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class | length_bytes int64 3 6.4M | extension stringclasses 4
values | content stringlengths 3 6.12M |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
f9c13841b86fe1881ba652a61f194752ac25c7e2 | 36c7a18fd72e5b57229bd8ba36493daf536a19ce | /tests/lean/run/blast_simp2.lean | 1839a8b7386b0bf6b38394554a7d8e1702f9d3c5 | [
"Apache-2.0"
] | permissive | YHVHvx/lean | 732bf0fb7a298cd7fe0f15d82f8e248c11db49e9 | 038369533e0136dd395dc252084d3c1853accbf2 | refs/heads/master | 1,610,701,080,210 | 1,449,128,595,000 | 1,449,128,595,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 117 | lean | set_option blast.recursor false
definition tst1 (a b : Prop) : a ∧ b ∧ true → b ∧ a :=
by blast
print tst1
|
b58e2c30255b6f7d06ceb090f4b3e3fbdee7cd97 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /tests/lean/run/macro2.lean | d315a7a4ba74da401600e7afc4ffdd795b23a7f3 | [
"Apache-2.0"
] | permissive | mhuisi/lean4 | 28d35a4febc2e251c7f05492e13f3b05d6f9b7af | dda44bc47f3e5d024508060dac2bcb59fd12e4c0 | refs/heads/master | 1,621,225,489,283 | 1,585,142,689,000 | 1,585,142,689,000 | 250,590,438 | 0 | 2 | Apache-2.0 | 1,602,443,220,000 | 1,585,327,814,000 | C | UTF-8 | Lean | false | false | 353 | lean | new_frontend
notation a `**`:50 b:50 => b * a * b
notation "~" a => a+a
namespace Foo
notation "~~" a => a+a
end Foo
syntax term "+++":60 term:59 : term
syntax "<|" term "|>" : term
macro_rules
| `($a +++ $b) => `($a + $b + $b)
macro_rules
| `(<| $x |>) => `($x +++ 1 ** 2)
#check <| 2 |>
#check <| ~2 |>
#check... |
8a0aa253a5542e7d238ebea081033ebd17a98d3d | 6094e25ea0b7699e642463b48e51b2ead6ddc23f | /tests/lean/run/impbug4.lean | 22e2371947d2ce54ef7b5e1f3817a1d5bab7b8a6 | [
"Apache-2.0"
] | permissive | gbaz/lean | a7835c4e3006fbbb079e8f8ffe18aacc45adebfb | a501c308be3acaa50a2c0610ce2e0d71becf8032 | refs/heads/master | 1,611,198,791,433 | 1,451,339,111,000 | 1,451,339,111,000 | 48,713,797 | 0 | 0 | null | 1,451,338,939,000 | 1,451,338,939,000 | null | UTF-8 | Lean | false | false | 646 | lean | prelude
-- category
definition Prop := Type.{0}
constant eq {A : Type} : A → A → Prop
infix `=`:50 := eq
constant ob : Type.{1}
constant mor : ob → ob → Type.{1}
inductive category : Type :=
mk : Π (id : Π (A : ob), mor A A),
(Π (A B : ob) (f : mor A A), id A = f) → category
definition id (Cat : category) := ... |
6e172311599c29f38d8f9bdd0e6af8ba2e86b7f1 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/data/indicator_function.lean | 48f97d076427fb2ec02a7e23d1fe0b9c6166ed7c | [
"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 | 11,718 | lean | /-
Copyright (c) 2020 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
-/
import algebra.group.pi
import group_theory.group_action
import data.support
import data.finset.lattice
/-!
# Indicator function
`indicator (s : set α) (f : α → β) (a... |
77a8b6b08fe9d74eaf30fb60f5718511fd22e0d9 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/order/basic.lean | 3cfd352996eb7ed9ca3fb8b818f5eeb0db6059e7 | [
"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 | 20,287 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Mario Carneiro
-/
import data.subtype
import data.prod
open function
/-!
# Basic definitions about `≤` and `<`
## Definitions
### Predicates on functions
- `monotone... |
fde271df0049b2a7d48848abfdbd47cb065cbc24 | 29cc89d6158dd3b90acbdbcab4d2c7eb9a7dbf0f | /Exercises 7/24_exercise_sheet.lean | 23900b4c4c6ce0f664fc8cba7f4d63dcbafecaa2 | [] | no_license | KjellZijlemaker/Logical_Verification_VU | ced0ba95316a30e3c94ba8eebd58ea004fa6f53b | 4578b93bf1615466996157bb333c84122b201d99 | refs/heads/master | 1,585,966,086,108 | 1,549,187,704,000 | 1,549,187,704,000 | 155,690,284 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,370 | lean | /- Exercise 2.4: Functional Programming — Metaprogramming -/
open expr
open tactic
/- Question 1: A term exploder -/
/- In this exercise, we develop a string format for the `expr` metatype. By default, there is no
`has_repr` instance to print a nice string. For example: -/
#eval (expr.app (expr.var 0) (expr.var 1)... |
31cf7950528c290ebbff47d185eed36d1070a95f | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/probability/notation.lean | 4c4d31f9632c7e1f2ce478ab7d955d69fe5644da | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 2,058 | 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 measure_theory.function.conditional_expectation.real
/-! # Notations for probability theory
This file defines the following notations, for functions `X,Y`, measu... |
67ae7808b754ae87774d64be7d6b668bf789f6d9 | ebb7367fa8ab324601b5abf705720fd4cc0e8598 | /homotopy/splice.hlean | 53cb2f45e5315d6fa49945b2d0ef66ab6489aff3 | [
"Apache-2.0"
] | permissive | radams78/Spectral | 3e34916d9bbd0939ee6a629e36744827ff27bfc2 | c8145341046cfa2b4960ef3cc5a1117d12c43f63 | refs/heads/master | 1,610,421,583,830 | 1,481,232,014,000 | 1,481,232,014,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,111 | hlean | /-
Copyright (c) 2016 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
Given a sequence of LES's, we want to splice them together.
... -> G_{1,k+1} -> G_{1,k} -> ... -> G_{1,1} -> G_{1,0}
... -> G_{2,k+1} -> G_{2,k} -> ... -> G_{2,1} ... |
c46745169535fb006abb868004c816d0f2ef310d | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/lie/solvable.lean | 88bb281acdadd4803e5d1b1439ba579207cdfd30 | [
"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 | 13,856 | 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.abelian
import algebra.lie.ideal_operations
import order.hom.basic
/-!
# Solvable Lie algebras
Like groups, Lie algebras admit a natural concept of sol... |
1ab1e9beb63c5b4b2231d07c2c01439f6edb6464 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/analysis/calculus/iterated_deriv.lean | 2b5968487d56800b18f0a18feb829915cdd7b82e | [
"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 | 14,452 | lean | /-
Copyright (c) 2020 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.cont_diff
/-!
# One-dimensional iterated derivatives
We define the `n`-th derivative of a function `f ... |
3b6d3cd7af64e61d49ff05f46d35261ec81c3712 | 554a228c368610a5d1be723291978b3bd38450ba | /fib.lean | 931f561f19f7e26e22af39dd10509584a01bfd1d | [] | no_license | wudcscheme/fib | e55b49ee803bf863cf47ceb2c0f43650826e28ff | 74fcd824aaf75c4705785a5a802791b889196118 | refs/heads/master | 1,678,988,835,876 | 1,431,792,926,000 | 1,431,792,926,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,332 | lean | import logic standard classical data.nat data.list
open decidable nat list
namespace fib
definition fib : ℕ → ℕ,
fib 0 := 0,
fib 1 := 1,
fib (succ (succ n)) := fib n + fib (succ n)
/-
fₙ ≤ fₙ₊₁
-/
private theorem nondecreasing'' : ∀ n : ℕ, fib n ≤ fib (succ n),
nondecreas... |
9f08870876e832d5518b49d490c7a81a38fb3013 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/group_theory/group_action/group.lean | ab1d85d8eddaf17839d1c5fb85aac376f0508825 | [
"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 | 10,849 | 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.hom.aut
import group_theory.group_action.units
/-!
