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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
177a3e874da2c082b4c68a5f1e70960947d5ace2 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/interactive/proof_qed.lean | a4a25ec1fb8c5ba2c68e50135ba44468174229fb | [
"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 | 283 | lean | import logic
open eq.ops
set_option pp.notation false
section
variable {A : Type}
variables {a b c d e : A}
theorem tst : a = b → b = c → c = d → d = e → a = e :=
take H1 H2 H3 H4,
have e1 : a = c,
proof
@eq.trans _ _ _ _ H1 H2
∎,
e1 ⬝ H3 ⬝ H4
end
|
0fab270517609fb5fdb47fbeeff187420ecf52e1 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/tactic/lift.lean | 457223a8c8befa16acc2e3045ffae5590dee8105 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 10,064 | lean | /-
Copyright (c) 2019 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import tactic.rcases
/-!
# lift tactic
This file defines the `lift` tactic, allowing the user to lift elements from one type to another
under a specified conditi... |
d2cfd13aafbfe5a6df5ce540c505a28afe57aefd | 36c7a18fd72e5b57229bd8ba36493daf536a19ce | /tests/lean/simplifier_norm_num.lean | 2d3eb385fec3ee5a5d0731e22f1146f91193668e | [
"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 | 1,773 | lean | import algebra.simplifier
open algebra
open simplifier.numeral
set_option simplify.max_steps 5000000
universe l
constants (A : Type.{l}) (A_comm_ring : comm_ring A)
attribute A_comm_ring [instance]
#simplify eq env 0 (0:A) + 1
#simplify eq env 0 (1:A) + 0
#simplify eq env 0 (1:A) + 1
#simplify eq env 0 (0:A) + 2
#si... |
6c7abc38bb0ff97cc1aa150f97ee0749583d9af4 | 3dc4623269159d02a444fe898d33e8c7e7e9461b | /.github/workflows/geo/src/finite_products.lean | a8e7b0079ea1d86a57a388d8f95d964b6eacaa56 | [] | 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 | 7,595 | lean | /-
Copyright (c) 2020 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki
-/
import category_theory.limits.shapes.finite_products
import category_theory.limits.shapes.binary_products
import category_theory.limits.shapes.terminal
import ... |
fa05dee73d63ffff63b62e6637fbe2aa8a2cf604 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/tactic/interval_cases.lean | 22c5d73ca06a4396797a6e81f227e174a5474326 | [
"Apache-2.0"
] | permissive | dupuisf/mathlib | 62de4ec6544bf3b79086afd27b6529acfaf2c1bb | 8582b06b0a5d06c33ee07d0bdf7c646cae22cf36 | refs/heads/master | 1,669,494,854,016 | 1,595,692,409,000 | 1,595,692,409,000 | 272,046,630 | 0 | 0 | Apache-2.0 | 1,592,066,143,000 | 1,592,066,142,000 | null | UTF-8 | Lean | false | false | 10,943 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Scott Morrison
Case bashing on variables in finite intervals.
