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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
107222dc7142ce8fd28084af49a0c70030a959cd | 0845ae2ca02071debcfd4ac24be871236c01784f | /library/init/data/array/basic.lean | b976784c51fd00efb810503a99aee7b851b69326 | [
"Apache-2.0"
] | permissive | GaloisInc/lean4 | 74c267eb0e900bfaa23df8de86039483ecbd60b7 | 228ddd5fdcd98dd4e9c009f425284e86917938aa | refs/heads/master | 1,643,131,356,301 | 1,562,715,572,000 | 1,562,715,572,000 | 192,390,898 | 0 | 0 | null | 1,560,792,750,000 | 1,560,792,749,000 | null | UTF-8 | Lean | false | false | 14,042 | lean | /-
Copyright (c) 2018 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.data.nat.basic init.data.fin.basic init.data.uint
import init.data.repr init.data.tostring init.control.id
import init.util
universes u ... |
a773d8c2992a76ed5fb982c1474615f93c06301f | bd57135d92f6f3b771aae7ca08550ff8719ec590 | /src/principal_ideal_domain.lean | 12ecaec428021438dce9b69039f2cc8623e80f30 | [] | no_license | simonjwinwood/kbb | 109775572d17fceb93ee2419905bbecff776ebd2 | b5ff345e1022aee40dfda406c1c0631a9bba9c03 | refs/heads/master | 1,585,550,843,265 | 1,537,509,365,000 | 1,537,509,365,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,338 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
More stuff for Principal Ideal Domains and Unique Factorization Domains
- PIDs are Noetherian
- PIDs are UFDs
-/
import
ring_theory.principal_ideal_domain
ring_the... |
c4a702ae85dd56c9ca749cf03c4564a7b84ed12f | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/analysis/inner_product_space/dual.lean | 428dcaba144cfdcf202ec9f54220d589ef1e6696 | [
"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 | 6,469 | lean | /-
Copyright (c) 2020 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import analysis.inner_product_space.projection
import analysis.normed_space.dual
/-!
# The Fréchet-Riesz representation theorem
We consider inner product spaces, ... |
e17fdac55c5323b5b17b9f3500899789adfce8b5 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/analysis/convex/extrema.lean | 340be610d6774c6da1e703a1342cec0b5e82e1a0 | [
"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 | 4,216 | lean | /-
Copyright (c) 2020 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import analysis.convex.function
import topology.algebra.affine
import topology.local_extr
import topology.metric_space.basic
/-!
# Minima and maxima of convex func... |
ce4c29abd081bd00529de3100f7b41b6c3b67b63 | e9078bde91465351e1b354b353c9f9d8b8a9c8c2 | /short_prop_trunc.hlean | b8a64f38824e772ce91c2193286c1c2c0da727bb | [
"Apache-2.0"
] | permissive | EgbertRijke/leansnippets | 09fb7a9813477471532fbdd50c99be8d8fe3e6c4 | 1d9a7059784c92c0281fcc7ce66ac7b3619c8661 | refs/heads/master | 1,610,743,957,626 | 1,442,532,603,000 | 1,442,532,603,000 | 41,563,379 | 0 | 0 | null | 1,440,787,514,000 | 1,440,787,514,000 | null | UTF-8 | Lean | false | false | 5,849 | hlean | import types.eq types.pi hit.colimit types.nat.hott hit.trunc cubical.square hprop_trunc
open eq is_trunc unit quotient seq_colim pi nat equiv sum
/-
Trying a different construction of the propositional truncation
Original proof length of "is_hprop truncX": 163 lines
Proof length here: 76 lines
-/
/- HELPER L... |
89b1186b226c80b938d28ab14718d594f916613e | 8b9f17008684d796c8022dab552e42f0cb6fb347 | /tests/lean/hott/rw_eta.hlean | 152b85fb5375915e58840d659f90e8da5dbd731d | [
"Apache-2.0"
] | permissive | chubbymaggie/lean | 0d06ae25f9dd396306fb02190e89422ea94afd7b | d2c7b5c31928c98f545b16420d37842c43b4ae9a | refs/heads/master | 1,611,313,622,901 | 1,430,266,839,000 | 1,430,267,083,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 815 | hlean | open eq is_equiv funext
constant f : nat → nat → nat
example : (λ x y : nat, f x y) = f :=
rfl
namespace hide
variables {A : Type} {B : A → Type} {C : Πa, B a → Type}
definition homotopy2 [reducible] (f g : Πa b, C a b) : Type :=
Πa b, f a b = g a b
notation f `∼2`:50 g := homotopy2 f g
definition eq_of_homotopy2... |
8eb6db73ad6692c0a018dd9d6dd111cdd80acec9 | 2fbe653e4bc441efde5e5d250566e65538709888 | /src/topology/algebra/ordered.lean | c21566074fc4ca5a59fa0fa80f43c5e6e764d3ee | [
"Apache-2.0"
] | permissive | aceg00/mathlib | 5e15e79a8af87ff7eb8c17e2629c442ef24e746b | 8786ea6d6d46d6969ac9a869eb818bf100802882 | refs/heads/master | 1,649,202,698,930 | 1,580,924,783,000 | 1,580,924,783,000 | 149,197,272 | 0 | 0 | Apache-2.0 | 1,537,224,208,000 | 1,537,224,207,000 | null | UTF-8 | Lean | false | false | 75,828 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
-/
import tactic.tfae
import order.liminf_limsup
import data.set.intervals
import topology.algebra.group
import topology.constructions
... |
bf03a38b64632fd04db169a9045747d62f32d615 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/exact_tac1.lean | 5b061055ffd2816ce74843d0966f3a679e55398f | [
"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 | 321 | lean | open tactic list
example (a b : nat) : a = a :=
by do
a ← get_local `a,
r ← mk_app `eq.refl [a],
exact r
set_option pp.all true
example (a b : nat) (f : nat → nat) : a = b → f a = f b :=
by do
intro `H,
H ← get_local `H,
f ← get_local `f,
r ← mk_app `congr_arg [f, H],
trace r,
exact r
|
fdb2b287df0d11c3984b3aef4bfcbdd2c65e611b | 432d948a4d3d242fdfb44b81c9e1b1baacd58617 | /src/topology/continuous_function/basic.lean | 3813dca32cb83152b5835284455d8ec0e9e982b4 | [
"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 | 7,513 | lean | /-
Copyright © 2020 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri
-/
import topology.subset_properties
import topology.tactic
import topology.algebra.ordered
/-!
# Continuous bundled map
In this file we define the type `continuous... |
dcc90d4eb655adbcd872fc9198b87ebc6653bf58 | 649957717d58c43b5d8d200da34bf374293fe739 | /src/topology/algebra/uniform_ring.lean | 4d187a161744c344b3845fbf17c2638fbb178113 | [
"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 | 7,538 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
Theory of topological rings with uniform structure.
-/
import topology.algebra.group_completion topology.algebra.ring
open classical set lattice filte... |
4cb4f88ec00f87c8d98297f863fc60e461f60606 | c8af905dcd8475f414868d303b2eb0e9d3eb32f9 | /src/data/cpi/concretion/default.lean | 0640f3a75966c052ea3a0cdfdc32d2517ed2fb4f | [
"BSD-3-Clause"
] | permissive | continuouspi/lean-cpi | 81480a13842d67ff5f3698643210d8ed5dd08de4 | 443bf2cb236feadc45a01387099c236ab2b78237 | refs/heads/master | 1,650,307,316,582 | 1,587,033,364,000 | 1,587,033,364,000 | 207,499,661 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 40 | lean | import data.cpi.concretion.pseudo_apply
|
4950cff934e862521a582f074e300c39e1fcea72 | 07c76fbd96ea1786cc6392fa834be62643cea420 | /library/init/datatypes.lean | 010fb258ca3b802d61c521691616d03ef3dd4fca | [
"Apache-2.0"
] | permissive | fpvandoorn/lean2 | 5a430a153b570bf70dc8526d06f18fc000a60ad9 | 0889cf65b7b3cebfb8831b8731d89c2453dd1e9f | refs/heads/master | 1,592,036,508,364 | 1,545,093,958,000 | 1,545,093,958,000 | 75,436,854 | 0 | 0 | null | 1,480,718,780,000 | 1,480,718,780,000 | null | UTF-8 | Lean | false | false | 3,152 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
Basic datatypes
-/
prelude
notation `Prop` := Type.{0}
notation [parsing_only] `Type'` := Type.{_+1}
notation [parsing_only] `Type₊` := Type.{_+1}
notation `... |
ff86b46a596194eded7c9495f68c7fedaf099001 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/geometry/manifold/real_instances.lean | 1e6bb31e4910b648ce9f10df50cd972d6c05430b | [
"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 | 15,989 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import geometry.manifold.smooth_manifold_with_corners
import linear_algebra.finite_dimensional
import analysis.normed_space.real_inner_product
/-!