# Group actions applied to various types of group
This file contains lemmas about `smul` on `group_wit... |
2a2187d4cc2c05bf507e5b2c8f8216f1504298aa | 02fbe05a45fda5abde7583464416db4366eedfbf | /library/init/control/state.lean | 7c5b61588be5a59fa526a71679b13507df8ce3cb | [
"Apache-2.0"
] | permissive | jasonrute/lean | cc12807e11f9ac6b01b8951a8bfb9c2eb35a0154 | 4be962c167ca442a0ec5e84472d7ff9f5302788f | refs/heads/master | 1,672,036,664,637 | 1,601,642,826,000 | 1,601,642,826,000 | 260,777,966 | 0 | 0 | Apache-2.0 | 1,588,454,819,000 | 1,588,454,818,000 | null | UTF-8 | Lean | false | false | 7,775 | 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, Sebastian Ullrich
The state monad transformer.
-/
prelude
import init.control.alternative init.control.lift
import init.control.id init.control.except
univer... |
159ce8f64a0ad1e6298e996b7c2d0eb91cd3d4ab | cb1829c15cd3d28210f93507f96dfb1f56ec0128 | /introduction/summer2017/overview.lean | f02e4a92d554296e505e7a3f17fd44eaeb23e676 | [] | no_license | williamdemeo/LEAN_wjd | 69f9f76e35092b89e4479a320be2fa3c18aed6fe | 13826c75c06ef435166a26a72e76fe984c15bad7 | refs/heads/master | 1,609,516,630,137 | 1,518,123,893,000 | 1,518,123,893,000 | 97,740,278 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,166 | lean | -- Chapter 1. Overview
#check "hello, world!"
-- page 6
namespace hide
inductive nat: Type
| zero: nat
| succ: nat → nat
def add: nat → nat → nat
| m nat.zero := m
| m (nat.succ n) := nat.succ (add m n)
#eval add nat.zero (nat.succ (nat.succ nat.zero))
end hide
def double (n: ℕ) : ℕ := n + n
#check double
#pr... |
7efa161ca14ad4fb556d5aa1b7de26882cecbdcf | 968e2f50b755d3048175f176376eff7139e9df70 | /examples/pred_logic/unnamed_429.lean | a59a2969f20dee120191dd02f74579e3b94c23ff | [] | 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 | 415 | lean | example : ∀ p q : Prop, p ∧ q ↔ q ∧ p :=begin
intros r s, -- Assume `r : Prop` and `s : Prop`. It suffices to prove `r ∧ s ↔ s ∧ r`.
split; -- By iff intro., it suffices to prove 1. `r ∧ s → s ∧ r` and 2. `s ∧ r → r ∧ s`. We'll use the same proof in each case.
{ intro h, exact ⟨h.2, h.1⟩, }, -- Assume the anteced... |
73dc5834ed8b68b28365fc1bda72f358b131f411 | c31182a012eec69da0a1f6c05f42b0f0717d212d | /src/rescale/Tinv.lean | 73556793fa9dfdc406a73c9a5b00cf0222d6b2e7 | [] | no_license | Ja1941/lean-liquid | fbec3ffc7fc67df1b5ca95b7ee225685ab9ffbdc | 8e80ed0cbdf5145d6814e833a674eaf05a1495c1 | refs/heads/master | 1,689,437,983,362 | 1,628,362,719,000 | 1,628,362,719,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,463 | lean | import pseudo_normed_group.Tinv
import rescale.CLC
open_locale classical nnreal
noncomputable theory
local attribute [instance] type_pow
open opposite ProFiltPseuNormGrpWithTinv category_theory
universe variable u
variables (r : ℝ≥0) (V : SemiNormedGroup) [normed_with_aut r V] [fact (0 < r)]
variables (r' : ℝ≥0) [fac... |
76b3581396efec361d80dae10a06a39c28b71322 | 3dc4623269159d02a444fe898d33e8c7e7e9461b | /.github/workflows/geo/src/com.lean | 3ab19ce44168359cb3d8763dc47cdd64fac07c36 | [] | no_license | Or7ando/lean | cc003e6c41048eae7c34aa6bada51c9e9add9e66 | d41169cf4e416a0d42092fb6bdc14131cee9dd15 | refs/heads/master | 1,650,600,589,722 | 1,587,262,906,000 | 1,587,262,906,000 | 255,387,160 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,308 | lean | /- Author: E.W.Ayers
Show that the open covers for a topological space form a basis for a grothendieck topology.
-/
import topology.category.Top.opens
import category_theory.limits.lattice
import category_theory.limits.limits
import category_theory.limits.shapes.pullbacks
import .grothendieck
universes u
open cate... |
70f8717732d8851233bc60c48337a14f5976eaf7 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/measure_theory/integral/integral_eq_improper.lean | 29e6a17f7b7af8677115c0a4a53ddc486f63ffba | [
"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 | 22,190 | 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 measure_theory.integral.interval_integral
import order.filter.at_top_bot
/-!
# Links between an integral and its "improper" version
In its current state,... |
bd32c72f9a7c2d671c6641e1195a972d310a3579 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/category_theory/limits/shapes/finite_limits.lean | db6672e8d014f554087aeafacc790a2bb047fcca | [
"Apache-2.0"
] | permissive | gebner/mathlib | eab0150cc4f79ec45d2016a8c21750244a2e7ff0 | cc6a6edc397c55118df62831e23bfbd6e6c6b4ab | refs/heads/master | 1,625,574,853,976 | 1,586,712,827,000 | 1,586,712,827,000 | 99,101,412 | 1 | 0 | Apache-2.0 | 1,586,716,389,000 | 1,501,667,958,000 | Lean | UTF-8 | Lean | false | false | 2,003 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.limits.shapes.products
import category_theory.discrete_category
import data.fintype.basic
universes v u
open category_theory
namespace catego... |
f78e1a8a74b8126361b3d13bc2c741fb189087d8 | 38bf3fd2bb651ab70511408fcf70e2029e2ba310 | /src/category_theory/monad/adjunction.lean | dfc3421482c5939e53da96d6cd7369d3141b86ab | [
"Apache-2.0"
] | permissive | JaredCorduan/mathlib | 130392594844f15dad65a9308c242551bae6cd2e | d5de80376088954d592a59326c14404f538050a1 | refs/heads/master | 1,595,862,206,333 | 1,570,816,457,000 | 1,570,816,457,000 | 209,134,499 | 0 | 0 | Apache-2.0 | 1,568,746,811,000 | 1,568,746,811,000 | null | UTF-8 | Lean | false | false | 5,579 | 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 `... |
9e3ad3a5dccfdbb758159cf8cd64916e41089bda | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/prvCtor.lean | 18a978732c4dbefe7f5e2b6199b883b3d71c65df | [
"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 | 534 | lean | import Lean
private def a := 10
#check a
structure Name (x : String) where
private mk ::
val : String := x
deriving Repr
def n1 : Name "hello" := {}
def n2 : Name "hello" := ⟨"hello"⟩
def n3 : Name "hello" := Name.mk "hello"
open Lean in
#eval id (α := CoreM Unit) do modifyEnv fun env => { env with header.... |
0602167f0232328ea529ab40c286d5206e980305 | 9a0b1b3a653ea926b03d1495fef64da1d14b3174 | /tidy/lib/num.lean | c96becf8dcb1ff5ed08ada19aec88b4e1d82d8fa | [
"Apache-2.0"
] | permissive | khoek/mathlib-tidy | 8623b27b4e04e7d598164e7eaf248610d58f768b | 866afa6ab597c47f1b72e8fe2b82b97fff5b980f | refs/heads/master | 1,585,598,975,772 | 1,538,659,544,000 | 1,538,659,544,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,282 | lean | import data.nat.basic
import data.pnat
lemma nat.succ_pred (n : ℕ) (h : n ≠ 0) : nat.succ (nat.pred n) = n :=
begin
cases n,
contradiction,
simp
end
def fin.with_max (n m : ℕ) (h : m ≠ 0): fin m :=
⟨ min n (m-1), begin
have p := min_le_right n (nat.pred m),
have q := nat.lt_suc... |
705febac7b8ae4765206714ece0a88577137af2c | b561a44b48979a98df50ade0789a21c79ee31288 | /src/Lean/Meta/Tactic/Simp/Main.lean | 815c622bf2d938b0918cdc3240349a54c5cc6de8 | [
"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 | 21,135 | 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.Meta.Transform
import Lean.Meta.Tactic.Replace
import Lean.Meta.Tactic.Util
import Lean.Meta.Tactic.Clear
import Lean.Meta.Tactic.Simp.Types
imp... |
2c2cbc6bdadaf20cd531d7987e5bda4690dde908 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/combinatorics/derangements/finite.lean | 49ecd92338d599b134b811cca4e20302be0bdc37 | [
"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 | 4,720 | lean | /-
Copyright (c) 2021 Henry Swanson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Henry Swanson
-/
import combinatorics.derangements.basic
import data.fintype.card
import tactic.delta_instance
import tactic.ring
/-!