In particular, `interval_cases n`
1) inspects hypotheses looking for lower and upper bounds of the form `a ≤ n` and `n < ... |
34373a6a4860e9e438ae1e25a556e98a152cf14a | 217bb195841a8be2d1b4edd2084d6b69ccd62f50 | /tests/playground/unionfind2.lean | 86b6e2964598229e088dd4948b9fbcfb2c6939a1 | [
"Apache-2.0"
] | permissive | frank-lesser/lean4 | 717f56c9bacd5bf3a67542d2f5cea721d4743a30 | 79e2abe33f73162f773ea731265e456dbfe822f9 | refs/heads/master | 1,589,741,267,933 | 1,556,424,200,000 | 1,556,424,281,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,363 | lean | def StateT' (m : Type → Type) (σ : Type) (α : Type) := σ → m (α × σ)
namespace StateT'
variables {m : Type → Type} [Monad m] {σ : Type} {α β : Type}
@[inline] protected def pure (a : α) : StateT' m σ α := λ s, pure (a, s)
@[inline] protected def bind (x : StateT' m σ α) (f : α → StateT' m σ β) : StateT' m σ β := λ s, d... |
6ec3b334b82f5d5022c889604e3f0eddddc6f874 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/order/filter/filter_product.lean | f0cab51a69c73a296020d5933ec38df76c027a4b | [
"Apache-2.0"
] | permissive | hikari0108/mathlib | b7ea2b7350497ab1a0b87a09d093ecc025a50dfa | a9e7d333b0cfd45f13a20f7b96b7d52e19fa2901 | refs/heads/master | 1,690,483,608,260 | 1,631,541,580,000 | 1,631,541,580,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,073 | lean | /-
Copyright (c) 2019 Abhimanyu Pallavi Sudhir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Abhimanyu Pallavi Sudhir, Yury Kudryashov
-/
import order.filter.ultrafilter
import order.filter.germ
/-!
# Ultraproducts
If `φ` is an ultrafilter, then the space of germs ... |
94c8fb5a2a9fde5f4f1aec74d1809f6d0836f946 | 6f1049e897f569e5c47237de40321e62f0181948 | /src/solutions/03_forall_or.lean | d75896e27e870be16066ee331867a50b5e0e5bf0 | [
"Apache-2.0"
] | permissive | anrddh/tutorials | f654a0807b9523608544836d9a81939f8e1dceb8 | 3ba43804e7b632201c494cdaa8da5406f1a255f9 | refs/heads/master | 1,655,542,921,827 | 1,588,846,595,000 | 1,588,846,595,000 | 262,330,134 | 0 | 0 | null | 1,588,944,346,000 | 1,588,944,345,000 | null | UTF-8 | Lean | false | false | 8,865 | lean | import data.real.basic
import algebra.pi_instances
set_option pp.beta true
/-
In this file, we'll learn about the ∀ quantifier, and the disjunction
operator ∨ (logical OR).
Let P be a predicate on a type X. This means for every mathematical
object x with type X, we get a mathematical statement P x.
In Lean, P x ha... |
fba38427e271c25d259d3e2a0dca010422413b3b | f1b175e38ffc5cc1c7c5551a72d0dbaf70786f83 | /algebra/group_power.lean | 8de2c7b6246f613c2e9d46b3159405651129252a | [
"Apache-2.0"
] | permissive | mjendrusch/mathlib | df3ae884dd5ce38c7edf452bcbfd3baf4e3a6214 | 5c209edb7eb616a26f64efe3500f2b1ba95b8d55 | refs/heads/master | 1,585,663,284,800 | 1,539,062,055,000 | 1,539,062,055,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 21,383 | lean | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis
The power operation on monoids and groups. We separate this from group, because it depends on
nat, which in turn depends on other parts of algebra.
