner/mathlib | eab0150cc4f79ec45d2016a8c21750244a2e7ff0 | cc6a6edc397c55118df62831e23bfbd6e6c6b4ab | refs/heads/master | 1,625,574,853,976 | 1,586,712,827,000 | 1,586,712,827,000 | 99,101,412 | 1 | 0 | Apache-2.0 | 1,586,716,389,000 | 1,501,667,958,000 | Lean | UTF-8 | Lean | false | false | 8,117 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import data.set.finite group_theory.coset
universes u v w
variables {α : Type u} {β : Type v} {γ : Type w}
/-- Typeclass for types with a scalar multiplication operatio... |
cd8ec5f560c3cd24cb8c02007ed49a70ec311b38 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/algebra/algebra/basic.lean | d84eb9352c739769436245250f561ec0a7e78a40 | [
"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 | 52,967 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov
-/
import algebra.iterate_hom
import data.equiv.ring_aut
import algebra.module.basic
import linear_algebra.basic
/-!
# Algebras over commutative semirings
In th... |
7f84155f1ca1ac388286fdeb418886f7f7bf16f5 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/calculus/fderiv_analytic.lean | 59431d132384c12ed4988e893149aa771d63073c | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 7,315 | lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import analysis.analytic.basic
import analysis.calculus.deriv.basic
import analysis.calculus.cont_diff_def
/-!
# Frechet derivatives of analytic functions.
> THIS... |
c82a8878956b3ed6f53c0e0243ef194ce2225831 | 274748215b6d042f0d9c9a505f9551fa8e0c5f38 | /src/topology/noetherian.lean | 4c8176da053346861024b24f06e04a0d7e9958ad | [
"Apache-2.0"
] | permissive | ImperialCollegeLondon/M4P33 | 878ecb515c77d20cc799ff1ebd78f1bf4fd65c12 | 1a179372db71ad6802d11eacbc1f02f327d55f8f | refs/heads/master | 1,607,519,867,193 | 1,583,344,297,000 | 1,583,344,297,000 | 233,316,107 | 59 | 4 | Apache-2.0 | 1,579,285,778,000 | 1,578,788,367,000 | Lean | UTF-8 | Lean | false | false | 10,236 | lean | /-
Noetherian topological spaces
-/
-- this import gives us irreducible topological spaces
import topology.subset_properties
-- this gives us the type of open sets in a top space
import topology.opens
open set
open_locale classical
@[simp]
lemma irred_iff_not_union_closed {X : Type*} [topological_space X] (Y : ... |
62e1d7aa785453f47380f4e4fa65b668f448237a | 12dabd587ce2621d9a4eff9f16e354d02e206c8e | /world05/level05.lean | f7baab4ce47e12a97badfc9d2c8f9a9ac5833f42 | [] | no_license | abdelq/natural-number-game | a1b5b8f1d52625a7addcefc97c966d3f06a48263 | bbddadc6d2e78ece2e9acd40fa7702ecc2db75c2 | refs/heads/master | 1,668,606,478,691 | 1,594,175,058,000 | 1,594,175,058,000 | 278,673,209 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 79 | lean | example (P Q : Type) : P → (Q → P) :=
begin
intro p,
intro q,
exact p,
end
|
33d7a4dfce0fc3066595b8d569fe3aeca9229319 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/topology/sheaves/sheaf_condition/unique_gluing.lean | 2a57389de3247ea8c5dea4ebb708a99502c3dcd4 | [
"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 | 11,612 | lean | /-
Copyright (c) 2021 Justus Springer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Justus Springer
-/
import topology.sheaves.forget
import category_theory.limits.shapes.types
import topology.sheaves.sheaf
import category_theory.types
/-!
# The sheaf condition in t... |
6a5493cf118289f3495d950bc12b001bf6e4fcba | e0f9ba56b7fedc16ef8697f6caeef5898b435143 | /test/norm_cast_lemma_order.lean | 4ce15a39c8483c33c495e54494759ccefd20981f | [
"Apache-2.0"
] | permissive | anrddh/mathlib | 6a374da53c7e3a35cb0298b0cd67824efef362b4 | a4266a01d2dcb10de19369307c986d038c7bb6a6 | refs/heads/master | 1,656,710,827,909 | 1,589,560,456,000 | 1,589,560,456,000 | 264,271,800 | 0 | 0 | Apache-2.0 | 1,589,568,062,000 | 1,589,568,061,000 | null | UTF-8 | Lean | false | false | 647 | lean | import data.nat.cast tactic.norm_cast
constant ℝ : Type
@[instance] constant real.add_monoid : add_monoid ℝ
@[instance] constant real.has_one : has_one ℝ
-- set_option trace.simplify.rewrite true
set_option pp.notation false
set_option pp.numerals false
-- should work
#eval norm_cast.numeral_to_coe `(0 : ℝ)
#eval no... |
263bf1c7bed5f56bbe9aca8ae549b77ef9908702 | 3f1a1d97c03bb24b55a1b9969bb4b3c619491d5a | /leanpkg/leanpkg/resolve.lean | 60a1bc0d1f0f51feb576221a8c63bb716a7dadbe | [
"Apache-2.0"
] | permissive | praveenmunagapati/lean | 00c3b4496cef8e758396005013b9776bb82c4f56 | fc760f57d20e0a486d14bc8a08d89147b60f530c | refs/heads/master | 1,630,692,342,183 | 1,515,626,222,000 | 1,515,626,222,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,956 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Gabriel Ebner
-/
import leanpkg.manifest system.io leanpkg.proc leanpkg.git
variable [io.interface]
namespace leanpkg
def assignment := list (string × string)
namespace assign... |
9ef71401a769b098e9633697ee23dcb9f22f5423 | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /src/Lean/Compiler/IR/Borrow.lean | 71c49ebc3985ad7da109275d98201ddfea9b7151 | [
"Apache-2.0"
] | permissive | WojciechKarpiel/lean4 | 7f89706b8e3c1f942b83a2c91a3a00b05da0e65b | f6e1314fa08293dea66a329e05b6c196a0189163 | refs/heads/master | 1,686,633,402,214 | 1,625,821,189,000 | 1,625,821,258,000 | 384,640,886 | 0 | 0 | Apache-2.0 | 1,625,903,617,000 | 1,625,903,026,000 | null | UTF-8 | Lean | false | false | 11,063 | 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.ExportAttr
import Lean.Compiler.IR.CompilerM
import Lean.Compiler.IR.NormIds
namespace Lean
namespace IR
namespace Borrow
namespace O... |
438beb7dc9d3623dd856c2ea32b4976a57e33159 | 2f8bf12144551bc7d8087a6320990c4621741f3d | /library/init/lean/parser/command.lean | 0ccac4a8e231f15cda7ca2fd4ea0d6a7db41820b | [
"Apache-2.0"
] | permissive | jesse-michael-han/lean4 | eb63a12960e69823749edceb4f23fd33fa2253ce | fa16920a6a7700cabc567aa629ce4ae2478a2f40 | refs/heads/master | 1,589,935,810,594 | 1,557,177,860,000 | 1,557,177,860,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,963 | lean | /-
Copyright (c) 2018 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Sebastian Ullrich
Command parsers
-/
prelude
import init.lean.parser.declaration
namespace Lean
namespace Parser
open Combinators MonadParsec
open Parser.HasTokens Parser.HasV... |
21b131c83a4201a0821b16cb67de5f4e852cb16c | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/ring_theory/non_zero_divisors.lean | e41bf9dbb67680f8649fbbf2662abcc09c54bceb | [] | 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 | 3,090 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Devon Tuma
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.group_theory.submonoid.operations
import Mathlib.group_theory.submonoid.membership
import... |
563e8f83a03b89668cf108583354291c6b3b42e1 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/list/defs.lean | 183faff24693a573fa2868132be8b2a7483e5489 | [
"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 | 40,682 | lean | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
import data.option.defs
import logic.basic
import tactic.cache
import data.rbmap.basic
import ... |
39c085951dbd2934413595c839e2d83cdad94d0c | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/limits/bicones.lean | a6a8efb89f27678505085c5486f752fafc5fad71 | [
"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 | 4,659 | lean | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import category_theory.limits.cones
import category_theory.fin_category
/-!