# Derangements on fintypes
This file contains lem... |
cef82a649bc280dafc8804f259e0f58a4250bd02 | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/real/nnreal.lean | 4912b549d1267e4bb6183fee3c076d6efa5ff875 | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 28,263 | lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import algebra.linear_ordered_comm_group_with_zero
import algebra.big_operators.ring
import data.real.basic
import data.indicator_function
import algebra.algebra.basi... |
bc73d69ed78d1eb919373520d4cfd4c8785cbd9d | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/277a.lean | c02d1d4ab8caa44a7c347f7e0bc531c339101c2d | [
"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 | 86 | lean | set_option hygiene false
infixl:67 " <>< " => nonexistant
#eval (1 <>< 11 : UInt64)
|
d6667f9c42ec89d605a0c9d2cec65d3ea738db86 | e6b8240a90527fd55d42d0ec6649253d5d0bd414 | /src/group_theory/coset.lean | 14031b5e2cb3d0e6166d614911e992b07f35f4aa | [
"Apache-2.0"
] | permissive | mattearnshaw/mathlib | ac90f9fb8168aa642223bea3ffd0286b0cfde44f | d8dc1445cf8a8c74f8df60b9f7a1f5cf10946666 | refs/heads/master | 1,606,308,351,137 | 1,576,594,130,000 | 1,576,594,130,000 | 228,666,195 | 0 | 0 | Apache-2.0 | 1,576,603,094,000 | 1,576,603,093,000 | null | UTF-8 | Lean | false | false | 9,161 | 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 data.equiv.basic data.quot
open set function
variable {α : Type*}
@[to_additive left_add_coset]
def left_coset [has_m... |
6eed3e7fec66c4c5646c4f9c387bbb8d0f0f254f | 367134ba5a65885e863bdc4507601606690974c1 | /src/algebra/char_p/quotient.lean | f88c9e00f3f470cb2500009a1151e374d6e6ee07 | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 1,449 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Eric Wieser
-/
import algebra.char_p.basic
import algebra.ring_quot
/-!
# Characteristic of quotients rings
-/
universes u v
namespace char_p
theorem quotient (R : Type u) [... |
84ced526ce54b38e89bfb12468ed200b77c99188 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/induction_tactic_delta.lean | 022521d978462775a43a0e189903d6963977e1cd | [
"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 | 379 | lean | open tactic
-- This test makes sure that [foo'] is not unfolded in the major premise,
-- since [foo'] is the type of the major premise of the provided recursor.
inductive foo (n : nat)
| mk : foo
definition foo' := @foo 0
definition foo'.rec := @foo.rec
example : Pi (x : foo'), x = x :=
by do x ← intro `x,
in... |
28e90b5c4ab9bb9ea387fedb8fb242c79f173cf5 | bb31430994044506fa42fd667e2d556327e18dfe | /src/data/set/pairwise.lean | 510c54cb4e6cc13c9660fff8c6e1db2658f97621 | [
"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 | 18,572 | 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 logic.relation
import logic.pairwise
import data.set.lattice
/-!
# Relations holding pairwise
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to thi... |
7ffeec22fbee26a497103ad86966c2e471b241ae | a4673261e60b025e2c8c825dfa4ab9108246c32e | /tests/lean/run/stxKindInsideNamespace.lean | bcd5d6556cf78f8db03e906312f44c0c0e6dc86a | [
"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 | 258 | lean | import Lean
namespace Foo
syntax[foo] "bla!" term : term
macro_rules[foo]
| `(bla! $x) => pure x
#check bla! 10
macro "foo!" x:term : term => pure x
#check foo! 10
elab "boo!" x:term : term =>
Lean.Elab.Term.elabTerm x none
#check boo! 20
end Foo
|
77eac93b6a626571510627f45b195933aa7dad71 | abd85493667895c57a7507870867b28124b3998f | /src/data/list/basic.lean | 5aec3f1e63e8ce3ce2027ef4ed1be2bec3fc58ad | [
"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 | 155,114 | lean | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
import algebra.group
import deprecated.group
import data.nat.basic
/-!
# Basic properties of ... |
317b082771b120ad52903975ba1671cd21e1c35f | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/ring_theory/coprime.lean | 8cbe6a31c5ba8094d80c85dacf86aca9719d127f | [
"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 | 11,480 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Ken Lee, Chris Hughes
-/
import tactic.ring
import algebra.big_operators.basic
import data.fintype.basic
import data.int.gcd
import data.set.disjointed
/-!
# Coprime elements of... |
e52ddb4e73e58f6c87e122ed0405b44ce47b1b17 | d5bef83c55d40cb88f9a01b755c882a93348a847 | /tests/lean/run/coe_to_fn.lean | c79b6e32f33cc01ee0be2cd5f4b1169d5a57ad77 | [
"Apache-2.0"
] | permissive | urkud/lean | 587d78216e1f0c7f651566e9e92cf8ade285d58d | 3526539070ea6268df5dd373deeb3ac8b9621952 | refs/heads/master | 1,660,171,634,921 | 1,657,873,466,000 | 1,657,873,466,000 | 249,789,456 | 0 | 0 | Apache-2.0 | 1,585,075,263,000 | 1,585,075,263,000 | null | UTF-8 | Lean | false | false | 671 | lean | universes u v w
structure equiv (α : Type u) (β : Type v) :=
(f : α → β) (g : β → α)
infix ` ≃ `:50 := equiv
variables {α : Type u} {β : Type v} {γ : Type w}
instance: has_coe_to_fun (α ≃ β) (λ _, α → β) := ⟨equiv.f⟩
@[symm] def equiv.inv : α ≃ β → β ≃ α
| ⟨f,g⟩ := ⟨g,f⟩
local postfix `⁻¹` := equiv.inv
-- coe_fn... |
7e8db2b23c268ab13999481e7bcac52bea72e462 | 968e2f50b755d3048175f176376eff7139e9df70 | /examples/prop_logic_theory/unnamed_2631.lean | 10ef0f4f580037a55f30537e6878e67b52c1eaea | [] | 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 | 676 | lean | import logic.basic
variables {p q : Prop}
local attribute [instance] classical.prop_decidable
-- BEGIN
example : ¬(p ∧ q) → ¬p ∨ ¬ q :=
begin
assume h₁ : ¬(p ∧ q), -- Assume `h₁ : ¬(p ∧ q)`. It sfufice to prove `¬p ∨ ¬q`.
by_contradiction h₂, -- For a contradiciton, assume `h₂ : ¬(¬p ∨ ¬q)`. It suffices ... |
75f69005f5956ef77d541ae781111d9c5ab8dd3f | 205f0fc16279a69ea36e9fd158e3a97b06834ce2 | /EXAMS/Exam2-Review.lean | b655e288a247b15a1ba6bab14e0f2bc8d04b4a71 | [] | no_license | kevinsullivan/cs-dm-lean | b21d3ca1a9b2a0751ba13fcb4e7b258010a5d124 | a06a94e98be77170ca1df486c8189338b16cf6c6 | refs/heads/master | 1,585,948,743,595 | 1,544,339,346,000 | 1,544,339,346,000 | 155,570,767 | 1 | 3 | null | 1,541,540,372,000 | 1,540,995,993,000 | Lean | UTF-8 | Lean | false | false | 8,258 | lean | /-
You need to understand the following
elements of automated predicate logic
for Exam 2
Suppose P and Q are arbitrary propositions
(i.e., P Q : Prop) and T and V are arbitrary
types (i.e., T V : Type).