# Constructi... |
ed63f93eec03eff0921bda4c2ea99e783e8d2c3b | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /tests/lean/run/e1.lean | 889a2d8d1e3901cd10be5e562008704634e27198 | [
"Apache-2.0"
] | permissive | codyroux/lean | 7f8dff750722c5382bdd0a9a9275dc4bb2c58dd3 | 0cca265db19f7296531e339192e9b9bae4a31f8b | refs/heads/master | 1,610,909,964,159 | 1,407,084,399,000 | 1,416,857,075,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 320 | lean | definition Prop : Type.{1} := Type.{0}
constant eq : forall {A : Type}, A → A → Prop
constant N : Type.{1}
constants a b c : N
infix `=`:50 := eq
check a = b
constant f : Prop → N → N
constant g : N → N → N
precedence `+`:50
infixl + := f
infixl + := g
check a + b + c
constant p : Prop
check p + a + b + c
|
01e6c048d0c3c28732d469b58e0ea9d44eb35be5 | bdd56e6eb0f467437e368d613de75299495d4054 | /src/category_theory/group_object.lean | a04c8b55923eff52b287db3d328990b086eb8827 | [] | no_license | truong111000/formalabstracts | 49a04c268ccee136e48e24e9d5dcb6fedea4b53e | 93a89a5c05c6fbc23eb9b914b60dcc353e609cd2 | refs/heads/master | 1,589,551,767,824 | 1,555,708,723,000 | 1,555,708,723,000 | 182,326,292 | 0 | 0 | null | 1,555,708,332,000 | 1,555,708,331,000 | null | UTF-8 | Lean | false | false | 980 | lean | -- Copyright (c) 2019 Jesse Han. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Jesse Han
import .finite_limits
open category_theory category_theory.limits category_theory.limits.binary_product
category_theory.limits.finite_limits
universes u v
local inf... |
8ab0b8f71048d944599d11b3ef028b0039c11e00 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/data/bool.lean | 8a3bd60b01424d19ed9c12876c47e13c66ce115b | [
"Apache-2.0"
] | permissive | gebner/mathlib | eab0150cc4f79ec45d2016a8c21750244a2e7ff0 | cc6a6edc397c55118df62831e23bfbd6e6c6b4ab | refs/heads/master | 1,625,574,853,976 | 1,586,712,827,000 | 1,586,712,827,000 | 99,101,412 | 1 | 0 | Apache-2.0 | 1,586,716,389,000 | 1,501,667,958,000 | Lean | UTF-8 | Lean | false | false | 4,644 | 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, Jeremy Avigad
-/
prefix `!`:90 := bnot
namespace bool
@[simp] theorem coe_sort_tt : coe_sort.{1 1} tt = true := eq_true_intro rfl
@[simp] theorem coe_sort_... |
c454bfe15aa2af44d09749aed6798a0c9328d66f | b561a44b48979a98df50ade0789a21c79ee31288 | /src/Init/Core.lean | 4f70638f02245b48fca57d85ad15eddc02d37a1f | [
"Apache-2.0"
] | permissive | 3401ijk/lean4 | 97659c475ebd33a034fed515cb83a85f75ccfb06 | a5b1b8de4f4b038ff752b9e607b721f15a9a4351 | refs/heads/master | 1,693,933,007,651 | 1,636,424,845,000 | 1,636,424,845,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 36,029 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
notation, basic datatypes and type classes
-/
prelude
import Init.Prelude
import Init.SizeOf
universe u v w
def inline {α : Sort u} (a : α) : α := a
@[inli... |
31a026abac16cf77fa30d34a058b565c75f3a8a7 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /library/data/default.lean | 74699fae3a577d61bd7a98ff37f6df95d5c1b22a | [
"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 | 309 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
-/
import .empty .unit .bool .num .string .nat .int .rat .fintype
import .prod .sum .sigma .option .list .finset .set .stream
import .fin .real .complex
|
3583f7d5b91d93f89910fa872df06975cd6c54d6 | 6b2a480f27775cba4f3ae191b1c1387a29de586e | /group_rep_2/Tools/bilinear_over_comm_ring.lean | 1c234fef27bfe510e6337298cced954e33f919c2 | [] | no_license | Or7ando/group_representation | a681de2e19d1930a1e1be573d6735a2f0b8356cb | 9b576984f17764ebf26c8caa2a542d248f1b50d2 | refs/heads/master | 1,662,413,107,324 | 1,590,302,389,000 | 1,590,302,389,000 | 258,130,829 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 3,385 | lean | import data.fintype.basic
import data.set.function
import .sum_tools
import data.equiv.basic
import linear_algebra.bilinear_form
universe variables u v w
open finset
open_locale big_operators
/--
# Je n'aime pas du tout l'utilisation du produit scalaire car je prefere avoir une notion spécifique
-/
variables {G :Ty... |
e40a24f9e3737f94db814c028717d24e0fdf7914 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/ring_theory/ideal/basic.lean | 31cc795eb9cf91e8a85f4b2a7cbfb03ec40cdb4b | [
"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 | 23,400 | 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.associated
import linear_algebra.basic
import order.zorn
import order.atoms
import order.compactly_generated
import tactic.abel
imp... |
a2c674ff7db80e14422e11294e2518f890948dfc | 9dd3f3912f7321eb58ee9aa8f21778ad6221f87c | /tests/lean/run/induction_on_aux_rec_bug.lean | 9aae543dc5ee4464b5a76c5959c709b4982b167b | [
"Apache-2.0"
] | permissive | bre7k30/lean | de893411bcfa7b3c5572e61b9e1c52951b310aa4 | 5a924699d076dab1bd5af23a8f910b433e598d7a | refs/heads/master | 1,610,900,145,817 | 1,488,006,845,000 | 1,488,006,845,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 814 | lean | namespace test
universe variables u v
variables {α : Type u} {β : Type v}
inductive Perm : list α → list α → Prop
| nil : Perm [] []
| skip : Π (x : α) {l₁ l₂ : list α}, Perm l₁ l₂ → Perm (x::l₁) (x::l₂)
| swap : Π (x y : α) (l : list α), Perm (y::x::l) (x::y::l)
| trans : Π {l₁ l₂ l₃ : list α}, Perm l₁ l₂ → Perm ... |
9967b530fb00eeb9a034b8746558c9a821abf73b | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/hott/892.hlean | 706f99890155582025e8de31b9e4dfa1403af4ed | [
"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 | 305 | hlean | open is_trunc unit
protected definition trunc.elim {n : trunc_index} {A : Type} {P : Type}
[Pt : is_trunc n P] (H : A → P) : trunc n A → P :=
trunc.rec H
attribute trunc.rec [recursor 6]
attribute trunc.elim [recursor 6]
example (x : trunc -1 unit) : unit :=
begin
induction x, exact star
end
|
dd6de6f801e742a71521580ca0d837b34156de74 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/group_theory/coset.lean | d819565908fa677ac729021479fa21f07b98f7cf | [
"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 | 11,239 | lean | /-
Copyright (c) 2018 Mitchell Rowett. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Rowett, Scott Morrison
-/
import group_theory.subgroup
open set function
variable {α : Type*}
/-- The left coset `a*s` corresponding to an element `a : α` and a subset `s ... |
9a61ffb42665ce14c6c22e02404d47ad3ed85e09 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/measure_theory/function/l2_space.lean | ff3d49ae545a3ced41e28850f857ecbce440dc42 | [
"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 | 10,210 | 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.inner_product_space.basic
import measure_theory.integral.set_integral
/-! # `L^2` space
If `E` is an inner product space over `𝕜` (`ℝ` or `ℂ`), then `L... |