# Bicones
Given a category `J`, a walking `bicone J` is a category whose objects are the objec... |
e8c5dd4d43b4f0ccbd235e96fa20e84962af429d | 01ae0d022f2e2fefdaaa898938c1ac1fbce3b3ab | /categories/types/finite.lean | 8cc0b0549c8a82c6635a68599bd0dc32c2cbc54d | [] | no_license | PatrickMassot/lean-category-theory | 0f56a83464396a253c28a42dece16c93baf8ad74 | ef239978e91f2e1c3b8e88b6e9c64c155dc56c99 | refs/heads/master | 1,629,739,187,316 | 1,512,422,659,000 | 1,512,422,659,000 | 113,098,786 | 0 | 0 | null | 1,512,424,022,000 | 1,512,424,022,000 | null | UTF-8 | Lean | false | false | 591 | 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 ..types
import ..full_subcategory
import ..util.finite
namespace categories.types
open categories
open categories.util.finite
definition... |
f67bf8d9f7ea5091e4a8653b929b0e32990f2aa3 | 08bd4ba4ca87dba1f09d2c96a26f5d65da81f4b4 | /src/Lean/Server/AsyncList.lean | 72e0fc629da75b7ca677f7603bf482834388b959 | [
"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 | 3,921 | lean | /-
Copyright (c) 2020 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki
-/
import Init.System.IO
namespace IO
universe u v
/-- An async IO list is like a lazy list but instead of being *unevaluated* `Thunk`s,
`delayed` suffixes are... |
42fbbe3fb1a0159ef319931f9f54f626bbfe7dd0 | 690889011852559ee5ac4dfea77092de8c832e7e | /src/category_theory/monoidal/of_has_finite_products.lean | 9054e3b15ae81f007d4768650fa801c9dc5ab4e5 | [
"Apache-2.0"
] | permissive | williamdemeo/mathlib | f6df180148f8acc91de9ba5e558976ab40a872c7 | 1fa03c29f9f273203bbffb79d10d31f696b3d317 | refs/heads/master | 1,584,785,260,929 | 1,572,195,914,000 | 1,572,195,913,000 | 138,435,193 | 0 | 0 | Apache-2.0 | 1,529,789,739,000 | 1,529,789,739,000 | null | UTF-8 | Lean | false | false | 1,946 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Simon Hudon
-/
import category_theory.monoidal.category
import category_theory.limits.shapes.finite_products
import category_theory.limits.shapes.binary_products
import... |
720d73860b552222bd2a5ec7ec1adf29a183e139 | 02005f45e00c7ecf2c8ca5db60251bd1e9c860b5 | /src/algebra/lie/abelian.lean | 9fe41b96d86e48b5b7debd07a89857d685cea570 | [
"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 | 7,805 | lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import algebra.lie.of_associative
import algebra.lie.ideal_operations
/-!
# Trivial Lie modules and Abelian Lie algebras
The action of a Lie algebra `L` on a module `M` i... |
95bee0acb8435590821c5774120b52791137965c | da3a76c514d38801bae19e8a9e496dc31f8e5866 | /library/init/meta/mk_dec_eq_instance.lean | a61a3a363d0431a4f41027a23d48c5b4b13ff82a | [
"Apache-2.0"
] | permissive | cipher1024/lean | 270c1ac5781e6aee12f5c8d720d267563a164beb | f5cbdff8932dd30c6dd8eec68f3059393b4f8b3a | refs/heads/master | 1,611,223,459,029 | 1,487,566,573,000 | 1,487,566,573,000 | 83,356,543 | 0 | 0 | null | 1,488,229,336,000 | 1,488,229,336,000 | null | UTF-8 | Lean | false | false | 5,228 | 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
Helper tactic for showing that a type has decidable equality.
-/
prelude
import init.meta.contradiction_tactic init.meta.constructor_tactic
import init.meta.i... |
c40f241fd5e2f3f7f542dd73cf5e600ebe3b7bf7 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/ring_theory/witt_vector/witt_polynomial.lean | c7fac8cfdf5a6a50645bb5f3e31ad389d61e9e2b | [
"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 | 10,804 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-/
import algebra.char_p.invertible
import data.fintype.card
import data.mv_polynomial.variables
import data.mv_polynomial.comm_ring
import data.mv_pol... |
8960c61a253e2339bf9860e5457765bee2799700 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/topology/metric_space/hausdorff_dimension.lean | ba277a6b4c64bd4d10d5460f6aaf6f8bf714adab | [
"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 | 22,787 | lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import measure_theory.measure.hausdorff
/-!
# Hausdorff dimension
The Hausdorff dimension of a set `X` in an (extended) metric space is the unique number
`dimH s ... |
26119b0e10dc64810a5fb7d4b29adfcc225efd2b | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/ring_theory/witt_vector/truncated_auto.lean | 08abb692eed2c3d593af865417499ebae366663e | [] | 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 | 16,512 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.ring_theory.witt_vector.init_tail
import Mathlib.tactic.equiv_rw
import Ma... |
7690d71a993dc83aaafd8e48cb33139b826505ec | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/1258.lean | add8dceff455c20c9df962bd78f4989093a880eb | [
"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 | 188 | lean | constant P : list ℕ → list ℕ → Prop
lemma foo (xs : list ℕ) : Π (ns : list ℕ), P xs ns
| [] := sorry
| (n::ns) := begin clear foo, cases xs, exact sorry, exact sorry end
|
1359fe5b5cc21e641b97c4f4dcdf9f1c79fb1962 | 076f5040b63237c6dd928c6401329ed5adcb0e44 | /instructor-notes/2019.10.03.review.lean | eb5f66fb04c877b4607011342de67c19687df98e | [] | no_license | kevinsullivan/uva-cs-dm-f19 | 0f123689cf6cb078f263950b18382a7086bf30be | 09a950752884bd7ade4be33e9e89a2c4b1927167 | refs/heads/master | 1,594,771,841,541 | 1,575,853,850,000 | 1,575,853,850,000 | 205,433,890 | 4 | 9 | null | 1,571,592,121,000 | 1,567,188,539,000 | Lean | UTF-8 | Lean | false | false | 4,168 | lean |
namespace review
/-
The identity function for any type:
a *polymorphic* identity function.
