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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
8c7cd34f8e6a55f98f1c8d10e1cac6fad0ac77ee | 048b0801f6dafb6486ca4f22bd0957671c3002ff | /src/repl.lean | 18577458b24355ff3733dfd9f7f21fea0d0069b1 | [
"Apache-2.0"
] | permissive | Scikud/lean-gym | e0782e36389ecfa1605a0c12dc95f67014a0fa05 | a1ca851b7c09eca1f72be2d059e3ed5536348b0b | refs/heads/main | 1,693,940,033,482 | 1,633,522,864,000 | 1,633,522,864,000 | 419,793,692 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,776 | lean | /-
Copyright (c) 2021 OpenAI. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author(s): Stanislas Polu, Jesse Michael Han
REPL implementation to interact with Lean through stdio at a specific
declaration.
-/
import tactic
import data.string.basic
import all
import util.io
impo... |
2dff509f083d8218b1bf035d772e75f6bcb55dad | 843cffbd2a25fd01677509247a92e9e8b33bec48 | /5. Tactics.lean | 2a92898fcb1c8f88f19f0a0aa66713085afe0b65 | [] | no_license | AlexandruBosinta/MyLeanPlayground | 9a78eba4a5c7a2b82edf84e1794a966f53f06c4f | 5dc50a590d784bfc27e7fb37b6361a6dcc1b2790 | refs/heads/master | 1,586,230,010,351 | 1,542,487,422,000 | 1,542,487,422,000 | 158,016,626 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,245 | lean | --import tactic.finish
namespace Three
open classical
variables p q r s : Prop
-- commutativity of ∧ and ∨
example : p ∧ q ↔ q ∧ p := begin
split,
intro hpq,
split,
exact hpq.right,
exact hpq.left,
intro hqp,
split,
exact hqp.right,
exact hqp.left,
end
exam... |
b476d636f84edb4b6f5840a9e48722e409df7cd6 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/monoidal/types_auto.lean | 247464a768a030187183e243235d685b0dce8ee7 | [] | 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 | 2,123 | lean | /-
Copyright (c) 2018 Michael Jendrusch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Jendrusch, Scott Morrison
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.monoidal.of_chosen_finite_products
import Mathlib.cat... |
b7a1e24bff3a256f5a74175a3179a55ca0e64cc1 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/def5.lean | b4698d6a2d05eb0b40940df7b3047908fc972e7b | [
"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 | 178 | lean | --
def fib : Nat → Nat
| 0 | 1 => 1
| n+2 => fib n + fib (n+1)
example : fib 0 = 1 := rfl
example : fib 1 = 1 := rfl
example (n : Nat) : fib (n+2) = fib n + fib (n+1) := rfl
|
11122a1f0d335b07cafe5ec2e6271825acf0ba17 | 8e381650eb2c1c5361be64ff97e47d956bf2ab9f | /src/spectrum_of_a_ring/strucutre_sheaf_stalks.lean | d200b02bfe5761842e0e6f9e08719ca1ee9bc1ee | [] | no_license | alreadydone/lean-scheme | 04c51ab08eca7ccf6c21344d45d202780fa667af | 52d7624f57415eea27ed4dfa916cd94189221a1c | refs/heads/master | 1,599,418,221,423 | 1,562,248,559,000 | 1,562,248,559,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,757 | lean | /-
Stalks of the structure sheaf are local rings.
-/
import ring_theory.ideals
import to_mathlib.localization.local_rings
import to_mathlib.localization.localization_of_iso
import to_mathlib.localization.localization_alt
import spectrum_of_a_ring.structure_presheaf_stalks
import spectrum_of_a_ring.structure_sheaf
im... |
e3385d59d0cd4f94573a254ba60fbcbf6073ee22 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/order/category/BoundedDistribLattice.lean | ecac2f1ba4af5d27cd0ac86b6bc03cf6666fcfa2 | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 3,721 | 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.category.BoundedLattice
import order.category.DistribLattice
/-!
# The category of bounded distributive lattices
This defines `BoundedDistribLattice`, the ... |
bfd160596ba049e02a9e9436f3d61db188933506 | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /stage0/src/Init/System/IO.lean | 9553e435090df66028cf27f9130279763d87806d | [
"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 | 19,517 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Luke Nelson, Jared Roesch, Leonardo de Moura, Sebastian Ullrich
-/
prelude
import Init.Control.EState
import Init.Control.Reader
import Init.Data.String
import Init.Data.ByteArr... |
c60cd027b683cb5fe3d4551edb0b9d2c338ad2e3 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/algebra/category/CommRing/limits.lean | 0b672ed685a123e46012db15080e7429d58dcaf4 | [
"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 | 5,081 | 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 algebra.category.CommRing.basic
import category_theory.limits.types
import category_theory.limits.preserves
import ring_theory.subring
import algebra.pi_instan... |
a122fbce745189bf121504d61a685d706c5f1f33 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/monad/products.lean | 3892166c71a90586a1d38fc2ee7f2aa2ed82b5a7 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,746 | lean | /-
Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.over
import Mathlib.category_theory.limits.preserves.basic
import Mathlib.categ... |
ea3b76defe460e7226629c700ddc35a4fe50b986 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/data/real/irrational.lean | cf7e6951bb56f9107b5caef39ac64dc16407694e | [
"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 | 9,185 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Yury Kudryashov.
-/
import data.real.basic
import data.rat.sqrt
import ring_theory.int.basic
import data.polynomial.eval... |
6fb191aaca49843c1a0196d3d3e3f666d6cdaeb7 | bb31430994044506fa42fd667e2d556327e18dfe | /src/topology/algebra/order/field.lean | 2b9eeecfab668f1f30511a6ea834e3a78ed897ea | [
"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 | 16,435 | lean | /-
Copyright (c) 2022 Benjamin Davidson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Benjamin Davidson, Devon Tuma, Eric Rodriguez, Oliver Nash
-/
import tactic.positivity
import topology.order.basic
import topology.algebra.field
/-!
# Topologies on linear ordered... |
bcfc07031c3d4604e8aeed096214f6976415c1ed | 94e33a31faa76775069b071adea97e86e218a8ee | /src/number_theory/arithmetic_function.lean | b3eb74b4ab2311324beb2fea322b4ff4a17bb403 | [
"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 | 37,260 | lean | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import algebra.big_operators.ring
import number_theory.divisors
import data.nat.squarefree
import algebra.invertible
import data.nat.factorization.basic
/-!
# Arithm... |
4b2fcc0d53541bd2aeb249553254377499afcb81 | 7bf54883c04ff2856c37f76a79599ceb380c1996 | /non-mathlib/numbers.lean | e319ec83f1f5083c577c4b95f6abae436d68e539 | [] | no_license | anonymousLeanDocsHosting/lean-polynomials | 4094466bf19acc0d1a47b4cabb60d8c21ddb2b00 | 361ef4cb7b68ef47d43b85cfa2d13f2ea0a47613 | refs/heads/main | 1,691,112,899,935 | 1,631,819,522,000 | 1,631,819,522,000 | 405,448,439 | 0 | 2 | null | null | null | null | UTF-8 | Lean | false | false | 3,865 | lean | import field_definition
import field_results
def two (f : Type) [myfld f] : f := (myfld.one .+ myfld.one)
def four (f : Type) [myfld f] : f := ((two f) .+ (two f))
/- We have to add an additional stipulation that our fields are not of characteristic 2.-/
/- The quadratic formula is not defined for fields where 1 + 1... |
c2b1cf2e6a3a919b27a674bcfc4e1e31b28930a3 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/polynomial/cardinal.lean | 6bd5486e7f972e2d6c7e8882931980d53a5a53af | [
"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 | 957 | lean | /-
Copyright (c) 2021 Chris Hughes, Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Junyan Xu
-/
import data.polynomial.basic
import set_theory.cardinal.ordinal
/-!