7963279a0bef6b8b4874b9fc14b67616d5bd08e9 | 592ee40978ac7604005a4e0d35bbc4b467389241 | /Library/generated/mathscheme-lean/AddCommMonWithMultSemigroup.lean | 9380eeab85680eeab60fd69d446f90f5ef3e2950 | [] | no_license | ysharoda/Deriving-Definitions | 3e149e6641fae440badd35ac110a0bd705a49ad2 | dfecb27572022de3d4aa702cae8db19957523a59 | refs/heads/master | 1,679,127,857,700 | 1,615,939,007,000 | 1,615,939,007,000 | 229,785,731 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,951 | lean | import init.data.nat.basic
import init.data.fin.basic
import data.vector
import .Prelude
open Staged
open nat
open fin
open vector
section AddCommMonWithMultSemigroup
structure AddCommMonWithMultSemigroup (A : Type) : Type :=
(times : (A → (A → A)))
(zero : A)
(plus : (A → (A → A)))
(... |
b802ec5db1e3cc0a342c48052e60513982bea3ef | ce6917c5bacabee346655160b74a307b4a5ab620 | /src/ch5/ex0717.lean | b4eea6224b37e626c1c7d6c2f13c39381320656d | [] | 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 | 510 | lean | import data.list.basic
open list
universe u
variables {α : Type} (x y z : α) (xs ys zs : list α)
def mk_symm (xs : list α) := xs ++ reverse xs
@[simp] theorem reverse_mk_symm (xs : list α) :
reverse (mk_symm xs) = mk_symm xs :=
by simp [mk_symm]
example (xs ys : list ℕ) :
reverse (xs ++ mk_symm ys) = mk_symm y... |
a3379e3a32e316c3dde05dddc8593eac189fa85b | 1a2aed113dcb5f1c07ae98040953fba5e6563624 | /lean_root/src/math_challenges.lean | de906817765fdfb912499141c8ec7b83dae19d24 | [
"Apache-2.0"
] | permissive | kevindoran/lean | 61d9fb90363b04587624036136482b29e3c16ebd | 77e755095a31e3a214010eb48a61e48d65dfdec9 | refs/heads/master | 1,670,372,072,769 | 1,598,920,365,000 | 1,598,920,365,000 | 264,824,992 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,098 | lean | import data.real.basic
import tactic
set_option pp.implicit true
-- Make simp display the steps used.
set_option trace.simplify.rewrite true
-- # 1
namespace problem1
-- let X, Y, Z be sets.
variables {X Y Z : Type}
-- a function f : X → Y is *injective* if f(a) = f(b) → a = b for all a,b in X.
def injective (f :... |
e18f5e19fbaf53c63a4e69138ea394317ac4816d | dc06cc9775d64d571bf4778459ec6fde1f344116 | /src/analysis/calculus/mean_value.lean | 576fe6614b52feb0f6908525f752348362ce10f4 | [
"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 | 7,660 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
The mean value inequality: a bound on the derivative of a function implies that this function
is Lipschitz continuous for the same bound.
-/
import analysis.calcu... |
e2ddc2d81c418d5c10b1e9bb9f4ef50320309801 | 626e312b5c1cb2d88fca108f5933076012633192 | /src/data/matrix/basic.lean | 077cf1c05d1cbcd39ce3ecc5038b8bb093108044 | [
"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 | 59,384 | lean | /-
Copyright (c) 2018 Ellen Arlt. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ellen Arlt, Blair Shi, Sean Leather, Mario Carneiro, Johan Commelin, Lu-Ming Zhang
-/
import algebra.big_operators.pi
import algebra.module.pi
import algebra.module.linear_map
import algeb... |
301be4e8cf077a671d8274a6914e88193d11ec23 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/dfinsupp.lean | 9d674452a03d206ed2adccebc8431b20fc781b09 | [] | 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 | 43,892 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.module.pi
import Mathlib.algebra.big_operators.basic
import Mathlib.data.set.... |
b1ead6bc50d9dd66f4b017904ba3125897d4e346 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /library/init/util.lean | 4e48c61c8bf9e8e828148a823407fec3f94ed266 | [
"Apache-2.0"
] | permissive | GaloisInc/lean | aa1e64d604051e602fcf4610061314b9a37ab8cd | f1ec117a24459b59c6ff9e56a1d09d9e9e60a6c0 | refs/heads/master | 1,592,202,909,807 | 1,504,624,387,000 | 1,504,624,387,000 | 75,319,626 | 2 | 1 | Apache-2.0 | 1,539,290,164,000 | 1,480,616,104,000 | C++ | UTF-8 | Lean | false | false | 1,626 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.meta.format
universes u
/-- This function has a native implementation that tracks time. -/
def timeit {α : Type u} (s : string) (f : th... |
8135376dc7506b66874cb8b864b2ea37ee4a249d | e39f04f6ff425fe3b3f5e26a8998b817d1dba80f | /category_theory/category.lean | a7766a76f5f4b8eb36fb7c41b3ff190d707e25a1 | [
"Apache-2.0"
] | permissive | kristychoi/mathlib | c504b5e8f84e272ea1d8966693c42de7523bf0ec | 257fd84fe98927ff4a5ffe044f68c4e9d235cc75 | refs/heads/master | 1,586,520,722,896 | 1,544,030,145,000 | 1,544,031,933,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,261 | 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... |
0dafa43c904cf4218c4c2e16835b27fe1cd7e56e | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/data/rbtree/main_auto.lean | 60f97e4afbbe0de4bf99e5ebe3ef3a4d751e8674 | [] | 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 | 9,780 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.Lean3Lib.data.rbtree.find
import Mathlib.Lean3Lib.data.rbtree.insert
import Mathl... |
9a72e11dccca233476dfc091dfeac31dbb642d99 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/set_theory/game/impartial.lean | 71eb179387037495ab75d142c6fdcd4e10b97d04 | [] | 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 | 4,132 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.set_theory.game.winner
import Mathlib.tactic.nth_rewrite.default
import Mathlib.tactic.equiv_rw
i... |
315500cf8fefcab3cb8d2f9b7d42d0ad8f159f39 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/algebra/char_p.lean | 37a683be3da4c0abcb955f79b0a2ec2c79805deb | [
"Apache-2.0"
] | permissive | dupuisf/mathlib | 62de4ec6544bf3b79086afd27b6529acfaf2c1bb | 8582b06b0a5d06c33ee07d0bdf7c646cae22cf36 | refs/heads/master | 1,669,494,854,016 | 1,595,692,409,000 | 1,595,692,409,000 | 272,046,630 | 0 | 0 | Apache-2.0 | 1,592,066,143,000 | 1,592,066,142,000 | null | UTF-8 | Lean | false | false | 10,854 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Kenny Lau, Joey van Langen, Casper Putz
-/
import data.fintype.basic
import data.nat.choose
import data.int.modeq
import algebra.module.basic
import algebra.iterate_hom
/-!
# Characteristi... |
84cba6bf600d50248dde31a22c26a612ab094822 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/algebra/free.lean | e09bbb40f2b71697399d77ad366d057b8f477e9f | [
"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 | 23,133 | 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 data.equiv.basic
import control.applicative
import control.traversable.basic
import algebra.group.hom
/-!
# Free constructions
## Main definitions
* `free_magma α`: f... |
9c1ad4eb7ffe2ef67989a51dd7a9c7c033439350 | f4bff2062c030df03d65e8b69c88f79b63a359d8 | /src/game/sup_inf/lub_prodSets.lean | 38e06ea562afe7542c42bae8d8621dc3fc324b4e | [
"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 | 1,189 | lean | import ..sup_inf.supProdConst
import ..sets.sets_level09
namespace xena -- hide
/-
# Chapter 3 : Sup and Inf
## Level 9
An intermediary result to be used in the next level.
