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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
f0e5b9eb907263b2b2ed23636b2aed4e6a3af1ef | b7f22e51856f4989b970961f794f1c435f9b8f78 | /library/theories/analysis/ivt.lean | 527a3ebfc07875dba7d6282e16b8a60976335d30 | [
"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 | 9,677 | lean | /-
Copyright (c) 2015 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
The intermediate value theorem.
-/
import .real_limit
open real analysis set classical topology
noncomputable theory
private definition inter_sup (a b : ℝ) (f : ℝ → ... |
1e33183485e780d46151a83608f5f35f954f9490 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/group_theory/submonoid/center.lean | 483e9f1bec8c69b8cf41e4c131124f03add38d9f | [
"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 | 4,486 | lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import group_theory.submonoid.operations
/-!
# Centers of magmas and monoids
## Main definitions
* `set.center`: the center of a magma
* `submonoid.center`: the center o... |
c65f60cfac9bc739ce25caf2823e42f8f69605ad | bb31430994044506fa42fd667e2d556327e18dfe | /src/data/finsupp/defs.lean | ac9ae1845a73b6e6abbc6e8badedcbf1f85c039a | [
"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 | 39,969 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Scott Morrison
-/
import algebra.indicator_function
import group_theory.submonoid.basic
/-!
# Type of functions with finite support
For any type `α` and any type `M` ... |
8e15fd48f43652f2a4cc180dac6a8f8d57c8dea8 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/geometry/manifold/diffeomorph.lean | 0ece1a4cae809a6fff901d46c074d723257aa3f8 | [
"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 | 19,776 | lean | /-
Copyright © 2020 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri, Yury Kudryashov
-/
import geometry.manifold.times_cont_mdiff_map
/-!
# Diffeomorphisms
This file implements diffeomorphisms.
## Definitions
* `diffeomorph I I' M ... |
942972e127bfca359e44a5caef47c21490c36642 | 4aca55eba10c989f0d58647d3c2f371e7da44355 | /src/set_finset_fintype.lean | e19ead7ca6b7a8fd3e4b85523d025e759d594fe7 | [] | no_license | eric-wieser/l534zhan-my_project | f9fc75fb5454405e1a2fa9b56cf96c355f6f2336 | febc91e76b7b00fe2517f258ca04d27b7f35fcf3 | refs/heads/master | 1,689,218,910,420 | 1,630,439,440,000 | 1,630,439,440,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,753 | lean | /-
Copyright (c) 2021 Lu-Ming Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Lu-Ming Zhang.
-/
import tactic
import data.finset.basic
import data.fintype.card
/-!
This file supplements things about `set`, `finset`, `fintype`, that are current missing i... |
c3ec71955debfe62add29a0aad193c76dc9aec04 | 432d948a4d3d242fdfb44b81c9e1b1baacd58617 | /src/data/polynomial/degree/definitions.lean | e212344aefcbe145440f58725a0e18d01d5b19b9 | [
"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 | 38,928 | 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.monomial
import data.nat.with_bot
/-!
# Theory of univariate polynomials
The definitions include
... |
cdd876984f06ce29aac94079e4b8c8ca4df66a66 | 32da3d0f92cab08875472ef6cacc1931c2b3eafa | /src/algebra/module/basic.lean | 29afb41e8975adf84cccabd13161a1915da4b761 | [
"Apache-2.0"
] | permissive | karthiknadig/mathlib | b6073c3748860bfc9a3e55da86afcddba62dc913 | 33a86cfff12d7f200d0010cd03b95e9b69a6c1a5 | refs/heads/master | 1,676,389,371,851 | 1,610,061,127,000 | 1,610,061,127,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 20,109 | lean | /-
Copyright (c) 2015 Nathaniel Thomas. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nathaniel Thomas, Jeremy Avigad, Johannes Hölzl, Mario Carneiro
-/
import algebra.big_operators.basic
import algebra.group.hom
import algebra.ring.basic
import data.rat.cast
import g... |
540bf5fc4b57f8cd86ad15d8d54aa0c183b1ca88 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/category_theory/monad/adjunction.lean | 947d6320f66b653a57e92c613bfac8797c3d0390 | [
"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 | 6,112 | 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 `... |
0a6b93768960ded7db86d91f019d739977d46e8b | 1dd482be3f611941db7801003235dc84147ec60a | /src/measure_theory/decomposition.lean | c6225ec79922cd82ce4fe1038302c2d9994d2c73 | [
"Apache-2.0"
] | permissive | sanderdahmen/mathlib | 479039302bd66434bb5672c2a4cecf8d69981458 | 8f0eae75cd2d8b7a083cf935666fcce4565df076 | refs/heads/master | 1,587,491,322,775 | 1,549,672,060,000 | 1,549,672,060,000 | 169,748,224 | 0 | 0 | Apache-2.0 | 1,549,636,694,000 | 1,549,636,694,000 | null | UTF-8 | Lean | false | false | 8,552 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Hahn decomposition theorem
TODO:
* introduce finite measures (into nnreal)
* show general for signed measures (into ℝ)
-/
import measure_theory.measure_space
local at... |
7f2126e969e478b7394a849a9eefdd222f6aefc8 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /test/set.lean | bbeebd5240130ade8af07daf14c91c93780c66cf | [
"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 | 1,344 | lean | import data.matrix.notation
example (x : ℕ) (h : x = 3) : x + x + x = 9 :=
begin
set y := x with ←h_xy,
guard_hyp y : ℕ := x,
guard_hyp h_xy : x = y,
guard_hyp h : y = 3,
guard_target y + y + y = 9,
set! z : ℕ := y,
guard_target y + y + y = 9,
simp [h]
end
example : true :=
let X1 := (![![1, 0], ![0,... |
1a178f69fb65f99fdf6bcad631508e866689eb36 | e39f04f6ff425fe3b3f5e26a8998b817d1dba80f | /analysis/measure_theory/outer_measure.lean | 58858557c09454a779c01132ca2215777c81ed26 | [
"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 | 18,153 | 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
Outer measures -- overapproximations of measures
-/
import order.galois_connection algebra.big_operators algebra.module
analysis.ennreal analysi... |
09e8cda76271d8a484724b4dcf0cd51e419f7b24 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/order/complete_lattice.lean | 0dd7476e66d5988be78769b3bbb57a00d6b497c6 | [] | 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 | 52,378 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.order.bounds
import Mathlib.PostPort
universes u_6 l u_1 u_2 u_4 u_5 u_3
namespace Mathl... |
771b323bd64eb64aa977adbdf32df4309f7549a2 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/control/lawful_fix.lean | 64df81a2c9ad0e1975001b40f9115d8952dc65f3 | [
"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 | 7,647 | lean | /-
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import data.stream.init
import tactic.apply
import control.fix
import order.omega_complete_partial_order
/-!
# Lawful fixed point operators
This module defines the laws r... |
88fb5d70209851cfdf272e005706a03655ae3091 | bdb33f8b7ea65f7705fc342a178508e2722eb851 | /data/nat/basic.lean | 977621feae3c7a4fb47f2572a040e130cbe020aa | [
"Apache-2.0"
] | permissive | rwbarton/mathlib | 939ae09bf8d6eb1331fc2f7e067d39567e10e33d | c13c5ea701bb1eec057e0a242d9f480a079105e9 | refs/heads/master | 1,584,015,335,862 | 1,524,142,167,000 | 1,524,142,167,000 | 130,614,171 | 0 | 0 | Apache-2.0 | 1,548,902,667,000 | 1,524,437,371,000 | Lean | UTF-8 | Lean | false | false | 19,057 | lean | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
Basic operations on the natural numbers.