# Cardinality of Polynomial Ring
The reuslt in this file is that the cardinalit... |
7e43069183eed420203434cd52af406524fbfaa8 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/eq13.lean | 099d288158896923e66a72de81aac6ba83fee6aa | [
"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 | 325 | lean | open nat
definition f : nat → nat → nat
| f _ 0 := 0
| f 0 _ := 1
| f _ _ := arbitrary nat
theorem f_zero_right : ∀ a, f a 0 = 0
| f_zero_right 0 := rfl
| f_zero_right (succ a) := rfl
theorem f_zero_succ (a : nat) : f 0 (a+1) = 1 :=
rfl
theorem f_succ_succ (a b : nat) : f (a+1) (b+1) = arbitrary nat :=
rfl
|
9647b7d9c87551adbdca9601b2b4565600af3f1b | 5719a16e23dfc08cdea7a5bf035b81690f307965 | /src/Init/Lean/Elab/App.lean | c22483744930097e445169eff137afefb7131b12 | [
"Apache-2.0"
] | permissive | postmasters/lean4 | 488b03969a371e1507e1e8a4df9ebf63c7cbe7ac | f3976fc53a883ac7606fc59357d43f4b51016ca7 | refs/heads/master | 1,655,582,707,480 | 1,588,682,595,000 | 1,588,682,595,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 29,215 | 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
-/
prelude
import Init.Lean.Util.FindMVar
import Init.Lean.Elab.Term
import Init.Lean.Elab.Binders
namespace Lean
namespace Elab
namespace Term
/--
Auxiliar... |
98785f76041861b3ddcbe613506e121d5b787c59 | 432d948a4d3d242fdfb44b81c9e1b1baacd58617 | /src/set_theory/pgame.lean | 5351826fa3501060e310c721ffaf93f7e97a95ad | [
"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 | 41,403 | lean | /-
Copyright (c) 2019 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Mario Carneiro, Isabel Longbottom, Scott Morrison
-/
import logic.embedding
import data.nat.cast
import data.fin
/-!
# Combinatorial (pre-)games.
The basic theory of com... |
68a4449106d7846a69cea1a0a82be61cf3ccf594 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/topology/uniform_space/uniform_convergence.lean | e392848b8f21db40cec8d334369414e6167b59a4 | [
"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 | 16,752 | 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 topology.uniform_space.basic
/-!
# Uniform convergence
A sequence of functions `Fₙ` (with values in a metric space) converges uniformly on a set `s` t... |
9b134df18e855c4436cdcc35092978ae6f51a670 | 4a1811b87c1a16ede17c8d4db9267aa4c6a01a83 | /README.lean | 3dc6843c76795cd874845051cd920bd6fb96b97e | [] | no_license | xu-hao/tranql-haskell | fb34ec63f92c1627d39111deca45566d6c128714 | 41903cd0cd94a3650fd828ab62395df75309f55b | refs/heads/master | 1,587,955,791,233 | 1,553,191,562,000 | 1,553,191,562,000 | 174,006,347 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,521 | lean | namespace rational
inductive rational : Type
| frac : int -> int -> rational
def rational_div : rational → rational → rational
| (rational.frac a b) (rational.frac c d) := rational.frac (a * d) (b * c)
def rational_one : rational := rational.frac 1 1
def rational_add : rational → rational → rational
| (rational.fr... |
2cc71a1454f6f6f254fb0c49fe55de17d9ba965e | 5e3548e65f2c037cb94cd5524c90c623fbd6d46a | /src_icannos_totilas/aops/2004-IMO-Problem_2.lean | 9f6cf687719349edf5c6c323243254d13007e260 | [] | no_license | ahayat16/lean_exos | d4f08c30adb601a06511a71b5ffb4d22d12ef77f | 682f2552d5b04a8c8eb9e4ab15f875a91b03845c | refs/heads/main | 1,693,101,073,585 | 1,636,479,336,000 | 1,636,479,336,000 | 415,000,441 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 348 | lean | import data.real.basic
import data.polynomial.basic
import data.polynomial.eval
theorem exo (f: polynomial real):
let f_fun (x: real) := polynomial.eval x f in
(forall (a b c: real), a*b + b*c + c*a = 0 -> f_fun(a - b) + f_fun(b - c) + f_fun(c - a) = 2*f_fun(a + b + c))
<-> (exists c1 c2, forall x, f_fun x = c1 ... |
86ba4ccb1844e3ca3468e66df0253dc42e7867db | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/tactic/omega/nat/neg_elim.lean | 206b33915667de13196b316904d39649e0b0d43d | [
"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 | 4,007 | lean | /-
Copyright (c) 2019 Seul Baek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Seul Baek
Negation elimination.
-/
import tactic.omega.nat.form
namespace omega
namespace nat
local notation x ` =* ` y := form.eq x y
local notation x ` ≤* ` y := form.le x y
local nota... |
14d6d965a3f28061c92e1df6df1cc6d5aebc868a | 4727251e0cd73359b15b664c3170e5d754078599 | /src/category_theory/monoidal/Mon_.lean | c25d0535bdc4f0afd57c751569b84c7e4d93a2e8 | [
"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 | 18,564 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.monoidal.braided
import category_theory.monoidal.discrete
import category_theory.monoidal.coherence_lemmas
import category_theory.limits.shapes... |
37e448bd32a117ac66f3f21cb7c555268871c67f | c31182a012eec69da0a1f6c05f42b0f0717d212d | /src/for_mathlib/kronecker.lean | 2780c65ab1c0d633238d004ab25327a6aa0d0754 | [] | 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 | 3,417 | lean | import linear_algebra.matrix
/-!
# Kronecker product of matrices
TODO: this should probably become a bilinear map
we might want to vary coefficient rings
-/
open_locale big_operators
namespace matrix
variables {l m n o l' m' n' o' R: Type*}
variables [fintype l] [fintype m] [fintype n] [fintype o]
variables [fint... |
4ee3848eb162f1a5498c9283e14d2788e982c06b | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/category_theory/yoneda.lean | e1e87474c25d5b321d3ddd2d3c4e00aae36210b6 | [
"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 | 6,699 | 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 category_theory.opposites
import category_theory.hom_functor
/-!
# The Yoneda embedding
The Yoneda embedding as a functor `yoneda : C ⥤ (Cᵒᵖ ⥤ Type v₁)`,
alo... |
616e4536e3af526aa434fa521ddada63a2e049c6 | a4673261e60b025e2c8c825dfa4ab9108246c32e | /tests/lean/PPRoundtrip.lean | 384f9a55db43b2ca984ec0dd0598e25b5d6c992a | [
"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 | 2,766 | lean | import Lean
open Lean
open Lean.Elab
open Lean.Elab.Term
open Lean.Elab.Command
open Lean.Format
open Lean.Meta
def checkM (stx : TermElabM Syntax) (optionsPerPos : OptionsPerPos := {}) : TermElabM Unit := do
let opts ← getOptions
let stx ← stx
let e ← elabTermAndSynthesize stx none <* throwErrorIfErrors
let stx' ← ... |
9695e29568b7ad1e6a2fa9e2d4678e3ceff0938c | 0845ae2ca02071debcfd4ac24be871236c01784f | /library/init/data/hashable.lean | 85f69aa511d95c398643a98987e7fb0fe08266e1 | [
"Apache-2.0"
] | permissive | GaloisInc/lean4 | 74c267eb0e900bfaa23df8de86039483ecbd60b7 | 228ddd5fdcd98dd4e9c009f425284e86917938aa | refs/heads/master | 1,643,131,356,301 | 1,562,715,572,000 | 1,562,715,572,000 | 192,390,898 | 0 | 0 | null | 1,560,792,750,000 | 1,560,792,749,000 | null | UTF-8 | Lean | false | false | 648 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.data.uint init.data.string
universes u
class Hashable (α : Type u) :=
(hash : α → USize)
export Hashable (hash)
@[extern cpp "lean::u... |
6d0fed00801b359cafec13b05bd0206d56deb72d | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/geometry/manifold/sheaf/basic.lean | 5c4722153c10212b2ee4c07a48ac2e6a6d193cff | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 4,285 | lean | /-
Copyright © 2023 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import geometry.manifold.local_invariant_properties
import topology.sheaves.local_predicate
/-! # Generic construction of a sheaf from a `local_invariant_prop` on a ... |
eecb9a5abbe494ccf4398b53fcb848b96b9e71fb | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/measure_theory/function/l1_space.lean | 80b6a243cb362bf0ca4954f6b4927726c2bab48d | [
"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 | 51,902 | lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
-/
import measure_theory.function.lp_order
/-!