-/
-- main result in lemma sup_mem_prod_of_sets
-- begin hide
--def mem_prod_sets (A : set ℝ) (B : set ℝ) := { x : ℝ | ∃ y ∈ A, ∃ z ∈ B, x = y... |
45a448313815f94f2c2c5c4c9293e8ab3eaec552 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/polynomial/eval.lean | c583a720f61b64eb65752f5e41ef2af9ed9fbf8e | [
"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 | 34,933 | 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.degree.definitions
import data.polynomial.induction
/-!
# Theory of univariate polynomials
> THIS... |
d2dfa5115a79ef05d869eb8403653cbd381f5a01 | e9dbaaae490bc072444e3021634bf73664003760 | /src/Arith/Field.lean | d512651d4701bb410344bfe9082d74a11f9670a0 | [
"Apache-2.0"
] | permissive | liaofei1128/geometry | 566d8bfe095ce0c0113d36df90635306c60e975b | 3dd128e4eec8008764bb94e18b932f9ffd66e6b3 | refs/heads/master | 1,678,996,510,399 | 1,581,454,543,000 | 1,583,337,839,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,746 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Selsam
Proving equalities in fields, building on:
1. https://github.com/coq/coq/blob/master/plugins/setoid_ring/Field_theory.v
-/
import Init.Data.Nat
import Init.Data.... |
00735ff7139dac58846fa39209a960fcaf70b11b | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/lie/cartan_subalgebra.lean | 460f04376cb0b383c65145eb18bcbd20cf32f2fd | [
"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 | 4,361 | lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import algebra.lie.nilpotent
import algebra.lie.normalizer
/-!
# Cartan subalgebras
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corres... |
ddd3a8262527e8e5ede731bd256124ca1b14457c | 7282d49021d38dacd06c4ce45a48d09627687fe0 | /tests/lean/tst1.lean | 86eb5854513f262bee48230ff0bc579084962a8e | [
"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 | 1,166 | lean | import if_then_else
-- Define a "fake" type to simulate the natural numbers. This is just a test.
variable N : Type
variable lt : N -> N -> Bool
variable zero : N
variable one : N
variable two : N
variable three : N
infix 50 < : lt
axiom two_lt_three : two < three
definition vector (A : Type) (n : N) : Type := forall (... |
32456e2d617966802d8dce06ac13353297f02f27 | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /tests/lean/run/elabCmd.lean | 43d1cb40c0da3b5e8d0db1ebf3ebdc6ec46ef0aa | [
"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 | 697 | lean | import Lean
open Lean
open Lean.Elab
open Lean.Elab.Term
def getCtors (c : Name) : TermElabM (List Name) := do
env ← getEnv;
match env.find? c with
| some (ConstantInfo.inductInfo val) =>
pure val.ctors
| _ => pure []
def elabAnonCtor (args : Syntax) (τ : Expr) : TermElabM Expr := do
match τ.getAppFn with
| Exp... |
7e66d95a09aefed93e3b283de417da225fd68151 | efa51dd2edbbbbd6c34bd0ce436415eb405832e7 | /20161026_ICTAC_Tutorial/ex46.lean | 3181632d48f4329860dc14dd3ba29a83a82e79ac | [
"Apache-2.0"
] | permissive | leanprover/presentations | dd031a05bcb12c8855676c77e52ed84246bd889a | 3ce2d132d299409f1de269fa8e95afa1333d644e | refs/heads/master | 1,688,703,388,796 | 1,686,838,383,000 | 1,687,465,742,000 | 29,750,158 | 12 | 9 | Apache-2.0 | 1,540,211,670,000 | 1,422,042,683,000 | Lean | UTF-8 | Lean | false | false | 329 | lean | /- Calculational environment -/
variables (a b c d e : ℕ)
variable h1 : a = b
variable h2 : b = c + 1
variable h3 : c = d
variable h4 : e = 1 + d
include h3
example : a = e :=
calc
a = b : h1
... = c + 1 : h2
... = d + 1 : by rewrite h3
... = 1 + d : nat.add_comm d 1
... = e : eq.s... |
99815e2ffd55488a388ec57b6803dd5a7747c7a7 | 1fd908b06e3f9c1252cb2285ada1102623a67f72 | /algebra/group.lean | b7a5e08bb87ffb598d3e860439bab5ac2f7cdbc2 | [
"Apache-2.0"
] | permissive | avigad/hott3 | 609a002849182721e7c7ae536d9f1e2956d6d4d3 | f64750cd2de7a81e87d4828246d1369d59f16f43 | refs/heads/master | 1,629,027,243,322 | 1,510,946,717,000 | 1,510,946,717,000 | 103,570,461 | 0 | 0 | null | 1,505,415,620,000 | 1,505,415,620,000 | null | UTF-8 | Lean | false | false | 18,290 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
-/
import ..init .classes
universes u v w
hott_theory
namespace hott
section binary
variables {α : Type u} {β : Type v}
variable f : α → α → ... |
8b3cb282203f5de569ff57c0d164586e45767164 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /tests/lean/run/809.lean | a99ddbf37fba212c4286db5b08e8cbfd26b2438a | [
"Apache-2.0"
] | permissive | davidmueller13/lean | 65a3ed141b4088cd0a268e4de80eb6778b21a0e9 | c626e2e3c6f3771e07c32e82ee5b9e030de5b050 | refs/heads/master | 1,611,278,313,401 | 1,444,021,177,000 | 1,444,021,177,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 743 | lean | import data.finset data.num data.nat data.int algebra.ring
open finset num nat int algebra
check @finset.insert _ _ 1 (@finset.empty ℕ)
check '{1, 2, 3} -- finset num
check ('{1, 2, 3} : finset ℕ)
check ('{1, 2, 3} : finset ℕ) -- finset ℕ
check ('{1, 2, 3} : finset ℤ) -- finset ℤ
example : finset nat... |
53667c40c0878c3b4e110d6ec5f0c8ec20af24e0 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/struct_inst_typed.lean | 02de514f66569c921a6cb98e6755e62dc32010bf | [
"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 | 200 | lean |
#check { fst := 10, snd := 20 : Nat × Nat }
structure S :=
(x : Nat) (y : Bool) (z : String)
#check { x := 10, y := true, z := "hello" : S }
#check { fst := "hello", snd := "world" : Prod _ _ }
|
aecb3d227014b3b8dc9ca8b11ce24f04a29cda52 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /library/init/nat.lean | 5937bc9934cef511c5dce57699fdc09fcc33eb74 | [
"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 | 9,893 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura
-/
prelude
import init.relation init.tactic init.num
open eq.ops decidable or
notation `ℕ` := nat
namespace nat
protected definition rec_... |
b5c8a448c43f837eb856c1b3d66c2f18f070521d | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /library/data/real/basic.lean | c232fa882da3df7782670042cc7cb02d351f7837 | [
"Apache-2.0"
] | permissive | davidmueller13/lean | 65a3ed141b4088cd0a268e4de80eb6778b21a0e9 | c626e2e3c6f3771e07c32e82ee5b9e030de5b050 | refs/heads/master | 1,611,278,313,401 | 1,444,021,177,000 | 1,444,021,177,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 41,010 | lean | /-
Copyright (c) 2015 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Robert Y. Lewis
The real numbers, constructed as equivalence classes of Cauchy sequences of rationals.
This construction follows Bishop and Bridges (1985).
The construction of the rea... |
2da0c1c0ac676ded88886a500673ef55eca69066 | c8af905dcd8475f414868d303b2eb0e9d3eb32f9 | /src/data/fin_fn.lean | 6b9b837429d6789554e969dec8f81b7463aa587e | [
"BSD-3-Clause"
] | permissive | continuouspi/lean-cpi | 81480a13842d67ff5f3698643210d8ed5dd08de4 | 443bf2cb236feadc45a01387099c236ab2b78237 | refs/heads/master | 1,650,307,316,582 | 1,587,033,364,000 | 1,587,033,364,000 | 207,499,661 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 21,901 | lean | import algebra.pi_instances algebra.half_ring data.finset
/-- A function which is defined everywhere, but only has "interesting" values in
a finite set of locations.