Know the following forms, how to prove them,
how to use proofs of them, and how to do these
things in Lean.
... |
ca8152f93f9ca31587aba57230a4268c1196d306 | 4bcaca5dc83d49803f72b7b5920b75b6e7d9de2d | /src/Lean/Meta/IndPredBelow.lean | 2a36cd3fdc823e7d23a371eff9dbed32ef2a1e56 | [
"Apache-2.0"
] | permissive | subfish-zhou/leanprover-zh_CN.github.io | 30b9fba9bd790720bd95764e61ae796697d2f603 | 8b2985d4a3d458ceda9361ac454c28168d920d3f | refs/heads/master | 1,689,709,967,820 | 1,632,503,056,000 | 1,632,503,056,000 | 409,962,097 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 25,663 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dany Fabian
-/
import Lean.Meta.Constructions
import Lean.Meta.Transform
import Lean.Meta.Tactic
import Lean.Meta.Match.Match
import Lean.Meta.Reduce
namespace Lean.Meta.IndPr... |
419af182468047db0f52f5c107f88aada0cf3089 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/ematch_loop.lean | d54b9ddd54e470f670e99ec6a4d8a8f2b31aeb7e | [
"Apache-2.0"
] | permissive | leanprover-community/lean | 12b87f69d92e614daea8bcc9d4de9a9ace089d0e | cce7990ea86a78bdb383e38ed7f9b5ba93c60ce0 | refs/heads/master | 1,687,508,156,644 | 1,684,951,104,000 | 1,684,951,104,000 | 169,960,991 | 457 | 107 | Apache-2.0 | 1,686,744,372,000 | 1,549,790,268,000 | C++ | UTF-8 | Lean | false | false | 1,534 | lean | constant f : nat → nat
constant p : nat → Prop
/- The following axiom produces a matching loop -/
axiom fax : ∀ x, f (: f x :) = nat.succ x
axiom px : ∀ x, p x
attribute [ematch] fax
set_option trace.smt.ematch true
lemma ex1 (a b c : nat) : f a = b → p a :=
begin [smt]
intros, iterate {ematch},
ematch_using [px... |
e2880fc507de4aa86c0eed0fe51c9f88963d6acc | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Meta/MatchUtil.lean | 06d1a924c49ef21ff12914988a640124a651ec45 | [
"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 | 2,017 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Util.Recognizers
import Lean.Meta.Basic
namespace Lean.Meta
@[inline] def testHelper (e : Expr) (p : Expr → MetaM Bool) : MetaM Bool := do
i... |
f82cf45d49bbc25066cb6335efa077a1def3bc6a | c777c32c8e484e195053731103c5e52af26a25d1 | /src/data/polynomial/ring_division.lean | d833e027586a3e3f29d63c30469a0b822a99cd9c | [
"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 | 45,188 | 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, Johan Commelin
-/
import algebra.char_zero.infinite
import data.polynomial.algebra_map
import data.polynomial.degree.lemmas
... |
61d95212e4b83d8f2c4fc1cd3dfc6bed3486bcc1 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/qpf/multivariate/basic.lean | c3fb19eb08e4e735d6bdd0b0377dcb6abf9c905b | [] | 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 | 7,738 | lean | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad, Simon Hudon
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.pfunctor.multivariate.basic
import Mathlib.PostPort
universes u u_1 l
nam... |
a4e99a093202dd63bb24be13634f4f864f1aea64 | 2a70b774d16dbdf5a533432ee0ebab6838df0948 | /_target/deps/mathlib/src/data/complex/exponential.lean | db18ee90a0598248bf1524a0db4e48382545965e | [
"Apache-2.0"
] | permissive | hjvromen/lewis | 40b035973df7c77ebf927afab7878c76d05ff758 | 105b675f73630f028ad5d890897a51b3c1146fb0 | refs/heads/master | 1,677,944,636,343 | 1,676,555,301,000 | 1,676,555,301,000 | 327,553,599 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 61,310 | 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
-/
import algebra.geom_sum
import data.nat.choose.sum
import data.complex.basic
/-!
# Exponential, trigonometric and hyperbolic trigonometric funct... |
7ab0b5a867ad52e4749950424ef3e3f64a6c082a | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /src/Lean/Meta/Tactic/Split.lean | 271f2d3ef15c338ad114c8686e97ff7588ea8270 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | EdAyers/lean4 | 57ac632d6b0789cb91fab2170e8c9e40441221bd | 37ba0df5841bde51dbc2329da81ac23d4f6a4de4 | refs/heads/master | 1,676,463,245,298 | 1,660,619,433,000 | 1,660,619,433,000 | 183,433,437 | 1 | 0 | Apache-2.0 | 1,657,612,672,000 | 1,556,196,574,000 | Lean | UTF-8 | Lean | false | false | 15,283 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.Match.MatchEqs
import Lean.Meta.Tactic.Generalize
namespace Lean.Meta
namespace Split
def getSimpMatchContext : MetaM Simp.Context :=
... |
2ad330ff909b734f7559582d6e9e743fc34c1253 | 80b18137872dad7c3df334b9069d70935b4224f3 | /src/algebra/big_operators.lean | 689af00eee4468033cde944a33f518a9a0335d6f | [
"Apache-2.0"
] | permissive | Jack-Pumpkinhead/mathlib | 1bcf5692d355dc397847791c137158f01b407535 | da8b23f907f750528539bffa604875b98717fb93 | refs/heads/master | 1,621,299,949,262 | 1,585,480,767,000 | 1,585,480,767,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 42,278 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Some big operators for lists and finite sets.
-/
import tactic.tauto data.list.defs data.finset data.nat.enat
universes u v w
variables {α : Type u} {β : Type v} {γ : ... |
0c0c3f9915786e54e05a8ce430e96c7a9dd2094f | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /tests/lean/run/eq16.lean | 284f773ae68196e22a6b9a6b649e14584045c947 | [
"Apache-2.0"
] | permissive | tjiaqi/lean | 4634d729795c164664d10d093f3545287c76628f | d0ce4cf62f4246b0600c07e074d86e51f2195e30 | refs/heads/master | 1,622,323,796,480 | 1,422,643,069,000 | 1,422,643,069,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 435 | lean | import data.list
open list
variable {A : Type}
set_option pp.implicit true
definition append : list A → list A → list A,
append nil l := l,
append (h :: t) l := h :: (append t l)
theorem append_nil (l : list A) : append nil l = l :=
rfl
theorem append_cons (h : A) (t l : list A) : append (h :: t) l = h :: (app... |
1d46e107e19c9ea792a27e4e3ff7e2453174d880 | 7b02c598aa57070b4cf4fbfe2416d0479220187f | /homotopy/smash_adjoint.hlean | 8d23779798a1b5bd096f3b478e95a499b8e4afbe | [
"Apache-2.0"
] | permissive | jdchristensen/Spectral | 50d4f0ddaea1484d215ef74be951da6549de221d | 6ded2b94d7ae07c4098d96a68f80a9cd3d433eb8 | refs/heads/master | 1,611,555,010,649 | 1,496,724,191,000 | 1,496,724,191,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 26,549 | hlean | -- Authors: Floris van Doorn
-- in collaboration with Egbert, Stefano, Robin, Ulrik
/- the adjunction between the smash product and pointed maps -/
import .smash .susp ..pointed
open bool pointed eq equiv is_equiv sum bool prod unit circle cofiber prod.ops wedge is_trunc
function unit sigma susp sphere
namespac... |
e17826ca1ec2402567c4ff5f6d5fe811ab8a9f37 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /tests/bench/rbmap.lean | ec624b260239e12e75593bd1a562c9f721bdf349 | [
"Apache-2.0"
] | permissive | mhuisi/lean4 | 28d35a4febc2e251c7f05492e13f3b05d6f9b7af | dda44bc47f3e5d024508060dac2bcb59fd12e4c0 | refs/heads/master | 1,621,225,489,283 | 1,585,142,689,000 | 1,585,142,689,000 | 250,590,438 | 0 | 2 | Apache-2.0 | 1,602,443,220,000 | 1,585,327,814,000 | C | UTF-8 | Lean | false | false | 2,900 | 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
