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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
a152c8ff6dcc72ba741b5f08ed805d706e9dff8e | 4c630d016e43ace8c5f476a5070a471130c8a411 | /data/fin.lean | d25f9198aa92547c60f88015b29fa40d42a96262 | [
"Apache-2.0"
] | permissive | ngamt/mathlib | 9a510c391694dc43eec969914e2a0e20b272d172 | 58909bd424209739a2214961eefaa012fb8a18d2 | refs/heads/master | 1,585,942,993,674 | 1,540,739,585,000 | 1,540,916,815,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,973 | lean | /-
Copyright (c) 2017 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Robert Y. Lewis
More about finite numbers.
-/
import data.nat.basic
open fin nat
/-- `fin 0` is empty -/
def fin_zero_elim {C : Sort*} : fin 0 → C :=
λ x, false.elim $ nat.not_lt_ze... |
a59207bc566487ef4e25293ce1c9a9262037ae2d | c777c32c8e484e195053731103c5e52af26a25d1 | /src/analysis/normed_space/star/spectrum.lean | c9cf202ad89d56509ad1c0de00375395de306407 | [
"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 | 7,928 | lean | /-
Copyright (c) 2022 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import analysis.normed_space.star.basic
import analysis.normed_space.spectrum
import analysis.special_functions.exponential
import algebra.star.star_alg_hom
/-! # Spec... |
279b6e79a652c4b57f86d0e96bb4a425e445943e | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/data/list/perm.lean | 54167f16979e9ed2356c4519c749f5894f2e7f2f | [
"Apache-2.0"
] | permissive | hamdysalah1/mathlib | b915f86b2503feeae268de369f1b16932321f097 | 95454452f6b3569bf967d35aab8d852b1ddf8017 | refs/heads/master | 1,677,154,116,545 | 1,611,797,994,000 | 1,611,797,994,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 47,765 | 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.list.bag_inter
import data.list.erase_dup
import data.list.zip
import logic.relation
import data.nat.factorial
/... |
9395dd1515db0ad818f988e3bc05128e2677b174 | fcf3ffa92a3847189ca669cb18b34ef6b2ec2859 | /src/world2/level5.lean | 7b106957bda5a155f5919e5266b3b8814b4ac38c | [
"Apache-2.0"
] | permissive | nomoid/lean-proofs | 4a80a97888699dee42b092b7b959b22d9aa0c066 | b9f03a24623d1a1d111d6c2bbf53c617e2596d6a | refs/heads/master | 1,674,955,317,080 | 1,607,475,706,000 | 1,607,475,706,000 | 314,104,281 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 358 | lean | import mynat.definition
import mynat.add
import world2.level1
import world2.level3
namespace mynat
lemma succ_eq_add_one (a : mynat) : succ(a) = a + 1 :=
begin [nat_num_game]
induction a with d hd,
{
rw zero_add,
rw one_eq_succ_zero,
refl,
},
{
rw succ_add,
rw h... |
30279ffe38a2f679e0af307d8804a400a637a75c | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/data/nat/dist.lean | 770e7c724aef4f8630a1489122547256d82f0d52 | [
"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 | 4,171 | lean | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Jeremy Avigad
-/
import data.nat.basic
/-!
# Distance function on ℕ
This file defines a simple distance function on naturals from truncated substraction.
-/
nam... |
f438a7c265797ca688860bbe48a008a9da2db274 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/limits/has_limits.lean | 00a7c55546d82ba9da0adb51c924c9119a698efd | [
"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 | 45,767 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Mario Carneiro, Scott Morrison, Floris van Doorn
-/
import category_theory.limits.is_limit
import category_theory.category.ulift
/-!
# Existence of limits and colimits
>... |
7af7df92390b9d0ae05b14410bd53a453449917b | f3849be5d845a1cb97680f0bbbe03b85518312f0 | /library/init/data/sigma/lex.lean | cdd4617365606c324578dc75b69425729c42d77b | [
"Apache-2.0"
] | permissive | bjoeris/lean | 0ed95125d762b17bfcb54dad1f9721f953f92eeb | 4e496b78d5e73545fa4f9a807155113d8e6b0561 | refs/heads/master | 1,611,251,218,281 | 1,495,337,658,000 | 1,495,337,658,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,833 | 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.sigma.basic init.meta
universes u v
namespace sigma
section
variables {α : Type u} {β : α → Type v}
variable (r : α → α → Prop... |
56e8ca78a981679f35fd5c631ab989b53a101c6c | 30b012bb72d640ec30c8fdd4c45fdfa67beb012c | /data/real/nnreal.lean | 042f23bc9b910c39c3405b88d911da93d626de45 | [
"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 | 15,427 | lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
Nonnegative real numbers.
-/
import data.real.basic order.lattice
section discrete_field
@[simp] lemma inv_eq_zero {α} [discrete_field α] (a : α) : a⁻¹ = 0 ↔ a = 0 :=... |
ca0252373cac1ac0a01d35c840c2510795b55802 | 49bd2218ae088932d847f9030c8dbff1c5607bb7 | /src/topology/metric_space/closeds.lean | 093ed0970b0aa971b73e0cb14f0867358c05cb95 | [
"Apache-2.0"
] | permissive | FredericLeRoux/mathlib | e8f696421dd3e4edc8c7edb3369421c8463d7bac | 3645bf8fb426757e0a20af110d1fdded281d286e | refs/heads/master | 1,607,062,870,732 | 1,578,513,186,000 | 1,578,513,186,000 | 231,653,181 | 0 | 0 | Apache-2.0 | 1,578,080,327,000 | 1,578,080,326,000 | null | UTF-8 | Lean | false | false | 22,451 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Sébastien Gouëzel
-/
import topology.metric_space.hausdorff_distance topology.opens analysis.specific_limits
/-!
# Closed subsets
This file defines the metric and emetric space st... |
ba0915615fee453037d4af80b863cb85f4e22cf0 | 159fed64bfae88f3b6a6166836d6278f953bcbf9 | /Structure/Forgetfulness.lean | 7ad46a3ed900c75a27964299eee40b98b1ac03e3 | [
"MIT"
] | permissive | SReichelt/lean4-experiments | 3e56830c8b2fbe3814eda071c48e3c8810d254a8 | ff55357a01a34a91bf670d712637480089085ee4 | refs/heads/main | 1,683,977,454,907 | 1,622,991,121,000 | 1,622,991,121,000 | 340,765,677 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 15,194 | lean | -- An abstract formalization of "isomorphism is equality up to relabeling"
-- -------------------------------------------------------------------------
--
-- See `README.md` for more info.
--
-- This file contains some definitions related to truncation and quotients.
import Structure.Basic
open Morphisms
open HasS... |
d97e9ff88bc3410a25c3ace473fc577a0bd147f5 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/adjunction/over.lean | d709fed80a2173ff114fddc338218e9ebd096d66 | [
"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 | 1,737 | lean | /-
Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import category_theory.limits.shapes.binary_products
import category_theory.monad.products
import category_theory.over
/-!
# Adjunctions related to the over category
> ... |
6b7af7636a2079b8ce41eed621b94a0360d4b4f3 | 200b12985a863d01fbbde6abfc9326bb82424a8b | /src/propLogic/Ex004.lean | 9ef0e9eb3419099f956c12cc628e438eb7e9c5af | [] | no_license | SvenWille/LeanLogicExercises | 38eacd36733ac48e5a7aacf863c681c9a9a48271 | 2dbc920feadd63bbc50f87e69646c0081db26eba | refs/heads/master | 1,629,676,667,365 | 1,512,161,459,000 | 1,512,161,459,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 173 | lean |
theorem Ex004(a b c : Prop):(a → (b ∧ c)) → (a → b) :=
assume H1:(a → (b ∧ c)),
assume H2:a,
have A:b ∧ c, from H1 H2,
show b, from and.elim_left A
|
e5862c5690a44186118e045ac106ceec4fdec069 | 22e97a5d648fc451e25a06c668dc03ac7ed7bc25 | /src/data/list/defs.lean | 51925f98457ff76e899ad62dceeb73641fed6762 | [
"Apache-2.0"
] | permissive | keeferrowan/mathlib | f2818da875dbc7780830d09bd4c526b0764a4e50 | aad2dfc40e8e6a7e258287a7c1580318e865817e | refs/heads/master | 1,661,736,426,952 | 1,590,438,032,000 | 1,590,438,032,000 | 266,892,663 | 0 | 0 | Apache-2.0 | 1,590,445,835,000 | 1,590,445,835,000 | null | UTF-8 | Lean | false | false | 20,481 | 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
Extra definitions on lists.