This is used to define a basic vector space, where every defined basis is
known. -/
structure fin_fn (α : Type*) (β : Type*) [has_zero β] :=... |
a98a193cde72c90bac37419144fe4433c81b3ddc | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /08_Building_Theories_and_Proofs.org.31.lean | e989e266c7b1f4fdbdbd225ee3656c4084a38e09 | [] | no_license | cjmazey/lean-tutorial | ba559a49f82aa6c5848b9bf17b7389bf7f4ba645 | 381f61c9fcac56d01d959ae0fa6e376f2c4e3b34 | refs/heads/master | 1,610,286,098,832 | 1,447,124,923,000 | 1,447,124,923,000 | 43,082,433 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 68 | lean | import standard
import data.nat
open - [notations] [coercions] nat
|
36f4df3fc6879105f54d2d5edbf5dbc4af726032 | 947b78d97130d56365ae2ec264df196ce769371a | /src/Init/Data/Repr.lean | a38a7e199091b3db39d532aeab8664f19db88b26 | [
"Apache-2.0"
] | permissive | shyamalschandra/lean4 | 27044812be8698f0c79147615b1d5090b9f4b037 | 6e7a883b21eaf62831e8111b251dc9b18f40e604 | refs/heads/master | 1,671,417,126,371 | 1,601,859,995,000 | 1,601,860,020,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,824 | 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.String.Basic
import Init.Data.UInt
import Init.Data.Nat.Div
open Sum Subtype Nat
universes u v
class HasRepr (α : Type u) :=
(repr... |
6c138d19520faed307af5a70fc9f274440a904ba | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/analysis/normed_space/bounded_linear_maps.lean | e1827d37bd6468dc13b27e45b59509a729db6ba9 | [
"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 | 24,601 | 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 analysis.normed_space.multilinear
import analysis.normed_space.units
import analysis.asymptotics.asymptotics
/-!
# Bounded linear maps
This f... |
929ad79305e8e6a97d3d34702ce0ae13625fef3e | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/linear_algebra/clifford_algebra/conjugation.lean | 218cba523cd0c88a990ef502e2723a1619b26169 | [
"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 | 5,036 | lean | /-
Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import linear_algebra.clifford_algebra.basic
import algebra.module.opposites
/-!
# Conjugations
This file defines the grade reversal and grade involution functions on mul... |
d4c809412970ccfe7569fa8f2ffb143f11ba4dd7 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/data/finset/to_set.lean | 432b15f2ae9bfdbac66974b662fedfa00f0d6730 | [
"Apache-2.0"
] | permissive | soonhokong/lean-osx | 4a954262c780e404c1369d6c06516161d07fcb40 | 3670278342d2f4faa49d95b46d86642d7875b47c | refs/heads/master | 1,611,410,334,552 | 1,474,425,686,000 | 1,474,425,686,000 | 12,043,103 | 5 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 4,040 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
Interactions between finset and set.
-/
import data.finset.comb data.set.function
open nat eq.ops set
namespace finset
variable {A : Type}
variable [deceq : deci... |
2fa45b9075d863dbdaafb151a289593718556871 | b3fced0f3ff82d577384fe81653e47df68bb2fa1 | /src/data/equiv/algebra.lean | 63fbe5eb243063292d45d429b2c51d5cb3fa2f41 | [
"Apache-2.0"
] | permissive | ratmice/mathlib | 93b251ef5df08b6fd55074650ff47fdcc41a4c75 | 3a948a6a4cd5968d60e15ed914b1ad2f4423af8d | refs/heads/master | 1,599,240,104,318 | 1,572,981,183,000 | 1,572,981,183,000 | 219,830,178 | 0 | 0 | Apache-2.0 | 1,572,980,897,000 | 1,572,980,896,000 | null | UTF-8 | Lean | false | false | 19,470 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Callum Sutton
-/
import data.equiv.basic algebra.field
/-!
# equivs in the algebraic hierarchy
In the first part there are theorems of the following
form: if `α` has... |
0f07dccfc98132a439de25c91c5a3fd74bd58d5e | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/polynomial/hasse_deriv.lean | 33fea89cf089738ead16c9fbd63e8b7574a625cb | [
"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 | 10,362 | lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import algebra.polynomial.big_operators
import data.nat.choose.cast
import data.nat.choose.vandermonde
import data.polynomial.derivative
/-!
# Hasse derivative of p... |
e180df6857be91e2abdba2337964170867f496c1 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/order/boolean_algebra.lean | cac14b317c45971b68e59ea8de93166310ab7606 | [
"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 | 3,766 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Type class hierarchy for Boolean algebras.
-/
import order.bounded_lattice
set_option old_structure_cmd true
universes u v
variables {α : Type u} {w x y z : α}
/-- S... |
e83a43e8a62ea272988638e5d52f3e2859ec65a8 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/logic/is_empty.lean | 1bf9adb34daeba4f1e86528556243fef9a1aee1f | [
"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 | 3,384 | lean | /-
Copyright (c) 2021 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import logic.basic
import tactic.protected
/-!
# Types that are empty
In this file we define a typeclass `is_empty`, which expresses that a type has no elements.... |
9be98ab7170498a7a94fe4dc8e141cc071ea37b4 | 453dcd7c0d1ef170b0843a81d7d8caedc9741dce | /group_theory/subgroup.lean | 3df4714570abc00432b03eceec2747034a081f7e | [
"Apache-2.0"
] | permissive | amswerdlow/mathlib | 9af77a1f08486d8fa059448ae2d97795bd12ec0c | 27f96e30b9c9bf518341705c99d641c38638dfd0 | refs/heads/master | 1,585,200,953,598 | 1,534,275,532,000 | 1,534,275,532,000 | 144,564,700 | 0 | 0 | null | 1,534,156,197,000 | 1,534,156,197,000 | null | UTF-8 | Lean | false | false | 14,965 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mitchell Rowett, Scott Morrison, Johan Commelin, Mario Carneiro
-/
import group_theory.submonoid
open set function
variables {α : Type*} {β : Type*} {a a₁ a₂ b c: α}
... |
9e3d74ba8e399547a8c2c2b551f22a2b89bd62fc | 4727251e0cd73359b15b664c3170e5d754078599 | /src/measure_theory/measure/haar_lebesgue.lean | 6d9e86eb8b61c24b0cede7f8579e5ada5c24a2ee | [
"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 | 40,069 | lean | /-
Copyright (c) 2021 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Sébastien Gouëzel
-/
import measure_theory.measure.lebesgue
import measure_theory.measure.haar
import linear_algebra.finite_dimensional
import analysis.normed_space... |
f6e6b328c981bbb67fe3b0b77bfc8b24fe7c4567 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/data/nat/factorial/basic.lean | 6860e7000836f3abeb31e0b551a71468e4b79b39 | [
"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 | 14,778 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Chris Hughes, Floris van Doorn, Yaël Dillies
-/
import data.nat.basic
import data.nat.pow
/-!
# Factorial and variants
This file defines the factorial, along with the... |
ea0f9bf63ffe80857e1fc29289d01d88a4149bae | 94e33a31faa76775069b071adea97e86e218a8ee | /src/group_theory/perm/cycle/concrete.lean | 4e20b7e894866c69f17ec038d039adc64ecd8517 | [
"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 | 19,607 | lean | /-
Copyright (c) 2021 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
import data.list.cycle
import group_theory.perm.cycle.type
import group_theory.perm.list
/-!