# Integrable functions and `L¹` space
In the first part of this file, the predicate `integrable` is defined and basic pro... |
40ef6a39f1327aaedada310122e3d1f807622fb8 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/linear/basic.lean | cd01f81bef101a48e1f631d7648f24a7cb8a3358 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 4,684 | 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.preadditive.basic
import algebra.module.linear_map
import algebra.invertible
import algebra.algebra.basic
/-!
# Linear categories
An `R`-line... |
38a83938c8da23751ef8f90fa8050774aafb03f2 | 2f291cee459e0e7f5af2abd1034c11b969936560 | /src/power_series_mk_is_lin_map.lean | 67a74662f4618518ccbff2269b6d376f0f32e19b | [] | no_license | mo271/faulhaber | be5a22e717f59b5a0a5b1f1e1acf61ff768c5400 | 2e39d9cb7bc6fc400a818b2581ee921d41a7871a | refs/heads/master | 1,678,216,700,259 | 1,613,991,672,000 | 1,613,991,672,000 | 338,251,172 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 485 | lean | import algebra.module.linear_map
import ring_theory.power_series.basic
variables {σ R : Type*}
variables (R) [semiring R]
/-
theorem linear_map_test :
is_linear_map R (λ (z:R), z) :=
begin
refine {map_add := _, map_smul := _},
intros,
simp,
intros,
simp,
end
-/
theorem pow_series_mk_is_lin_map (R :Type) [se... |
a98442b0afe89b578baa869a46dc00fad2df8924 | 53618200bef52920c1e974173f78cd378d268f3e | /hott/types/pointed.hlean | 918ec139b42505ab0b8a1b68da466afaedfdf9dd | [
"Apache-2.0"
] | permissive | sayantangkhan/lean2 | cc41e61102e0fcc8b65e8501186dcca40b19b22e | 0fc0378969678eec25ea425a426bb48a184a6db0 | refs/heads/master | 1,590,323,112,724 | 1,489,425,932,000 | 1,489,425,932,000 | 84,854,525 | 0 | 0 | null | 1,489,425,509,000 | 1,489,425,509,000 | null | UTF-8 | Lean | false | false | 40,487 | hlean | /-
Copyright (c) 2014-2016 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer, Floris van Doorn
Ported from Coq HoTT
The basic definitions are in init.pointed
-/
import .nat.basic ..arity ..prop_trunc
open is_trunc eq prod sigma nat equ... |
11c044fded1e464af0459cc6bb59887f205a85af | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /stage0/src/Lean/Elab/App.lean | 4c7342378ad5f2d5cb19587ad77a6d4717f43602 | [
"Apache-2.0"
] | permissive | WojciechKarpiel/lean4 | 7f89706b8e3c1f942b83a2c91a3a00b05da0e65b | f6e1314fa08293dea66a329e05b6c196a0189163 | refs/heads/master | 1,686,633,402,214 | 1,625,821,189,000 | 1,625,821,258,000 | 384,640,886 | 0 | 0 | Apache-2.0 | 1,625,903,617,000 | 1,625,903,026,000 | null | UTF-8 | Lean | false | false | 42,717 | 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.Util.FindMVar
import Lean.Parser.Term
import Lean.Elab.Term
import Lean.Elab.Binders
import Lean.Elab.SyntheticMVars
import Lean.Elab.Arg
names... |
e5eb39d2d6119c2ab9be596d82061d4e3ac201f3 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/algebra/big_operators/pi.lean | 645da4b9bbe4e7c154edbb76e33a7c18f97345a5 | [
"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 | 3,334 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot
-/
import algebra.ring.pi
import algebra.big_operators
import data.fintype.basic
import algebra.group.prod
/-!
# Big operators for Pi Types
This file contains... |
3fb2cf655d8e25af51104b9b04e999a87217a53d | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/ring_theory/norm.lean | a9ee578b28db79664f530da6572c9089de428c50 | [
"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 | 13,148 | lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import field_theory.primitive_element
import linear_algebra.determinant
import linear_algebra.finite_dimensional
import linear_algebra.matrix.charpoly.minpoly
import linea... |
3b47529fe0ca211d851ceb9172e978222f1ffd42 | 29cc89d6158dd3b90acbdbcab4d2c7eb9a7dbf0f | /24_lecture.lean | 95ffb3fe5ff8d7cdf8edb1593f6aab50f28333cb | [] | 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 | 4,393 | lean | /- Lecture 2.4: Functional Programming — Metaprogramming -/
/- Tactics -/
example : true :=
by tactic.triv
example : true := by do
tactic.trace "Hello, Metacosmos!",
tactic.triv
meta def hello_world : tactic unit := do
tactic.trace "Hello, Metacosmos!",
tactic.triv
example : true := by hello_world
run_c... |
471ece3e616102cbe4bf0382d4338df9674c9b41 | 130c49f47783503e462c16b2eff31933442be6ff | /src/Lean/PrettyPrinter/Formatter.lean | 6204668262caecbf1c6447b5b4bd8e7eb8eefd04 | [
"Apache-2.0"
] | permissive | Hazel-Brown/lean4 | 8aa5860e282435ffc30dcdfccd34006c59d1d39c | 79e6732fc6bbf5af831b76f310f9c488d44e7a16 | refs/heads/master | 1,689,218,208,951 | 1,629,736,869,000 | 1,629,736,896,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 21,388 | lean | /-
Copyright (c) 2020 Sebastian Ullrich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
-/
import Lean.CoreM
import Lean.Parser.Extension
import Lean.KeyedDeclsAttribute
import Lean.ParserCompiler.Attribute
import Lean.PrettyPrinter.Basic
/-!
The for... |
5fda41b7aaf5f6e0ed703d78c50428ec17cac5d5 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/topology/metric_space/hausdorff_distance.lean | 23d51502044bb8980fd979ad57096ac1bc428536 | [
"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 | 32,532 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Sébastien Gouëzel
-/
import topology.metric_space.isometry topology.instances.ennreal
topology.metric_space.lipschitz
/-!