-/
import data.option.defs
import logic.basic
import tactic.cache
n... |
16c95b56a934fe2c7d7ee169ef588df572364559 | 626e312b5c1cb2d88fca108f5933076012633192 | /src/ring_theory/polynomial/cyclotomic.lean | ed57de3bbf5824cc1822262220693f6b975ca854 | [
"Apache-2.0"
] | permissive | Bioye97/mathlib | 9db2f9ee54418d29dd06996279ba9dc874fd6beb | 782a20a27ee83b523f801ff34efb1a9557085019 | refs/heads/master | 1,690,305,956,488 | 1,631,067,774,000 | 1,631,067,774,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 30,769 | lean | /-
Copyright (c) 2020 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
import field_theory.splitting_field
import ring_theory.roots_of_unity
import algebra.polynomial.big_operators
import number_theory.arithmetic_function
import data.... |
9ac21567b84114f393a95a0b041739e74c1fc800 | 88892181780ff536a81e794003fe058062f06758 | /src/lib/nat.lean | 1b7551e1fec3ab7df52c8024b0bcc7ff13f345f5 | [] | no_license | AtnNn/lean-sandbox | fe2c44280444e8bb8146ab8ac391c82b480c0a2e | 8c68afbdc09213173aef1be195da7a9a86060a97 | refs/heads/master | 1,623,004,395,876 | 1,579,969,507,000 | 1,579,969,507,000 | 146,666,368 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,892 | lean | import lib.tactics
import data.nat.basic
import algebra.field
import algebra.group
open nat
@[simp]
lemma zero_lt_succ {n : ℕ} : 0 < n + 1 := by {
induction n with n ih,
{ exact less_than_or_equal.refl _ },
{ exact less_than_or_equal.step ih } }
@[simp]
lemma nat_div_self {n : ℕ} : (n + 1) / (n + 1) = 1 := beg... |
c61c5de823f97fad08cd1632a1cf8c13d76aee48 | b00eb947a9c4141624aa8919e94ce6dcd249ed70 | /stage0/src/Lean/Meta/Match/Match.lean | 50b026574cd937d78c83309b107c8f23f3bb7e0b | [
"Apache-2.0"
] | permissive | gebner/lean4-old | a4129a041af2d4d12afb3a8d4deedabde727719b | ee51cdfaf63ee313c914d83264f91f414a0e3b6e | refs/heads/master | 1,683,628,606,745 | 1,622,651,300,000 | 1,622,654,405,000 | 142,608,821 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 40,334 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Util.CollectLevelParams
import Lean.Util.Recognizers
import Lean.Compiler.ExternAttr
import Lean.Meta.Check
import Lean.Meta.Closure
import Lean... |
160deade70a5f82d66657cd9d9ae96388ac7f846 | 4fa161becb8ce7378a709f5992a594764699e268 | /src/algebra/continued_fractions/convergents_equiv.lean | 06aecbc2cf707d48fe32905df2c2d96ad2751fba | [
"Apache-2.0"
] | permissive | laughinggas/mathlib | e4aa4565ae34e46e834434284cb26bd9d67bc373 | 86dcd5cda7a5017c8b3c8876c89a510a19d49aad | refs/heads/master | 1,669,496,232,688 | 1,592,831,995,000 | 1,592,831,995,000 | 274,155,979 | 0 | 0 | Apache-2.0 | 1,592,835,190,000 | 1,592,835,189,000 | null | UTF-8 | Lean | false | false | 20,597 | lean | /-
Copyright (c) 2020 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import algebra.continued_fractions.continuants_recurrence
import algebra.continued_fractions.terminated_stable
import tactic.linarith
/-!
# Equivalence of Recursi... |
91350d2c4cd4aca73466c1ffcecc93510dec4d1b | ea11767c9c6a467c4b7710ec6f371c95cfc023fd | /src/monoidal_categories/monoidal_functor.lean | 886e2dd3f7eb92c69bca82bd66fdcc9b5718b282 | [] | no_license | RitaAhmadi/lean-monoidal-categories | 68a23f513e902038e44681336b87f659bbc281e0 | 81f43e1e0d623a96695aa8938951d7422d6d7ba6 | refs/heads/master | 1,651,458,686,519 | 1,529,824,613,000 | 1,529,824,613,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,636 | 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 .monoidal_category
open categories
open categories.functor
open categories.natural_transformation
open categories.monoidal_category
open ca... |
9976e795f97cca362bc0674de06694bc512cddcc | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/category_theory/types.lean | 227eef7d0477c0ee3d014b7856fa6d2d4dfed3f1 | [
"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 | 3,133 | 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, Johannes Hölzl
import category_theory.functor_category
import category_theory.fully_faithful
import data.equiv.basic
namespace category_theory
... |
7b1ff5f55b47bf17db924b7190f6f937007a1ff4 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/algebra/ordered_group.lean | e763b716956c57c66cd7f9ff3262d8a38ae03049 | [
"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 | 67,826 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl
-/
import algebra.group.with_one
import algebra.group.type_tags
import order.bounded_lattice
set_option old_structure_c... |
48fa5964e27ea6d31e7ee1e718b9b4c2cc8e4d0f | bb31430994044506fa42fd667e2d556327e18dfe | /src/ring_theory/ideal/local_ring.lean | 3f53ef4a90068ba937a8ad5be0fc18ba48c10c06 | [
"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 | 15,543 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Chris Hughes, Mario Carneiro
-/
import algebra.algebra.basic
import ring_theory.ideal.operations
import ring_theory.jacobson_ideal
/-!
# Local rings
Define local rings as com... |
dc33fc1814acdd446c9dafc3a0e8b3da93caeb6f | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/1952.lean | 5a6aa28dd88a01ada7f069691f484a44297f3a8a | [
"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 | 433 | lean | structure foo :=
(fn : nat → nat)
(fn_ax : ∀ a : nat, fn a = a)
/-
set_option pp.all true
set_option pp.universes false -- universes are probably irrelevant
set_option pp.purify_metavars false
set_option trace.type_context.is_def_eq true
set_option trace.type_context.is_def_eq_detail true
-/
def bl... |
7aacc1e8264f956f6c5b4a32f7088f56070be9e1 | ad0c7d243dc1bd563419e2767ed42fb323d7beea | /data/fin.lean | 582504167c06ffc11fefb8854a53e1d78561dc9a | [
"Apache-2.0"
] | permissive | sebzim4500/mathlib | e0b5a63b1655f910dee30badf09bd7e191d3cf30 | 6997cafbd3a7325af5cb318561768c316ceb7757 | refs/heads/master | 1,585,549,958,618 | 1,538,221,723,000 | 1,538,221,723,000 | 150,869,076 | 0 | 0 | Apache-2.0 | 1,538,229,323,000 | 1,538,229,323,000 | null | UTF-8 | Lean | false | false | 3,028 | lean | import data.nat.basic
open fin nat
namespace fin
variable {n : ℕ}
/-- The greatest value of `fin (n+1)` -/
def last (n : ℕ) : fin (n+1) := ⟨_, n.lt_succ_self⟩
theorem le_last (i : fin (n+1)) : i ≤ last n :=
le_of_lt_succ i.is_lt
/-- Embedding of `fin n` in `fin (n+1)` -/
def raise (k : fin n) : fin (n + 1) := ⟨va... |
c2f4de5567b54f8b2cee8cc60684742fe7123990 | 77c5b91fae1b966ddd1db969ba37b6f0e4901e88 | /src/ring_theory/polynomial/homogeneous.lean | 3b232b09b29f3a32bbc6a631f0bc574f767e00d9 | [
"Apache-2.0"
] | permissive | dexmagic/mathlib | ff48eefc56e2412429b31d4fddd41a976eb287ce | 7a5d15a955a92a90e1d398b2281916b9c41270b2 | refs/heads/master | 1,693,481,322,046 | 1,633,360,193,000 | 1,633,360,193,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,907 | 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 algebra.algebra.operations
import data.fintype.card
import algebra.direct_sum.algebra
/-!