# Properties of cyclic permutations constructed from lists/cycles
In... |
42f71d4d9e800b91bae38cceddb06949b0d4697e | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/number_theory/zsqrtd/gaussian_int.lean | b2560a8959462d2274029585dd0944ba744506a5 | [
"Apache-2.0"
] | permissive | ramonfmir/mathlib | c5dc8b33155473fab97c38bd3aa6723dc289beaa | 14c52e990c17f5a00c0cc9e09847af16fabbed25 | refs/heads/master | 1,661,979,343,526 | 1,660,830,384,000 | 1,660,830,384,000 | 182,072,989 | 0 | 0 | null | 1,555,585,876,000 | 1,555,585,876,000 | null | UTF-8 | Lean | false | false | 12,630 | 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 number_theory.zsqrtd.basic
import data.complex.basic
import ring_theory.principal_ideal_domain
import number_theory.legendre_symbol.quadratic_reciprocity
/-!
# Gau... |
7cb3f6c04f4e9db680fc525c85cf4a2ad24f7e0d | 37da0369b6c03e380e057bf680d81e6c9fdf9219 | /hott/homotopy/imaginaroid.hlean | 9f545e92151ff3f0ff8cbda55506a6c9a3c2a8fe | [
"Apache-2.0"
] | permissive | kodyvajjha/lean2 | 72b120d95c3a1d77f54433fa90c9810e14a931a4 | 227fcad22ab2bc27bb7471be7911075d101ba3f9 | refs/heads/master | 1,627,157,512,295 | 1,501,855,676,000 | 1,504,809,427,000 | 109,317,326 | 0 | 0 | null | 1,509,839,253,000 | 1,509,655,713,000 | C++ | UTF-8 | Lean | false | false | 8,508 | hlean | /-
Copyright (c) 2016 Ulrik Buchholtz and Egbert Rijke. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ulrik Buchholtz, Egbert Rijke
Cayley-Dickson construction via imaginaroids
-/
import algebra.group cubical.square types.pi .hopf
open eq eq.ops equiv susp hopf poi... |
36caffca9236a875b70cd5a69f282acf5c96e16a | 8cb37a089cdb4af3af9d8bf1002b417e407a8e9e | /library/init/meta/congr_lemma.lean | 72546770920ebf9f8ed918f72016d8c3f6a58570 | [
"Apache-2.0"
] | permissive | kbuzzard/lean | ae3c3db4bb462d750dbf7419b28bafb3ec983ef7 | ed1788fd674bb8991acffc8fca585ec746711928 | refs/heads/master | 1,620,983,366,617 | 1,618,937,600,000 | 1,618,937,600,000 | 359,886,396 | 1 | 0 | Apache-2.0 | 1,618,936,987,000 | 1,618,936,987,000 | null | UTF-8 | Lean | false | false | 6,328 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.meta.tactic init.meta.format init.function
/-- This is a kind attached to an argument of a congruence lemma that tells the simplifier h... |
1c8788ac9588ec1625654a3dac6d189ce6e1690d | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/polynomial/default.lean | 05858af734dd8070f5205926ece93b015ebd2cd7 | [
"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 | 187 | lean | import data.polynomial.algebra_map
import data.polynomial.field_division
import data.polynomial.derivative
import data.polynomial.identities
import data.polynomial.integral_normalization
|
75bba76ae7131642706b3539bec1a7ec107e9e35 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/probability/probability_mass_function/basic.lean | 63f3d6ce1df8c4b7e18ddc518de1d91903fae399 | [
"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 | 10,477 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Devon Tuma
-/
import topology.instances.ennreal
import measure_theory.measure.measure_space
/-!
# Probability mass functions
This file is about probability mass funct... |
9ad6795937422b38397c27a155fb298818d2fb0b | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/proof_qed_improved.lean | 79dd6ea812e63634786cc556e0ac6cdae28e4c8b | [
"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 | 295 | lean | example (a b c : nat) (f : nat → nat → nat) (H₁ : a = b) (H₂ : b = c) : f (f a a) (f b b) = f (f c c) (f c c) :=
have h : a = c, from eq.trans H₁ H₂,
proof
calc f (f a a) (f b b) = f (f c c) (f b b) : by rewrite h
... = f (f c c) (f c c) : by rewrite H₂
qed
|
dddea344ab3f876d0a7487ce4876ccfe578169f6 | f00cc9c04d77f9621aa57d1406d35c522c3ff82c | /tests/lean/run/apply2.lean | 08016cb2cd3cc660345b624bf84d9ab791c3b6eb | [
"Apache-2.0"
] | permissive | shonfeder/lean | 444c66a74676d74fb3ef682d88cd0f5c1bf928a5 | 24d5a1592d80cefe86552d96410c51bb07e6d411 | refs/heads/master | 1,619,338,440,905 | 1,512,842,340,000 | 1,512,842,340,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 176 | lean | open tactic
example (p q : Prop) : p → q → p ∧ q ∧ p :=
by do
intros,
c₁ ← return (expr.const `and.intro []),
iterate_at_most 10 (apply c₁ <|> assumption)
|
5e0a01bb3e1168c2558021b5f4dc7a9229ca892f | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/combinatorics/double_counting.lean | c500b6f7b8bdf37229379428e333f93c79bb6023 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 5,152 | lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import algebra.big_operators.order
/-!
# Double countings
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
... |
42f31df03c00a4014708a7f5c3e3f4f289be2276 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/tactic/converter/apply_congr.lean | 5074c3dd992133625317e01142f612ed9ada6f35 | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 3,342 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lucas Allen, Scott Morrison
-/
import tactic.interactive
import tactic.converter.interactive
/-!
## Introduce the `apply_congr` conv mode tactic.
`apply_congr` will apply congruence ... |
ae9a4b87de916dd21ba60b2017cc31f41951c7be | 437dc96105f48409c3981d46fb48e57c9ac3a3e4 | /src/topology/instances/ennreal.lean | 0c1a8f33938c97832b591e6e0f42c3b183d18e47 | [
"Apache-2.0"
] | permissive | dan-c-k/mathlib | 08efec79bd7481ee6da9cc44c24a653bff4fbe0d | 96efc220f6225bc7a5ed8349900391a33a38cc56 | refs/heads/master | 1,658,082,847,093 | 1,589,013,201,000 | 1,589,013,201,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 38,596 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
-/
import topology.instances.nnreal
/-!