-/
prelude
import Init.Data.Option.Basic
import Init.Data.List.BasicAux
import Init.Data.String
import Init.System.IO
universes u v w w'
inductive color
| Re... |
e4cbd392b4cb484ff831ec2b6fab763eceac08d5 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/hott/488.hlean | d4ed79afe8a3b7979925cdfb3da37dd289bd189f | [
"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 | 239 | hlean | constants {A B : Type} {P : B → Type} {f : A → B}
(rec_on : Π(b : B) (H : Πa, P (f a)) (H2 : Πa, H a = H a), P b)
example (b : B) (H : Πa, P (f a)) : P b :=
begin
fapply (rec_on b),
{exact H},
{clear b, apply sorry}
end
|
678256397ac1dbbbd12eeae862494fd6ced4d720 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/free_algebra_auto.lean | 9b4ae3801de072c3224bb63dd2257701e2b69653 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,301 | lean | /-
Copyright (c) 2020 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Scott Morrison, Adam Topaz.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.algebra.subalgebra
import Mathlib.algebra.monoid_algebra
import Mathlib.lin... |
fee800f1159ef5798a26810bf8faa6851b50bcdf | 3bd26f8e9c7eeb6ae77ac4ba709b5b3c65b8d7cf | /fin_seq.lean | 81cc5955c9dfdade97451c89c125207813ddeff7 | [] | no_license | koba-e964/lean-work | afac5677efef6905fce29cac44f36f309c3bcd62 | 6ab0506b9bd4e5a2e1ba6312d4ac6bdaf6ae1594 | refs/heads/master | 1,659,773,150,740 | 1,659,289,453,000 | 1,659,289,453,000 | 100,273,655 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,981 | lean | def fin_seq (k: nat) (t: Type) := fin k -> t
namespace fin_seq
def push {t k} (v: t) (a: fin_seq k t): fin_seq (k + 1) t
| ⟨val, is_lt⟩ :=
begin
cases val with val',
exact v, -- arg(0) = v
apply a,
existsi val',
apply nat.lt_of_succ_lt_succ,
exact is_lt,
end
def pop {t k} (a: fin_seq (k +... |
a12b99e0ff019121ba39fe4dde78390a9bfadf85 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/analysis/fourier.lean | 2738621452e30f48241d12e95ae906a017b6fe7d | [
"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 | 8,206 | 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 measure_theory.function.continuous_map_dense
import measure_theory.function.l2_space
import measure_theory.measure.haar
import analysis.complex.circle
import... |
28c3eb7719121012bbe59511a9905a82b97446df | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/topology/instances/ennreal.lean | 349e1040ebc96dbc05e746d82fdb8312c0f3fd3c | [
"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 | 35,444 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
Extended non-negative reals
-/
import topology.instances.nnreal data.real.ennreal
noncomputable theory
open classical set lattice filter metric
open_locale classical
ope... |
9908c7e61de3396829ba4c69eaaa4afb3a795296 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/get_unused_name.lean | 5be4eb45f90b0ba9e847594c36bd7030e4a27f4c | [
"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 | 333 | lean | open tactic
example (a b c : nat) : a = c → a + b = b + c :=
by do
n1 ← get_unused_name `a,
n2 ← get_unused_name `b,
n3 ← get_unused_name `c,
n4 ← get_unused_name `d,
intro n1,
n5 ← get_unused_name `a,
trace n1 >> trace n2 >> trace n3 >> trace n4 >> trace n5,
get_local `a >>= subst,
`[apply add_comm]... |
707a9a6bb93fbdb43a749eaee1477892adb41f92 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/order/filter/n_ary.lean | 6a9515f4282badbe927a9fff4ea898f7d8a6743c | [
"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 | 17,519 | 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 order.filter.prod
/-!
# N-ary maps of filter
This file defines the binary and ternary maps of filters. This is mostly useful to define pointwise
operations on fi... |
d137eea8febb42444a82a8bef22f0be65d538832 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/elab9.lean | 37a6dcb48679aa35a750e3604fa4a0b93ffdd2de | [
"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 | 278 | lean | set_option pp.notation false
set_option pp.implicit true
set_option pp.numerals false
set_option pp.binder_types true
check λ (A : Type*) [has_add A] [has_zero A] (a : A) (H : a + 0 = a) [has_add A] (H : a = 0 + 0), a + a
check λ (a b : nat) (H : a > b) [has_lt nat], a < b
|
a1f9e85d2acf0268278e9f4123c24ab03ea5c4a5 | acc85b4be2c618b11fc7cb3005521ae6858a8d07 | /order/basic.lean | c4ae8fa28560916a44a8d0278505defe17ff9514 | [
"Apache-2.0"
] | permissive | linpingchuan/mathlib | d49990b236574df2a45d9919ba43c923f693d341 | 5ad8020f67eb13896a41cc7691d072c9331b1f76 | refs/heads/master | 1,626,019,377,808 | 1,508,048,784,000 | 1,508,048,784,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,445 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
-/
open eq function
/- TODO: automatic construction of dual definitions / theorems -/
universes u v w
variables {α : Type u} {β : Type v} {γ : Type w}
section monotone
v... |
457102517aedcfa1b64c0aa9aee85cdea28a286c | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/data/array/slice_auto.lean | 5bf21d0d02a6ca96dfbf6f1b00e58f3e0f6f9be8 | [] | 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 | 1,066 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.data.nat.default
import Mathlib.Lean3Lib.init.data.array.basic
import Mathlib.Lean3Lib.init.data.nat.lemmas
... |
9b79a1a8a9361941293b9ca55b5111cf5feaa9a8 | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/algebra/group/hom.lean | eeee3d3b3f9ffa16e006c6accf2912386720918d | [
"Apache-2.0"
] | permissive | ChrisHughes24/mathlib | 98322577c460bc6b1fe5c21f42ce33ad1c3e5558 | a2a867e827c2a6702beb9efc2b9282bd801d5f9a | refs/heads/master | 1,583,848,251,477 | 1,565,164,247,000 | 1,565,164,247,000 | 129,409,993 | 0 | 1 | Apache-2.0 | 1,565,164,817,000 | 1,523,628,059,000 | Lean | UTF-8 | Lean | false | false | 21,997 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Kevin Buzzard, Scott Morrison, Johan Commelin, Chris Hughes,
Johannes Hölzl, Yury Kudryashov
Homomorphisms of multiplicative and additive (semi)groups and monoids.
... |
b4d714e0037844d8581fcb1f8d65a521c89eba6e | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/pprod.lean | c2c7dd6d65ecbce7405abf91afcc3dc34c5fdb0b | [
"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 | 324 | lean | /-
Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
/-!
# Extra facts about `pprod`
-/
variables {α : Sort*} {β : Sort*}
@[simp] lemma pprod.mk.eta {p : pprod α β} : pprod.mk p.1 p.2 = p :=
pprod.cases_on p (λ a b, rfl)
|
9ac0cdad4a7e05830541a12305ac42180c474a25 | a047a4718edfa935d17231e9e6ecec8c7b701e05 | /src/algebra/field_power.lean | e2f5b54ca40f20199364820311b8f33b0a4c8c54 | [
"Apache-2.0"
] | permissive | utensil-contrib/mathlib | bae0c9fafe5e2bdb516efc89d6f8c1502ecc9767 | b91909e77e219098a2f8cc031f89d595fe274bd2 | refs/heads/master | 1,668,048,976,965 | 1,592,442,701,000 | 1,592,442,701,000 | 273,197,855 | 0 | 0 | null | 1,592,472,812,000 | 1,592,472,811,000 | null | UTF-8 | Lean | false | false | 5,540 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
Integer power operation on fields.