-/
import logic.basic algebra.order data.option
universe u
namespace na... |
3b1e12252ac7bf5590eae8d2d95497667d0b9831 | 6e8de6b43162bef473b4a0bd93b71db886df98ce | /src/pregeom/basis.lean | 0cd9218d023cd42d5b7a85e0a4a23ad63f5beea2 | [
"Unlicense"
] | permissive | adamtopaz/comb_geom | 38ec6fde8d2543f56227ec50cdfb86cac6ac33c1 | e16b629d6de3fbdea54a528755e7305dfb51e902 | refs/heads/master | 1,668,613,552,530 | 1,593,199,940,000 | 1,593,199,940,000 | 269,824,442 | 6 | 0 | Unlicense | 1,593,119,545,000 | 1,591,404,975,000 | Lean | UTF-8 | Lean | false | false | 7,321 | lean | import order.zorn
import tactic
import .basic
import ..helpers
import data.set
open_locale classical
variables {T : Type*} [pregeom T]
namespace pregeom
namespace basis
open has_cl
/--
A set `S` is independent if for all `x ∈ S`, the element `x` is not contained in
`cl (S - {x})`
-/
def is_indep (S : set T) := ∀... |
2e27e20964247289ba78a8f39be541bc4ecb8a3d | 48f4f349e1bb919d14ab7e5921d0cfe825f4c423 | /fabstract/Bauer_A_InjBaireNat/toposes.lean | 8979d5e03a42d4677d59b124b932278099f922ff | [] | no_license | thalesant/formalabstracts-2017 | fdf4ff90d30ab1dcb6d4cf16a068a997ea5ecc80 | c47181342c9e41954aa8d41f5049965b5f332bca | refs/heads/master | 1,584,610,453,925 | 1,528,277,508,000 | 1,528,277,508,000 | 136,299,625 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 841 | lean | -- an incomplete definition of toposes
import meta_data
.categories
run_cmd tactic.skip -- temporary fix
unfinished nno_structure : category → Type :=
{ description := "natural numbers object in a category",
sources := [cite.Website "https://ncatlab.org/nlab/show/natural+numbers+object"] }
structur... |
1cda5e2c7278f7c73c3c5bc4669308ca17d9bd4d | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/data/rat/default.lean | 33d5888eec2c4f0da80ba4c39ebc9c7d2656bff1 | [
"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 | 326 | lean | /-
Copyright (c) 2019 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import data.rat.basic
import data.rat.order
import data.rat.cast
import data.rat.floor
import data.rat.meta_defs
/-!
# Default Imports to Work With Rational Numbe... |
bb952dd0c8f53c6df7a74d2ba130f15ce177625e | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/geometry/manifold/charted_space.lean | 8e18a77915d6e0b9fe004dab29c9177487332f85 | [
"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 | 43,241 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import topology.local_homeomorph
/-!
# Charted spaces
A smooth manifold is a topological space `M` locally modelled on a euclidean space (or a euclidean
half-... |
428200340ddffa7b54d1a2fb1ba44d0bcef48f51 | 01ae0d022f2e2fefdaaa898938c1ac1fbce3b3ab | /categories/adjunctions/examples/functor_categories.lean | 619d5238da8b746cb8519e24a0760a364e663a89 | [] | no_license | PatrickMassot/lean-category-theory | 0f56a83464396a253c28a42dece16c93baf8ad74 | ef239978e91f2e1c3b8e88b6e9c64c155dc56c99 | refs/heads/master | 1,629,739,187,316 | 1,512,422,659,000 | 1,512,422,659,000 | 113,098,786 | 0 | 0 | null | 1,512,424,022,000 | 1,512,424,022,000 | null | UTF-8 | Lean | false | false | 854 | 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 ...adjunctions
open categories
open categories.functor
open categories.natural_transformation
open categories.products
open categories.isomorphism
open ca... |
700c87ea17d17787b3ed25d9d833249e808b6eca | dcf093fda1f51c094394c50e182cfb9dec39635a | /wlog.lean | 06a06370a68a118c7e20c6660843e355d1f5bb5b | [] | no_license | dselsam/cs103 | 7ac496d0293befca95d3045add91c5270a5d291f | 31ab9784a6f65f226efb702a0da52f907c616a71 | refs/heads/master | 1,611,092,644,140 | 1,492,571,015,000 | 1,492,571,015,000 | 88,693,969 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,695 | lean | import data.nat data.set
open nat set
variable {T : Type}
/-
Lemma 2: A Δ B ⊆ (A ∪ B) – (A ∩ B)
Proof of Lemma 2: We will show that for any x ∈ A Δ B, x ∈ (A ∪ B) – (A ∩ B). Consider any
x ∈ A Δ B. Then either x ∈ A and x ∉ B, or x ∈ B and x ∉ A. Assume without loss of generality that
x ∈ A and x ∉ B. Since x ∈ A, x ... |
72ea96fbb4eef777a2fe7628e0aba560c90b78f2 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/ring_theory/power_series/basic.lean | 64057659cb4e8739eb85b1c2ee0262d1b1d89700 | [
"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 | 75,248 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Kenny Lau
-/
import algebra.big_operators.nat_antidiagonal
import data.finsupp.interval
import data.mv_polynomial.basic
import data.polynomial.algebra_map
import data.p... |
c2671dfc79e53d9b505fa331e53013f2a1d96f68 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/algebra/lie/basic.lean | bb4a258425fd7c3390e59644b43321fa9e2e9f4e | [
"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 | 28,872 | lean | /-
Copyright (c) 2019 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import tactic.noncomm_ring
import data.equiv.module
import data.bracket
/-!
# Lie algebras
This file defines Lie rings and Lie algebras over a commutative ring together w... |
910f2774c76df8b9e574d83045c22df8365b9c10 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/instances/sign.lean | 2ddc6e4e4d487045be87970e3584ed50d5ceaed8 | [
"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 | 1,656 | lean | /-
Copyright (c) 2022 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import data.sign
import topology.order.basic
/-!
# Topology on `sign_type`
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding... |
fca76bd92c527b6cbbb20d6b4b95ef895420da48 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/category/Quiv.lean | 2bcf0b8f1830809671fb25d3ea525c95f4aaade9 | [
"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 | 3,173 | lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.adjunction.basic
import category_theory.category.Cat
import category_theory.path_category
/-!
# The category of quivers
The category of (bund... |
30280abd9a98d9e7537a71adb1bb35dac705b467 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/algebra/ring_bigops.lean | 0b5d468d8cb58f30a2df200271a9b8fee1977c2f | [
"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 | 6,088 | lean | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
Properties of finite sums and products in various structures, including ordered rings and fields.
There are two versions of every theorem: one for finsets, and one for fin... |
ed17a759b0de8f3abf261247f699590e92603e40 | abd85493667895c57a7507870867b28124b3998f | /src/group_theory/quotient_group.lean | 816f600248cedd2a82fbc1aa0c6157a0e6de9082 | [
"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 | 7,199 | lean | /-
Copyright (c) 2018 Kevin Buzzard and Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Patrick Massot.
This file is to a certain extent based on `quotient_module.lean` by Johannes Hölzl.