# Homogeneous polynomials
A multivariate... |
d654be97dd5e93a3660286ae04036420b8276091 | 3dd1b66af77106badae6edb1c4dea91a146ead30 | /library/standard/prop_decidable.lean | 9c469d7662c48a5ad4f399de9427fbe12d9116d8 | [
"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 | 792 | 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 classical hilbert decidable
using decidable
-- Excluded middle + Hilbert implies every proposition is decidable
-- First, we show that (decidable... |
2e3efe5f75f8ff9b24b41b6f45f8c2dd6745cc15 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/lake/Lake/Build/Library.lean | c804a011a87cdc7dbd3d9102f95f4d495009aa99 | [
"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 | 3,759 | lean | /-
Copyright (c) 2022 Mac Malone. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mac Malone
-/
import Lake.Build.Common
import Lake.Build.Targets
/-! # Library Facet Builds
Build function definitions for a library's builtin facets.
-/
namespace Lake
/-! ## Build Lea... |
37ef3313ae5b0c8a65dec7179cd2b9aa8bb55eb0 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/order/monoid/cancel/defs.lean | 84ff915afcc98c064063d7d7e02f7a4c736e10cd | [
"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 | 4,140 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl
-/
import algebra.order.monoid.defs
/-!
# Ordered cancellative monoids
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> ht... |
9803003f2f55c8d3b7127db3a83c1c3219630816 | 3618c6e11aa822fd542440674dfb9a7b9921dba0 | /scratch/coprod_mul_test.lean | 7b92eb0676cc364f79c96c5e9a1e7f8de52db98a | [] | no_license | ChrisHughes24/single_relation | 99ceedcc02d236ce46d6c65d72caa669857533c5 | 057e157a59de6d0e43b50fcb537d66792ec20450 | refs/heads/master | 1,683,652,062,698 | 1,683,360,089,000 | 1,683,360,089,000 | 279,346,432 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 29,904 | lean | import data.list.chain data.int.basic tactic data.list.basic
variables {ι : Type*} {G : ι → Type*} [Π i, monoid (G i)]
open list
def reduced (l : list (Σ i, G i)) : Prop :=
l.chain' (λ a b, a.1 ≠ b.1) ∧ ∀ a : Σ i, G i, a ∈ l → a.2 ≠ 1
@[simp] lemma reduced_nil : reduced ([] : list (Σ i, G i)) :=
⟨list.chain'_nil, λ... |
702a0fae07cfa8383bbb3c4fed5a5847ceecf693 | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /src/Lean/Environment.lean | 209c4ea06c8cc992840b1e0844ebc87a5fda7245 | [
"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 | 30,227 | 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 Std.Data.HashMap
import Lean.Data.SMap
import Lean.Declaration
import Lean.LocalContext
import Lean.Util.Path
import Lean.Util.FindExpr
import Lean.U... |
d5a6f837e63d0f11e1a724d8cb1f5f6a09a5d27a | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/inner_product_space/spectrum.lean | 6c3e285e142f5aeb7aa1d4be96f32a21657e83d1 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 13,411 | lean | /-
Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import analysis.inner_product_space.rayleigh
import analysis.inner_product_space.pi_L2
import algebra.direct_sum.decomposition
import linear_algebra.eigenspace.minp... |
6c51a5ead4efe122ae2ef978aa3d217fb7e60643 | 8d65764a9e5f0923a67fc435eb1a5a1d02fd80e3 | /src/algebra/group_power/lemmas.lean | 26d99b6ec89007c6e7f7c861cb787ce3814f18dd | [
"Apache-2.0"
] | permissive | troyjlee/mathlib | e18d4b8026e32062ab9e89bc3b003a5d1cfec3f5 | 45e7eb8447555247246e3fe91c87066506c14875 | refs/heads/master | 1,689,248,035,046 | 1,629,470,528,000 | 1,629,470,528,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 35,010 | lean | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis
-/
import algebra.group_power.basic
import algebra.invertible
import algebra.opposites
import data.list.basic
import data.int.cast
import data.equiv.basic... |
34564c0975cd2b51c394f7a27062f3f9242c0e7f | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/ring_theory/trace.lean | 8aa14624757627a6627266d7a68b45ae00b96ca6 | [
"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 | 22,538 | 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 linear_algebra.matrix.bilinear_form
import linear_algebra.matrix.charpoly.minpoly
import linear_algebra.determinant
import linear_algebra.finite_dimensional
import ... |
679f13379964009826e7b079b2fa03bd6fd2f9fd | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/congr_error_msg.lean | 541e9f7a7a6ec00cceb698088847adb9fc2436c5 | [
"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 | 794 | lean | open nat
definition g : nat → nat → nat :=
sorry
definition R : nat → nat → Prop :=
sorry
lemma C₁ [congr] : g 0 1 = g 1 0 := -- ERROR
sorry
lemma C₂ [congr] (a b : nat) : g a b = 0 := -- ERROR
sorry
lemma C₃ [congr] (a b : nat) : R (g a b) (g 0 0) := -- ERROR
sorry
lemma C₄ [congr] (A B : Type) : (A → B) = (λ a... |
5f5a817db125e2da36ccbdd0d736e89afbaddd69 | abd85493667895c57a7507870867b28124b3998f | /src/measure_theory/l1_space.lean | 6ad3af90c405c3049405bcbdb63f6bf1c580dbbb | [
"Apache-2.0"
] | permissive | pechersky/mathlib | d56eef16bddb0bfc8bc552b05b7270aff5944393 | f1df14c2214ee114c9738e733efd5de174deb95d | refs/heads/master | 1,666,714,392,571 | 1,591,747,567,000 | 1,591,747,567,000 | 270,557,274 | 0 | 0 | Apache-2.0 | 1,591,597,975,000 | 1,591,597,974,000 | null | UTF-8 | Lean | false | false | 28,714 | 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.ae_eq_fun
/-!