We h... |
298e50cf2e8283190ead2b21cb3aed9b13828d44 | 32fa6b3db8c34b5b2996ed46f2eef23e6cd58023 | /matrix.lean | 458407426524c885649d42faee90cdce42381e4e | [] | no_license | skbaek/strassen | 3568459f9aa85beb9d3a653e92225bd9518985a5 | 396c94805360b10896d436813c1e4d0190885840 | refs/heads/master | 1,587,522,553,720 | 1,549,860,051,000 | 1,549,860,051,000 | 170,051,087 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,474 | lean | import .vector
variables {k m n p : nat} {α β : Type} [ring α] [ring β]
open tactic vector
def matrix (α : Type) [ring α] (m n : nat) : Type := vector (vector α n) m
namespace matrix
def add : ∀ {m n : nat}, matrix α m n →
matrix α m n → matrix α m n
| 0 n A B := nil
| (m+1) n A B :=
let A' : matrix α m n... |
4cef70f4fb1f94542c4ba65821ea3bbe198581a9 | 2c1ae42b7676ac4a573a53b902feb68be1ea98f7 | /src/Intro.lean | 0ce1d8c5041f6a34e24c3c911701c0f4ad2fdf93 | [] | no_license | rodrigogribeiro/lean-tutorial | 67d9793fdfba1ddd418ec5c29c30564ff3f4987a | 564254d582181d08eedf241781ab5a4c9ce8d832 | refs/heads/master | 1,610,252,605,463 | 1,447,618,793,000 | 1,447,618,793,000 | 43,224,821 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,219 | lean | import standard
import data.sigma
open nat bool prod sigma
check 3
check tt
-- some logic using lean
theorem and_commutative(p q:Prop) : p ∧ q → q ∧ p:=
assume Hpq : p ∧ q,
have Hp : p, from and.elim_left Hpq,
have Hq : q, from and.elim_right Hpq,
show q ∧ p, from and.intro Hq Hp
theorem implies_chai... |
a7dd15f2290a5d11b01ca64725ee536a939e7aca | 4727251e0cd73359b15b664c3170e5d754078599 | /src/ring_theory/jacobson.lean | 9edb5dd598b612c4c6f956ab676ac0dbca745e97 | [
"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 | 34,257 | lean | /-
Copyright (c) 2020 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Devon Tuma
-/
import ring_theory.localization.away
import ring_theory.ideal.over
import ring_theory.jacobson_ideal
/-!
# Jacobson Rings
The following conditions are equivalent for a ring ... |
276dc3625f938abd976935d1907d25f4a53723b4 | 30b012bb72d640ec30c8fdd4c45fdfa67beb012c | /ring_theory/principal_ideal_domain.lean | 886a2296945694f7109e96a472e76884bd1ab3ca | [
"Apache-2.0"
] | permissive | kckennylau/mathlib | 21fb810b701b10d6606d9002a4004f7672262e83 | 47b3477e20ffb5a06588dd3abb01fe0fe3205646 | refs/heads/master | 1,634,976,409,281 | 1,542,042,832,000 | 1,542,319,733,000 | 109,560,458 | 0 | 0 | Apache-2.0 | 1,542,369,208,000 | 1,509,867,494,000 | Lean | UTF-8 | Lean | false | false | 9,781 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Chris Hughes, Morenikeji Neri
-/
import algebra.euclidean_domain
import ring_theory.ideals ring_theory.noetherian ring_theory.unique_factorization_domain
variables {α : Type*}
open set... |
14a3cc9d8db86d11d6b228c9e2136132bb259433 | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/tactic6.lean | 1a6121158df9047d2b79ec5b5f5a2b45d6f3bf1e | [
"Apache-2.0"
] | permissive | codyroux/lean0.1 | 1ce92751d664aacff0529e139083304a7bbc8a71 | 0dc6fb974aa85ed6f305a2f4b10a53a44ee5f0ef | refs/heads/master | 1,610,830,535,062 | 1,402,150,480,000 | 1,402,150,480,000 | 19,588,851 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 523 | lean | (* import("tactic.lua") *)
theorem T (a b c : Bool): a → b /\ c → c /\ a /\ b := _.
conj_hyp
apply and_intro
(* Focus(Then(show_tac(), conj_tac(), show_tac(), assumption_tac()), 2) *)
exact
done
theorem T2 (a b c : Bool): a → b /\ c → c /\ a /\ b := _.