-/
import group_theory.coset
universes u v
names... |
15b0ea16c3cc473f8101c7b727a450411f94f6dd | a89b8d3c600409f2f752bc9ab5c96ac20787cfef | /library/init/meta/interactive.lean | 7c75f841f32b5873bfc7e72a8a44999da230a85a | [
"Apache-2.0"
] | permissive | Armael/lean | 0211a95f4db2a69189073497500e170660b5284e | 49bc0ef0fd04242242f81ebdb0912ce6daed5a65 | refs/heads/master | 1,611,565,828,709 | 1,496,958,664,000 | 1,497,031,159,000 | 93,794,727 | 0 | 0 | null | 1,496,958,642,000 | 1,496,958,642,000 | null | UTF-8 | Lean | false | false | 31,213 | 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.rewrite_tactic init.meta.simp_tactic
import init.meta.smt.congruence_closure init.category.combinators
import init... |
4e84c31ada19c656b68df29e8f08aca7701c1660 | f3849be5d845a1cb97680f0bbbe03b85518312f0 | /library/init/data/list/basic.lean | 36b44d167aaa38311237092e65b31bdb28b85017 | [
"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 | 8,865 | 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.logic init.data.nat.basic
open decidable list
universes u v w
instance (α : Type u) : inhabited (list α) :=
⟨list.nil⟩
variables {α : ... |
3977c6990a006882c93b803e8f1c16ef005b399e | 5749d8999a76f3a8fddceca1f6941981e33aaa96 | /src/measure_theory/simple_func_dense.lean | e6040bf12920b7e8edc49d1fb60dfc360866f52c | [
"Apache-2.0"
] | permissive | jdsalchow/mathlib | 13ab43ef0d0515a17e550b16d09bd14b76125276 | 497e692b946d93906900bb33a51fd243e7649406 | refs/heads/master | 1,585,819,143,348 | 1,580,072,892,000 | 1,580,072,892,000 | 154,287,128 | 0 | 0 | Apache-2.0 | 1,540,281,610,000 | 1,540,281,609,000 | null | UTF-8 | Lean | false | false | 15,104 | lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
Show that each Borel measurable function can be approximated,
both pointwise and in L¹ norm, by a sequence of simple functions.
-/
import measure_theory.l1_space
noncom... |
8ee6fac8f537ce73ac3f441ae223e55bddd35d02 | bb31430994044506fa42fd667e2d556327e18dfe | /src/number_theory/cyclotomic/basic.lean | 652614ab0c3fc422d59792e8d615ae8e5257747c | [
"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 | 31,523 | lean | /-
Copyright (c) 2021 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
import ring_theory.polynomial.cyclotomic.basic
import number_theory.number_field.basic
import algebra.char_p.algebra
import field_theory.galois
/-!
# Cyclotomic e... |
b0f55d0a2534e793585e262d608a922f0cd0bf16 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/simp_rw.lean | cb9325926f71b38e89f057442a37bf11ef1138d7 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,912 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
The `simp_rw` tactic, a mix of `simp` and `rewrite`.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.tactic.core
import Mathlib.PostPort
namesp... |
d18246e3277bbbfc4b2b455afe06a3fd060963ec | c777c32c8e484e195053731103c5e52af26a25d1 | /src/data/polynomial/laurent.lean | bcdfada8689be5fe32b97500803ee293db33e896 | [
"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 | 20,023 | lean | /-
Copyright (c) 2022 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import data.polynomial.algebra_map
import ring_theory.localization.basic
/-! # Laurent polynomials
We introduce Laurent polynomials over a semiring `R`. Mathematic... |
bf3e4addf9bede13b09a88860930a64a22e6b98f | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/apply_tac1.lean | 5dd4d6a963280ee08563614248636adc33ca63d5 | [
"Apache-2.0"
] | permissive | codyroux/lean0.1 | 1ce92751d664aacff0529e139083304a7bbc8a71 | 0dc6fb974aa85ed6f305a2f4b10a53a44ee5f0ef | refs/heads/master | 1,610,830,535,062 | 1,402,150,480,000 | 1,402,150,480,000 | 19,588,851 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 558 | lean | import tactic.
import Int.
variable f : Int -> Int -> Bool
variable P : Int -> Int -> Bool
axiom Ax1 (x y : Int) (H : P x y) : (f x y)
theorem T1 (a : Int) : (P a a) → (f a a).
apply Ax1.
exact.
done.
variable b : Int
axiom Ax2 (x : Int) : (f x b)
(*
simple_tac = Repeat(OrElse(assumption_tac(), apply... |
eec3ef731847137947b154f572ae51b50ddeb141 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/data/finset/prod.lean | 885a9af98772b701e68fc665998cf4d6412fa7fa | [
"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 | 10,235 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Oliver Nash
-/
import data.finset.card
/-!
# Finsets in product types
This file defines finset constructions on the product type `α × β`. Bewar... |
a1d190d38ea34cb07495f58b7e8fada6e2379009 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/category_theory/sites/sieves.lean | 39430023d16d300f4f782c6c187370199487eb26 | [
"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 | 23,489 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, E. W. Ayers
-/
import category_theory.over
import category_theory.limits.shapes.finite_limits
import category_theory.yoneda
import order.complete_lattice
import data.set.l... |
790ade46de75f82d92b5e346021c8e10ba426f30 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/1367.lean | a71567c5c12f2048eb1e6b01e511abc951e36a1f | [
"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 | 160 | lean | def two := 2
notation "𝟚" => two
/- 𝟚 : Nat -/
#check 𝟚
def three (_ : Nat) := 3
notation "𝟛" => three
/- three 10 : Nat -/
#check 𝟛 10
|
17150df5c32d5bb7a47b5840c1822e3b7bdf0a28 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/linear_algebra/basic.lean | 0ba16eac1dd6750df3bbefbaf5162ee9e2f419d4 | [
"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 | 83,668 | 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, Kevin Buzzard, Yury Kudryashov, Frédéric Dupuis,
Heather Macbeth
-/
import algebra.big_operators.pi
import algebra.module.hom
import algebra.module.pr... |
5ff730660f4904a1efe3cbc63ff74cc50986a472 | ce6917c5bacabee346655160b74a307b4a5ab620 | /src/ch4/ex0302.lean | 868a0805b21b7d8e083842d916739e7c94436ad7 | [] | 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 | 316 | lean | 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 h1 h2 h3 h4
theorem T : a = e :=
calc
a = b : by rw h1
... = c + 1 : by rw h2
... = d + 1 : by rw h3
... = 1 + d : by rw add_comm
... = e : by rw h4
|
2fec5eae11f482ae2a012790937e5bc7c1632f8b | f4bff2062c030df03d65e8b69c88f79b63a359d8 | /src/game/order/level04.lean | d76304f781d3166270bf0f39c0b3c0d0c1a4f8c5 | [
"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 | 825 | lean | import game.order.level03
namespace xena -- hide
/-
# Chapter 2 : Order
## Level 4
This level invites you to work out a property of the absolute value.
In Lean the absolute value of $x$ is denoted by `abs x`.
For ease of use, a notation can be used around that definition as below.
Feel free to use the triangle ine... |
3fedbb9338068f6de61d4d3b5ad3a88ee623156e | 618003631150032a5676f229d13a079ac875ff77 | /src/data/list/tfae.lean | e32f1ab4ad1dd55e7d1d1ec6d3bb702fffb8a817 | [
"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 | 1,842 | lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Simon Hudon
-/
import data.list.basic
namespace list
/- tfae: The Following (propositions) Are Equivalent -/
def tfae (l : list Prop) : Prop := ∀ x ∈ l, ∀ y ∈ l, x ↔ ... |
3b9fe655d6b31879b4155f26c8f2b262ee628005 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/goal.lean | f9ed94d74b7215b79cd4c8e1e6979bf3f75e92f1 | [
"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 | 113 | lean | import logic
open tactic
theorem T {a b c d : Prop} (H : a) (H : b) (H : c) (H : d) : a
:= by state; assumption
|
c63cfeec72b3082457a971a8093c1038e9ab9b1a | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/algebra/order.lean | 399aa491d641356d640f08acd4138393d6fd293c | [
"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 | 18,094 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
Weak orders "≤", strict orders "<", and structures that include both.