# Extended non-negative reals
-/
noncomputable theory
open classical set filter metric
open_locale classical
open_locale topologi... |
17172e44a642fb315d30d8516c75265f91141788 | a721fe7446524f18ba361625fc01033d9c8b7a78 | /src/principia/experimental/oldint/le.lean | 2ab231393360975a9bbc691454b19e656d33c8fd | [] | no_license | Sterrs/leaning | 8fd80d1f0a6117a220bb2e57ece639b9a63deadc | 3901cc953694b33adda86cb88ca30ba99594db31 | refs/heads/master | 1,627,023,822,744 | 1,616,515,221,000 | 1,616,515,221,000 | 245,512,190 | 2 | 0 | null | 1,616,429,050,000 | 1,583,527,118,000 | Lean | UTF-8 | Lean | false | false | 9,701 | lean | import .basic
import .mul
namespace hidden
namespace oldint
open mynat
def le: oldint → oldint → Prop
| (of_nat a) (of_nat b) := a ≤ b
| (of_nat a) -[1+ b] := false
| -[1+ a] (of_nat b) := true
| -[1+ a] -[1+ b] := b ≤ a
instance: has_le oldint := ⟨le⟩
variables {m n k x y z : oldint}
variables {a b c : mynat}
@... |
7a7d2070933f088574a4b5cff7ffdceab0f495ca | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/protected.lean | c7b4c27cc196386ab9bdefcbbbbf3df8b39e2168 | [
"Apache-2.0"
] | permissive | soonhokong/lean-osx | 4a954262c780e404c1369d6c06516161d07fcb40 | 3670278342d2f4faa49d95b46d86642d7875b47c | refs/heads/master | 1,611,410,334,552 | 1,474,425,686,000 | 1,474,425,686,000 | 12,043,103 | 5 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 108 | lean | namespace foo
protected definition C := true
definition D := true
end foo
open foo
check foo.C
check D
|
30605e6459b414bc16c39039feed4121d3e98431 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/num_norm1.lean | 6a2f3e3c6431fffd369e27c98661be607e8eeb9f | [
"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 | 8,615 | lean | import data.real
open real
/-
variable {A : Type}
variable [s : linear_ordered_field A]
include s-/
notation `A` := real
example : (-1 :A) * 1 = -1 := by norm_num
example : (-2 :A) * 1 = -2 := by norm_num
example : (-2 :A) * -1 = 2 := by norm_num
example : (-2 :A) * -2 = 4 := by norm_num
example : (1 : A) * 0 = 0 := ... |
d8689d51a6a41b4b0601ee263f28e28580d7500e | 3dd1b66af77106badae6edb1c4dea91a146ead30 | /tests/lean/run/ind3.lean | 27cc3c794ea34f946c505a228e338ffe14b0a8e2 | [
"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 | 444 | lean | inductive tree (A : Type) : Type :=
| node : A → forest A → tree A
with forest (A : Type) : Type :=
| nil : forest A
| cons : tree A → forest A → forest A
check tree.{1}
check forest.{1}
check tree_rec.{1 1}
check forest_rec.{1 1}
print "==============="
inductive group : Type :=
| mk_group : Π (carrier : Type) (mu... |
261a57f32dcf7824bd49e209b5a12a8af92b1906 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/monad/monadicity.lean | 3caeaa2ad27b2911f03465a40cd610a2ff795e29 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 15,334 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import category_theory.limits.preserves.shapes.equalizers
import category_theory.limits.shapes.reflexive
import category_theory.monad.coequalizer
import category_theory.... |
29445287b75240906fe73e01e46bc9a779cb1a16 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/ordmap/ordnode_auto.lean | 83f040142124b703d7f7704c5c77fe8afcf5b2f0 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 33,685 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.list.defs
import Mathlib.data.nat.psub
import Mathlib.PostPort
universes u l u_1 u_2 ... |
e45329778e3f75d447603fd07883c921f931e0fd | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /stage0/src/Lean/Compiler/InferType.lean | 3960cc762b10df6e2d92f7e871e5e9d2b07361b2 | [
"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 | 6,602 | lean | /-
Copyright (c) 2022 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Compiler.LCNFTypes
import Lean.Compiler.Util
namespace Lean.Compiler
class MonadInferType (m : Type → Type) where
inferType : Expr → m Expr
... |
ba9e1f453ad7977b694f60de92e972fe511de066 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/category_theory/abelian/diagram_lemmas/four.lean | 6bb067fc43cb0f41aa989f4df137ea10afd9f794 | [
"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 | 7,742 | lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import category_theory.abelian.pseudoelements
/-!
# The four and five lemmas
Consider the following commutative diagram with exact rows in an abelian category:
```
A... |
211343a08b5d467449cbef8ede3c8ec41ff94160 | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /src/Lean/Server/Watchdog.lean | 17691f24f370c82831f59ff7324a1f0607dbd663 | [
"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 | 24,902 | lean | /-
Copyright (c) 2020 Marc Huisinga. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Marc Huisinga, Wojciech Nawrocki
-/
import Init.System.IO
import Init.Data.ByteArray
import Std.Data.RBMap
import Lean.Elab.Import
import Lean.Data.Lsp
import Lean.Server.Utils
impor... |
fcd9db134c9addaeffce77c1d23ceadc804898a6 | 4727251e0cd73359b15b664c3170e5d754078599 | /archive/imo/imo2005_q4.lean | 76ea4b2f299f678a38cf38d8723fd573ce09fb8d | [
"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 | 4,444 | 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 field_theory.finite.basic
/-!
# IMO 2005 Q4
Problem: Determine all positive integers relatively prime to all the terms of the infinite sequence
`a n = 2 ^ ... |
9fe3f2e6d4d3695cec6c22503e86ed316a0f09cf | 097294e9b80f0d9893ac160b9c7219aa135b51b9 | /instructor/functions/syntax/function_syntax_styles.lean | 3532d91e52e2e44ccde113f7f40a0b92f6d1dddd | [] | no_license | AbigailCastro17/CS2102-Discrete-Math | cf296251be9418ce90206f5e66bde9163e21abf9 | d741e4d2d6a9b2e0c8380e51706218b8f608cee4 | refs/heads/main | 1,682,891,087,358 | 1,621,401,341,000 | 1,621,401,341,000 | 368,749,959 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,715 | lean | -- Function expressions / lambda abstraction
-- anonymous functions
#check λ (n : ℕ), 0
#check λ (n : ℕ), n
#check λ (a b : ℕ), a+b
#check λ (a b c x: ℕ), a*x^2 + b*x + c
-- Function *application* expressions
#check (λ (n : ℕ), 0) 5
#check (λ (n : ℕ), n) 5
#check (λ (a b : ℕ), a+b) 3 2
#check (λ (a b c x: ℕ), a*x^2... |
b865e4240f0116c9ddfe5c04315831e589b027f9 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/topology/metric_space/isometry.lean | 37e013925d5fe0c3fcc5a50f8d436694aac9b29e | [
"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 | 19,909 | lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Isometries of emetric and metric spaces
Authors: Sébastien Gouëzel
-/
import topology.metric_space.antilipschitz
/-!
# Isometries
We define isometries, i.e., maps between emetric spaces th... |
cbfae6b6347471786be8a7c520ccf5be97ecc5e7 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/algebra/default_auto.lean | 83f8ca5345e7e6213d09fb2b6bdc8e955bd96f8b | [] | 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 | 265 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.algebra.functions
namespace Mathlib
end Mathlib |
6507b26f2bc126b0c72157cc4aec5515b90db747 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/deprecated/subgroup.lean | 13df2d1dd716ff9dd427076a150ddfa1eae02058 | [
"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 | 28,629 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mitchell Rowett, Scott Morrison, Johan Commelin, Mario Carneiro,
Michael Howes
-/
import group_theory.subgroup
import deprecated.submonoid
open set function
variabl... |
b191d4c59cb5ff769491a7286bcfdffcb683980e | f5f7e6fae601a5fe3cac7cc3ed353ed781d62419 | /src/category_theory/instances/measurable_space.lean | 3e8a839bfa49b231357b0a29bbab1ef6e47712ae | [
"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 | 891 | lean | /- Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Basic setup for measurable spaces.
-/
import category_theory.instances.topological_spaces
import measure_theory.borel_space
open category_theory
universes u v
namesp... |
cc676c5f29fd299094ce5e877901a473e27aebee | 842b7df4a999c5c50bbd215b8617dd705e43c2e1 | /nat_num_game/src/Advanced_Addition_World/adv_add_wrld9.lean | 790fe97e1c50ce1c806f6a9453a8590ee8560056 | [] | no_license | Samyak-Surti/LeanCode | 1c245631f74b00057d20483c8ac75916e8643b14 | 944eac3e5f43e2614ed246083b97fbdf24181d83 | refs/heads/master | 1,669,023,730,828 | 1,595,534,784,000 | 1,595,534,784,000 | 282,037,186 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 107 | lean | theorem succ_ne_zero (a : ℕ) : nat.succ a ≠ 0 :=
begin
symmetry,
exact nat.zero_ne_succ a,
end
|
2c283e2f617181b95fc8bd1ca2348befd41a6aee | 5e3548e65f2c037cb94cd5524c90c623fbd6d46a | /src_icannos_totilas/topologie-espaces-normés/cpge_ten_01.lean | a919b2893f9d4f5a0c3bb25bd2173f1efb482b82 | [] | no_license | ahayat16/lean_exos | d4f08c30adb601a06511a71b5ffb4d22d12ef77f | 682f2552d5b04a8c8eb9e4ab15f875a91b03845c | refs/heads/main | 1,693,101,073,585 | 1,636,479,336,000 | 1,636,479,336,000 | 415,000,441 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 586 | lean | import topology.basic
import algebra.module.basic
import algebra.module.submodule
import analysis.normed_space.basic
-- Montrer que tout fermé peut s'écrire comme intersection d'une suite décroissante
-- d'ouverts.