Key points: type parameters (i.e.,
polymorphism); type inference; and
implicit type arguments.
-/
def id (α : Type) (a : α) : α := a
/-
Examples of its use. Note how we
have to specific type argument
values explicitly--bool... |
ed386d166429d936deaff54bf94a642c2c39edf6 | 5fbbd711f9bfc21ee168f46a4be146603ece8835 | /lean/natural_number_game/inequality/14.lean | b869bc989bf83537a047465daf86b25d27b1cef4 | [
"LicenseRef-scancode-warranty-disclaimer"
] | no_license | goedel-gang/maths | 22596f71e3fde9c088e59931f128a3b5efb73a2c | a20a6f6a8ce800427afd595c598a5ad43da1408d | refs/heads/master | 1,623,055,941,960 | 1,621,599,441,000 | 1,621,599,441,000 | 169,335,840 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 169 | lean | theorem add_le_add_left (a b : mynat) (h : a ≤ b) (t : mynat) :
t + a ≤ t + b :=
begin
rw add_comm t a,
rw add_comm t b,
exact add_le_add_right a b h t,
end
|
56671e650876be4cbef479f60001e62abde17de7 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /src/Init/Classical.lean | 480eb14d4c51e575faafe065252e0bc9ea5a9f8b | [
"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 | 5,574 | 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
-/
prelude
import Init.Core
import Init.NotationExtra
universe u v
/-! # Classical reasoning support -/
namespace Classical
noncomputable def indefiniteDes... |
238bf43b26dc8a541823009bfbef4c91d4c1a2ba | 3863d2564418bccb1859e057bf5a4ef240e75fd7 | /hott/types/fiber.hlean | 700602e7bc7e9015dcbe3eec2b3f281d6112fa8b | [
"Apache-2.0"
] | permissive | JacobGross/lean | 118bbb067ff4d4af48a266face2c7eb9868fa91c | eb26087df940c54337cb807b4bc6d345d1fc1085 | refs/heads/master | 1,582,735,011,532 | 1,462,557,826,000 | 1,462,557,826,000 | 46,451,196 | 0 | 0 | null | 1,462,557,826,000 | 1,447,885,161,000 | C++ | UTF-8 | Lean | false | false | 6,256 | 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
Ported from Coq HoTT
Theorems about fibers
-/
import .sigma .eq .pi
open equiv sigma sigma.ops eq pi
structure fiber {A B : Type} (f : A → B) (b : B) :=
(point :... |
9b481d9d74dff51c0e89f7580636b20289ea69fa | a7eef317ddec01b9fc6cfbb876fe7ac00f205ac7 | /src/analysis/calculus/inverse.lean | 9ba67554f06e4c92e391f547f25b671fdfe007ef | [
"Apache-2.0"
] | permissive | kmill/mathlib | ea5a007b67ae4e9e18dd50d31d8aa60f650425ee | 1a419a9fea7b959317eddd556e1bb9639f4dcc05 | refs/heads/master | 1,668,578,197,719 | 1,593,629,163,000 | 1,593,629,163,000 | 276,482,939 | 0 | 0 | null | 1,593,637,960,000 | 1,593,637,959,000 | null | UTF-8 | Lean | false | false | 21,677 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov.
-/
import analysis.calculus.deriv
import topology.local_homeomorph
import topology.metric_space.contracting
/-!
# Inverse function theorem
In this file we prove the... |
e24c5d40ec5e0cfe6de5c3d5e8174ab25b21afac | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/data/equiv/encodable/basic.lean | cbb813a0cba6071f00bdf1f5b7e28682f1b73a22 | [
"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 | 18,108 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Mario Carneiro
-/
import data.equiv.nat
import order.rel_iso
import order.directed
/-!
# Encodable types
This file defines encodable (constructively countab... |
5def2125664fa5bcfcc0467aaa0105de486aff0f | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/new_obtain3.lean | e44a084af6b438bef285daf08326f5ceb36e1760 | [
"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 | 600 | lean | import data.set
open set function eq.ops
variables {X Y Z : Type}
lemma image_compose (f : Y → X) (g : X → Y) (a : set X) : (f ∘ g) ' a = f ' (g ' a) :=
ext (take z,
iff.intro
(assume Hz : z ∈ (f ∘ g) ' a,
obtain x (Hx₁ : x ∈ a) (Hx₂ : f (g x) = z), from Hz,
have Hgx : g x ∈ g ' a, from mem_image Hx... |
77dc054c11bacfc5cf0757757584f565b7fb457f | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/topology/metric_space/gromov_hausdorff_realized.lean | 911125846cb3ac023846d8bbc86e72111f40a9e3 | [
"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 | 27,420 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import topology.metric_space.gluing
import topology.metric_space.hausdorff_distance
import topology.continuous_function.bounded
/-!
# The Gromov-Hausdorff dist... |
a75aecbd2c29dc20e633487f475a36dfe1c7aacb | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/topology/continuous_on.lean | 5d8a922818c9f3a5e500e92edb9907a5d07cbbde | [
"Apache-2.0"
] | permissive | hikari0108/mathlib | b7ea2b7350497ab1a0b87a09d093ecc025a50dfa | a9e7d333b0cfd45f13a20f7b96b7d52e19fa2901 | refs/heads/master | 1,690,483,608,260 | 1,631,541,580,000 | 1,631,541,580,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 47,594 | 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`
* `co... |
c53dedbbfee3e0463400fd6aa1e3a16817f6c628 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/tactic/abel.lean | 7815857ad7b7499ce5c7695efb5e5c6f01320996 | [
"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 | 15,313 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import tactic.norm_num
/-!
# The `abel` tactic
Evaluate expressions in the language of additive, commutative monoids and groups.