# Integrable functions and `L¹` space
In the first part of this file, the predicate `integrable` is defined and basic properties o... |
a673db704c0dec7b8dadb0ea10a28aa4ce075fcb | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/measure_theory/function/ae_eq_of_integral.lean | 7467c3405dfd11a97c02c7639c7efb7cd462f166 | [
"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 | 27,988 | lean | /-
Copyright (c) 2021 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import analysis.normed_space.dual
import measure_theory.function.strongly_measurable
import measure_theory.integral.set_integral
/-! # From equality of integrals to equ... |
5f2c522095fd61954ff4877bdad1d6153515239e | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /tests/lean/appParserIssue.lean | a7f7a759a719f5086c05c91e123f573be9706bf7 | [
"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 | 334 | lean | def f (x : Nat) (g : Nat → Nat) := g x
new_frontend
#check f 1 fun x => x -- should work
#check f 1 (fun x => x) -- should work
#check f 1 $ fun x => x -- should work
syntax "foo" term:max term:max : term
macro_rules `(foo $x $y) => `(f $x $y)
#check foo 1 (fun x => x) -- should work
#check foo 1 fun x => x -- ... |
a1b2796cf7a8a6e4d2877e98aefc51efd2b9dd35 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/pfunctor/univariate/M.lean | 8a2be6295b3f8c333a2c6c7d6d03728e72908b44 | [
"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 | 21,995 | 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... |
05b23c28d940be5cf07b141bf55b2771c7eb88f6 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/category_theory/limits/lattice.lean | a5169cb7fc792de7e03fb5bc940155360062c4f5 | [
"Apache-2.0"
] | permissive | rmitta/mathlib | 8d90aee30b4db2b013e01f62c33f297d7e64a43d | 883d974b608845bad30ae19e27e33c285200bf84 | refs/heads/master | 1,585,776,832,544 | 1,576,874,096,000 | 1,576,874,096,000 | 153,663,165 | 0 | 2 | Apache-2.0 | 1,544,806,490,000 | 1,539,884,365,000 | Lean | UTF-8 | Lean | false | false | 1,545 | 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.limits.limits
import order.complete_lattice
universes u
open category_theory
open lattice
namespace category_theory.limits
variables {α : T... |
73943730ae9a328b7f7749e3dc8cf84e965076c7 | 9ad8d18fbe5f120c22b5e035bc240f711d2cbd7e | /src/commutative_algebra/book/sec_rings.lean | d0d3e5020312e935b03b8c8bd2b4553f03a12004 | [] | no_license | agusakov/lean_lib | c0e9cc29fc7d2518004e224376adeb5e69b5cc1a | f88d162da2f990b87c4d34f5f46bbca2bbc5948e | refs/heads/master | 1,642,141,461,087 | 1,557,395,798,000 | 1,557,395,798,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,629 | lean | import algebra.ring algebra.pi_instances data.rat data.real.basic data.complex.basic
import data.nat.prime ring_theory.subring data.zsqrtd.gaussian_int data.zmod.basic
import ring_theory.subring
import topology.constructions topology.algebra.continuous_functions topology.instances.real
import data.mv_polynomial
import... |
192ae53700dfe3cd6684a8172a85888c9db00bc0 | b70031c8e2c5337b91d7e70f1e0c5f528f7b0e77 | /src/data/fintype/card.lean | f244f16d894e308948ea8ab8591e36ed59faadc6 | [
"Apache-2.0"
] | permissive | molodiuc/mathlib | cae2ba3ef1601c1f42ca0b625c79b061b63fef5b | 98ebe5a6739fbe254f9ee9d401882d4388f91035 | refs/heads/master | 1,674,237,127,059 | 1,606,353,533,000 | 1,606,353,533,000 | 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.
Author: Mario Carneiro
-/
import data.fintype.basic
import algebra.big_operators.ring
/-!
Results about "big operations" over a `fintype`, and consequent
results about cardinalities of certain... |
857c42a89071381eeebfb49d218d194a7ec4318c | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /test/congrm.lean | 57a20017a9c4278001e22411618179b80a5bb364 | [
"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 | 4,894 | lean | import tactic.congrm
variables {X : Type*} [has_add X] [has_mul X] (a b c d : X) (f : X → X)
example (H : a = b) : f a + f a = f b + f b :=
by congrm f _ + f _; exact H
example {g : X → X} (H : a = b) (H' : c + f a = c + f d) (H'' : f d = f b) :
f (g a) * (f d + (c + f a)) = f (g b) * (f b + (c + f d)) :=
begin
... |
e3c1ebc75095298e3f37ba65a377473a923e2cba | 33340b3a23ca62ef3c8a7f6a2d4e14c07c6d3354 | /dlo/sqe.lean | d68885b416dd311c977c09e3c8b03f290c5973f5 | [] | no_license | lclem/cooper | 79554e72ced343c64fed24b2d892d24bf9447dfe | 812afc6b158821f2e7dac9c91d3b6123c7a19faf | refs/heads/master | 1,607,554,257,488 | 1,578,694,133,000 | 1,578,694,133,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,128 | lean | import .formula .basic .dense_linear_order
open list --dnf
def get_lb : atom_dlo → option term_dlo
| (_ =' _) := none
| ((term_dlo.var 0) <' (term_dlo.var 0)) := none
| ((term_dlo.var (n+1)) <' (term_dlo.var 0)) := some (term_dlo.var n)
| ((term_dlo.cst b) <' (term_dlo.var 0)) := some (term_dlo.cst b)
| (_ <' (term_... |
617f6c03ac599f079fac0e037257edd654f8e939 | f5f7e6fae601a5fe3cac7cc3ed353ed781d62419 | /src/ring_theory/ideal_operations.lean | 5c0281349fbc5b367590f467cd9e22de8dcaeafe | [
"Apache-2.0"
] | permissive | EdAyers/mathlib | 9ecfb2f14bd6caad748b64c9c131befbff0fb4e0 | ca5d4c1f16f9c451cf7170b10105d0051db79e1b | refs/heads/master | 1,626,189,395,845 | 1,555,284,396,000 | 1,555,284,396,000 | 144,004,030 | 0 | 0 | Apache-2.0 | 1,533,727,664,000 | 1,533,727,663,000 | null | UTF-8 | Lean | false | false | 24,786 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
More operations on modules and ideals.
-/
import ring_theory.ideals data.nat.choose order.zorn
import linear_algebra.tensor_product
import data.equiv.algebra
import ring_theory.... |
2f637602b7d8cb3f04b31fd7b59b0f9c009ce3ff | 29cc89d6158dd3b90acbdbcab4d2c7eb9a7dbf0f | /Exercises week 3/hw13.lean | a2c4aa8b1c1204343252b4721eb1ede5b8b7ad76 | [] | no_license | KjellZijlemaker/Logical_Verification_VU | ced0ba95316a30e3c94ba8eebd58ea004fa6f53b | 4578b93bf1615466996157bb333c84122b201d99 | refs/heads/master | 1,585,966,086,108 | 1,549,187,704,000 | 1,549,187,704,000 | 155,690,284 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 177 | lean | begin
apply iff.intro,
assume hpq,
apply and.intro,
assume a,
have b := and.left (hpq a),
show p a, from b,
assume a,
have c := and.right (hpq a),
show q a, from c,
assume hpq,
|
c065ecd6a10815755f78bb4198049642040e8720 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/explicit_delimiters.lean | a46af934aa2edb3c8eb617795c70dd9c23a6c556 | [
"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 | 172 | lean | example p : false := trivial -- Error
def main proof : false := trivial -- Error
example (p : false) := trivial
def main' (proof : false) := trivial
example := trivial
|
b92d254f61aaac2fb21d7153fdf48c6570d97d6f | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/lie/classical.lean | 35377c6ab8c1c371b70d1fd0a7e5f47ca14e78e4 | [] | 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 | 14,048 | lean | /-
Copyright (c) 2020 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.invertible
import Mathlib.algebra.lie.skew_adjoint
import Mathlib.linear_algebra.matrix
i... |
98457e783762a04d1ec0ee93d76a2866eedfc8eb | c3e8fac5ab7ca328e55bccf82a0207a97f96678c | /lean/src/concrete_syntax.lean | eef29ad3f0057b1bc643446e836d7b1933192cad | [
"Unlicense"
] | permissive | Rotsor/brainfuck | 941bb33862ce3e9d61f0454db5ca02942f4b5775 | 3e6f30f298b8ba76d0bc71b8b5a47cedaf2f0b97 | refs/heads/master | 1,619,718,778,100 | 1,532,913,653,000 | 1,532,913,653,000 | 121,682,141 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 23,937 | lean | import .byte
import .unix
import .ast
universes u v
namespace brainfuck
namespace concrete_syntax
def string : Type := list byte
instance : has_append(string) := ⟨ list.append ⟩
instance : has_repr(string) :=
⟨ λ l, list.as_string (list.map (λ (x : fin _), char.of_nat x.val) l) ⟩
def lparen... |
1c46f68fe12bc702a97673266bc1f4bf749f1e55 | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /tests/lean/notation4.lean | 5f63b2ee606192bd9f26c2bdb60c3ed69ab3434d | [
"Apache-2.0"
] | permissive | tjiaqi/lean | 4634d729795c164664d10d093f3545287c76628f | d0ce4cf62f4246b0600c07e074d86e51f2195e30 | refs/heads/master | 1,622,323,796,480 | 1,422,643,069,000 | 1,422,643,069,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 342 | lean | import logic data.sigma
open sigma
inductive list (T : Type) : Type := nil {} : list T, cons : T → list T → list T open list notation h :: t := cons h t notation `[` l:(foldr `,` (h t, cons h t) nil) `]` := l
check ∃ (A : Type₁) (x y : A), x = y
check ∃ (x : num), x = 0
check Σ (x : num), x = 10
check Σ (A : Type₁),... |
b82ed6b19e235dce49402ea8fb5c00bd29bbfa19 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/limits/shapes/pullbacks.lean | ff1a2095c1adfacd55c5607734c2022321655af2 | [
"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 | 93,846 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Markus Himmel, Bhavik Mehta, Andrew Yang
-/
import category_theory.limits.shapes.wide_pullbacks
import category_theory.limits.shapes.binary_products
/-!