theorem exo {R E: Type*} [normed_field R] [normed_group E] [normed_space R E] :
forall A: set E, is... |
45300c2485dd05d929e5218605069beae4b7f6eb | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/ring_theory/subsemiring/basic.lean | 76063edf304e2dce2872f470dca643fbb84ef902 | [
"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 | 47,003 | 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 algebra.module.basic
import algebra.ring.equiv
import algebra.ring.prod
import algebra.order.ring.inj_surj
import algebra.group_ring_action.subobjects
import... |
15b2a2a1d2c4eabae92d9ced5b9b5a3a15e1657e | 827124860511172deb7ee955917c49b2bccd1b3c | /data/containers/map.lean | 17ef4490281cbca4f5bac0a0f76972cfb1cb4246 | [] | no_license | joehendrix/lean-containers | afec24c7de19c935774738ff3a0415362894956c | ef6ff0533eada75f18922039f8312badf12e6124 | refs/heads/master | 1,624,853,911,199 | 1,505,890,599,000 | 1,505,890,599,000 | 103,489,962 | 1 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 2,239 | lean | /- This defines a map from key to values. -/
import .set
namespace data.containers
/-- A key value pair -/
structure binding (K : Type _) (A: Type _) :=
(key : K)
(value : A)
namespace binding
section
parameters {K : Type _} [has_preordering K]
parameters { A: Type _}
def cmp (x y : binding K A) : ordering := ha... |
3ae721a23cdf851666052c9b46bf21080d441869 | 83c8119e3298c0bfc53fc195c41a6afb63d01513 | /library/init/meta/format.lean | d29d279943fdaf3deb2aff5b2c2b41827af9dcdb | [
"Apache-2.0"
] | permissive | anfelor/lean | 584b91c4e87a6d95f7630c2a93fb082a87319ed0 | 31cfc2b6bf7d674f3d0f73848b842c9c9869c9f1 | refs/heads/master | 1,610,067,141,310 | 1,585,992,232,000 | 1,585,992,232,000 | 251,683,543 | 0 | 0 | Apache-2.0 | 1,585,676,570,000 | 1,585,676,569,000 | null | UTF-8 | Lean | false | false | 6,160 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.meta.options init.function init.data.to_string
universes u v
inductive format.color
| red | green | orange | blue | pink | cyan | grey... |
1a5b93edef273d23e9f42f318f8024323d65e8bf | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/data/finset/basic.lean | c45861de58ec9238dfb2b3673957f43bca921d73 | [
"Apache-2.0"
] | permissive | ramonfmir/mathlib | c5dc8b33155473fab97c38bd3aa6723dc289beaa | 14c52e990c17f5a00c0cc9e09847af16fabbed25 | refs/heads/master | 1,661,979,343,526 | 1,660,830,384,000 | 1,660,830,384,000 | 182,072,989 | 0 | 0 | null | 1,555,585,876,000 | 1,555,585,876,000 | null | UTF-8 | Lean | false | false | 124,975 | 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, Minchao Wu, Mario Carneiro
-/
import data.int.basic
import data.multiset.finset_ops
import tactic.apply
import tactic.monotonicity
import tacti... |
475d407a5a5a6f7aa6e92ba3cad8ce5e8fce17de | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/logic/embedding.lean | 411a59308fce9088d2d70e5ba57ea974f6825099 | [
"Apache-2.0"
] | permissive | waynemunro/mathlib | e3fd4ff49f4cb43d4a8ded59d17be407bc5ee552 | 065a70810b5480d584033f7bbf8e0409480c2118 | refs/heads/master | 1,693,417,182,397 | 1,634,644,781,000 | 1,634,644,781,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 15,402 | 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 data.equiv.basic
import data.set.basic
import data.sigma.basic
/-!
# Injective functions
-/
universes u v w x
namespace function
/-- `α ↪ β... |
86138464bb3919f42960243d56845d6c953dc8e9 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/measure_theory/covering/besicovitch.lean | 838ed37d0037124c69a37247ec6c5346a040dc0f | [
"Apache-2.0"
] | permissive | ramonfmir/mathlib | c5dc8b33155473fab97c38bd3aa6723dc289beaa | 14c52e990c17f5a00c0cc9e09847af16fabbed25 | refs/heads/master | 1,661,979,343,526 | 1,660,830,384,000 | 1,660,830,384,000 | 182,072,989 | 0 | 0 | null | 1,555,585,876,000 | 1,555,585,876,000 | null | UTF-8 | Lean | false | false | 60,316 | lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import measure_theory.covering.differentiation
import measure_theory.covering.vitali_family
import measure_theory.integral.lebesgue
import measure_theory.measur... |
97248212957f8c1324ef140b377e408abd80e7ae | efa51dd2edbbbbd6c34bd0ce436415eb405832e7 | /20170116_POPL/meta/ex1.lean | ade0a889f3dcdcae71cfb1141fd4782316f3a01d | [
"Apache-2.0"
] | permissive | leanprover/presentations | dd031a05bcb12c8855676c77e52ed84246bd889a | 3ce2d132d299409f1de269fa8e95afa1333d644e | refs/heads/master | 1,688,703,388,796 | 1,686,838,383,000 | 1,687,465,742,000 | 29,750,158 | 12 | 9 | Apache-2.0 | 1,540,211,670,000 | 1,422,042,683,000 | Lean | UTF-8 | Lean | false | false | 3,984 | lean | open tactic
/-
Hover over tactics to view their types.
The notation `id is a "name quotation".
For example `foo.bar is syntax sugar for
(name.mk_string "bar" (name.mk_string "foo" name.anonymous))
-/
example (p q : Prop) : p → q → q ∧ p :=
by do
h₁ ← intro `h₁,
h₂ ← intro `h₂,
trace_state,
constructor... |
69f651e937702045e8930b35117e0087f0d153f2 | 65b579fba1b0b66add04cccd4529add645eff597 | /simple.lean | e190aff9a12e156e6eadad68ea047b0aae6cbda9 | [] | no_license | teodorov/sf_lean | ba637ca8ecc538aece4d02c8442d03ef713485db | cd4832d6bee9c606014c977951f6aebc4c8d611b | refs/heads/master | 1,632,890,232,054 | 1,543,005,745,000 | 1,543,005,745,000 | 108,566,115 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 235 | lean | import system.io
def fib : ℕ → ℕ
| 0 := 1
| 1 := 1
| (n+2) := fib n + fib (n + 1)
def main : io unit :=
io.print_ln "hello" >>
io.print_ln ("toto", 6) >>
io.print_ln (fib 7)
#eval fib 7
--lean --run simple.lean |
3025ca084e41b5bcc804c8a93db3240544c8f74c | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/MonadControl_tutorial.lean | d2bef986300360b48a474912dde8cb15b7275eca | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 1,038 | lean | namespace Tutorial
/- This file contains the code examples that are used in the
monad control docstring in "How `MonadControl` works" in src/Init/Control/Basic.lean -/
def σ := Nat
@[reducible]
def β := String
opaque foo : ∀ {α}, IO α → IO α
opaque bar : StateT σ IO β
def mapped_foo : StateT σ IO β := do
let s ← ... |
e804b6d94c44c4df5aa79fa6af6ab381df4f491c | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/data/nat/pairing.lean | bba3e45d9bd4dff397f81d8974c327fc1d141b09 | [
"Apache-2.0"
] | permissive | soonhokong/lean-osx | 4a954262c780e404c1369d6c06516161d07fcb40 | 3670278342d2f4faa49d95b46d86642d7875b47c | refs/heads/master | 1,611,410,334,552 | 1,474,425,686,000 | 1,474,425,686,000 | 12,043,103 | 5 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 3,509 | 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
Elegant pairing function.
-/
import data.nat.sqrt data.nat.div
open prod decidable
namespace nat
definition mkpair (a b : nat) : nat :=
if a < b then b*b + a... |
79d4445f6b3cac82f6f0b753e3d8f4d05e46744c | ce6917c5bacabee346655160b74a307b4a5ab620 | /src/ch3/ex0205.lean | c5d39a9541d0059eebd604f05ab12c09ee996b64 | [] | 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 | 102 | lean | constants p q : Prop
lemma t1 : p → q → p :=
assume hp : p,
assume hq : q,
show p, from hp
|
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