# Hausdorff distance
The Hausdorff distance on sub... |
66bfff5be64c5d72b81a25354b2cb80aef950bef | 08a8ee10652ba4f8592710ceb654b37e951d9082 | /src/hott/types/pi.lean | b33e82d9d4c5ceee333a4a2ae3cc57a7822c87a4 | [
"Apache-2.0"
] | permissive | felixwellen/hott3 | e9f299c84d30a782a741c40d38741ec024d391fb | 8ac87a2699ab94c23ea7984b4a5fbd5a7052575c | refs/heads/master | 1,619,972,899,098 | 1,509,047,351,000 | 1,518,040,986,000 | 120,676,559 | 0 | 0 | null | 1,518,040,503,000 | 1,518,040,503,000 | null | UTF-8 | Lean | false | false | 14,945 | lean | /-
Copyright (c) 2014-15 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Floris van Doorn
Partially ported from Coq HoTT
Theorems about pi-types (dependent function spaces)
-/
import .sigma hott.arity hott.cubical.square
universe u
hott_theory
names... |
02292d4a8f4cac8a62651f6cef4f529cc5f7c2f6 | 31e8ce8c3f972f4102a087008fd33dee6f2d7dfe | /test.lean | b8ecc5eb23a7d6c453a931a9664bbf6607fa8f69 | [
"MIT"
] | permissive | sakas--/lean-tauto | 6ca908abde99b252c9a3fdce5c0e98871ebbcc26 | 3cc5c1349f9204f3b798ea8cdb6e4f36ed2d1b25 | refs/heads/master | 1,610,549,743,092 | 1,488,258,185,000 | 1,488,258,185,000 | 76,671,935 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,771 | lean | /- TODO : add some test from ILTP library
-/
import .tauto
open tauto
section test
variables {A B C D E F : Prop}
example : true :=
by tauto >> tactic.trace "test1 succeeded"
example : A → A :=
by tauto >> tactic.trace "test2 succeeded"
example : A ∧ B → B ∧ A :=
by tauto >> tactic.trace "test3 succeeded"
exampl... |
3c164379309363d3243fcc86891203ab9a9c69c4 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/algebra1.lean | c26351671d604001f47c2607c3c3708d0ffc45af | [
"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 | 3,225 | lean | import logic
namespace experiment
definition Type1 := Type.{1}
section
variable {A : Type}
variable f : A → A → A
variable one : A
variable inv : A → A
local infixl `*` := f
local postfix `^-1`:100 := inv
definition is_assoc := ∀ a b c, (a*b)*c = a*b*c
definition is_id := ∀ a, a*one = a
de... |
ba84b1b81775c5ec3d4f60f495acb261ff434dbd | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebraic_geometry/Spec.lean | eff89cbd23173716bc3c10c51fe48ff61b2ed737 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 15,761 | 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 ring_theory.localization.localization_localization
im... |
6f77c5e97fd1371345e549309a2824819ead4c0a | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/category/PartialFun.lean | 46ffcb1b33c11180b1db35e0cb026c84450856bc | [
"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 | 6,487 | 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 category_theory.category.Pointed
import data.pfun
/-!
# The category of types with partial functions
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to ... |
f58d729c2a9055db3057d001e552c6da8ad459f5 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/fin/interval.lean | af0d1b267af69db33d5ebc728e099f6a0e9b81ba | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 5,031 | lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import data.nat.interval
import data.finset.locally_finite
/-!
# Finite intervals in `fin n`
This file proves that `fin n` is a `locally_finite_order` and calculates th... |
2a644ddf247415684c5255028bf6ad8da95f14c3 | 5ca7b1b12d14c4742e29366312ba2c2ef8201b21 | /world_experiments/used_to_be_level2_stupid_exact_tactic.lean | 734633b51b99890a04a02a4cff4bafc913df7bea | [
"Apache-2.0"
] | permissive | MatthiasHu/natural_number_game | 2e464482ef3001863430b0336133b6697b275ba3 | 2d764f72669ae30861f6a1057fce0257f3e466c4 | refs/heads/master | 1,609,719,110,419 | 1,576,345,737,000 | 1,576,345,737,000 | 240,296,314 | 0 | 0 | Apache-2.0 | 1,581,608,357,000 | 1,581,608,356,000 | null | UTF-8 | Lean | false | false | 2,673 | lean | import mynat.definition -- Imports the natural numbers. -- hide
import mynat.mul -- hide
namespace mynat -- hide
/-
# World 1: Tutorial world
## level 2: the `exact` tactic.
Delete the `sorry` below and let's look at the box
on the top right. It should look like this:
```
a b : mynat,
h : 2 * a = b + 7
⊢ 2 * a = b... |
1d3929613fc0a310c3711532ab6fcaf66ca37d8e | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/tactic/swap_var.lean | 85d285695841a6a909b5800303a4243140faf42d | [
"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 | 1,950 | lean | /-
Copyright (c) 2022 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
import tactic.interactive
/-!
# Swap bound variable tactic
This files defines a tactic `swap_var` whose main purpose is to be a weaker
version of `wlog` that jugg... |
6b58efb295d7f4c56129592c6799b057048b106d | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/algebra/continued_fractions/computation/terminates_iff_rat.lean | 87c1281554f0f446c78aa9478a8fa9b166b5d6ba | [
"Apache-2.0"
] | permissive | ayush1801/mathlib | 78949b9f789f488148142221606bf15c02b960d2 | ce164e28f262acbb3de6281b3b03660a9f744e3c | refs/heads/master | 1,692,886,907,941 | 1,635,270,866,000 | 1,635,270,866,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,318 | lean | /-
Copyright (c) 2020 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import algebra.continued_fractions.computation.approximations
import algebra.continued_fractions.computation.correctness_terminating
import data.rat
/-!
# Termina... |
9247301bb425fcf1ff3aaa5f91ff45171e58e04e | ce6917c5bacabee346655160b74a307b4a5ab620 | /src/ch4/ex0407.lean | a7594c5d8527429f5371b98f6c3b2eaa01f8e769 | [] | 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 | 150 | lean | variables (α : Type) (p q : α → Prop)
example (h : ∃ x, p x ∧ q x) : ∃ x, q x ∧ p x :=
let ⟨w, hpw, hqw⟩ := h in ⟨w, hqw, hpw⟩
|
93b7f5cfd40030cceb7baaba0b4a590071018b15 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/normed/field/infinite_sum.lean | 67888a205379ce48eb3d326193ea94de053b2279 | [
"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 | 6,116 | 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.field.basic
import analysis.normed.group.infinite_sum
/-! # Multiplying two infinite sums in a normed ring
> THIS FILE IS SYNCHRONIZED WI... |
b503bcbeb074c6a8a6efa2cd4112c13c454ccbaf | c3f2fcd060adfa2ca29f924839d2d925e8f2c685 | /library/init/nat.lean | a6cb271a47f5b2da111f3c15377d96c554d1fa50 | [
"Apache-2.0"
] | permissive | respu/lean | 6582d19a2f2838a28ecd2b3c6f81c32d07b5341d | 8c76419c60b63d0d9f7bc04ebb0b99812d0ec654 | refs/heads/master | 1,610,882,451,231 | 1,427,747,084,000 | 1,427,747,429,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,699 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.nat
Authors: Floris van Doorn, Leonardo de Moura
-/
prelude
import init.wf init.tactic init.num
open eq.ops decidable
namespace nat
notation `ℕ` := nat
inductive lt ... |
3171d7be86e6ddb8e93c825c0a3b188b2e4aa02e | 8034095e1be60c0b8f6559c39220bd537d1f9933 | /lambda/parsing.lean | cbb9f2a61918f5ec5ad008a8fa4e7bd0c3e86af0 | [] | no_license | teodorov/lambda | 40c573e2dd268824641702d9f94cf61e019ae6c5 | 4dc4d595dd0ee20c59913ef0171fd33eb0d637a1 | refs/heads/master | 1,585,318,070,303 | 1,530,364,515,000 | 1,530,364,515,000 | 146,645,753 | 1 | 0 | null | 1,535,569,435,000 | 1,535,569,434,000 | null | UTF-8 | Lean | false | false | 2,342 | lean | import data.buffer.parser
import lambda.types
open parser types
namespace parsing
def whitespaces := " \t\n\x0d".to_list
def reserved_chars :=
[' ', ',', 'λ', '(', ')', ':', '-']
def WordChar : parser char :=
sat (λ c, list.all (reserved_chars ++ whitespaces) (≠ c))
def LF := ch $ char.of_nat 10
def CR := ch $ char... |
abe83213324fcb23f6cc2e8e5f3a1c39d1c563d6 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/smt_tests3.lean | 780ff728ce18b82f23528a97d91f19fa485af4a7 | [
"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 | 675 | lean | def f : nat → nat
| 0 := 1
| (n+1) := f n + 1
lemma ex(a : nat) : f a ≠ 0 :=
begin
induction a,
dsimp [f], intro x, contradiction,
dsimp [f],
change nat.succ (f a_n) ≠ 0,
apply nat.succ_ne_zero
end
lemma ex2 (a : nat) : f a ≠ 0 :=
begin [smt]
induction a,
{ intros, ematch_using [f] },
{ iterate {... |
857eca2a5233b789a823d14ff85a0c55661424b5 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/algebra/punit_instances.lean | b89b2b62e897c55ecc41978cde12e9548f4f1c92 | [
"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 | 2,819 | lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import algebra.module.basic
/-!