-/
namespace tactic
namespace ab... |
d2dbe58937d458a59d277f74df7597124aeeaf38 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/topology/metric_space/emetric_space.lean | 03f5963a474711393dae900cbb99bfdf3a075459 | [
"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 | 36,158 | 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.real.nnreal data.real.ennreal
import topology.uniform_space.separation topology.u... |
68bf117b3cefae42db7fe7dc624ab4d9e6247db9 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/category_theory/abelian/transfer.lean | 80335de073b91bc93938fc41d8c98bd3582bc53d | [
"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 | 8,013 | lean | /-
Copyright (c) 2022 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.preadditive.additive_functor
import category_theory.abelian.basic
import category_theory.limits.preserves.shapes.kernels
import category_theory... |
8d8ce3358bb508819e8bd80f962fc6f20e48ef7e | ebb7367fa8ab324601b5abf705720fd4cc0e8598 | /algebra/subgroup.hlean | 0f64dbfbcdd8f6fed6b9617ccdc5419e6cd08b91 | [
"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 | 13,262 | hlean | /-
Copyright (c) 2015 Egbert Rijke. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Egbert Rijke
Basic concepts of group theory
-/
import algebra.group_theory
open eq algebra is_trunc sigma sigma.ops prod trunc
namespace group
/- #Subgroups -/
... |
023b02185f4b2b953fab05bea487505633243c5f | c46a31beec236d29b6c02e7d7683691bcfbb3014 | /src/quiz05.lean | ebad2064d0009513a1ae800d0265953f11584c88 | [] | no_license | UVM-M52/quiz-5-maddiestrauss | a88b9bfbdd486a521ee280f9b7b551bcb48f23c6 | 214529615e08bbcdd3d6600c89432ec985e6ba3a | refs/heads/master | 1,617,897,187,103 | 1,584,922,038,000 | 1,584,922,038,000 | 248,787,429 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 690 | lean | -- Math 52: Quiz 5
-- Open this file in a folder that contains 'utils'.
import utils
open classical
definition divides (a b : ℤ) : Prop := ∃ (k : ℤ), b = a * k
local infix ∣ := divides
axiom not_3_divides : ∀ (m : ℤ), ¬ (3 ∣ m) ↔ 3 ∣ m - 1 ∨ 3 ∣ m + 1
lemma not_3_divides_of_3_divides_minus_1 :
∀ (m : ℤ), 3 ∣ m - 1... |
2f94ed2c2e131e353617bad4876fb64f86611efe | 6b02ce66658141f3e0aa3dfa88cd30bbbb24d17b | /stage0/src/Lean/Elab/Tactic/Match.lean | a8bc42d33c3d83c12f0e8ff80215fc05c56a1d35 | [
"Apache-2.0"
] | permissive | pbrinkmeier/lean4 | d31991fd64095e64490cb7157bcc6803f9c48af4 | 32fd82efc2eaf1232299e930ec16624b370eac39 | refs/heads/master | 1,681,364,001,662 | 1,618,425,427,000 | 1,618,425,427,000 | 358,314,562 | 0 | 0 | Apache-2.0 | 1,618,504,558,000 | 1,618,501,999,000 | null | UTF-8 | Lean | false | false | 2,781 | 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.Parser.Term
import Lean.Elab.Match
import Lean.Elab.Tactic.Basic
import Lean.Elab.Tactic.Induction
namespace Lean.Elab.Tactic
open Meta
/- Era... |
91499248892f9a4940e53d579bcb7b825d05b7c0 | 1d265c7dd8cb3d0e1d645a19fd6157a2084c3921 | /src/lessons/hello.lean | 0220c38b676a8266515a894fde22754df0169259 | [
"MIT"
] | permissive | hanzhi713/lean-proofs | de432372f220d302be09b5ca4227f8986567e4fd | 4d8356a878645b9ba7cb036f87737f3f1e68ede5 | refs/heads/master | 1,585,580,245,658 | 1,553,646,623,000 | 1,553,646,623,000 | 151,342,188 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 810 | lean | /-theorem interesting: 1 = 1 := rfl. -/
#check ¬ (1 = 0)
#check ∀ T: Type, ∀ t: T, t = t
lemma zeqz: 0 = 0 := rfl
lemma oeqo: 1 = 1 := rfl
theorem helloTheorem: "hello" = "hello" := rfl
theorem twooneone: 2 = 1 + 1 := rfl
theorem tthof: 2 + 3 = 1 + 4 := rfl
theorem holeqhl: "Hello " ++ "Logic!" = "Hello Logic!" := rf... |
fe84228d837bc05acb9d02a4bd54ed253365ff90 | 398b53a5e02ce35196531591f84bb2f6b034ce5a | /tpil/chapter7.lean | c5369ebdb5f27884ff74e96d17ef350556150f41 | [
"MIT"
] | permissive | crockeo/math-exercises | 64f07a9371a72895bbd97f49a854dcb6821b18ab | cf9150ef9e025f1b7929ba070a783e7a71f24f31 | refs/heads/master | 1,607,910,221,030 | 1,581,231,762,000 | 1,581,231,762,000 | 234,595,189 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,726 | lean | ------------------
-- Random Notes --
--
-- 7.1. Enumerated Types
--
namespace s71
inductive weekday : Type
| sunday : weekday
| monday : weekday
| tuesday : weekday
| wednesday : weekday
| thursday : weekday
| friday : weekday
| saturday : weekday
namespace weekday
def next (d : w... |
74c6570f22e36671a591e216724484b8524314ef | 4bcaca5dc83d49803f72b7b5920b75b6e7d9de2d | /stage0/src/Lean/Elab/LetRec.lean | c4f79476de35a8bc477f9687410288471ec78dbc | [
"Apache-2.0"
] | permissive | subfish-zhou/leanprover-zh_CN.github.io | 30b9fba9bd790720bd95764e61ae796697d2f603 | 8b2985d4a3d458ceda9361ac454c28168d920d3f | refs/heads/master | 1,689,709,967,820 | 1,632,503,056,000 | 1,632,503,056,000 | 409,962,097 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,035 | 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.Attributes
import Lean.Elab.Binders
import Lean.Elab.DeclModifiers
import Lean.Elab.SyntheticMVars
import Lean.Elab.DeclarationRange
names... |
f467d4315b75b5df4d981900e73401961242e342 | 649957717d58c43b5d8d200da34bf374293fe739 | /src/data/padics/padic_norm.lean | 41412020e459afb2ad38bd4b611581952989bbc1 | [
"Apache-2.0"
] | permissive | Vtec234/mathlib | b50c7b21edea438df7497e5ed6a45f61527f0370 | fb1848bbbfce46152f58e219dc0712f3289d2b20 | refs/heads/master | 1,592,463,095,113 | 1,562,737,749,000 | 1,562,737,749,000 | 196,202,858 | 0 | 0 | Apache-2.0 | 1,562,762,338,000 | 1,562,762,337,000 | null | UTF-8 | Lean | false | false | 13,302 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
Define the p-adic valuation on ℤ and ℚ, and the p-adic norm on ℚ
-/
import data.rat.basic algebra.gcd_domain algebra.field_power
import ring_theory.multiplicity tact... |
37a6de63f334c4c00210ff2b71ef563d13456bad | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/big_operators/multiset/lemmas.lean | dadbcc8381e52f263406dc5ad28551b0e01dc46a | [
"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 | 1,427 | lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Bhavik Mehta, Eric Wieser
-/
import data.list.big_operators.lemmas
import algebra.big_operators.multiset.basic
/-! # Lemmas about `multiset.sum` and `multiset.prod` requir... |
4157b974268ac1f222b2c6934f5a78624202b2b3 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/number_theory/legendre_symbol/mul_character.lean | 820fc0682d8136fa9c1809b789c47e416f64aa67 | [
"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 | 16,071 | lean | /-
Copyright (c) 2022 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
import ring_theory.integral_domain
/-!