-/
import logic.eq logic.connectives algebra.binary algebra.priority
open eq function
variables {A :... |
36e902bddb5e8f6fbb0e44dda96e5b97b46c7a8f | 6214e13b31733dc9aeb4833db6a6466005763162 | /src/qiaux.lean | 08b8960c1fad2991cc877c70abfe76b5530c9227 | [] | no_license | joshua0pang/esverify-theory | 272a250445f3aeea49a7e72d1ab58c2da6618bbe | 8565b123c87b0113f83553d7732cd6696c9b5807 | refs/heads/master | 1,585,873,849,081 | 1,527,304,393,000 | 1,527,304,393,000 | 154,901,199 | 1 | 0 | null | 1,540,593,067,000 | 1,540,593,067,000 | null | UTF-8 | Lean | false | false | 12,338 | lean | -- auxilliary definitions and lemmas used for termination of QI
import .definitions1
def prop.num_quantifiers: prop → ℕ
| (prop.term t) := 0
| (prop.not P) := P.num_quantifiers
| (prop.and P₁ P₂) := P₁.num_quantifiers + P₂.num_quantifiers
| (prop.or P₁ P₂) := P₁.num_quantifiers + P₂.num_quanti... |
510c7ab1f3bc70c9463aae9a88c63997310df1df | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/closed/zero.lean | 720938c6f74b6ed55cbdda25d08b84e66453f253 | [
"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 | 2,102 | 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.closed.cartesian
import category_theory.punit
import category_theory.conj
import category_theory.limits.shapes.zero_objects
/-!
# A cartesian clo... |
da364b5b2f781bea74deec9dcbb2c13ed0b32614 | 9d00e4b237465921fb33aa10eed92a2495ca2e46 | /testProofs.lean | 357c21733ba996670c4dc1257052f493f346b697 | [] | no_license | Bpalkmim/LeanNatD | 7756abf1ed7b0e7a3e3b9d16ad756018f5c70c7c | 2e73bb44e44b955839e7a0874cd7013fbfb9c4e3 | refs/heads/master | 1,610,999,141,530 | 1,475,515,895,000 | 1,475,515,895,000 | 69,893,600 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,397 | lean | namespace testProofs
-- Requer os namespaces
open implRules
open andRules
open orRules
open negBotRules
print " "
print "Provas AVANÇADAS - início"
print " "
constants A B C D : Prop
--- Termos úteis
variable a : Proof A
variable b : Proof B
variable NEGb : Proof (neg B)
variable c : Proof C
variable NEGc : Proof (... |
d394718d02289a99ecf68853fbb3147270442760 | 8c95816d6379a6864848d68ce735a5700c1cbbc3 | /src/smt2/syntax.lean | e1ba8309636648df49e5afa0502ff4e4cb90a014 | [
"Apache-2.0"
] | permissive | aqjune/smt2_interface | f00ed0a4317d7c9112deb0806c8e89e6512a901e | 598848a7a6fa47520fadcfe1b16891053a296084 | refs/heads/master | 1,631,518,664,718 | 1,524,489,340,000 | 1,524,489,340,000 | 115,204,811 | 0 | 0 | null | 1,514,043,428,000 | 1,514,043,427,000 | null | UTF-8 | Lean | false | false | 5,443 | lean | namespace smt2
@[reducible] def symbol : Type := string
@[reducible] def identifier : Type := string
inductive special_constant : Type
| number : int → special_constant
| bitvec : nat → int → special_constant
| string : string → special_constant
| bool : bool → special_constant
def hexdigit (n:nat) : char :=
char.of... |
b3155c9c3966eabcbec609d0f25a0e084db8456f | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/geometry/manifold/instances/real.lean | 0ee93ba3e67e1dbcf95fe971b9397a85bcc8a980 | [
"Apache-2.0"
] | permissive | hikari0108/mathlib | b7ea2b7350497ab1a0b87a09d093ecc025a50dfa | a9e7d333b0cfd45f13a20f7b96b7d52e19fa2901 | refs/heads/master | 1,690,483,608,260 | 1,631,541,580,000 | 1,631,541,580,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,573 | 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.algebra.smooth_functions
import linear_algebra.finite_dimensional
import analysis.normed_space.pi_Lp
/-!
# Constructing examples of ma... |
f537b222dcb27bb38a9cf7130896712c60ae92a6 | 968e2f50b755d3048175f176376eff7139e9df70 | /examples/prop_logic_theory/unnamed_287.lean | 8d76a4cf08814b609200f11a6c6731d5f3aeeb8d | [] | no_license | gihanmarasingha/mth1001_sphinx | 190a003269ba5e54717b448302a27ca26e31d491 | 05126586cbf5786e521be1ea2ef5b4ba3c44e74a | refs/heads/master | 1,672,913,933,677 | 1,604,516,583,000 | 1,604,516,583,000 | 309,245,750 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 367 | lean | variables p q : Prop
-- BEGIN
example (h : p ∧ q) : q ∧ p :=
begin
have h₂ : p, from h.left,
have h₃ : q, from h.right,
exact and.intro h₃ h₂,
end
-- END
Alternatively, one can use the 'anonymous constructor' notation ``⟨h₃, h₂⟩`` in place of
``and.intro h₃ h₂``. Here, ``⟨`` and ``⟩`` are written as ``\<`` and `... |
cc5bfbb21a51084f37bfd1ea2e98602c8da7f743 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/nasty_sizeof.lean | c7a73d1719dbca5088942341243658e43c3f7329 | [
"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 | 100 | lean | def nasty_sizeof : list nat → nat
| [] := 100000000
| (a::as) := nasty_sizeof as + 100000000
|
8ccdb664159dd6976cbe03e34bf9c4535a7ea206 | e0f9ba56b7fedc16ef8697f6caeef5898b435143 | /src/tactic/finish.lean | 288eee9ac7a43991770eced808e119f7b1bc866c | [
"Apache-2.0"
] | permissive | anrddh/mathlib | 6a374da53c7e3a35cb0298b0cd67824efef362b4 | a4266a01d2dcb10de19369307c986d038c7bb6a6 | refs/heads/master | 1,656,710,827,909 | 1,589,560,456,000 | 1,589,560,456,000 | 264,271,800 | 0 | 0 | Apache-2.0 | 1,589,568,062,000 | 1,589,568,061,000 | null | UTF-8 | Lean | false | false | 23,095 | lean | /-
Copyright (c) 2017 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Jesse Michael Han
-/
import tactic.hint
/-!