# Instances on punit
This file collects facts about algebraic structures on the one-element type, e.g. that it is a
commutative ring.
-/
uni... |
d83e2c1cef915554ede387b503d382dc941c842f | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /13_More_Tactics.org.7.lean | 568227ea2a38ccc2dc2cdb20bc12ecf120d56796 | [] | 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 | 209 | lean | import standard
import data.nat
open nat
example (x y : ℕ) (H : succ x = succ y) : x = y :=
by injection H with H'; exact H'
example (x y : ℕ) (H : succ x = succ y) : x = y :=
by injection H; assumption
|
c1da96fb776bb00bac1cb38bc7d193bad77bf5ee | 07c76fbd96ea1786cc6392fa834be62643cea420 | /hott/types/lift.hlean | 9db711a4598a422f70e8959df55c4fd329f0d7cb | [
"Apache-2.0"
] | permissive | fpvandoorn/lean2 | 5a430a153b570bf70dc8526d06f18fc000a60ad9 | 0889cf65b7b3cebfb8831b8731d89c2453dd1e9f | refs/heads/master | 1,592,036,508,364 | 1,545,093,958,000 | 1,545,093,958,000 | 75,436,854 | 0 | 0 | null | 1,480,718,780,000 | 1,480,718,780,000 | null | UTF-8 | Lean | false | false | 6,360 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Floris van Doorn
Theorems about lift
-/
import ..function
open eq equiv is_equiv is_trunc pointed
namespace lift
universe variables u v
variables {A : Type.{u}} (z z' : lift.{... |
5740b6dd2cf173a704fbbb7051dca8d082739168 | fecda8e6b848337561d6467a1e30cf23176d6ad0 | /src/category_theory/over.lean | a575f4f650eca6ba16a3d7ef3590fcf139754fbe | [
"Apache-2.0"
] | permissive | spolu/mathlib | bacf18c3d2a561d00ecdc9413187729dd1f705ed | 480c92cdfe1cf3c2d083abded87e82162e8814f4 | refs/heads/master | 1,671,684,094,325 | 1,600,736,045,000 | 1,600,736,045,000 | 297,564,749 | 1 | 0 | null | 1,600,758,368,000 | 1,600,758,367,000 | null | UTF-8 | Lean | false | false | 9,773 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Bhavik Mehta
-/
import category_theory.comma
import category_theory.punit
import category_theory.reflects_isomorphisms
/-!
# Over and under categories
Over (and under... |
b368afeb84ac777d889597b39758ac35362cee6d | cc5bb0a18c45fa529fc8bf0365b1fbf48464c5a8 | /library/init/data/int/order.lean | 4fcad5b7cb2131c632dbe1317b52d1afe2796ff6 | [
"Apache-2.0"
] | permissive | mk12/lean | 6bb58b9f3cfe312236b41779478d345399f00918 | 092fc89333160661c4c5a6295f3054cafff4341e | refs/heads/master | 1,609,531,450,083 | 1,501,275,267,000 | 1,501,278,025,000 | 98,760,144 | 0 | 0 | null | 1,501,364,485,000 | 1,501,364,485,000 | null | UTF-8 | Lean | false | false | 13,012 | 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 order relation on the integers.
-/
prelude
import init.data.int.basic
namespace int
private def nonneg (a : ℤ) : Prop := int.cases_on a (assume n, true) (assume n, ... |
4ef45ed77a3cdfb1a2628f7282273d165f4e9a66 | 423cba856b0cf4755b74f3fea3f0a0c5656379fd | /src/pipes/tactic.lean | 856d7200f9c588d973b9f5d31c62c02ee75b1086 | [] | no_license | cipher1024/lean-pipes | e221aafa8f127ab8f2dabe12897427eefd762b36 | 3db1d792b987113b07578f21de26c23826809e0c | refs/heads/master | 1,609,627,565,606 | 1,526,931,011,000 | 1,526,931,011,000 | 99,382,224 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 662 | lean |
namespace tactic
open lean.parser interactive interactive.types
open tactic.interactive (generalize cases_arg_p)
local postfix `?`:9000 := optional
local postfix `*`:9000 := many
lemma cast_eq_of_heq {α β} {x : α} {y : β}
(h : α = β)
(h' : cast h x = y)
: x == y :=
by { subst β, subst y, symmetry, simp [cast_heq]... |
89fb1f5931e9397195fd645dcabe027170014db7 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/number_theory/primorial.lean | c12caa9bf03502a468b4f056f6e1f95ffbc43116 | [] | 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 | 1,435 | lean | /-
Copyright (c) 2020 Patrick Stevens. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Stevens
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.tactic.ring_exp
import Mathlib.data.nat.parity
import Mathlib.data.nat.choose.sum
import ... |
71135d17fc27614fe867317ee4645eb2af1a5b65 | 2d34dfb0a1cc250584282618dc10ea03d3fa858e | /src/for_mathlib/free_abelian_group.lean | d175eac349143e3110a1af43906e860d1cbfea98 | [] | no_license | zeta1999/lean-liquid | 61e294ec5adae959d8ee1b65d015775484ff58c2 | 96bb0fa3afc3b451bcd1fb7d974348de2f290541 | refs/heads/master | 1,676,579,150,248 | 1,610,771,445,000 | 1,610,771,445,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 12,305 | lean | import group_theory.free_abelian_group
import data.finsupp.basic
noncomputable theory
open_locale big_operators
namespace int
variables {A : Type*} [add_comm_group A]
def cast_add_hom' (a : A) : ℤ →+ A :=
add_monoid_hom.mk' (λ n, n • a) $ λ m n, add_smul _ _ _
@[simp] lemma cast_add_hom'_apply (a : A) (n : ℤ) : c... |
475960cbc2772c4bdfd3d3ee6d513747173272cc | c46a31beec236d29b6c02e7d7683691bcfbb3014 | /src/utils/cmp.lean | 3001e1915acfdc54b4ba7cd0d4914cea0220fe6d | [] | no_license | UVM-M52/quiz-5-maddiestrauss | a88b9bfbdd486a521ee280f9b7b551bcb48f23c6 | 214529615e08bbcdd3d6600c89432ec985e6ba3a | refs/heads/master | 1,617,897,187,103 | 1,584,922,038,000 | 1,584,922,038,000 | 248,787,429 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,905 | lean |
section
variables {α : Type*} [semiring α]
theorem mul_two_eq_add_self (x : α) : x * 2 = x + x :=
show x * (1 + 1) = x + x, by rw [mul_add, mul_one]
theorem two_mul_eq_add_self (x : α) : 2 * x = x + x :=
show (1 + 1) * x = x + x, by rw [add_mul, one_mul]
end
namespace linear_ordered_ring
variables (α : Type*) [i :... |
f57cf1ec28cb7dab958bd480612701237fdb69e6 | 297c4ceafbbaed2a59b6215504d09e6bf201a2ee | /finset/to_set.lean | e5b18fffda5e39f702c14c8d08171515bef8de6e | [] | no_license | minchaowu/Kruskal.lean3 | 559c91b82033ce44ea61593adcec9cfff725c88d | a14516f47b21e636e9df914fc6ebe64cbe5cd38d | refs/heads/master | 1,611,010,001,429 | 1,497,935,421,000 | 1,497,935,421,000 | 82,000,982 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,476 | lean | import .logic .comb
open set classical
namespace finset
variable {A : Type}
variable [deceq : decidable_eq A]
definition to_set (s : finset A) : set A := λx, x ∈ s
-- def ts := @to_set A
instance finset_to_set_coe : has_coe (finset A) (set A) := ⟨to_set⟩
variables (s t : finset A) (x y : A)
theorem mem_eq_mem_to_... |
8d7b9b046dc074cf5e730a8277a2f028f9179cf3 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/pequiv.lean | e83da726cc7faf5c73c2d0adf05125f95af6ff82 | [
"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 | 12,894 | lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import data.set.lattice
/-!