# Pullbacks
>... |
945b81a8dae9206854338bd6dfe2b2f4add44049 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/559.lean | 30d88237b1ec9750cf3245dce8c5211f847a3cd9 | [
"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 | 278 | lean | import algebra.ordered_field
open algebra
section sequence_c
parameter Q : Type
parameter lof_Q : linear_ordered_field Q
definition to_lof [instance] : linear_ordered_field Q := lof_Q
include to_lof
theorem foo (a b : Q) : a + b = b + a := !add.comm
end sequence_c
|
d4846863baaefcea350fbc3583fe31f507e8e26f | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/data/polynomial/monomial.lean | 9adb9c3b53d8c8ebbe9aa9b6375f4b9d872a0486 | [
"Apache-2.0"
] | permissive | abentkamp/mathlib | d9a75d291ec09f4637b0f30cc3880ffb07549ee5 | 5360e476391508e092b5a1e5210bd0ed22dc0755 | refs/heads/master | 1,682,382,954,948 | 1,622,106,077,000 | 1,622,106,077,000 | 149,285,665 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,384 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
-/
import data.polynomial.coeff
/-!
# Univariate monomials
Preparatory lemmas for degree_basic.
-/
noncomputable theory
n... |
bcbd9255944f73a2d545ead9f3e4a7190165f50a | e447aba4f95cefc4e26736a59e4781640deafcc5 | /src/congruence_groups.lean | b774829f121bfe43c8850523417e8a34bf040e87 | [
"Unlicense"
] | permissive | Eloitor/four-squares-modular-forms | 45674978910900ac4b773316d2642774ecad3f7e | f1eaa559640b75371149f5fe819869babeb60aa2 | refs/heads/main | 1,677,012,829,783 | 1,611,628,491,000 | 1,611,628,491,000 | 321,801,679 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,236 | lean |
import linear_algebra.special_linear_group
import data.zmod.basic
open matrix
lemma det_2x2 (M : matrix (fin 2) (fin 2) ℤ) : M.det = M 0 0 * M 1 1 - M 1 0 * M 0 1 :=
calc M.det = ((1 : units ℤ) * (_ * (_ * 1))) + (((-1 : units ℤ) * (_ * (_ * 1))) + 0) : refl M.det
... = M 0 0 * M 1 1 - M 1 0 * M 0 1 : by { simp, rin... |
a438625888d3152b796c4674a40ceb211ee6118b | a46270e2f76a375564f3b3e9c1bf7b635edc1f2c | /8.9.3.lean | e637dd4c73fe035cf633cf7d222a5f23ed42ed4a | [
"CC0-1.0"
] | permissive | wudcscheme/lean-exercise | 88ea2506714eac343de2a294d1132ee8ee6d3a20 | 5b23b9be3d361fff5e981d5be3a0a1175504b9f6 | refs/heads/master | 1,678,958,930,293 | 1,583,197,205,000 | 1,583,197,205,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,598 | lean | universe u
namespace hidden
inductive list (α : Type u)
| nil {} : list
| cons : α → list → list
namespace list
notation `[` l:(foldr `,` (h t, cons h t) nil) `]` := l
variable {α : Type}
notation h :: t := cons h t
def append: list α -> list α -> list α
| nil t := t
| (h::s) t := h::(append s t... |
9d53ba5619a8d1e77e3fd40a8cdb6e07f03de0d2 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/buffer/parser/numeral.lean | af91eeba878d24a59ac18abfef066e697695ee1c | [
"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 | 5,096 | lean | /-
Copyright (c) 2020 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
import data.buffer.parser.basic
/-!
# Numeral parsers
This file expands on the existing `nat : parser ℕ` to provide parsers into any type `α` that
can be represen... |
0d2ebbe664c999416d53fb1e6cd037aed39fe0c2 | e953c38599905267210b87fb5d82dcc3e52a4214 | /hott/hit/trunc.hlean | c877c1b70baaf3176f2c1bca980b890c3310e231 | [
"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 | 4,890 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
n-truncation of types.
Ported from Coq HoTT
-/
/- The hit n-truncation is primitive, declared in init.hit. -/
import types.sigma types.pointed
open is_trunc eq ... |
28530cd7cea3552ecb89c670b002835583449374 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/ring_theory/polynomial/bernstein.lean | 8d4f2331c648f802fca0f05130375224586ade61 | [
"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 | 15,852 | 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 data.polynomial.derivative
import data.nat.choose.sum
import ring_theory.polynomial.pochhammer
import data.polynomial.algebra_map
import linear_algebra.linear_... |
584656f5a552290abbaeb1c820355d4a4ece361b | dc06cc9775d64d571bf4778459ec6fde1f344116 | /src/algebraic_geometry/presheafed_space.lean | ea843f9da5690b76af3f98bf5387cf8cd0ff3ed0 | [
"Apache-2.0"
] | permissive | mgubi/mathlib | 8c1ea39035776ad52cf189a7af8cc0eee7dea373 | 7c09ed5eec8434176fbc493e0115555ccc4c8f99 | refs/heads/master | 1,642,222,572,514 | 1,563,782,424,000 | 1,563,782,424,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,907 | 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 topology.Top.presheaf
universes v u
open category_theory
open Top
open topological_space
open opposite
variables (C : Type u) [𝒞 : category.{v+1} C]
inc... |
0b3c75ec6350619dfc217d1e951bbfd89fc14d20 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/topology/continuous_function/units.lean | c88dc320c5ce34c94c5c642f939a41a79686a91f | [
"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 | 3,654 | lean | /-
Copyright (c) 2022 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import analysis.normed_space.units
import algebra.algebra.spectrum
import topology.continuous_function.algebra
/-!
# Units of continuous functions
This file concerns ... |
25a9eec62cfe9c46eb075f28f70eba7f4282976c | a7eef317ddec01b9fc6cfbb876fe7ac00f205ac7 | /test/noncomm_ring.lean | c8b49f0feabeeb835b541b598baa511ce56e3cd7 | [
"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 | 2,686 | lean | import tactic.noncomm_ring
local notation `⁅`a`,` b`⁆` := a * b - b * a
local infix ` ⚬ `:70 := λ a b, a * b + b * a
variables {R : Type*} [ring R]
variables (a b c : R)
example : (a + b) * c = a * c + b * c := by noncomm_ring
example : a * (b + c) = a * b + a * c := by noncomm_ring
example : a - b = a + -b := by no... |
0ca3c45013578c1372f4d2d06bf30c6ba4e29c17 | 618003631150032a5676f229d13a079ac875ff77 | /src/algebra/floor.lean | 4ce37e95d237a6480e51cd4745bf96daaf59940b | [
"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 | 9,809 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kevin Kappelmann
-/
import tactic.linarith
import tactic.abel
import algebra.ordered_group
/-!
# Floor and Ceil
## Summary
We define `floor`, `ceil`, and `nat_ceil` f... |
0e94c52058e1d6ae0585c60a95134ad31d10501f | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/linear_algebra/projective_space/independence.lean | f210d15c03dc1bd7144f0b044b1d99d8225ee9d2 | [
"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 | 4,646 | lean | /-
Copyright (c) 2022 Michael Blyth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Blyth
-/
import linear_algebra.projective_space.basic
/-!