# Multiplicative characters of finite rings and fields
Let `R` and `R'` be a commutative rings.
A *multiplicative character* of... |
c53d0c7b537adc9765ec378c89894cd31474ff3f | c777c32c8e484e195053731103c5e52af26a25d1 | /src/measure_theory/function/simple_func.lean | 9051f119f2976536646e598ba9f04506a7b2df2e | [
"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 | 46,935 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl
-/
import measure_theory.constructions.borel_space
import algebra.indicator_function
import algebra.support
/-!
# Simple functions
A function `f` from ... |
255d8a0d8cf223a7dc14966a4ebb2959f0598897 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/order/pilex.lean | b56c521dafe1f88d2f255ff1c82aa8ad8932967e | [
"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 | 3,760 | 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.order.pi
import order.well_founded
import order.min_max
/-!
# Lexicographic order on Pi types
This file defines the lexicographic relation for Pi types ... |
57538d75678eae6446fc14235e06022c1ba699ec | 367134ba5a65885e863bdc4507601606690974c1 | /src/ring_theory/polynomial/homogeneous.lean | cf6c82c759c372e8c0167187aaaf10bb9e0e67a9 | [
"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 | 8,061 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import data.mv_polynomial
import data.fintype.card
/-!
# Homogeneous polynomials
A multivariate polynomial `φ` is homogeneous of degree `n`
if all monomials occuri... |
a110c23d45d050648deebb7d19a400f2589c4fba | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/order/filter/partial_auto.lean | 1f48fe69f5be1f42822a85746f45e2cd6ab0845d | [] | 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 | 6,718 | lean | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
Extends `tendsto` to relations and partial functions.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.order.filter.basic
import Mathlib.Post... |
c734f11ed00ccb1c8026e4130fa84e92646f0e07 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /src/Init/Data/String/Basic.lean | ce463f91e46e217df228d636b4bd0913b3359d7f | [
"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 | 15,597 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import Init.Data.List.Basic
import Init.Data.Char.Basic
import Init.Data.Option.Basic
universes u
structure String :=
(data : List Char)
abbrev Str... |
5a3a06e5ca6d2b7c26d6fcc10a336a7dd5f86aea | 4727251e0cd73359b15b664c3170e5d754078599 | /src/number_theory/lucas_lehmer.lean | cbef60a48fff04d74c25a32e835d4746b2e20dda | [
"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 | 17,261 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Scott Morrison, Ainsley Pahljina
-/
import data.nat.parity
import data.pnat.interval
import data.zmod.basic
import group_theory.order_of_element
import ring_theory.fint... |
cc0974cb279d3110e82c9ba81db13d436824b335 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/punit.lean | 86c16356489a6c62c6bcdeb81e3743883183227c | [
"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 | 3,352 | lean | /-
Copyright (c) 2018 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.functor.const
import category_theory.discrete_category
/-!
# The category `discrete punit`
We define `star : C ⥤ discrete punit... |
5301781bfb7ce5014194d647e115fcc68922c075 | 934eae675a9d997202bb021816325184e7d694aa | /_notes/Languages/lean/myproject/pierce3.lean | 046f067d862c3978671c214086e6fb7c5cf06d44 | [] | no_license | philzook58/philzook58.github.io | da78841df4ffd9a19c81e0eab833983d95a64b70 | 76000a5847bd6ee41dff25937ae916835bbcf03f | refs/heads/master | 1,692,951,958,916 | 1,692,631,945,000 | 1,692,631,945,000 | 91,513,884 | 9 | 4 | null | 1,677,330,791,000 | 1,494,977,989,000 | Jupyter Notebook | UTF-8 | Lean | false | false | 2,478 | lean | /-
The thing about lambdas is that binders are complicated and kind of distraction from some of the main points.
It is also interesting to see how a bunch of stuff works and some different angles of definition.
-/
namespace Term0
inductive term where
| true_ : term
| false_ : term
| ITE (x y z: term): term
... |
3d458c413e39aa309dc7277a75ad74d693a5e4dc | f20db13587f4dd28a4b1fbd31953afd491691fa0 | /library/init/data/default.lean | a2b496e9cd381275dc63e387ed80a7ca3e318edc | [
"Apache-2.0"
] | permissive | AHartNtkn/lean | 9a971edfc6857c63edcbf96bea6841b9a84cf916 | 0d83a74b26541421fc1aa33044c35b03759710ed | refs/heads/master | 1,620,592,591,236 | 1,516,749,881,000 | 1,516,749,881,000 | 118,697,288 | 1 | 0 | null | 1,516,759,470,000 | 1,516,759,470,000 | null | UTF-8 | Lean | false | false | 455 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.data.basic init.data.sigma init.data.nat init.data.char init.data.string
import init.data.list init.data.sum init.data.subtype init.data... |
6b8866a57a67d4472ec0f3ff21322b30648036d1 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/number_theory/padics/ring_homs.lean | 6e7189506bb30a364400761018a0578463f83c88 | [
"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 | 24,480 | lean | /-
Copyright (c) 2020 Johan Commelin, Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-/
import number_theory.padics.padic_integers
/-!
# Relating `ℤ_[p]` to `zmod (p ^ n)`
In this file we establish connections betwee... |
bcf0c9a471cc134b8a7a00328b48c2f0a1366d64 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /src/Lean/Data/Xml/Parser.lean | c5f774485857db0bf88b3fbf37456bbb8d0b822c | [
"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 | 15,241 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Dany Fabian
-/
import Lean.Data.Parsec
import Lean.Data.Xml.Basic
open IO
open System
open Lean
namespace Lean
namespace Xml
namespace Parser
open Lean.Parsec
open Parsec.Pars... |
0192298d95201e55d89fb99b11e205a64fadd225 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/box_integral/box/basic.lean | 71807a3aa84a418f50476ce81f95071b93c69088 | [
"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 | 18,009 | lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import data.set.intervals.monotone
import topology.algebra.order.monotone_convergence
import topology.metric_space.basic
/-!