# The `finish` family of tactics
These tactics do straightforward things: they call the simplifier, split conjunctive assump... |
7b709dfe85aac511821becb5ea3d4535077d1d68 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Util/Profile.lean | d247970b1f355cfeb09aeb7d79520535346014cd | [
"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 | 1,785 | lean | /-
Copyright (c) 2019 Sebastian Ullrich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Sebastian Ullrich
-/
import Lean.Data.Options
namespace Lean
register_builtin_option profiler : Bool := {
defValue := false
group := "profiler"
descr := "show execution... |
4e582cdc9dc30ccb797bec22cb0eb75cdb47e38b | 9dd3f3912f7321eb58ee9aa8f21778ad6221f87c | /tests/lean/run/even_perf.lean | 5914dea3f3cb96abdc93f140802245ec062206c8 | [
"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 | 194 | lean | open nat
def even : nat → bool
| 0 := tt
| (succ 0) := ff
| (succ (succ n)) := even n
vm_eval even 0
vm_eval even 1
vm_eval even 2
vm_eval even 10000
vm_eval even 10001
|
f7c053aa8da2f9f3523fe9a0778988ec32fb75c1 | 8b9f17008684d796c8022dab552e42f0cb6fb347 | /tests/lean/run/match_tac3.lean | 38844920dbb09f5abd4a39cc1025facd4d0f178e | [
"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 | 219 | lean | import data.nat
open nat
theorem tst (a b : nat) (H : a = 0) : a + b = b :=
begin
revert H,
match a with
| zero := λ H, by rewrite zero_add
| (n+1) := λ H, nat.no_confusion H
end
end
print definition tst
|
2be5898f74cb01df82e1c48559f4f953cba22c1d | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/analysis/special_functions/exp_log.lean | f4fbe4629d175b633ac9d600a30f9f802afdc516 | [
"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 | 31,468 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne
-/
import data.complex.exponential
import analysis.complex.basic
import analysis.calculus.mean_value
import measure_theory.bo... |
d712bc8007de3d2f0246f7a99063f72d5ce2fa70 | 9bf90df35bb15a2f76571e35c48192142a328c40 | /src/ch7.lean | edda5cd3b966e210822513e0540defa079f3d9da | [] | no_license | ehaskell1/set_theory | ed0726520e84990d5f3180bafa0a3674ed31fb5e | e6c829c4dd953d98c9cba08f9f79784cd91794fb | refs/heads/master | 1,693,282,405,362 | 1,636,928,916,000 | 1,636,928,916,000 | 428,055,746 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 100,092 | lean | import ch6
universe u
namespace Set
local attribute [irreducible] mem
structure part_order (R : Set) : Prop :=
(rel : R.is_rel)
(trans : R.transitive)
(irrefl : ∀ ⦃x : Set⦄, x.pair x ∉ R)
def part_le (R x y : Set) : Prop := x.pair y ∈ R ∨ x = y
-- Theorem 7A part a
theorem not_lt_and_gt_part {R : Set} (hR : R.part_... |
572998da86ea5e9d66ab324522f94b2f44c3482b | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /src/Lean/Compiler/ConstFolding.lean | 376d01825f9860c5e02b7988be87f4268b8affe5 | [
"Apache-2.0"
] | permissive | williamdemeo/lean4 | 72161c58fe65c3ad955d6a3050bb7d37c04c0d54 | 6d00fcf1d6d873e195f9220c668ef9c58e9c4a35 | refs/heads/master | 1,678,305,356,877 | 1,614,708,995,000 | 1,614,708,995,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,086 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Expr
import Lean.Compiler.Util
/- Constant folding for primitives that have special runtime support. -/
namespace Lean.Compiler
abbrev BinFol... |
ca5dfe0725a1cf1e93691ce0240fb933a790d029 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/measure_theory/integration_auto.lean | 46cd72987b90efae551cc222c002a11bd4540fed | [] | 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 | 72,675 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.measure_theory.measure_space
import Mathlib.measure_theory.borel_space
impo... |
e86ced63f2b05cf0f6f0f0dbff8eec92f17c44d6 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/analysis/convex/slope.lean | abe5e37c12a7aa10f381cc88a28b19db023175e6 | [
"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 | 10,423 | lean | /-
Copyright (c) 2021 Yury Kudriashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudriashov, Malo Jaffré
-/
import analysis.convex.function
import tactic.field_simp
/-!
# Slopes of convex functions
This file relates convexity/concavity of functions in a lin... |
f5420ed373ab784fb4606e50cc55d1a684199e07 | f3a5af2927397cf346ec0e24312bfff077f00425 | /src/game/world8/level13.lean | 1970ee6d9fd3ee3e88b1f8568316c998f87d7ea9 | [
"Apache-2.0"
] | permissive | ImperialCollegeLondon/natural_number_game | 05c39e1586408cfb563d1a12e1085a90726ab655 | f29b6c2884299fc63fdfc81ae5d7daaa3219f9fd | refs/heads/master | 1,688,570,964,990 | 1,636,908,242,000 | 1,636,908,242,000 | 195,403,790 | 277 | 84 | Apache-2.0 | 1,694,547,955,000 | 1,562,328,792,000 | Lean | UTF-8 | Lean | false | false | 688 | lean | import game.world8.level12 -- hide
namespace mynat -- hide
/-
# Advanced Addition World
## Level 13: `ne_succ_self`
The last level in Advanced Addition World is the statement
that $n\not=\operatorname{succ}(n)$. When you've done this
you've completed Advanced Addition World and can move on
to Advanced Multiplicatio... |
8674085142adeeb757cdfd94801179ae8d10a323 | 3618c6e11aa822fd542440674dfb9a7b9921dba0 | /src/no_letters.lean | 02f464641a42cea398b03f8c807274a08c9c9f60 | [] | 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 | 2,736 | lean | import P
import initial
/-!
# No letters
This file handles the case that all letters in `r` are in `T`
## Implementation Notes
Every function in this file uses an ad-hoc implementation of the
binary coproduct of `P (free_group T)` and `free_group Tᶜ`. It is implemented as
a `list (P (free_group ι) × free_group ι)`.
Th... |
1c314640fb48720f1813c2f70aef4f2c8d64e22e | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/tactic/omega/find_scalars.lean | bd4cfc962396a28d6a62425b6d08471575e2017c | [
"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 | 1,890 | lean | /-
Copyright (c) 2019 Seul Baek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Seul Baek
A tactic which performs Fourier–Motzkin elimination to find
a contradictory linear combination of input constraints.
-/
import tactic.omega.term data.list.min_max
open list.func... |
e478fdfd25642379d6bf6c6782bbe308dc1d43cb | c777c32c8e484e195053731103c5e52af26a25d1 | /src/analysis/locally_convex/with_seminorms.lean | a578827117d1d36f00ab916a7989c3b5f86f5a69 | [
"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 | 30,886 | lean | /-
Copyright (c) 2022 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll, Anatole Dedecker
-/
import analysis.seminorm
import analysis.locally_convex.bounded
import topology.algebra.filter_basis
import topology.algebra.module.locally_convex
/-!
#... |
46de19fc29e24716bef054ab2237cadab5a0ea5b | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/ring_theory/ideal/local_ring.lean | 8928de69e17230380167aef2cf4873d7077d14a9 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 15,282 | 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... |
52ddb17070154a0dbf711ba6eaebfa097a3b93fd | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/lake/examples/deps/bar/lakefile.lean | a180b75b235e85d5e3a9d932e067c9de48cac534 | [
"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 | 143 | lean | import Lake
open System Lake DSL
package bar
require foo from ".."/"foo"
lean_lib Bar
@[default_target]
lean_exe bar where
root := `Main
|
95cdc953362c6d5b514edfb601055bf0459e1a08 | 9db059bff49b1090a86ec0050ac6c577eb16ac67 | /src/exercises/algebraic_hierarchy.lean | 1ea6088eaff66bad1fec097efff2089b29807407 | [] | no_license | fpvandoorn/Harvard-tutoring | d64cd75c4c529009ee562c30e9cb245fe237e760 | a8846c08e32cdc7b91a7e28adfa5d9b2810088b0 | refs/heads/master | 1,680,870,428,641 | 1,617,022,194,000 | 1,617,022,194,000 | 330,297,467 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,722 | lean | /-
This is a file covering the material on Wednesday afternoon
at LFTCM2020. It's how to build some algebraic structures in Lean
This file has the excercise solutions replaced by `sorry`.
-/
import data.rat.basic -- we'll need the rationals at the end of this file
/-
As a mathematician I essentially always start my ... |
36e3ebe163a93921a2a565696ac5aaf5c37911bd | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /counterexamples/char_p_zero_ne_char_zero.lean | a567d155f59ec4b4fb80e0b3b3911d2b4374f906 | [
"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 | 1,171 | lean | /-
Copyright (c) 2022 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa, Eric Wieser
-/
import algebra.char_p.basic
/-! # `char_p R 0` and `char_zero R` need not coincide for semirings
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes... |
972d6f5fe1829c1823084fce4dd4ce8b9a207a1a | 82b86ba2ae0d5aed0f01f49c46db5afec0eb2bd7 | /stage0/src/Init/Control/StateRef.lean | 38fd9d21159f085ded41b295aafccbde96f05a7a | [
"Apache-2.0"
] | permissive | banksonian/lean4 | 3a2e6b0f1eb63aa56ff95b8d07b2f851072d54dc | 78da6b3aa2840693eea354a41e89fc5b212a5011 | refs/heads/master | 1,673,703,624,165 | 1,605,123,551,000 | 1,605,123,551,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,521 | 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, Sebastian Ullrich
The State monad transformer using IO references.