# Independence in Projective Space
In this file we define independence and dependence of families of elements in pro... |
633569b2ce71071c22195407b2a37af9433c330a | 7617a8700fc3eebd9200f1e620ee65b3565d2eff | /src/c0/dyn.lean | fa998ac0117707376eb7b38d257c8e7cf831e4fa | [] | no_license | digama0/vc0 | 9747eee791c5c2f58eb53264ca6263ee53de0f87 | b8b192c8c139e0b5a25a7284b93ed53cdf7fd7a5 | refs/heads/master | 1,626,186,940,436 | 1,592,385,972,000 | 1,592,385,972,000 | 158,556,766 | 5 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 17,242 | lean | -- Dynamic semantics
import c0.ast_ok
namespace c0
@[derive decidable_eq]
inductive value
| int : int32 → value
| bool : bool → value
| nil : value
| cons : value → value → value
| ref : option ℕ → value
| arr : ℕ → value → value
| named : ident → value → value
inductive addr
| ref : nat → addr
| var : ident → addr
... |
14a4e92d4b2e7aa41358976a4e7d987b5fa1f6ab | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/topology/quasi_separated.lean | 93b8a30bdbfb95ca0054c2797bad2a715b69f361 | [
"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 | 5,169 | 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 topology.subset_properties
import topology.separation
import topology.noetherian_space
/-!
# Quasi-separated spaces
A topological space is quasi-separated if the i... |
c1796e03bbe32df49f997c3a29dc9b9391ff7e5a | 432d948a4d3d242fdfb44b81c9e1b1baacd58617 | /src/tactic/aesop/search.lean | 7e5d7bfbf2b9eb4de10fdf0cf784e02a64c86d77 | [
"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 | 12,706 | lean | /-
Copyright (c) 2021 Jannis Limperg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jannis Limperg
-/
import data.list.sort
import tactic.aesop.config
import tactic.aesop.percent
import tactic.aesop.priority_queue
import tactic.aesop.tracing
import tactic.aesop.tree
... |
594270a10d7fa3c987592a73b1a77a74f878d6a6 | 7a0854479980a89e813e3c93d127f09a8e2c3a7e | /src/group/definitions.lean | 0cac3ea31c912b737c1b031e15cab4c4d9744ed8 | [] | no_license | cfbolz/group-theory-game | 020e382df58bf9a510dce38304f27400e4ef0b80 | b5282ce72a2a22e9ba1b48cee432ff3d77496040 | refs/heads/master | 1,668,643,052,237 | 1,594,820,769,000 | 1,594,820,769,000 | 279,899,736 | 0 | 0 | null | 1,594,825,474,000 | 1,594,825,473,000 | null | UTF-8 | Lean | false | false | 1,440 | lean | import tactic
/-!
Basic definitions in group theory.
The beginner mathematician should be looking in the files called
`theorems.lean` rather than these ones; the definitions are
rather more intimidating.
Source:
https://xenaproject.wordpress.com/2018/04/30/group-theory-revision/
-/
set_option old_structure_cmd tru... |
821a6bf087bb09d4e9680051daf68b957b6fb420 | 82e44445c70db0f03e30d7be725775f122d72f3e | /archive/arithcc.lean | d195c1331a8b2bfcbf9959e532460c152eb82acd | [
"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 | 12,199 | lean | /-
Copyright (c) 2020 Xi Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xi Wang
-/
import tactic.basic
/-!
# A compiler for arithmetic expressions
A formalization of the correctness of a compiler from arithmetic expressions to machine language
described by McC... |
1b593f894bed3ae7e12e5d30fc98c066bd06fdc8 | 86f6f4f8d827a196a32bfc646234b73328aeb306 | /examples/basics/unnamed_1549.lean | 7114cf2e9546b31f5e829add34c1bdee9e7c4524 | [] | no_license | jamescheuk91/mathematics_in_lean | 09f1f87d2b0dce53464ff0cbe592c568ff59cf5e | 4452499264e2975bca2f42565c0925506ba5dda3 | refs/heads/master | 1,679,716,410,967 | 1,613,957,947,000 | 1,613,957,947,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 199 | lean | import data.real.basic
variables a b : ℝ
-- BEGIN
example : min a b = min b a :=
begin
apply le_antisymm,
repeat {
apply le_min,
apply min_le_right,
apply min_le_left }
end
-- END |
1946f16f89a324a3d5ec5c6cd2c367b81d00637c | d436468d80b739ba7e06843c4d0d2070e43448e5 | /src/category_theory/monad/adjunction.lean | 268a3cc00f4b5e07e139d367742ea0f31a3a67dc | [
"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 | 5,656 | 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.monad.algebra
import category_theory.adjunction.fully_faithful
namespace category_theory
open category
universes v₁ v₂ u₁ u₂ -- declare the `... |
6724f2ffde9e6afd4e7bdaa9d44325e3513cca0c | 853df553b1d6ca524e3f0a79aedd32dde5d27ec3 | /src/ring_theory/free_ring.lean | 6e2a5c5cb1cbfe10115b99690e59c3301c163fb3 | [
"Apache-2.0"
] | permissive | DanielFabian/mathlib | efc3a50b5dde303c59eeb6353ef4c35a345d7112 | f520d07eba0c852e96fe26da71d85bf6d40fcc2a | refs/heads/master | 1,668,739,922,971 | 1,595,201,756,000 | 1,595,201,756,000 | 279,469,476 | 0 | 0 | null | 1,594,696,604,000 | 1,594,696,604,000 | null | UTF-8 | Lean | false | false | 3,896 | lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Johan Commelin
-/
import data.polynomial
universes u v
def free_ring (α : Type u) : Type u :=
free_abelian_group $ free_monoid α
namespace free_ring
variables (α : Type u)
i... |
062703a62c434d649a3d11e4a6a66a36d5715821 | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/topology/algebra/group.lean | 7d35421148cef990a6fde9c09e533c1b51a0fd51 | [
"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 | 13,675 | 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
Theory of topological groups.
-/
import data.equiv.algebra
import group_theory.quotient_group
import topology.algebra.monoid topology.o... |
9cae331ea70adc61714d3b356b3911f3a251d6b7 | fb7979075f5bf70a1e85f8b368da00001593254b | /Test.lean | 906949e0b5fffba3da118405205eed3143940028 | [] | no_license | PeterKementzey/example-lean4-pkg-using-Graph | 9e0c18596200187d269b7db9efba5546e5f0b604 | 204e17c4cbfa86a2426e4f099065a2e8f7bc491d | refs/heads/master | 1,687,026,900,466 | 1,625,933,058,000 | 1,625,933,058,000 | 376,614,994 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 241 | lean | import Graph.Graph -- This will only import the Graph structure and basic functionality, you can use `import Graph` to import all default algorithms
def g : Graph Nat Nat := (Graph.empty.addVertex 0).1
def main : IO Unit :=
IO.println g
|
0ce67b372be4ff2bfdef1f36528730ae4cd85170 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/computability/turing_machine.lean | 41921f89a6afc834c05a62419039f5c12dc8a872 | [
"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 | 109,990 | 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 algebra.order
import data.fintype.basic
import data.pfun
import tactic.apply_fun
import logic.function.iterate
/-!
# Turing machines
This file defines a sequ... |
518c60c0853a29b7356d892c497fea7e3094f3d9 | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/data/pfun.lean | 64e5bb8d1f5225de420ed36e52ea9b25b4fed692 | [
"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 | 22,203 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro, Jeremy Avigad
-/
import data.set.basic data.equiv.basic data.rel logic.relator
/-- `roption α` is the type of "partial values" of type `α`. It
is similar to `option α... |
d2709077973cd68b60ea439403636f1a54bf144f | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/order/filter/prod.lean | c674f22486f75ee080bbb80862659e31167c97e8 | [
"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 | 20,818 | lean | /-
Copyright (c) 2022 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johanes Hölzl, Patrick Massot, Yury Kudryashov, Kevin Wilson, Heather Macbeth
-/
import order.filter.basic
/-!