# Rectangular boxes in `ℝⁿ`
> THIS FI... |
460bf39465b5b3cbbda2e952a5109c28af1842b4 | 5d166a16ae129621cb54ca9dde86c275d7d2b483 | /tests/lean/run/xrewrite1.lean | abb7858300334e15b7939d93e9d5b0abec4931be | [
"Apache-2.0"
] | permissive | jcarlson23/lean | b00098763291397e0ac76b37a2dd96bc013bd247 | 8de88701247f54d325edd46c0eed57aeacb64baf | refs/heads/master | 1,611,571,813,719 | 1,497,020,963,000 | 1,497,021,515,000 | 93,882,536 | 1 | 0 | null | 1,497,029,896,000 | 1,497,029,896,000 | null | UTF-8 | Lean | false | false | 306 | lean | open nat tactic
constant zeroadd (a : nat) : 0 + a = a
meta definition xrewrite (th_name : name) : tactic unit :=
do th ← mk_const th_name,
rewrite_core semireducible tt tt occurrences.all ff th,
try reflexivity
example (a : nat) : (0 + a) + (0 + a) + (0 + a) = a + a + a :=
by xrewrite `zeroadd
|
55bf4952760efc8f8099de836075cf396f8ffc0c | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/335.lean | 396f55ab8fc6f8fd4aecc75e6f50e2ec9b073a5b | [
"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 | 613 | lean | opaque foo : {x : Nat} → Type
opaque bar : {T : Type} → ({x : T} → Type) → Type
structure Baz where
baz : {x : Nat} → Type
#check bar foo
#check fun (b : Baz) => bar b.baz
structure Ty where
ctx : Type
ty : ctx → Type
structure Tm where
ty : Ty
tm : ∀ {Γ}, ty.ty Γ
#check fun (Γ : Type)
(A : Ty)
(Actx : Γ ... |
e8cc4627a27beac529965ab245f7c672d67fe686 | 367134ba5a65885e863bdc4507601606690974c1 | /src/deprecated/submonoid.lean | ea136e56d84bb947f1ff3ff4ffdf7f47cfcb7ab9 | [
"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 | 20,246 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard
-/
import group_theory.submonoid.basic
import algebra.big_operators.basic
/-!
# Submonoids
This file defines ... |
8a2f45b8b5cb44f46d9989c1f448c0d552c6a3a3 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/topology/algebra/order/floor.lean | 2d23ea9abdb7acabb846dbdcd48c981c491732e3 | [
"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 | 9,570 | lean | /-
Copyright (c) 2020 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
import algebra.order.floor
import topology.algebra.order.basic
/-!
# Topological facts about `int.floor`, `int.ceil` and `int.fract`
This file proves statements... |
93605298e5fd1e3d89c137862c44c7aa43d447e5 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Init/Coe.lean | 1b83ca4198cfc7d9a74e55b007e0116e7c23daa4 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 13,312 | 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, Mario Carneiro
-/
prelude
import Init.Prelude
set_option linter.missingDocs true -- keep it documented
/-!
# Coercion
Lean uses a somewhat elaborate system ... |
70b92ca04a8f54bd1b317b94324e6116437f9117 | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/data/holor.lean | ead3071a3de04eacb2b017dd9ee5260ef3f35c64 | [
"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 | 14,793 | lean | /-
Copyright (c) 2018 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp
-/
import algebra.module.pi
import algebra.big_operators.basic
/-!
# Basic properties of holors
Holors are indexed collections of tensor coefficients. Confusin... |
8cf865dc3bdb9a4cd3a6deea0c93154aa99a3b36 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/group2.lean | 7a6509c3faeba2aecd59fa852272783f65f05116 | [
"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 | 1,698 | lean | import logic
section
variable {A : Type}
variable f : A → A → A
variable one : A
variable inv : A → A
local infixl `*` := f
local postfix `^-1`:100 := inv
definition is_assoc := ∀ a b c, (a*b)*c = a*b*c
definition is_id := ∀ a, a*one = a
definition is_inv := ∀ a, a*a^-1 = one
end
inducti... |
0df31f64431b75234cdac4a9756d39e966e49ee7 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/metric_space/hausdorff_dimension.lean | fbad19511cd6d049c87e64f5e96ee2e155fa898e | [
"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 | 22,966 | lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import analysis.calculus.cont_diff
import measure_theory.measure.hausdorff
/-!
# Hausdorff dimension
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to t... |
205418cb6f055d75af2a7b4b8a62bc99d61c9a8d | f4bff2062c030df03d65e8b69c88f79b63a359d8 | /src/game/order/level01.lean | b7b9d93a66910f02fdb9068e0cd6a50d4a8e3602 | [
"Apache-2.0"
] | permissive | adastra7470/real-number-game | 776606961f52db0eb824555ed2f8e16f92216ea3 | f9dcb7d9255a79b57e62038228a23346c2dc301b | refs/heads/master | 1,669,221,575,893 | 1,594,669,800,000 | 1,594,669,800,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 628 | lean | import game.sets.sets_level10
import data.real.basic
namespace xena -- hide
/-
# Chapter 2 : Order
## Level 1
This level aims to familiarize you with the use of the trichotomy property in
Lean, as it will come in handy in later levels.
This property is stated in Lean's mathlib is:
`lt_trichotomy : ∀ (a b : ?M_1),... |
add90246249cec8c1cdc70a286b04a7a073362c3 | d436468d80b739ba7e06843c4d0d2070e43448e5 | /src/topology/metric_space/gluing.lean | e652282b6123c84efccceccc22769286c7180b73 | [
"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 | 23,502 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Gluing metric spaces
Authors: Sébastien Gouëzel
Gluing two metric spaces along a common subset. Formally, we are given
Φ
γ ---> α
|
|Ψ
v
β
where hΦ : isometry Φ and hΨ : isom... |
3a8b481d7ef17c596b779ee5f416ed95f50a2122 | 77c5b91fae1b966ddd1db969ba37b6f0e4901e88 | /src/algebra/direct_sum/ring.lean | 8d6a415a8ad6178efa9cf2da582b8dddfbf7650f | [
"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 | 26,250 | 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 algebra.algebra.basic
import algebra.algebra.operations
import algebra.direct_sum.basic
import group_theory.subgroup.basic
/-!
# Additively-graded multiplicative st... |
16c4e9e640e027b58c8f47ac957f14d3e58fedbf | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/topology/metric_space/basic.lean | d27a5ed4c4592d0d1c56a2628c7eb45348b8e8f8 | [
"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 | 75,262 | lean | /-
Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Metric spaces.
Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
Many definitions and theorems expected on metric spaces are already introduced o... |
fc0264d2897a05663f1f6508352542d48c87754d | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/interval_cases_auto.lean | 160cd7275eba3812456037406479887f6ba32714 | [] | 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 | 4,429 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Scott Morrison
Case bashing on variables in finite intervals.