-/
prelude
import Init.System.IO
import Init.Control.State
def StateRefT' (ω : Type) (σ :... |
8a87f67569dedd2ee53b2555e0f5bdf98a088fbc | d29d82a0af640c937e499f6be79fc552eae0aa13 | /src/data/nat/totient.lean | 0e306e851b514da4226eae69f1c8fb285ec29962 | [
"Apache-2.0"
] | permissive | AbdulMajeedkhurasani/mathlib | 835f8a5c5cf3075b250b3737172043ab4fa1edf6 | 79bc7323b164aebd000524ebafd198eb0e17f956 | refs/heads/master | 1,688,003,895,660 | 1,627,788,521,000 | 1,627,788,521,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,650 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import algebra.big_operators.basic
import data.zmod.basic
/-!
# Euler's totient function
This file defines [Euler's totient function][https://en.wikipedia.org/wiki/Eule... |
e760b5f7d6a4fe6bf2153abd2ecd06449d302d6a | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/coe11.lean | 734f7c3c7d3b106eb7dc63172bb9a2de7fcf1a4b | [
"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 | 970 | lean | import algebra.category.basic
open category
inductive my_functor {obC obD : Type} (C : category obC) (D : category obD) : Type :=
mk : Π (obF : obC → obD) (homF : Π{A B : obC}, hom A B → hom (obF A) (obF B)),
(Π {A : obC}, homF (ID A) = ID (obF A)) →
(Π {A B C : obC} {f : hom A B} {g : hom B C}, homF (g ∘ f) =... |
92fdcc062e821175f211c9e6d899c9c1664f0e8d | 82b86ba2ae0d5aed0f01f49c46db5afec0eb2bd7 | /tests/lean/ppSyntax.lean | 76c4d66c4649e50b5101a5fd178bea9d893eccb1 | [
"Apache-2.0"
] | permissive | banksonian/lean4 | 3a2e6b0f1eb63aa56ff95b8d07b2f851072d54dc | 78da6b3aa2840693eea354a41e89fc5b212a5011 | refs/heads/master | 1,673,703,624,165 | 1,605,123,551,000 | 1,605,123,551,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 175 | lean | import Lean
open Lean
def test (stx : Unhygienic Syntax) : MetaM Unit :=
PrettyPrinter.ppTerm stx.run >>= IO.println
-- test imported `ParserDescr`
#eval test `(s!"hi!")
|
0183a5e0c755bf1163fd6192baa61c36fc741a12 | 1a2aed113dcb5f1c07ae98040953fba5e6563624 | /lean_root/src/tao_ch5.lean | 1895044d510ce2f6d765d14b22e399ce39a8a536 | [
"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 | 554 | lean |
import order.bounds
import data.real.basic
-- Consider reworking to be congruent with mathlib's bounds or ereals.
-- https://leanprover-community.github.io/mathlib_docs/order/bounds.html#lower_bounds
def has_infinite_sup (X : set ℝ) : Prop :=
X.nonempty ∧ ¬ (upper_bounds X).nonempty
def has_infinite_inf (X : set ℝ) ... |
e63b3c9a7ec3bafc5aafdf3a9b5a18faf12b75c7 | ad31a621913db8baff8c0518c10b76ef58a178c0 | /src/3_nat_equiv_nat_sq.lean | b60428ef9e9513ed9bc076c644383ff81e39dde3 | [] | no_license | shingtaklam1324/lean_blog | 0a881d38273bf8f45a8c837ebc131a2c529884fb | 730670bb1066d081a4c6a1494badb5f4be27cdbc | refs/heads/master | 1,668,249,864,724 | 1,592,876,934,000 | 1,592,876,934,000 | 274,282,996 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,458 | lean | import data.equiv.basic
data.nat.prime
data.nat.multiplicity
tactic
set_theory.schroeder_bernstein
open function nat
def to_fun : ℕ → ℕ × ℕ := λ x, (x,0)
def inv_fun' : ℕ × ℕ → ℕ := λ ⟨x,y⟩, 2^x * 3^y
lemma injective_to_fun : injective to_fun :=
begin
intros a b h,
unfold to_fun at h... |
93f7753de83a5f4fce328dcbf5f180013a38452f | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /08_Building_Theories_and_Proofs.org.10.lean | f9f1dec4e0a904b2967ae2901ff56da0c97259c8 | [] | 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 | 523 | lean | import standard
import data.examples.vector
open vector nat
-- BEGIN
variables (P : Π (n m : ℕ) (v : vector bool n) (w : vector bool m), Type)
(p : Π (n m : ℕ) (v : vector bool n) (w : vector bool m), P n m v w)
(n m : ℕ) (v : vector bool n) (w : vector bool m)
set_option pp.metavar_args false
eval (!p : P n m v w) ... |
2e3530188b722b8716e8eea90b89776ea26fa9d8 | a4673261e60b025e2c8c825dfa4ab9108246c32e | /stage0/src/Lean/Util/ReplaceLevel.lean | 0b892e18f57a772cc402771e96f9a4f3c51f63a4 | [
"Apache-2.0"
] | permissive | jcommelin/lean4 | c02dec0cc32c4bccab009285475f265f17d73228 | 2909313475588cc20ac0436e55548a4502050d0a | refs/heads/master | 1,674,129,550,893 | 1,606,415,348,000 | 1,606,415,348,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,421 | 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.Expr
namespace Lean
namespace Level
partial def replace (f? : Level → Option Level) (u : Level) : Level :=
match f? u with
| some v => v
... |
cf7ee9db4926f87fae87f006a5c01d69e2f389e2 | 66a6486e19b71391cc438afee5f081a4257564ec | /algebra/graded.hlean | d4f3f8536ed55e2b0ab30f2bca60e824d6e2d065 | [
"Apache-2.0"
] | permissive | spiceghello/Spectral | c8ccd1e32d4b6a9132ccee20fcba44b477cd0331 | 20023aa3de27c22ab9f9b4a177f5a1efdec2b19f | refs/heads/master | 1,611,263,374,078 | 1,523,349,717,000 | 1,523,349,717,000 | 92,312,239 | 0 | 0 | null | 1,495,642,470,000 | 1,495,642,470,000 | null | UTF-8 | Lean | false | false | 28,448 | hlean | /- Graded (left-) R-modules for a ring R. -/
-- Author: Floris van Doorn
import .left_module .direct_sum .submodule --..heq
open is_trunc algebra eq left_module pointed function equiv is_equiv prod group sigma sigma.ops nat
trunc_index property
namespace left_module
definition graded [reducible] (str : Type) (I :... |
7bfe4b8756c465b83975e855388a71366adee700 | 9b9a16fa2cb737daee6b2785474678b6fa91d6d4 | /src/category_theory/functor_category.lean | 4c5807678b42d985c1ff65c8b380560e6b3749da | [
"Apache-2.0"
] | permissive | johoelzl/mathlib | 253f46daa30b644d011e8e119025b01ad69735c4 | 592e3c7a2dfbd5826919b4605559d35d4d75938f | refs/heads/master | 1,625,657,216,488 | 1,551,374,946,000 | 1,551,374,946,000 | 98,915,829 | 0 | 0 | Apache-2.0 | 1,522,917,267,000 | 1,501,524,499,000 | Lean | UTF-8 | Lean | false | false | 2,683 | 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
import category_theory.natural_transformation
namespace category_theory
universes v₁ v₂ v₃ u₁ u₂ u₃ -- declare the `v`'s first; see... |
bf315045c531a8caac4931d89a08c6d562984ff2 | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /tests/lean/run/e8.lean | 73f1e2382d5a4600602e3604bf21a129640bbf73 | [
"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 | 835 | lean | precedence `+`:65
namespace nat
constant nat : Type.{1}
constant add : nat → nat → nat
infixl + := add
end nat
namespace int
open nat (nat)
constant int : Type.{1}
constant add : int → int → int
infixl + := add
constant of_nat : nat → int
coercion of_nat
end int
-- Open "only" the notation and decl... |
454997875d2784bb6b3867e16668380518ac2f86 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/algebraic_geometry/Spec.lean | 03a242b6849ba970706b6dd5d5de4daa26b28db9 | [
"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 | 8,643 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Justus Springer
-/
import algebraic_geometry.locally_ringed_space
import algebraic_geometry.structure_sheaf
import data.equiv.transfer_instance
/-!