# Product and coproduct filters
In this file we define `filter.prod f g... |
fdcd60de53e1cdd0d3ffc90199a0c584616fd255 | 42c01158c2730cc6ac3e058c1339c18cb90366e2 | /xenalib/polytac.lean | c5d4db54a478def5bead0fe9cfa821f42b7b6901 | [] | no_license | ChrisHughes24/xena | c80d94355d0c2ae8deddda9d01e6d31bc21c30ae | 337a0d7c9f0e255e08d6d0a383e303c080c6ec0c | refs/heads/master | 1,631,059,898,392 | 1,511,200,551,000 | 1,511,200,551,000 | 111,468,589 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,771 | lean | import tactic.norm_num
import analysis.real
open tactic
-- set_option trace.eqn_compiler.elim_match true
/-- If the target is ∀ x, X, return (x,X). Else fail. -/
meta def polytac : tactic unit :=
do t ← target, -- t now has type tactic expr
match expr.is_pi t with
| ff := tactic.fail "target is not a pi type in pol... |
9394855c3791ec7f03144b17b7e325110dd407aa | 5ca7b1b12d14c4742e29366312ba2c2ef8201b21 | /src/game/world4/level5.lean | 23616204dba83fc623ac90da780a86c5ccfe6f7c | [
"Apache-2.0"
] | permissive | MatthiasHu/natural_number_game | 2e464482ef3001863430b0336133b6697b275ba3 | 2d764f72669ae30861f6a1057fce0257f3e466c4 | refs/heads/master | 1,609,719,110,419 | 1,576,345,737,000 | 1,576,345,737,000 | 240,296,314 | 0 | 0 | Apache-2.0 | 1,581,608,357,000 | 1,581,608,356,000 | null | UTF-8 | Lean | false | false | 433 | lean | import game.world4.level4 -- hide
namespace mynat -- hide
/-
# Power World
## Level 5: `pow_add`
-/
/- Lemma
For all naturals $m$, $a$, $b$, we have $a^{m + n} = a ^ m a ^ n$.
-/
lemma pow_add (a m n : mynat) : a ^ (m + n) = a ^ m * a ^ n :=
begin [nat_num_game]
induction n with t ht,
rw [add_zero, pow_zero... |
bdcd0098b505a4c43b50c944b6c62316d517538a | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/pkg/prv/Prv/Foo.lean | 5a386ecd88a24c9f3b4373550fc0fa518621b97d | [
"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 | 145 | lean | structure Foo where
private val : Nat
name : String
#check { name := "leo", val := 15 : Foo }
#check { name := "leo", val := 15 : Foo }.val
|
84abba69fb57df3038044582b95a27cd2d5f5f31 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/category_theory/limits/shapes/equalizers.lean | 85859db0360d18bd449fcb831f517b8e5db55832 | [
"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 | 44,323 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Markus Himmel
-/
import category_theory.epi_mono
import category_theory.limits.has_limits
/-!
# Equalizers and coequalizers
This file defines (co)equalizers as specia... |
075be9a185bcf025dbf0521cb54284128d0af8ab | ca1ad81c8733787aba30f7a8d63f418508e12812 | /clfrags/src/hilbert/wr/or.lean | 45b12de5c8fee7af6232c3998fc2ce813d754c78 | [] | no_license | greati/hilbert-classical-fragments | 5cdbe07851e979c8a03c621a5efd4d24bbfa333a | 18a21ac6b2e890060eb4ae65752fc0245394d226 | refs/heads/master | 1,591,973,117,184 | 1,573,822,710,000 | 1,573,822,710,000 | 194,334,439 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 438 | lean | import core.connectives
namespace clfrags
namespace hilbert
namespace wr
namespace or
axiom d₁ : ∀ {a b : Prop}, a → or a b
axiom d₂ : ∀ {a : Prop}, or a a → a
axiom d₃ : ∀ {a b : Prop}, or a b → or b a
axiom d₄ : ∀ {a b c : Prop},... |
ece9056b836868d52f8954b17bca53e4abc2810a | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/analysis/normed_space/operator_norm.lean | 561b18f77f6695c0e631acf566a5bb67211402ef | [
"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 | 53,456 | lean | /-
Copyright (c) 2019 Jan-David Salchow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo
-/
import linear_algebra.finite_dimensional
import analysis.normed_space.linear_isometry
import analysis.normed_space.riesz_lemma
impor... |
95578bff67bdffb722c075d9edc4591170048754 | d436468d80b739ba7e06843c4d0d2070e43448e5 | /src/category_theory/category/default.lean | 8146076b0ded428cae5991d868516bf7b5f278e7 | [
"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 | 5,409 | 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, Johannes Hölzl, Reid Barton
Defines a category, as a typeclass parametrised by the type of objects.
Introduces notations
`X ⟶ Y` for the morphism spa... |
a31ff4f0ae61b7988a4c74b1428b522c6cbb38d9 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/tactic/congr.lean | b56676516052088cebb0b8cb62000829f9860481 | [
"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 | 8,637 | lean | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import tactic.lint
import tactic.ext
/-!
# Congruence and related tactics
This file contains the tactic `congr'`, which is an extension of `congr`, and various ... |
3d4e0e9b87a7f75744c50269d8d1a4deef6ecd5b | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /stage0/src/Init/Data/List/Basic.lean | 7f99cefe22ab1e2576da0841858b89165204807d | [
"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 | 11,639 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import Init.SimpLemmas
import Init.Data.Nat.Basic
open Decidable List
universe u v w
variable {α : Type u} {β : Type v} {γ : Type w}
namespace Lis... |
c9c63265ce89e0d04e2514d3dee4e061922e519d | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/algebra/gcd_monoid.lean | 1152cf97916e2beec26a6c5c822b055635ee4c6b | [
"Apache-2.0"
] | permissive | abentkamp/mathlib | d9a75d291ec09f4637b0f30cc3880ffb07549ee5 | 5360e476391508e092b5a1e5210bd0ed22dc0755 | refs/heads/master | 1,682,382,954,948 | 1,622,106,077,000 | 1,622,106,077,000 | 149,285,665 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 36,112 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker
TODO: Provide a GCD monoid instance for `ℕ`, port GCD facts about nats
TODO: Generalize normalization monoids commutative (cancellative) monoids with or... |
02d3bd574b6fe1d8bd6ab74a87c7e8c2f8fb961e | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/1373.lean | d277b5024c800725a7cf3be746dff91874d5a400 | [
"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 | 125 | lean | class Foo (d: Nat)
set_option checkBinderAnnotations false
inductive Bar [i: ∀ d', d ≤ d' → Foo d']
| mk: Bar (i:=i)
|
5bcaed3a029f511de6d6b8c09032b5115183da5c | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /tests/lean/hott/apply_class_issue.hlean | e36d28a2e3e493b1f4dbfd7776c711ce4bc7171e | [
"Apache-2.0"
] | permissive | tjiaqi/lean | 4634d729795c164664d10d093f3545287c76628f | d0ce4cf62f4246b0600c07e074d86e51f2195e30 | refs/heads/master | 1,622,323,796,480 | 1,422,643,069,000 | 1,422,643,069,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 307 | hlean | open truncation
context
parameters {P : Π(A : Type), A → Type}
definition my_contr {A : Type} [H : is_contr A] (a : A) : P A a := sorry
definition foo2
(A : Type)
(B : A → Type)
(a : A)
(x : B a)
(H : Π (a : A), is_contr (B a)) --(H : is_contr (B a))
: P (B a) x :=
by apply (@my_contr _ _)
end
|
96d8e511ab204adad37b5eb94bb233d010f7a518 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/category_theory/natural_isomorphism.lean | b0aa03fd8d6d89545d87a59234e677df9229668e | [
"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 | 7,493 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tim Baumann, Stephen Morgan, Scott Morrison, Floris van Doorn
-/
import category_theory.functor_category
import category_theory.isomorphism
/-!