In particular, `interval_cases n`
1) inspects hypotheses looking for lower and upper bounds of the form `a ≤ n` and `n < ... |
f8e2c5101e9fd80f1ffdc051d6dac98f0bfef5f0 | 969dbdfed67fda40a6f5a2b4f8c4a3c7dc01e0fb | /src/analysis/normed_space/basic.lean | 50864be84462792ab6ff8642a7cd086cdee581c9 | [
"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 | 59,450 | 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
-/
import topology.instances.nnreal
import topology.algebra.module
import topology.metric_space.antilipschitz
/-!
# Normed spaces
-/
variables {α : Typ... |
aad8e059c049261989fb23890e0373eee6cf0b09 | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/topology/sequences.lean | cb0fcc7e0f7eb6df3fdbfceb557071d63c30770d | [
"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 | 10,521 | lean | /-
Copyright (c) 2018 Jan-David Salchow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow
Sequences in topological spaces.
In this file we define sequences in topological spaces and show how they are related to
filters and the topology. In particular,... |
07fc0e8490e15520c7d3ecedd223738e383b8d66 | 8f209eb34c0c4b9b6be5e518ebfc767a38bed79c | /code/src/internal/Ant/main.lean | 3d76326a219bdc58bc4ab6aa22370f2dccdaf340 | [] | no_license | hediet/masters-thesis | 13e3bcacb6227f25f7ec4691fb78cb0363f2dfb5 | dc40c14cc4ed073673615412f36b4e386ee7aac9 | refs/heads/master | 1,680,591,056,302 | 1,617,710,887,000 | 1,617,710,887,000 | 311,762,038 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 54 | lean | import .eval
import .implies
import .map
import .rhss
|
05bcfd9fcb7dbce00a74dadad4d05937bafa9080 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/ring_theory/polynomial/content.lean | c7e32b7fb268cda9802092d41156d1735209997a | [
"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 | 17,143 | 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.gcd_monoid.finset
import data.polynomial.field_division
import data.polynomial.erase_lead
import data.polynomial.cancel_leads
/-!
# GCD structures on ... |
281ecc2431efe9822033d5b85d27632051c95ac0 | 432d948a4d3d242fdfb44b81c9e1b1baacd58617 | /src/ring_theory/polynomial/symmetric.lean | fcbd03d10cde6a200573de0fac6eb3961b68eac9 | [
"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 | 8,147 | lean | /-
Copyright (c) 2020 Hanting Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Hanting Zhang, Johan Commelin
-/
import tactic
import data.mv_polynomial.rename
import data.mv_polynomial.comm_ring
import algebra.algebra.subalgebra
/-!
# Symmetric Polynomials and El... |
3efa66e5baeb48cf4d8450f5ce934427e836a444 | 30b012bb72d640ec30c8fdd4c45fdfa67beb012c | /logic/function.lean | 16ea359e44e7b8ab5ea078b445cb3c7cd8ac7f9d | [
"Apache-2.0"
] | permissive | kckennylau/mathlib | 21fb810b701b10d6606d9002a4004f7672262e83 | 47b3477e20ffb5a06588dd3abb01fe0fe3205646 | refs/heads/master | 1,634,976,409,281 | 1,542,042,832,000 | 1,542,319,733,000 | 109,560,458 | 0 | 0 | Apache-2.0 | 1,542,369,208,000 | 1,509,867,494,000 | Lean | UTF-8 | Lean | false | false | 8,671 | lean | /-
Copyright (c) 2016 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
Miscellaneous function constructions and lemmas.
-/
import logic.basic data.option
universes u v w
namespace function
section
variables {α : Sort u} ... |
cabb525d41b24c07024086ae47bd04919b06cb8d | 07c6143268cfb72beccd1cc35735d424ebcb187b | /src/data/nat/prime.lean | 2de92d0b60ac693a1d5a7747fc7726daf6b61252 | [
"Apache-2.0"
] | permissive | khoek/mathlib | bc49a842910af13a3c372748310e86467d1dc766 | aa55f8b50354b3e11ba64792dcb06cccb2d8ee28 | refs/heads/master | 1,588,232,063,837 | 1,587,304,803,000 | 1,587,304,803,000 | 176,688,517 | 0 | 0 | Apache-2.0 | 1,553,070,585,000 | 1,553,070,585,000 | null | UTF-8 | Lean | false | false | 20,201 | 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, Jeremy Avigad, Mario Carneiro
-/
import data.nat.sqrt data.nat.gcd data.list.defs data.list.perm
import algebra.group_power
import tactic.wlog
/-!
# Prime n... |
53ff07b7bd3fbfcc6a9fb95e7246d0120ffeb500 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/computability/turing_machine.lean | 2d7bde5959a75ae6f389317cbcdab2be359d3ab6 | [
"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 | 109,935 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.fintype.basic
import data.pfun
import logic.function.iterate
import order.basic
import tactic.apply_fun
/-!
# Turing machines
This file defines a sequen... |
d00ac7c47e4b660eaf1a05f4790b9f9b57d1116d | 4bcaca5dc83d49803f72b7b5920b75b6e7d9de2d | /stage0/src/Lean/Elab/PatternVar.lean | 68fbcec77729d62721957e61e710117581bf9343 | [
"Apache-2.0"
] | permissive | subfish-zhou/leanprover-zh_CN.github.io | 30b9fba9bd790720bd95764e61ae796697d2f603 | 8b2985d4a3d458ceda9361ac454c28168d920d3f | refs/heads/master | 1,689,709,967,820 | 1,632,503,056,000 | 1,632,503,056,000 | 409,962,097 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,860 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.Match.MatchPatternAttr
import Lean.Elab.Arg
import Lean.Elab.MatchAltView
namespace Lean.Elab.Term
open Meta
inductive PatternVar where
... |
77415e1b02210946943c33844f2297f8ec5271fc | b7f22e51856f4989b970961f794f1c435f9b8f78 | /library/algebra/complete_lattice.lean | 0f434638aaa13bbafb56d230da5b7927df1786ee | [
"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 | 14,898 | 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
Complete lattices
TODO: define dual complete lattice and simplify proof of dual theorems.
-/
import algebra.lattice data.set.basic algebra.monotone
open set
... |
aec68c392635799b43b787d39dabf27fac583d51 | 856e2e1615a12f95b551ed48fa5b03b245abba44 | /src/measure_theory/measure_space.lean | a0e818be3444f84b54292c6bf94fdfc34f339f68 | [
"Apache-2.0"
] | permissive | pimsp/mathlib | 8b77e1ccfab21703ba8fbe65988c7de7765aa0e5 | 913318ca9d6979686996e8d9b5ebf7e74aae1c63 | refs/heads/master | 1,669,812,465,182 | 1,597,133,610,000 | 1,597,133,610,000 | 281,890,685 | 1 | 0 | null | 1,595,491,577,000 | 1,595,491,576,000 | null | UTF-8 | Lean | false | false | 54,401 | 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 measure_theory.outer_measure
import order.filter.countable_Inter
/-!