# $Spec$ as a funct... |
047811f855a6f9fa43391eccc3977247913f4fee | df561f413cfe0a88b1056655515399c546ff32a5 | /3-function-world/l2.lean | 7354d9484feaa04f5c83acbae3bf86c30ebdec29 | [] | no_license | nicholaspun/natural-number-game-solutions | 31d5158415c6f582694680044c5c6469032c2a06 | 1e2aed86d2e76a3f4a275c6d99e795ad30cf6df0 | refs/heads/main | 1,675,123,625,012 | 1,607,633,548,000 | 1,607,633,548,000 | 318,933,860 | 3 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 60 | lean | example : mynat → mynat :=
begin
intro n, exact 3*n+2,
end |
639e56ca4b9b858f54eb42513022c23a332f6302 | 19cc34575500ee2e3d4586c15544632aa07a8e66 | /src/data/complex/is_R_or_C.lean | 806129c557990c25f1891faa3a427cb52fdced0e | [
"Apache-2.0"
] | permissive | LibertasSpZ/mathlib | b9fcd46625eb940611adb5e719a4b554138dade6 | 33f7870a49d7cc06d2f3036e22543e6ec5046e68 | refs/heads/master | 1,672,066,539,347 | 1,602,429,158,000 | 1,602,429,158,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 25,802 | 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.normed_space.basic
import analysis.complex.basic
/-!
# `is_R_or_C`: a typeclass for ℝ or ℂ
This file defines the typeclass `is_R_or_C` intended t... |
bd3beffd2719d46c04b4522db7288ac0769ed4bd | 8d65764a9e5f0923a67fc435eb1a5a1d02fd80e3 | /src/analysis/calculus/fderiv_symmetric.lean | b5cd69507ceb803980a05f34619f918527fa64de | [
"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 | 19,573 | 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 analysis.calculus.deriv
import analysis.calculus.mean_value
import analysis.convex.topology
/-!
# Symmetry of the second derivative
We show that, over ... |
4e8fd4e4553dc74aaa102f0ddbd7eaf1704f1a28 | c61b91f85121053c627318ad8fcde30dfb8637d2 | /Chapter3/3-2.lean | 0d58ede3bbc6fa6b5f716f42150332dbad1efcfb | [] | no_license | robkorn/theorem-proving-in-lean-exercises | 9e2256360eaf6f8df6cdd8fd656e63dfb04c8cdb | 9c51da587105ee047a9db55d52709d881a39be7a | refs/heads/master | 1,585,403,341,988 | 1,540,142,619,000 | 1,540,142,619,000 | 148,431,678 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,666 | lean |
namespace hidden
constants p q : Prop
theorem t1 : p → q → p := λ hp : p, λ hq : q, hp
#print t1
theorem tt1 : p -> q -> p :=
assume hp : p,
assume hq : q,
show p, from hp
lemma ttt1 : p -> q -> q :=
λ hp : p,
assume hq : q,
show q, from hq
lemma tl ... |
f4ee1dc403450533bcbe6334f9e75822ece25d63 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/analysis/complex/basic.lean | 13ccea2e8b15c45be631a06e071a8ceef9845be7 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 15,055 | lean | /-
Copyright (c) Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import data.complex.determinant
import data.complex.is_R_or_C
/-!
# Normed space structure on `ℂ`.
This file gathers basic facts on complex numbers of an analytic ... |
fd860142c32124faba28e83d393a3233f774938d | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/varBinderUpdate.lean | 2710b16bdbead5b69a8e9cb2af4b58f3707fdcc0 | [
"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 | 805 | lean | namespace Ex1
variable {α : Type}
variable [Add α]
variable (α)
def f (a : α) := a + a
#check f Nat 5
variable {α}
def g (b : α) := b
#check g 5
#check f
#check g
end Ex1
namespace Ex2
variable {α β : Type}
variable (α)
def f (a : α) := a
def g (b : β) := b
#check f Nat 5
#check g 5
#check f
#check g
variable (α)
en... |
d4a486ee867fcb1bee28158cc9fc112208b2bf3f | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/analysis/asymptotics/specific_asymptotics.lean | 3d5227187c385a30e045cb188571f4debb164ca1 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 2,659 | lean | /-
Copyright (c) 2021 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
import analysis.normed_space.ordered
import analysis.asymptotics.asymptotics
/-!
# A collection of specific asymptotic results
This file contains specific lemma... |
39236753bf13ae60ee83c0824570ec0ff49b0bd4 | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /stage0/src/Lean/Meta/Basic.lean | e13bc96cc6c43d47589f38a802fcc5b500f43127 | [
"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 | tobiasgrosser/lean4 | ce0fd9cca0feba1100656679bf41f0bffdbabb71 | ebdbdc10436a4d9d6b66acf78aae7a23f5bd073f | refs/heads/master | 1,673,103,412,948 | 1,664,930,501,000 | 1,664,930,501,000 | 186,870,185 | 0 | 0 | Apache-2.0 | 1,665,129,237,000 | 1,557,939,901,000 | Lean | UTF-8 | Lean | false | false | 73,212 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Data.LOption
import Lean.Environment
import Lean.Class
import Lean.ReducibilityAttrs
import Lean.Util.ReplaceExpr
import Lean.Util.MonadBacktrac... |
a6f80a966f800e1091f924c420ef2f6a863951bb | 4727251e0cd73359b15b664c3170e5d754078599 | /src/topology/uniform_space/basic.lean | dab3dfc966d1edafcfcb7bae4c5aaa6ede61a4c2 | [
"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 | 74,190 | 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
-/
import order.filter.lift
import topology.subset_properties
/-!