-/
import algebra.group_with_zero_power
import tactic.linarith
universe u
@[simp] lemma ring_hom.map_fpow {K L : Type*} [division... |
684c4853c6257ce40522ae67044b73ec35b63db1 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /test/lint.lean | 28f6253d437ae2c686858825056dae8af9542eba | [
"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 | 4,567 | lean | import tactic.lint
import algebra.ring.basic
def foo1 (n m : ℕ) : ℕ := n + 1
def foo2 (n m : ℕ) : m = m := by refl
lemma foo3 (n m : ℕ) : ℕ := n - m
lemma foo.foo (n m : ℕ) : n ≥ n := le_refl n
instance bar.bar : has_add ℕ := by apply_instance -- we don't check the name of instances
lemma foo.bar (ε > 0) : ε = ε := r... |
6a023e3039ff85067e9a9bccbb999a1ea47f814e | 94637389e03c919023691dcd05bd4411b1034aa5 | /src/exam1/lin2k.lean | 40d19c8fc3c7bc8cf76f1ec85530416ce97d0f40 | [] | no_license | kevinsullivan/complogic-s21 | 7c4eef2105abad899e46502270d9829d913e8afc | 99039501b770248c8ceb39890be5dfe129dc1082 | refs/heads/master | 1,682,985,669,944 | 1,621,126,241,000 | 1,621,126,241,000 | 335,706,272 | 0 | 38 | null | 1,618,325,669,000 | 1,612,374,118,000 | Lean | UTF-8 | Lean | false | false | 8,698 | lean | import algebra.module.basic
import data.real.basic
/-
This is EXAM #1 for UVa CS 4501/6501, Spring
2021.
Ground rules are as follows:
- open book, notes, code, WWW
- no communication except with instructors
- don't post any part of an answer on Piazza
- use Piazza only to ask about errors or to request clarification... |
5bf50cb91415ca2278b43ebf0b3f1f9ff55c5fd1 | a7dd8b83f933e72c40845fd168dde330f050b1c9 | /src/data/opposite.lean | 4f2b9664c28f6ff995cd038f3eaa82933b6eaeff | [
"Apache-2.0"
] | permissive | NeilStrickland/mathlib | 10420e92ee5cb7aba1163c9a01dea2f04652ed67 | 3efbd6f6dff0fb9b0946849b43b39948560a1ffe | refs/heads/master | 1,589,043,046,346 | 1,558,938,706,000 | 1,558,938,706,000 | 181,285,984 | 0 | 0 | Apache-2.0 | 1,568,941,848,000 | 1,555,233,833,000 | Lean | UTF-8 | Lean | false | false | 2,398 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Reid Barton, Simon Hudon, Kenny Lau
Opposites.
-/
namespace opposite
universes v u -- declare the `v` first; see `category_theory.category` for an explanation
variabl... |
ba4a52b99766069e0d9c8b97d7be19223fee4c99 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/option/basic_auto.lean | f9f0073f4a470d655c2a4291864a68fd11b02e7c | [] | 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 | 18,124 | 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.tactic.basic
import Mathlib.PostPort
universes u_1 u_2 u_3
namespace Mathlib
namespace ... |
0b4bcc73a9617d7a384de91363e2edd784de01c0 | 6e4b1527dfc11d1b56419f0d747c66d3b258260b | /src/parsing/default.lean | ee371e974ffc59c1695df66ea09fa5b7f57ab81a | [
"Apache-2.0"
] | permissive | jroesch/parsing | 7860046a3b96dd3695f25e274034de518a2da7c6 | 8ac39e59498d33b674fda526bfef44af66ca9df8 | refs/heads/master | 1,626,501,031,276 | 1,508,386,101,000 | 1,508,386,101,000 | 107,495,434 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13 | lean | import .core
|
0ee558cd849c3178b55182d4778607b16a43e39d | 534c92d7322a8676cfd1583e26f5946134561b54 | /src/Exercises/01_Propositions/Q0106/Q0006.lean | 3b82920b28076911557ee37d8501b46bedd9b6e6 | [
"Apache-2.0"
] | permissive | kbuzzard/mathematics-in-lean | 53f387174f04d6077f434e27c407aee9425837f7 | 3fad7bb7e888dabef94921101af8671b78a4304a | refs/heads/master | 1,586,812,457,439 | 1,546,893,744,000 | 1,546,893,744,000 | 163,450,734 | 8 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 46 | lean | theorem very_easy : true :=
begin
sorry
end
|
057f2e6d38262f670d7afebeba36d35ba9a3bff3 | 842b7df4a999c5c50bbd215b8617dd705e43c2e1 | /nat_num_game/src/Advanced_Proposition_World/adv_prop_wrld1.lean | e5e1e46c156cdc8ee1b55b8e4d37e0df5e866668 | [] | 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 | 96 | lean | example (P Q : Prop) (p : P) (q : Q) : P ∧ Q :=
begin
split,
exact p,
exact q,
end |
81fdf517777cfdb6165bf287338ff29eafc0fd99 | 5fbbd711f9bfc21ee168f46a4be146603ece8835 | /lean/natural_number_game/function/1.lean | e34a35b5f25ca9977bba1cb3261709ac6242927b | [
"LicenseRef-scancode-warranty-disclaimer"
] | no_license | goedel-gang/maths | 22596f71e3fde9c088e59931f128a3b5efb73a2c | a20a6f6a8ce800427afd595c598a5ad43da1408d | refs/heads/master | 1,623,055,941,960 | 1,621,599,441,000 | 1,621,599,441,000 | 169,335,840 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 67 | lean | example (P Q : Type) (p : P) (h : P → Q) : Q :=
exact h p,
end
|
28ba89ba05c9ab1fd77176beaa22262a59247aef | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/bindersAbstractingUnassignedMVars.lean | e8f496d6f284d76cfd24c21ee43e53a2ea293d0d | [
"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 | 1,385 | lean | import Lean
open Lean
open Lean.Meta
def tst1 : MetaM Unit := do
withLocalDeclD `x (mkConst ``Nat) fun x =>
withLocalDeclD `y (mkConst ``Nat) fun y => do
let e ← mkForallFVars #[y, x] (← mkEq (← mkAdd x (← mkAdd x y)) x)
IO.println (← Meta.ppExpr e)
#eval tst1
def tst2 : MetaM Unit := do
let x ← mkFres... |
d99f94f46fa097b76e927de5849fd6ca684827cd | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/group_theory/order_of_element.lean | b6b3fd951457bd93ead213e25654f2a02758d178 | [
"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 | 36,366 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Julian Kuelshammer
-/
import algebra.pointwise
import group_theory.coset
import dynamics.periodic_pts
import algebra.iterate_hom
/-!
# Order of an element
This file d... |
33ef9ff9b486b9a90df5b9d10a76a870d186b71c | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/module/opposites.lean | f6f6a9ad0fcc285fca01b98ef08fbe41d80128ac | [
"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 | 1,674 | 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 algebra.module.equiv
import group_theory.group_action.opposite
/-!
# Module operations on `Mᵐᵒᵖ`
This file contains definitions that build on top of the group acti... |
094cd2f399b3152219fd75659286af2f91c4314e | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/simpBool.lean | 217526d2b2a96fb5fef1443f092a2e3d62fdc156 | [
"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 | 247 | lean | example (h : x ≠ true) : (x && y) = false := by
simp [h]
example (h : ¬ (x = true)) : (x && y) = false := by
simp [h]
example (h : x ≠ false) : (x && y) = y := by
simp [h]
example (h : ¬ (x = false)) : (x && y) = y := by
simp [h]
|
06d283366f4d0833cba2f6e14c72013d72a4067d | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/control/traversable/basic.lean | adbdd050a211c0adede3b0dc893819a24929d7aa | [
"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 | 9,536 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import control.functor
/-!
# Traversable type class
Type classes for traversing collections. The concepts and laws are taken from
<http://hackage.haskell.org/package/base... |
27aa2ae314b777ccdd7fee8469a289d83c2c293d | 54c9ed381c63410c9b6af3b0a1722c41152f037f | /Binport/Path.lean | 24b96a6b2e2a5c59ec1c1043ef9dc28a12f807dd | [
"Apache-2.0"
] | permissive | dselsam/binport | 0233f1aa961a77c4fc96f0dccc780d958c5efc6c | aef374df0e169e2c3f1dc911de240c076315805c | refs/heads/master | 1,687,453,448,108 | 1,627,483,296,000 | 1,627,483,296,000 | 333,825,622 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,468 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Selsam
Lean3 structure:
- <lean3>/library/init/data/nat/basic.tlean
- <mathlib3>/src/data/nat/basic.tlean
Lean4 structure:
- Lib4/Lean3Lib/data/nat/basic.olean
- Lib4... |
d4703416c6c2f38123c6bb06d41d911ca6438c59 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/topology/metric_space/basic.lean | 3f83a62b6836126f6909231a97b05f8c7acd8e9b | [
"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 | 75,044 | lean | /-
Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Metric spaces.
Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
Many definitions and theorems expected on metric spaces are already introduced o... |
fc1b51482c3377a1a6ffe54081236e339a147aef | 43390109ab88557e6090f3245c47479c123ee500 | /src/Geometry/tarski_7.lean | de28c962a702faa4d54eed7b32e0ddcb10864440 | [
"Apache-2.0"
] | permissive | Ja1941/xena-UROP-2018 | 41f0956519f94d56b8bf6834a8d39473f4923200 | b111fb87f343cf79eca3b886f99ee15c1dd9884b | refs/heads/master | 1,662,355,955,139 | 1,590,577,325,000 | 1,590,577,325,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 38,092 | lean | import geometry.tarski_6
open classical set
namespace Euclidean_plane
variables {point : Type} [Euclidean_plane point]
local attribute [instance, priority 0] prop_decidable
theorem col_of_perp {a b p q : point} : p ≠ q → R a p q → R b p q → col p a b :=
λ h, not_3dim (seven12b h.symm).symm (seven5 p q).2
theorem co... |
7b9521c1ec953103c41bc43bf440fe95cf88d248 | 2c096fdfecf64e46ea7bc6ce5521f142b5926864 | /src/Lean/Class.lean | 38edc2a5e0a9f834c30fced1106a636e09725ecc | [
"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 | Kha/lean4 | 1005785d2c8797ae266a303968848e5f6ce2fe87 | b99e11346948023cd6c29d248cd8f3e3fb3474cf | refs/heads/master | 1,693,355,498,027 | 1,669,080,461,000 | 1,669,113,138,000 | 184,748,176 | 0 | 0 | Apache-2.0 | 1,665,995,520,000 | 1,556,884,930,000 | Lean | UTF-8 | Lean | false | false | 5,088 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Attributes
namespace Lean
/-- An entry for the persistent environment extension for declared type classes -/
structure ClassEntry where
/-- ... |
3037402e675f18ef06c1015f63f31b943ceebddf | 1d265c7dd8cb3d0e1d645a19fd6157a2084c3921 | /src/other/odd_and_even.lean | a42e5bae15d60b15637c141507eeab4b9a078848 | [
"MIT"
] | permissive | hanzhi713/lean-proofs | de432372f220d302be09b5ca4227f8986567e4fd | 4d8356a878645b9ba7cb036f87737f3f1e68ede5 | refs/heads/master | 1,585,580,245,658 | 1,553,646,623,000 | 1,553,646,623,000 | 151,342,188 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 3,748 | lean | import data.set
import data.int.basic
def odd : ℤ → Prop := λ n, ∃ m, n = 2 * m + 1
def even : ℤ → Prop := λ n, ∃ m, n = 2 * m
theorem even_or_odd : ∀ n, (even n ∨ odd n) :=
begin
assume n,
apply @int.induction_on (λ n, even n ∨ odd n),
left, exact ⟨0, rfl⟩,
assume k,
assume h,
... |
076a01b593f33dc0aef3aa7c7ed92d37155ac161 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/data/set/countable.lean | f4b94e6dd83c01536869fea2b4411d4587a4efda | [
"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 | 10,386 | 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 data.equiv.list
import data.set.finite
/-!
# Countable sets
-/
noncomputable theory
open function set encodable
open classical (hiding some)
open_locale cla... |
c5bb0c305d11823628d159e8bdbc9107cf659c24 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/order/conditionally_complete_lattice.lean | dc46cae9c8bf24438eea1189af043144fc3c4c30 | [
"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 | 46,652 | lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import order.bounds
import data.set.intervals.basic
import data.set.finite
import data.set.lattice
/-!
# Theory of conditionally complete lattices.
A conditio... |
d2408ae3d43a4729e6e3f9baade25a2d853b5639 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /test/monotonicity.lean | 30ee14d29d5cadb12def0e878f889aa6ee5824c7 | [
"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 | 8,958 | lean | /-
Copyright (c) 2019 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import tactic.monotonicity
import tactic.norm_num
import algebra.order.ring.defs
import measure_theory.measure.lebesgue
import measure_theory.function.locally_integrable
im... |
594a9350333340d3e763e0740b72f012ddaa3a00 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/alex1.lean | eaeda355ba40106a295de91c9ee07c61f3e0ee8e | [
"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 | 734 | lean | universe u
/-- A curried function of exactly `n` arguments; `α → ... → α → β` -/
abbrev CurriedFun (α β : Type u) : Nat → Type u
| 0 => β
| n+1 => α → CurriedFun α β n
/-- A curried type function of `n` arguments, i.e., `Type u → Type u → ... → Type u` -/
abbrev CurriedTypeFun : Nat → Type (u+1)
:= CurriedFun... |
ce9c6c5dfc23ecec4cd7e46d9fe77164021ad22c | bb31430994044506fa42fd667e2d556327e18dfe | /src/analysis/complex/cauchy_integral.lean | 2cbc77d447e99afbdf9e112d91ba4270f84de836 | [
"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 | 37,659 | lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import measure_theory.measure.complex_lebesgue
import measure_theory.integral.divergence_theorem
import measure_theory.integral.circle_integral
import analysis.calc... |
abb414e0b13da3275910981fed711aa49f904259 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/order/liminf_limsup.lean | de79833ecd7586013cc57c4de8bb56ab5634b271 | [
"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 | 16,590 | lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Johannes Hölzl
Defines the Liminf/Limsup of a function taking values in a conditionally complete lattice, with
respect to an arbitrary filter.
We define `f.Lims... |
a2dff886fc7a0e4c04b111c9fb10df0e1c39dbb3 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/topology/metric_space/basic.lean | 9b2d9904744c2391a56ec9c0ef882604e7027acb | [
"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 | 70,239 | lean | /-
Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Metric spaces.
Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
Many definitions and theorems expected on metric spaces are already introduced o... |
60894fc1aa80c7736a984a1580a054b1449f1653 | 9cba98daa30c0804090f963f9024147a50292fa0 | /time/time.lean | 26ce44d1b30c19caf00f00143966e8c0e54c752f | [] | no_license | kevinsullivan/phys | dcb192f7b3033797541b980f0b4a7e75d84cea1a | ebc2df3779d3605ff7a9b47eeda25c2a551e011f | refs/heads/master | 1,637,490,575,500 | 1,629,899,064,000 | 1,629,899,064,000 | 168,012,884 | 0 | 3 | null | 1,629,644,436,000 | 1,548,699,832,000 | Lean | UTF-8 | Lean | false | false | 16,834 | lean | import ..phys_dimensions
import linear_algebra.affine_space.basic
--import ...math.affnKcoord.affnKcoord_std
import ...math.euclidnK.euclidnK_definitions
import ..scalar
open_locale affine
section foo
universes u
abbreviation time_frame := fm scalar 1 LENGTH
abbreviation time_space (f : time_frame) := spc scala... |
09480cba8f5592b315d361bb79ac460ee74f6a8f | bb31430994044506fa42fd667e2d556327e18dfe | /src/algebraic_geometry/function_field.lean | a56d5c1e1635c3c592b9f076baa2be3c124e4a3f | [
"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 | 8,174 | lean | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import algebraic_geometry.properties
/-!
# Function field of integral schemes
We define the function field of an irreducible scheme as the stalk of the generic point.
Thi... |
3c9b12e897f57e90f86c5c02d365e3dc0610d0b9 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebraic_geometry/projective_spectrum/scheme.lean | 4fc52b338df17b85e93e993858145b48973690e1 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 22,619 | lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
import algebraic_geometry.projective_spectrum.structure_sheaf
import algebraic_geometry.Spec
import ring_theory.graded_algebra.radical
/-!