# Natural isomorphisms
For the most pa... |
13a1743078a0a04cd0bbcdae13b68b48d07ba29c | e151e9053bfd6d71740066474fc500a087837323 | /src/hott/init/meta/simp_attr.lean | 52f0ee380d8860003b925d4a2922fec9d95e5ab4 | [
"Apache-2.0"
] | permissive | daniel-carranza/hott3 | 15bac2d90589dbb952ef15e74b2837722491963d | 913811e8a1371d3a5751d7d32ff9dec8aa6815d9 | refs/heads/master | 1,610,091,349,670 | 1,596,222,336,000 | 1,596,222,336,000 | 241,957,822 | 0 | 0 | Apache-2.0 | 1,582,222,839,000 | 1,582,222,838,000 | null | UTF-8 | Lean | false | false | 1,680 | lean | /-
Copyright (c) 2017 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner
-/
import .support
open tactic expr
namespace hott
private meta def open_pis : expr → tactic (expr × list expr) | e := do
e ← whnf e,
if e.is_pi then do
x ← mk_local... |
870fc037e8cc284652b3d6f65f70d7ab09bd8c5b | 7282d49021d38dacd06c4ce45a48d09627687fe0 | /tests/lean/simp19.lean | 24780bef37f0726e62bfa6d4e91b7d8eaa81c106 | [
"Apache-2.0"
] | permissive | steveluc/lean | 5a0b4431acefaf77f15b25bbb49294c2449923ad | 92ba4e8b2d040a799eda7deb8d2a7cdd3e69c496 | refs/heads/master | 1,611,332,256,930 | 1,391,013,244,000 | 1,391,013,244,000 | 16,361,079 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 878 | lean | import cast
variable vec : Nat → Type
variable concat {n m : Nat} (v : vec n) (w : vec m) : vec (n + m)
infixl 65 ; : concat
axiom concat_assoc {n1 n2 n3 : Nat} (v1 : vec n1) (v2 : vec n2) (v3 : vec n3) :
(v1 ; v2) ; v3 = cast (congr2 vec (symm (Nat::add_assoc n1 n2 n3)))
... |
40b4f87471b0219eb2e95c7fedbb0828a32ac330 | 92b1c7f0343a6a5cd36bc0f623a7490da3f1e0f3 | /src/stump/setup_definition.lean | 72694b4744b1998fe3ab407aaa370f9812d51fc5 | [
"Apache-2.0"
] | permissive | jtristan/stump-learnable | 717453eb590af16e60c7d3806cc9e66492fab091 | aa3c089f41602efa08d31ef6b41e549456186d57 | refs/heads/master | 1,625,630,634,360 | 1,607,552,106,000 | 1,607,552,106,000 | 218,629,406 | 15 | 2 | null | null | null | null | UTF-8 | Lean | false | false | 951 | lean | /-
Copyright © 2019, Oracle and/or its affiliates. All rights reserved.
-/
import measure_theory.measurable_space
import measure_theory.borel_space
import topology.instances.nnreal
import ..lib.basic
import ..lib.util
namespace stump
notation `ℍ` := nnreal
noncomputable
instance meas_ℍ: measurable_space ℍ :=
begin
... |
c0c914db83debe4d76b557e940407d588d8e0f90 | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/data/list/alist.lean | ce1b028b510b8d2606bc233780387220f31bd1dc | [
"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 | 10,660 | lean | /-
Copyright (c) 2018 Sean Leather. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sean Leather, Mario Carneiro
Association lists.
-/
import data.list.sigma
universes u v w
open list
variables {α : Type u} {β : α → Type v}
/-- `alist β` is a key-value map stored as ... |
500e5a755e51093f76ce4ba7e988b8641f5278cf | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/polynomial/field_division.lean | 80a36e70aad3d3e189f0221fe9632c1a6d8e241a | [
"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 | 18,894 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
-/
import data.polynomial.ring_division
import data.polynomial.derivative
import algebra.gcd_monoid
/-!
# Theory of univaria... |
4e35a6d27a7afd9e6248cd99ee932465ca15f4dc | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /stage0/src/Lean/Data.lean | 61f35a40feb2a3fd26291f12096d0722e31f66ef | [
"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 | 549 | lean | /-
Copyright (c) 2020 Sebastian Ullrich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
-/
import Lean.Data.Format
import Lean.Data.Json
import Lean.Data.JsonRpc
import Lean.Data.KVMap
import Lean.Data.LBool
import Lean.Data.LOption
import Lean.Data.L... |
ecf284fc4c9b7c490a40ec4082b83563940dcb01 | dfbb669f3f58ceb57cb207dcfab5726a07425b03 | /vscode-lean4/test/test-fixtures/orphan/factorial.lean | 3349b5ab5a278eb69a8b41039bb75d3e583535ee | [
"Apache-2.0"
] | permissive | leanprover/vscode-lean4 | 8bcf7f06867b3c1d42007fe6da863a7a17444dbb | 6ef0bfa668bdeaad0979e6df10551d42fcc01094 | refs/heads/master | 1,692,247,771,767 | 1,691,608,804,000 | 1,691,608,804,000 | 325,845,305 | 64 | 24 | Apache-2.0 | 1,694,176,429,000 | 1,609,435,614,000 | TypeScript | UTF-8 | Lean | false | false | 388 | lean |
/-- Return the the product of all positive integers less than or equal to the
input value -/
def factorial x :=
match x with
| 0 => 1
| n + 1 => (n + 1) * factorial n
/-- Return the sum of all the numbers in the given list. -/
def sum (x : List Nat) : Nat :=
match x with
| [] => 0
| a :: as => a + sum (... |
776c1f37550a56137f17695729fb8ac61cecc6b3 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/analysis/normed_space/is_R_or_C.lean | d0d42de322ac4bb7cd73be99356af75166498694 | [
"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 | 4,118 | lean | /-
Copyright (c) 2021 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä
-/
import data.complex.is_R_or_C
import analysis.normed_space.operator_norm
import analysis.normed_space.pointwise
/-!
# Normed spaces over R or C
This file is about resul... |
d92ed142d145ba691932654530af34ae1399dfde | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/setoid/partition.lean | 4bfc285e753560dd267ce07fa4e1aa8e8fd2f6e9 | [
"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 | 9,159 | lean | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston, Bryan Gin-ge Chen
-/
import data.setoid.basic
import data.set.lattice
/-!
# Equivalence relations: partitions
This file comprises properties of equivalence rel... |
df5ecbfa7016a7df1387adcea36d6092e770abc1 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /library/data/complex.lean | 74e2ad8287ecaa903e59c6aadfe6c6f493d471f5 | [
"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 | 12,369 | lean | /-
Copyright (c) 2015 Jacob Gross. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jacob Gross, Jeremy Avigad
The complex numbers.
-/
import data.real
open real eq.ops
record complex : Type :=
(re : ℝ) (im : ℝ)
notation `ℂ` := complex
namespace complex
variables (u... |
b82c0bf0208c3b651a2c2bccc5d99d18e3cedbf1 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/set_theory/cardinal.lean | 207aeaf4057d0db303b2e4b13f23e4e2fd1a119b | [
"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 | 52,267 | 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 data.set.countable
import set_theory.schroeder_bernstein
import data.fintype.card
import data.nat.enat
/-!
# Cardinal Number... |
1db5bf2d0e11f8472ec885c95cd3e4c12fd2a5c3 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/1650.lean | d43fe301752d52775f3135b7db4e56e4b1e98e29 | [
"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 | 459 | lean | def A : inhabited true → Type | ⟨t⟩ := inhabited (t = t)
def B (T : Type) (t : T) : Prop := t = t
def C {T x} : B T x := rfl
structure X :=
( x : inhabited true )
( y : A x )
( z : B _ y )
def test : X := {
x := ⟨let t := trivial in t⟩,
y := sorry,
z := C
}
constant T : nat → Type
open tactic
exam... |
ebf74c7e4c2b56f784f9f3a36259bb7f7bd49e8d | 26b8b0964ca8e1c2e203585ba5940f83fe05e48a | /src/tidy/auto_cast.lean | 8ed5207c04a7cabcd8f1a4f1520b9a3412ef5c7a | [] | no_license | jcommelin/lean-tidy | ef3cd32a3804221d93f0dff9e180bb2c52f4b143 | 9cecf497e90db64b5ea140ad6ae1603976dcd402 | refs/heads/master | 1,585,129,919,276 | 1,533,512,680,000 | 1,533,512,680,000 | 143,677,361 | 0 | 0 | null | 1,616,803,481,000 | 1,533,530,576,000 | Lean | UTF-8 | Lean | false | false | 456 | lean | -- Copyright (c) 2017 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Scott Morrison
import .tidy
open tactic
@[reducible] def {u} auto_cast {α β : Sort u} {h : α = β} (a : α) := cast h a
@[simp] lemma {u} auto_cast_identity {α : Sort u} (a : α)... |
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