# Partial Equivalences
In this file, we define partial equivalences `pequiv`, which are a bijection between a subset of `α`
and a subset of... |
77d4bfd3d944cc7979166314a8d1eee333376089 | 12dabd587ce2621d9a4eff9f16e354d02e206c8e | /world06/level02.lean | d913a782cd2039254116011c506f7824bf51bda6 | [] | no_license | abdelq/natural-number-game | a1b5b8f1d52625a7addcefc97c966d3f06a48263 | bbddadc6d2e78ece2e9acd40fa7702ecc2db75c2 | refs/heads/master | 1,668,606,478,691 | 1,594,175,058,000 | 1,594,175,058,000 | 278,673,209 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 67 | lean | lemma imp_self (P : Prop) : P → P :=
begin
intro p,
exact p,
end
|
8fef5465e0694ad94f0006cd1db82a3c04a5c96a | 28d9ae48dddad2ebe8cb28027b15e9c9d996e0ed | /src/pos_num.lean | 04f3b64b6ed44dbbbddef347c0e3779d27971177 | [] | no_license | ImperialCollegeLondon/british-natural-number-game | 0f76ac920488db62b3d391bd60d650e725f90938 | 593dede2c911e0651b8d177365180b659d7b2acf | refs/heads/master | 1,669,990,486,571 | 1,596,886,731,000 | 1,596,886,731,000 | 285,931,256 | 4 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 31,720 | lean | -- `pos_num` -- the British Natural Numbers.
-- The same as pnat
/- todo --
make nicer recursor to get less `one` and more `1`.
le world
add docstrings
add questions (these are solutions)
-/
import tactic
namespace xena
-- should be elsewhere
-- pnat inductive principle
@[elab_as_eliminator] def pnat'.ind... |
c239e7b09c54a5cf22c1bb1cd584581d9a570edf | a4673261e60b025e2c8c825dfa4ab9108246c32e | /src/Init/WF.lean | fd815d8aaf3b304a05de960cf7fd571a74ed0c7c | [
"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 | 11,258 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import Init.SizeOf
import Init.Data.Nat.Basic
universes u v
set_option codegen false
inductive Acc {α : Sort u} (r : α → α → Prop) : α → Prop :=
... |
b90cf681e23c7b1226a4813718d3d6c4831c5844 | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/data/multiset/basic.lean | f774e2106a3176623759e8dbb2c36f3f3e969e5f | [
"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 | 88,068 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
-/
import data.list.perm
import algebra.group_power
/-!
# Multisets
These are implemented as the quotient of a list by permutations.
## Notation
We define the ... |
cf1874c583fbf037d3670d72214041d7931d3085 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/nat/choose/default.lean | 807baa6363db8518feb48544dcd1012613e2e69c | [] | 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 | 174 | lean | import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.nat.choose.dvd
import Mathlib.data.nat.choose.sum
import Mathlib.PostPort
namespace Mathlib
|
016e56884bbd5b53e755cd7990021e99b38da057 | 8461211c55a0962f1c8b2e7537d535b4c68194a2 | /tao_analysis/02_natural_numbers.lean | d3c5718ddcd7c9159f29b00321bf8a70010a5bf8 | [] | no_license | alanhdu/lean-proofs | ba687a3d289c58cce9cf80a66f55bed2cdf4bdfb | a02cb9d0d2b6a6457f35247b89253d727f641531 | refs/heads/master | 1,598,769,649,392 | 1,575,379,585,000 | 1,575,379,585,000 | 218,293,755 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,333 | lean | inductive xnat : Type
| zero : xnat
| succ : xnat → xnat
namespace xnat
axiom succ_ne_zero : ∀ n : xnat, xnat.succ n ≠ xnat.zero
axiom succ_inj : ∀ {n m: xnat}, xnat.succ n = xnat.succ m → n = m
def add : xnat → xnat → xnat
| zero m := m
| (succ n) m := succ (add n m)
-- Lemma 2.2.2
theorem add_zero : ∀... |
394ab0986351f32cf6894a619df80560b3c9a9c2 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/linear_algebra/quadratic_form/real.lean | 8e172a1e9c1c58fbe933e5c4bcd8ac4d1456fb38 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 4,362 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Kexing Ying, Eric Wieser
-/
import linear_algebra.quadratic_form.isometry
import analysis.special_functions.pow
import data.real.sign
/-!
# Real quadratic forms
Sylvester's... |
13d971b1c15c0249af1705350bc09c1a7cfc1305 | ea5678cc400c34ff95b661fa26d15024e27ea8cd | /fermat's little theorem.lean | c0ce4a4b3d3091e0efcf4ce8a980adc6b47c256c | [] | no_license | ChrisHughes24/leanstuff | dca0b5349c3ed893e8792ffbd98cbcadaff20411 | 9efa85f72efaccd1d540385952a6acc18fce8687 | refs/heads/master | 1,654,883,241,759 | 1,652,873,885,000 | 1,652,873,885,000 | 134,599,537 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,916 | lean | import data.nat.modeq data.nat.basic data.nat.prime data.int.basic tactic.norm_num
def prime : ℤ → Prop := λ x,nat.prime (int.nat_abs x)
theorem prime_dvd_mul {p m n : ℤ} (pp : prime p) : p ∣ m * n ↔ p ∣ m ∨ p ∣ n :=begin
have H:int.nat_abs p ∣int.nat_abs m * int.nat_abs n ↔ int.nat_abs p ∣ int.nat_abs m ∨ int.nat... |
e9ef80a6195b66072a1146fffb208d1e9bff244f | 9d2e3d5a2e2342a283affd97eead310c3b528a24 | /src/for_mathlib/category_theory/isomorphism.lean | 69c00f649699a350e74aef756df0a4426d70f532 | [] | permissive | Vtec234/lftcm2020 | ad2610ab614beefe44acc5622bb4a7fff9a5ea46 | bbbd4c8162f8c2ef602300ab8fdeca231886375d | refs/heads/master | 1,668,808,098,623 | 1,594,989,081,000 | 1,594,990,079,000 | 280,423,039 | 0 | 0 | MIT | 1,594,990,209,000 | 1,594,990,209,000 | null | UTF-8 | Lean | false | false | 2,149 | lean | import category_theory.isomorphism
open category_theory
universes v u
variables {C : Type u} [category.{v} C]
namespace category_theory.iso
/-!
All these cancellation lemmas can be solved by `simp [cancel_mono]` (or `simp [cancel_epi]`),
but with the current design `cancel_mono` is not a good `simp` lemma,
because... |
dbc130dbabfcd1caa31fa7d5f746688dc9eb83e6 | acc85b4be2c618b11fc7cb3005521ae6858a8d07 | /data/prod.lean | 163a50e836138074c244e06ebd69977656e2e2fc | [
"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 | 1,044 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Extends theory on products
-/
universes u v
variables {α : Type u} {β : Type v}
-- copied from parser
@[simp] lemma prod.mk.eta : ∀{p : α × β}, (p.1, p.2) = p
| (a, b... |
b0c624c6846c35311c6de45c72d39c11612b4d2c | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/indicator_function.lean | d412f3c3e71eff53547ca64a439c3bb16c772193 | [
"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 | 26,507 | 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.support
/-!