# Proj as a scheme
> THIS FIL... |
9edbf6816f4dc16734f333eb3fb3f33b37f6456a | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /src/Lean/Elab/Binders.lean | 0532b3fa344a6f554614ef2992f66f9719a19d67 | [
"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 | 22,032 | 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.Elab.Term
import Lean.Elab.Quotation
namespace Lean
namespace Elab
namespace Term
open Meta
/--
Given syntax of the forms
a) (`:` term)... |
1cde45fb607e06a930380c852dc32bfe44545bfa | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/topology/order.lean | 48b3eef7ded724374612114ab36eac5205e39712 | [
"Apache-2.0"
] | permissive | fpvandoorn/mathlib | b21ab4068db079cbb8590b58fda9cc4bc1f35df4 | b3433a51ea8bc07c4159c1073838fc0ee9b8f227 | refs/heads/master | 1,624,791,089,608 | 1,556,715,231,000 | 1,556,715,231,000 | 165,722,980 | 5 | 0 | Apache-2.0 | 1,552,657,455,000 | 1,547,494,646,000 | Lean | UTF-8 | Lean | false | false | 32,110 | 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
Order on topological structures. Lattice structure, Galois connection, and applications.
-/
import topology.basic
open set filter lattice classical
loc... |
bd038340674be219b9d246b1e6f16077e981ba44 | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/category_theory/limits/limits.lean | 8cb87dbe81c0fecaa383d2aca44e5d47cb2024c8 | [
"Apache-2.0"
] | permissive | vaibhavkarve/mathlib | a574aaf68c0a431a47fa82ce0637f0f769826bfe | 17f8340912468f49bdc30acdb9a9fa02eeb0473a | refs/heads/master | 1,621,263,802,637 | 1,585,399,588,000 | 1,585,399,588,000 | 250,833,447 | 0 | 0 | Apache-2.0 | 1,585,410,341,000 | 1,585,410,341,000 | null | UTF-8 | Lean | false | false | 41,380 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Mario Carneiro, Scott Morrison, Floris van Doorn
-/
import category_theory.whiskering
import category_theory.yoneda
import category_theory.limits.cones
import category_the... |
e33a75edaa6fe09c332ba85555e9f3344c2b9fe9 | 7b4371534ac437ca8cfb325dd5c6638ff111d31a | /nat_util.lean | fa3aeb27fb893417fe8c2fb100af5495c7256a19 | [] | no_license | Shamrock-Frost/boolean_rings | 6d78294568b6b9ad7b9c67b5de5e9545227826da | 5da11beeaa37ec186c1deff946f2dbf7594fceb4 | refs/heads/master | 1,588,394,857,485 | 1,553,973,949,000 | 1,553,973,949,000 | 177,757,941 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,736 | lean | lemma nat.not_self_lt_lt_succ_self {a b : nat}
: a < b → b < a + 1 → false :=
begin
intros h1 h2,
cases nat.le.dest h1 with w h_1,
cases nat.le.dest h2 with w_1 h_2,
rw ← h_1 at h_2,
rw ← nat.succ_add at h_2,
apply nat.lt_irrefl (nat.succ a),
apply nat.lt_of_lt_of_le,
apply lt_add_of_pos_right (nat.s... |
956f3a35b58745dcb406810996209e9f3a2b3fbc | 9b9a16fa2cb737daee6b2785474678b6fa91d6d4 | /src/category_theory/eq_to_hom.lean | e8ef21cfae51b628fedd506618001088579018fa | [
"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 | 2,671 | lean | -- Copyright (c) 2018 Reid Barton. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Reid Barton, Scott Morrison
import category_theory.isomorphism
import category_theory.functor_category
universes v v' u u' -- declare the `v`'s first; see `category_theory.categor... |
f64e709ddf4795a8a1efdf99ce7985cb95bb12b2 | 38bf3fd2bb651ab70511408fcf70e2029e2ba310 | /src/ring_theory/power_series.lean | cb0e779e297799b5a8d5975bcf3983ea9e24f7a4 | [
"Apache-2.0"
] | permissive | JaredCorduan/mathlib | 130392594844f15dad65a9308c242551bae6cd2e | d5de80376088954d592a59326c14404f538050a1 | refs/heads/master | 1,595,862,206,333 | 1,570,816,457,000 | 1,570,816,457,000 | 209,134,499 | 0 | 0 | Apache-2.0 | 1,568,746,811,000 | 1,568,746,811,000 | null | UTF-8 | Lean | false | false | 56,804 | 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 data.finsupp order.complete_lattice algebra.ordered_group data.mv_polynomial
import algebra.order_functions
import ring_theory.ideal_operations
/-... |
d447cddb2e16b428f6002e2dc9c39e218d475e60 | ce4db867008cc96ee6ea6a34d39c2fa7c6ccb536 | /src/tokens.lean | 8b50999a3e62cb395b38ce691e89aca8a6a97415 | [] | no_license | PatrickMassot/lean-bavard | ab0ceedd6bab43dc0444903a80b911c5fbfb23c3 | 92a1a8c7ff322e4f575ec709b8c5348990d64f18 | refs/heads/master | 1,679,565,084,665 | 1,616,158,570,000 | 1,616,158,570,000 | 348,144,867 | 1 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 1,032 | lean | /-
Ce fichier réunit tous les mots clef introduits par les tactiques bavardes.
Ces mots ne peuvent plus servir à désigner des lemmes, objets ou hypothèses.
-/
precedence `applique`:0
precedence `appliqué`:0
precedence `à`:0
precedence `on`:0
precedence `obtient`:0
precedence `choisit`:0
precedence `que`:0
precedence ... |
a4f5046584a618bf2aae5df1c9f59576efd35609 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/pi_auto.lean | ac7dbdb90e93144c3fa4a51adf44dfc6217861c0 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,306 | lean | /-
Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot, Eric Wieser
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.tactic.split_ifs
import Mathlib.tactic.simpa
import Mathlib.algebra.... |
4fbc98617d68b8bff1939436f8d5d857500b7d40 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /tests/compiler/float.lean | a724ff5520fb096792400bf3a59f4e860e3b118c | [
"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 | 1,850 | lean |
def tst1 : IO Unit := do
IO.println (1 : Float)
IO.println ((1 : Float) + 2)
IO.println ((2 : Float) - 3)
IO.println ((3 : Float) * 2)
IO.println ((3 : Float) / 2)
IO.println (decide ((3 : Float) < 2))
IO.println (decide ((3 : Float) < 4))
IO.println ((3 : Float) == 2)
IO.println ((2 : Float) == 2)
... |
3976bb2304bc3961df4a899af603ffc2c65675b8 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /04_Quantifiers_and_Equality.org.7.lean | d5e9ef6a770d97035a1258d6a06978454d527b0b | [] | 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 | 891 | lean | /- page 50 -/
import standard
variables (A : Type) (p q : A → Prop)
variable r : Prop
/-
example : A → (∀ x : A, r) ↔ r :=
iff.intro (λ H, _)
(λ Hr Ha Ha, Hr)
-/
example : A → ((∀ x : A, r) ↔ r) :=
λ Ha, iff.intro (λ H, H Ha)
(λ Hr Ha, Hr)
example : (∀ x, p x ∨ r) ↔ (∀ x, p x) ∨ r ... |
b51feadb1cfd0999820402ab3c142366c79d9581 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/topology/uniform_space/uniform_embedding_auto.lean | 570751c1085c5473c7b18b7171c021ddde57deeb | [] | 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 | 11,609 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Sébastien Gouëzel, Patrick Massot
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.topology.uniform_space.cauchy
import Mathlib.topology.un... |
b43c8994b6cb42d91e234e978d53416e8bd91759 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/677.lean | da44566e0d407789ae26f87b18d7c64777d215c6 | [
"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 | 268 | lean | import Lean
open Lean
def encodeDecode [ToJson α] [FromJson α] (x : α) : Except String α := do
let json := toJson x
fromJson? json
#eval IO.ofExcept <| encodeDecode (Name.mkNum Name.anonymous 5)
#eval IO.ofExcept <| encodeDecode (Name.mkStr `bla "foo.boo")
|
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