# Measure spaces
Given a measurable space `α`, a measure on `α` is a fun... |
47e7fb77269f1896727cdb87fae20c0d680dc8c5 | 693339a8c7c9c4b3a7ef726ed5df540f77a2ee84 | /02-lean.lean | ac95c23fd217db0db9e48b53edd8a82ffb721443 | [
"MIT"
] | permissive | Jerrycaster/lean | d02d5f39131461758310b6dac20570ebdcb46913 | c2f7e07ad8415e0618bba2e7497f360117d238bc | refs/heads/master | 1,592,160,820,153 | 1,562,540,316,000 | 1,562,540,316,000 | 195,093,506 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,155 | lean | #check λ x : ℕ, x + 5
#reduce (λ x : ℕ, x + 5) 5
#reduce (λ x : ℕ, x / 5) 5
#reduce (λ x : ℕ, x - 10) 5
#reduce (λ x : ℤ, x - 10) 5
constants α β γ : Type
constant f : α → β
constant g : β → γ
constant h : α → α
constant H : γ → α
constants (a : α) (b : β) (c : γ)
#check λ x : α, b -- λ (x : α), b : α → β
#check (λ ... |
c0463939f2d72b42944a99ba07d9528f7844abe0 | ce6917c5bacabee346655160b74a307b4a5ab620 | /src/ch5/ex0217.lean | 4912599e858a9d9f5b8854983bd46bd2d1cf50d7 | [] | 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 | 88 | lean | example : 3 = 3 :=
begin
generalize : 3 = x,
revert x,
intro y,
reflexivity
end
|
0299fa3fa9d8f0846be8c878863c89379eb45757 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/direct_sum_auto.lean | 630ded420ae32ea38997bea1d0f9a506cc8e034f | [] | 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 | 6,946 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.dfinsupp
import Mathlib.PostPort
universes v w u₁ u_1
namespace Mathlib
/-!
# Direct sum
T... |
70b2d1a5f083cd5f891e55948a24d6272a126f0a | 037dba89703a79cd4a4aec5e959818147f97635d | /src/2020/relations/partition_challenge.lean | a522af5a416c4f6722ec96a5ce1fd6e469977fb8 | [] | no_license | ImperialCollegeLondon/M40001_lean | 3a6a09298da395ab51bc220a535035d45bbe919b | 62a76fa92654c855af2b2fc2bef8e60acd16ccec | refs/heads/master | 1,666,750,403,259 | 1,665,771,117,000 | 1,665,771,117,000 | 209,141,835 | 115 | 12 | null | 1,640,270,596,000 | 1,568,749,174,000 | Lean | UTF-8 | Lean | false | false | 7,638 | lean | import tactic
/-!
# The partition challenge!
Prove that equivalence relations on α are the same as partitions of α.
Three sections:
1) partitions
2) equivalence classes
3) the challenge
## Overview
Say `α` is a type, and `R` is a binary relation on `α`.
The following things are already in Lean:
reflexive R := ... |
f1eb7d5c1671814af9e6eddec46aa094d04557c6 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/run/inductive_pred.lean | 7f21caf0d244e57358c024fec15278bb690ff519 | [
"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 | 5,117 | lean | import Lean
open Lean
def checkGetBelowIndices (ctorName : Name) (indices : Array Nat) : MetaM Unit := do
let actualIndices ← Meta.IndPredBelow.getBelowIndices ctorName
if actualIndices != indices then
throwError "wrong indices for {ctorName}: {actualIndices} ≟ {indices}"
namespace Ex
inductive LE : Nat → Na... |
f6888e798cb4089ae94fb0117e23a00d6dfd4cb2 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/ring_theory/localization.lean | 84d80701c54290b48cd9bd5334d96207e32d8dd7 | [
"Apache-2.0"
] | permissive | lacker/mathlib | f2439c743c4f8eb413ec589430c82d0f73b2d539 | ddf7563ac69d42cfa4a1bfe41db1fed521bd795f | refs/heads/master | 1,671,948,326,773 | 1,601,479,268,000 | 1,601,479,268,000 | 298,686,743 | 0 | 0 | Apache-2.0 | 1,601,070,794,000 | 1,601,070,794,000 | null | UTF-8 | Lean | false | false | 64,629 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston
-/
import data.equiv.ring
import group_theory.monoid_localization
import ring_theory.algebraic
import ring_theory.integral_clos... |
a6e723b565995995f0b7099116973e4ae2af9de4 | 367134ba5a65885e863bdc4507601606690974c1 | /src/algebra/category/Group/Z_Module_equivalence.lean | 219b668008d2a1fc20257c4f03a7e05e6733d068 | [
"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 | 1,338 | 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 algebra.category.Module.basic
/-!
The forgetful functor from ℤ-modules to additive commutative groups is
an equivalence of categories.
TODO:
either use this ... |
a0088c32a2b9c2891af4c324071402b0eaf2d23b | ad3e8f15221a986da27c99f371922c0b3f5792b6 | /src/week-02/solutions/e03-relations.lean | 868893d1227cfd0556cb2aae75ac3d8387d2074a | [] | no_license | VArtem/lean-itmo | a0e1424c8cc4c2de2ac85ab6fd4a12d80e9b85f1 | dc44cd06f9f5b984d051831b3aaa7364e64c2dc4 | refs/heads/main | 1,683,761,214,467 | 1,622,821,295,000 | 1,622,821,295,000 | 357,236,048 | 12 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,840 | lean | import tactic
/-
Упражнения в этом файле взяты из курса Formalising Mathematics:
https://github.com/ImperialCollegeLondon/formalising-mathematics/blob/master/src/week_1/Part_D_relations.lean
Рассмотрим тип `α` и бинарные отношения над `α`: `R : α → α → Prop`.
Для бинарных отношений в Lean определены понятия рефлекси... |
f305135b4e4efebfe137eea78a66cc7b0143b80d | 4484372104c20d5ccb4c725f0a5708632be2bfaa | /Maths_Challenges/solutions/solution3.lean | 0657d3d8d2ace0381e2146380ae2c10bb0a633ba | [] | no_license | robertylewis/xena | 45eecd4a06b4248683e84f32fdd496f7a5ebb0ec | 8c7e9fc2662171fdaacfde871bdc032693df83ce | refs/heads/master | 1,606,353,192,576 | 1,576,659,298,000 | 1,576,659,298,000 | 228,918,214 | 0 | 0 | null | 1,576,701,677,000 | 1,576,701,677,000 | null | UTF-8 | Lean | false | false | 89 | lean | import data.real.basic
theorem challenge2 :
(2 : ℝ) + 2 ≠ 5 :=
begin
norm_num
end
|
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