# Indicator function
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
- `indi... |
a9bc6dcb09900af8b189f9f7f856874ef60bc8e6 | 72d99e722771bfc4f845b49212c0f743cf3f08df | /tests/lean/run/check_constants.lean | 9d29b68f7919553b4ccaef89104555611a9b9c6f | [
"Apache-2.0"
] | permissive | AtnNn/lean | c79fa061e300e0ebea0186d9f7db971e839e8955 | d97d77fd30601f06c751ca376c0cdddd59cf52f9 | refs/heads/master | 1,583,885,051,450 | 1,523,730,668,000 | 1,523,730,668,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,389 | lean | -- DO NOT EDIT, automatically generated file, generator scripts/gen_constants_cpp.py
import smt system.io
open tactic
meta def script_check_id (n : name) : tactic unit :=
do env ← get_env, (env^.get n >> return ()) <|> (guard $ env^.is_namespace n) <|> (attribute.get_instances n >> return ()) <|> fail ("identifier '" +... |
4a6cab2e9569cee7623364cdae891a2d21b9b58d | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/unfold_lemmas.lean | fbe281cd4587b99b2081d9cd3ba0c05b8b81a94e | [
"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 | 275 | lean | open nat well_founded
def gcd' : ℕ → ℕ → ℕ | y := λ x,
if h : y = 0 then
x
else
have x % y < y, by { apply mod_lt, cases y, contradiction, apply succ_pos },
gcd' (x % y) y
@[simp] lemma gcd_zero_right (x : nat) : gcd' 0 x = x :=
by { rw gcd', simp }
|
019bea9ba1a5ae2a0dbde881905b02af7626ee32 | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /tests/lean/run/new_compiler.lean | 9e2c2668a2ae18178fa2cfeeadebee0dd98704e1 | [
"Apache-2.0"
] | permissive | WojciechKarpiel/lean4 | 7f89706b8e3c1f942b83a2c91a3a00b05da0e65b | f6e1314fa08293dea66a329e05b6c196a0189163 | refs/heads/master | 1,686,633,402,214 | 1,625,821,189,000 | 1,625,821,258,000 | 384,640,886 | 0 | 0 | Apache-2.0 | 1,625,903,617,000 | 1,625,903,026,000 | null | UTF-8 | Lean | false | false | 1,745 | lean |
universe u v w r s
set_option trace.compiler.stage1 true
-- set_option pp.explicit true
set_option pp.binder_types false
-- set_option pp.proofs true
def foo (n : Nat) : Nat :=
let x := Nat.zero;
let x1 := Nat.succ x;
let x2 := Nat.succ x1;
let x3 := Nat.succ x2;
let x4 := Nat.succ x3;
let x5 := Nat.succ x4;
let x6... |
dac220e74c5de18553ca2c3af459b88d029edd4a | 432d948a4d3d242fdfb44b81c9e1b1baacd58617 | /src/analysis/normed_space/inner_product.lean | 545161c86d7b30068a5db446985673c45c8ba3dc | [
"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 | 127,431 | lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Sébastien Gouëzel, Frédéric Dupuis, Heather Macbeth
-/
import linear_algebra.bilinear_form
import linear_algebra.sesquilinear_form
import topology.metric_space.pi_Lp
imp... |
83be5aae1a88b203af1c0aa5f8f74e7d68f66725 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/category_theory/fully_faithful.lean | 59f29d818f4076d0e8f56b812e0b1855b66c4a72 | [
"Apache-2.0"
] | permissive | agjftucker/mathlib | d634cd0d5256b6325e3c55bb7fb2403548371707 | 87fe50de17b00af533f72a102d0adefe4a2285e8 | refs/heads/master | 1,625,378,131,941 | 1,599,166,526,000 | 1,599,166,526,000 | 160,748,509 | 0 | 0 | Apache-2.0 | 1,544,141,789,000 | 1,544,141,789,000 | null | UTF-8 | Lean | false | false | 8,059 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.natural_isomorphism
import data.equiv.basic
universes v₁ v₂ v₃ u₁ u₂ u₃ -- declare the `v`'s first; see `category_theory.category` for an expl... |
ab40fac4c556f89369efa81206a22a6e8d8e62f6 | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/measure_theory/decomposition/jordan.lean | a40b9c84209f1ae3ceffc8a7fe7a4662437319d8 | [
"Apache-2.0"
] | permissive | jumpy4/mathlib | d3829e75173012833e9f15ac16e481e17596de0f | af36f1a35f279f0e5b3c2a77647c6bf2cfd51a13 | refs/heads/master | 1,693,508,842,818 | 1,636,203,271,000 | 1,636,203,271,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 25,249 | lean | /-
Copyright (c) 2021 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import measure_theory.decomposition.signed_hahn
/-!
# Jordan decomposition
This file proves the existence and uniqueness of the Jordan decomposition for signed measures.
... |
db9b79ea01a32e27a69be4e564845e4247a39beb | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/ring_theory/free_ring.lean | 92008aab7ba9de5b6476ef7a345d4198c123dcce | [] | 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 | 2,714 | lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Johan Commelin
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.group_theory.free_abelian_group
import Mathlib.ring_theory.subring
import Mathlib.Pos... |
ffc2712283d8469a64492bb92266b603fb6f6d0c | 4727251e0cd73359b15b664c3170e5d754078599 | /src/combinatorics/double_counting.lean | 99e30deda21c4d5b9424a52c8be42fd12c5993f7 | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 3,532 | lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import algebra.big_operators.order
/-!
# Double countings
This file gathers a few double counting arguments.
## Bipartite graphs
In a bipartite graph (considered as a... |
17abb32280983c2018c77de2a2cc2ef8059eedd2 | 8d65764a9e5f0923a67fc435eb1a5a1d02fd80e3 | /src/data/pfunctor/univariate/M.lean | 74d227d020b07ad8ba5e76768939ae2bfb469542 | [
"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 | 22,062 | lean | /-
Copyright (c) 2017 Simon Hudon All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import data.pfunctor.univariate.basic
/-!
# M-types
M types are potentially infinite tree-like structures. They are defined
as the greatest fixpoint of a polynomial functo... |
11d443763ec1853db5df4738958c0cdcbba46bb1 | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/computability/tm_to_partrec.lean | 4c67003579f9d37fb55c3ce8bfb5e0325f9286b2 | [
"Apache-2.0"
] | permissive | ayush1801/mathlib | 78949b9f789f488148142221606bf15c02b960d2 | ce164e28f262acbb3de6281b3b03660a9f744e3c | refs/heads/master | 1,692,886,907,941 | 1,635,270,866,000 | 1,635,270,866,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 64,484 | lean | /-
Copyright (c) 2020 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import computability.halting
import computability.turing_machine
import data.num.lemmas
/-!
# Modelling partial recursive functions using Turing machines
This file ... |
54be8ac68ab5ca0db4ef9d1f84ffade14e652197 | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/tactic/group.lean | bc74780c84d5a97c60488910b75efdf038599869 | [
"Apache-2.0"
] | permissive | ayush1801/mathlib | 78949b9f789f488148142221606bf15c02b960d2 | ce164e28f262acbb3de6281b3b03660a9f744e3c | refs/heads/master | 1,692,886,907,941 | 1,635,270,866,000 | 1,635,270,866,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,690 | lean | /-
Copyright (c) 2020. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import tactic.ring
import tactic.doc_commands
/-!
# `group`
Normalizes expressions in the language of groups. The basic idea is to use the simplifier
to put everything into a prod... |
4fd2fa88d5f3988f2d2919f86802bd9c3859335c | 1437b3495ef9020d5413178aa33c0a625f15f15f | /data/finset.lean | 3afcdaaf2c3b495abc2167380960ceac420f52a5 | [
"Apache-2.0"
] | permissive | jean002/mathlib | c66bbb2d9fdc9c03ae07f869acac7ddbfce67a30 | dc6c38a765799c99c4d9c8d5207d9e6c9e0e2cfd | refs/heads/master | 1,587,027,806,375 | 1,547,306,358,000 | 1,547,306,358,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 72,938 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura, Jeremy Avigad, Minchao Wu, Mario Carneiro
Finite sets.