# Uniform spaces
Uniform spaces are a generalization of metric spaces ... |
f4734f85856dc89468616a6df80fba2d830e47ca | 618003631150032a5676f229d13a079ac875ff77 | /src/algebra/continued_fractions/default.lean | 5d91f70b04f0e4cb9b4bc5bae649d8adaf0b924c | [
"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 | 418 | lean | /-
Copyright (c) 2019 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 algebra.continued_fractions.convergents_equi... |
8375b6dd144448afdc3b3a3339b12d1ff4569bb4 | f618aea02cb4104ad34ecf3b9713065cc0d06103 | /src/data/real/nnreal.lean | a6b19fef03b78e0a647cb6134b388c612adfbaf6 | [
"Apache-2.0"
] | permissive | joehendrix/mathlib | 84b6603f6be88a7e4d62f5b1b0cbb523bb82b9a5 | c15eab34ad754f9ecd738525cb8b5a870e834ddc | refs/heads/master | 1,589,606,591,630 | 1,555,946,393,000 | 1,555,946,393,000 | 182,813,854 | 0 | 0 | null | 1,555,946,309,000 | 1,555,946,308,000 | null | UTF-8 | Lean | false | false | 15,608 | 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 algebra.field
local attribute [instance, priority 0] nat.cast_coe
local attribute [instance, priority... |
94095b040c2a3996e17558474de63291944949f9 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /src/Lean/Compiler/IR/EmitC.lean | db46c338bd66f7e7e8aaef1b1599acf3ba5a26b1 | [
"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 | 26,210 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Runtime
import Lean.Compiler.NameMangling
import Lean.Compiler.ExportAttr
import Lean.Compiler.InitAttr
import Lean.Compiler.IR.CompilerM
import... |
97e0361d753c7b2c3ef2096890ea1bed6465b672 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /tests/lean/run/nested_rec.lean | ba9a6c6eb8bcc6e35d64cbe4a90d5a769fc04218 | [
"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 | 1,254 | lean | open nat prod sigma
-- We will define the following example by well-foudned recursion
-- g 0 := 0
-- g (succ x) := g (g x)
definition g.F (x : nat) : (Π y, y < x → Σ r : nat, r ≤ y) → Σ r : nat, r ≤ x :=
nat.cases_on x
(λ f, ⟨zero, le.refl zero⟩)
(λ x₁ (f : Π y, y < succ x₁ → Σ r : nat, r ≤ y),
let... |
157f10823b3e969b77dc89f00052a279f2f42f3d | d7189ea2ef694124821b033e533f18905b5e87ef | /galois/subset/subset.lean | 0aefa8214b6e9c30e40310a5d20f1f37d585bf33 | [
"Apache-2.0"
] | permissive | digama0/lean-protocol-support | eaa7e6f8b8e0d5bbfff1f7f52bfb79a3b11b0f59 | cabfa3abedbdd6fdca6e2da6fbbf91a13ed48dda | refs/heads/master | 1,625,421,450,627 | 1,506,035,462,000 | 1,506,035,462,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,886 | lean | import galois.tactic
galois.list.preds
universes u v w
/-- Defines a subset of a type -/
def subset (A : Sort u) := A → Prop
namespace subset
section
parameter {A : Type u}
/-- A subset that is the same for all members of the type -/
def const (P : Prop) : subset A := λ _, P
/-- The subset with all memebers -... |
d445fe1289201770be00bbfbe6dc3777730002ac | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/topology/metric_space/closeds.lean | a1c8c58c7900fee86b1066b1fd9e8c970a400b1e | [
"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 | 21,278 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import topology.metric_space.hausdorff_distance
import topology.compacts
import analysis.specific_limits
/-!
# Closed subsets
This file defines the metric and... |
d3dfa8e3798f974d5101b84d508565f93fdf5137 | f083c4ed5d443659f3ed9b43b1ca5bb037ddeb58 | /data/int/basic.lean | 3ebc5874cb4ffddb419c89675661047f8438246c | [
"Apache-2.0"
] | permissive | semorrison/mathlib | 1be6f11086e0d24180fec4b9696d3ec58b439d10 | 20b4143976dad48e664c4847b75a85237dca0a89 | refs/heads/master | 1,583,799,212,170 | 1,535,634,130,000 | 1,535,730,505,000 | 129,076,205 | 0 | 0 | Apache-2.0 | 1,551,697,998,000 | 1,523,442,265,000 | Lean | UTF-8 | Lean | false | false | 45,056 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
The integers, with addition, multiplication, and subtraction.
-/
import data.nat.basic algebra.char_zero algebra.order_functions
open nat
namespace int
instance : inhab... |
016b3c36c71d9daaf233ec2e32c79d9095caf17c | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/analysis/box_integral/integrability.lean | 763a6ca1b9fd9ee54932d5ceda094ed60b4a205c | [
"Apache-2.0"
] | permissive | waynemunro/mathlib | e3fd4ff49f4cb43d4a8ded59d17be407bc5ee552 | 065a70810b5480d584033f7bbf8e0409480c2118 | refs/heads/master | 1,693,417,182,397 | 1,634,644,781,000 | 1,634,644,781,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 17,646 | lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import analysis.box_integral.basic
/-!
# McShane integrability vs Bochner integrability
In this file we prove that any Bochner integrable function is McShane inte... |
37f03c6d4fb7044f72e204909718abd0906f0c36 | 5df84495ec6c281df6d26411cc20aac5c941e745 | /src/formal_ml/lattice.lean | 5286969de64eed29f7d6e165a9d3056ee0d0bef4 | [
"Apache-2.0"
] | permissive | eric-wieser/formal-ml | e278df5a8df78aa3947bc8376650419e1b2b0a14 | 630011d19fdd9539c8d6493a69fe70af5d193590 | refs/heads/master | 1,681,491,589,256 | 1,612,642,743,000 | 1,612,642,743,000 | 360,114,136 | 0 | 0 | Apache-2.0 | 1,618,998,189,000 | 1,618,998,188,000 | null | UTF-8 | Lean | false | false | 2,183 | lean | import order.complete_lattice
lemma le_supr'' {α : Type*} {ι : Sort*} [_inst_1 : complete_lattice α] (s : ι → α) (i : ι) (x:α):
(x ≤ s i) → x ≤ supr s :=
begin
intro A1,
apply le_trans A1,
apply le_supr,
end
lemma infi_prop_def {α:Type*} [complete_lattice α]
{v:α} {P:Prop} (H:P):(⨅ (H2:P), v) = v :=
be... |
73333b948b59233ecc7ab2013a18f7320b62c501 | 07c6143268cfb72beccd1cc35735d424ebcb187b | /src/topology/uniform_space/cauchy.lean | c8afcb37a398bb6b938b1ac8a29a3460582d36a4 | [
"Apache-2.0"
] | permissive | khoek/mathlib | bc49a842910af13a3c372748310e86467d1dc766 | aa55f8b50354b3e11ba64792dcb06cccb2d8ee28 | refs/heads/master | 1,588,232,063,837 | 1,587,304,803,000 | 1,587,304,803,000 | 176,688,517 | 0 | 0 | Apache-2.0 | 1,553,070,585,000 | 1,553,070,585,000 | null | UTF-8 | Lean | false | false | 25,043 | 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
Theory of Cauchy filters in uniform spaces. Complete uniform spaces. Totally bounded subsets.
-/
import topology.uniform_space.basic topology.bases data... |
7a9b145721e7aaef36fb89bffb4aa82582f4bb0d | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/algebra/char_zero.lean | a775dc0f6aa41a35fc7f1087b4926967ebec18a7 | [
"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 | 6,244 | lean | /-
Copyright (c) 2014 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.nat.cast
import data.fintype.basic
import tactic.wlog
/-!
# Characteristic zero
A ring `R` is called of characteristic zero if every natural number `n`... |
4ed25c569f3335ca6088814c4b3aaa7d6fc0ce1e | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/ring_theory/polynomial/chebyshev/default.lean | 05ad32d9f4d117e867963225deb72d2c01434a72 | [
"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 | 46 | lean | import ring_theory.polynomial.chebyshev.basic
|
65aa2a07ece00f5c2b54bb3cdba0721c98d925ba | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/548.lean | 7b0b13e06c9b7f8869a388c8538477f29492b29a | [
"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 | 667 | lean | open nat
example (a b : nat) (P : nat → Prop) (H₁ : a = b) (H₂ : P a) : P b :=
begin
rewrite H₁ at *,
exact H₂
end
example (a b : nat) (P : nat → Prop) (H₀ : a = 0 → b = 1) (H₁ : a = 0) (H₂ : P b) : P 1 :=
begin
rewrite (H₀ H₁) at *,
exact H₂
end
example (a c : nat) (P : nat → Prop) (H₁ : P a) (b : nat) (H₂ ... |
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