-/
import logic.embedding order.boolean_algebra algebra.order_functions
data.multiset data.sigma.basi... |
c14e5a2665245a0b6c0524ea62c9ed76c5dc5b3e | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/record9.lean | 5c126635ec3737f9ec419856d8d72ec2a1f2204f | [
"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 | 127 | lean | constant {u} fibrant : Type u → Prop
structure {u} Fib : Type (u+1) :=
{type : Type u} (pred : fibrant type)
#check Fib.mk
|
d1355b66364515010ec0df75ffdc482f2a59dd8d | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/linear_algebra/projection.lean | d8f56f520278e01d478deb84e6eaff47a10b1aeb | [
"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 | 16,863 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import linear_algebra.quotient
import linear_algebra.prod
/-!
# Projection to a subspace
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file req... |
eee53b7f4d1b6729eb0cccb5000c900494f56ece | b3fced0f3ff82d577384fe81653e47df68bb2fa1 | /src/measure_theory/measure_space.lean | 7f218566327cc510c416d7f2e22353064ad77bfc | [
"Apache-2.0"
] | permissive | ratmice/mathlib | 93b251ef5df08b6fd55074650ff47fdcc41a4c75 | 3a948a6a4cd5968d60e15ed914b1ad2f4423af8d | refs/heads/master | 1,599,240,104,318 | 1,572,981,183,000 | 1,572,981,183,000 | 219,830,178 | 0 | 0 | Apache-2.0 | 1,572,980,897,000 | 1,572,980,896,000 | null | UTF-8 | Lean | false | false | 35,080 | 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
Measure spaces -- measures
Measures are restricted to a measurable space (associated by the type class `measurable_space`).
This allows us to prove equ... |
cbff6294c706baffbd1e6854b454e8763f71d183 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/sym/card.lean | f45e2c505f828ef8907e3cfd98e9823c8bb1d99b | [
"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 | 8,914 | lean | /-
Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta, Huỳnh Trần Khanh, Stuart Presnell
-/
import algebra.big_operators.basic
import data.finset.sym
import data.fintype.sum
/-!
# Stars and bars
> ... |
4228a9f12de7b1b81e1fecbd1f9f51c307ce5766 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/run/unification_hints.lean | 43e596e3b20a8794476a05b2fb725278a59e7a1b | [
"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 | 800 | lean | open list nat
namespace toy
constants (A : Type.{1}) (f h : A → A) (x y z : A)
attribute [irreducible]
noncomputable definition g (x y : A) : A := f z
@[unify]
noncomputable definition toy_hint (x y : A) : unification_hint :=
{ pattern := g x y ≟ f z,
constraints := [] }
open tactic
set_option trace.type_cont... |
170f78b97f82c8515a0a27293d1474be0ec00864 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /11_Tactic-Style_Proofs.org.39.lean | 75961cda53ad6e744550c5c78bb0fcf4b9b71c70 | [] | 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 | 165 | lean | import standard
import data.nat
open nat
-- BEGIN
example (a b c : nat) : a + b + c = a + c + b :=
begin
rewrite [add.assoc, {b + _}add.comm, -add.assoc]
end
-- END
|
6bc63951f3651df7d9dcd47b81c3afb522acc7d9 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/algebra/big_operators/ring.lean | 312adc17b6e5f3342c88cf77daabb57dceded4c5 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 11,181 | 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 algebra.big_operators.basic
import algebra.field.basic
import data.finset.pi
import data.finset.powerset
/-!
# Results about big operators with values in a (... |
f0e3a069a908e7027dc4ad1683a6cb453272943e | 205f0fc16279a69ea36e9fd158e3a97b06834ce2 | /src/04_Implication/00_intro.lean | 36eb698a6f0ff33ac6a7280cc56c557edfb1c8db | [] | 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 | 11,564 | lean | /-
Given any two propositions, P and Q, we can form
the proposition, P → Q. That is the syntax of an
implications.
If P and Q are propositions, we read P → Q as
P implies Q. A proof of a proposition, P → Q,
is a program that that converts any proof of P
into a proof of Q. The type of such a program
is P → Q.
-/
... |
043481018f5d438ff693c816ae2d6a467f8a772e | 02005f45e00c7ecf2c8ca5db60251bd1e9c860b5 | /src/ring_theory/polynomial/chebyshev/dickson.lean | 54c1b4bff9eda9d99f6d4ecf02cc518c9e5a4508 | [
"Apache-2.0"
] | permissive | anthony2698/mathlib | 03cd69fe5c280b0916f6df2d07c614c8e1efe890 | 407615e05814e98b24b2ff322b14e8e3eb5e5d67 | refs/heads/master | 1,678,792,774,873 | 1,614,371,563,000 | 1,614,371,563,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,094 | lean | /-
Copyright (c) 2021 Julian Kuelshammer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Kuelshammer
-/
import data.polynomial.eval
import ring_theory.polynomial.chebyshev.defs
/-!
# Dickson polynomials
The (generalised) Dickson polynomials are a family of po... |
c2b591e338745efa8d79f3426c47c4db2324e667 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/monoid_algebra.lean | f05ac5e98e3a28eb5b1b729b10ae80b785305775 | [] | 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 | 40,442 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury G. Kudryashov, Scott Morrison
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.algebra.basic
import Mathlib.linear_algebra.fin... |
0e3ceba81b10ca3c5df4967c74949c8f409a2e47 | 2a70b774d16dbdf5a533432ee0ebab6838df0948 | /_target/deps/mathlib/src/analysis/special_functions/trigonometric.lean | dc1d16dcd4e8b53def750c0c7951cbe99d9224f3 | [
"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 | 123,837 | 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, Benjamin Davidson
-/
import analysis.special_functions.exp_log
import data.set.intervals.infinite
import algebra.quadratic_d... |
290c34e60e56e8692e6969c144e3aadcdb0c1322 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/measure_theory/function/ae_measurable_sequence.lean | 90a71460a9acdc735e2269a02ecba7710283c46a | [
"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 | 6,354 | 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.measurable_space
/-!
# Sequence of measurable functions associated to a sequence of a.e.-measurable functions
> THIS FILE IS SYNCHRONIZED WITH MA... |
c15f13cac4fccbb9fa90cd4b5e6fbdbe4a3d2dca | df561f413cfe0a88b1056655515399c546ff32a5 | /8-inequality-world/l3.lean | a67eef6965de26cd7faa1f9999df5fd989bf3012 | [] | 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 | 156 | lean | theorem le_succ (a b : mynat) : a ≤ b → a ≤ (succ b) :=
begin
intro h,
cases h with c hc,
use c + 1,
rw add_one_eq_succ,
rw add_succ,
rw hc,
refl,
end |
6fdda07d5238c63aef27ecf6342c54a7743b11eb | 1b8f093752ba748c5ca0083afef2959aaa7dace5 | /src/category_theory/follow_your_nose.lean | 44169f1044a9ddadfd706337bd29c29680919a18 | [] | no_license | khoek/lean-category-theory | 7ec4cda9cc64a5a4ffeb84712ac7d020dbbba386 | 63dcb598e9270a3e8b56d1769eb4f825a177cd95 | refs/heads/master | 1,585,251,725,759 | 1,539,344,445,000 | 1,539,344,445,000 | 145,281,070 | 0 | 0 | null | 1,534,662,376,000 | 1,534,662,376,000 | null | UTF-8 | Lean | false | false | 1,179 | lean | import category_theory.natural_transformation
import category_theory.opposites
import category_theory.types
import category_theory.tactics.obviously
universes u₁ v₁
open tactic
def fyn_names :=
[ `category_theory.category.id,
`category_theory.functor.map,
`category_theory.nat_trans.app,
`category_theory.c... |
4295cda02a7aa09ba33ec5ea1655f043c7e833e0 | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/equiv/encodable/basic.lean | 874cee4c4b32c51feb1c336ee5646ce46546b35b | [
"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 | 14,920 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura, Mario Carneiro
Type class for encodable Types.
Note that every encodable Type is countable.
-/
import data.equiv.nat
import order.rel_iso
import order.directe... |
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