conj_hyp
apply and_intro
(* show_tac() *)
... |
9c4669baa34abe82240303011d5cbae475d6099d | 94e33a31faa76775069b071adea97e86e218a8ee | /src/testing/slim_check/functions.lean | 0e7283b3a477f333a86bc675b9d5fdc7fd9988db | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 19,547 | lean | /-
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import data.list.sigma
import data.int.range
import data.finsupp.basic
import data.finsupp.to_dfinsupp
import tactic.pretty_cases
import testing.slim_check.sampleable
impor... |
0482c02d9a2bfb5a0e066addf86f4270c553df61 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/control/lawful.lean | e4fe0d889d69e5d4084b8346a373a98d7b70a523 | [] | 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 | 11,676 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.control.monad
import Mathlib.Lean3Lib.init.meta.interactive
import Mathlib.Lean3Lib.init.control.state
i... |
f6249c440bf104baaea3e6337d473070a76931e5 | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/algebra/CommRing/colimits.lean | df9cebbb2469917166f91d77062e7e5647505930 | [
"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 | 12,138 | 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.CommRing.basic
import category_theory.limits.limits
universes u v
open category_theory
open category_theory.limits
-- [ROBOT VOICE]:
-- You should p... |
427561c49ba48d457570c6536417a046cadb5655 | bb31430994044506fa42fd667e2d556327e18dfe | /src/order/partition/finpartition.lean | c20d35dafaaaf174ed533fcf51c79abf7dbb0d78 | [
"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 | 19,685 | lean | /-
Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import algebra.big_operators.basic
import order.atoms.finite
import order.sup_indep
/-!
# Finite partitions
In this file, we define finite p... |
43ba02ac3f1c303889e5e60bfef139ce7b05ab57 | 5d166a16ae129621cb54ca9dde86c275d7d2b483 | /tests/lean/run/simplify_with_hypotheses.lean | 12aa24671fc912b6ea0222802ce8c8c98dfbb843 | [
"Apache-2.0"
] | permissive | jcarlson23/lean | b00098763291397e0ac76b37a2dd96bc013bd247 | 8de88701247f54d325edd46c0eed57aeacb64baf | refs/heads/master | 1,611,571,813,719 | 1,497,020,963,000 | 1,497,021,515,000 | 93,882,536 | 1 | 0 | null | 1,497,029,896,000 | 1,497,029,896,000 | null | UTF-8 | Lean | false | false | 646 | lean | open tactic
example (A : Type) (a₁ a₂ : A) (f : A → A) (H₀ : a₁ = a₂) : f a₁ = f a₂ := by do simp_using_hs >> try reflexivity
example (A : Type) (a₁ a₁' a₂ a₂' : A) (f : A → A) (H₀ : a₁' = a₂') (H₁ : f a₁ = a₁') (H₂ : f a₂ = a₂')
: f a₁ = f a₂ := by do simp_using_hs >> try reflexivity
constants (A : Type.{1}) (x y z... |
f12ad9e0b8789083ee5933443f8f0fec3cb9e0fe | 5d166a16ae129621cb54ca9dde86c275d7d2b483 | /tests/lean/run/assert_tac3.lean | 1633513167212ae260c7ba397073067859f1527b | [
"Apache-2.0"
] | permissive | jcarlson23/lean | b00098763291397e0ac76b37a2dd96bc013bd247 | 8de88701247f54d325edd46c0eed57aeacb64baf | refs/heads/master | 1,611,571,813,719 | 1,497,020,963,000 | 1,497,021,515,000 | 93,882,536 | 1 | 0 | null | 1,497,029,896,000 | 1,497,029,896,000 | null | UTF-8 | Lean | false | false | 811 | lean | open tactic
definition tst2 (a : nat) : a = a :=
by do
assert `x (expr.const `nat []),
rotate 1,
trace_state,
a ← get_local `a,
mk_app `eq.refl [a] >>= exact,
a ← get_local `a,
exact a,
return ()
#print tst2
definition tst3 (a b : nat) : a = a :=
by do
define `x (expr.const `nat []),
ro... |
45d00d1c688fbcb8845fe94788c52beac33ef2de | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Expr.lean | e03f24ce17eb1c7c2d8dbd087e89945a1d6d10d9 | [
"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 | 62,592 | lean | /-
Copyright (c) 2018 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Data.KVMap
import Lean.Level
namespace Lean
/-- Literal values for `Expr`. -/
inductive Literal where
/-- Natural number literal -/
| natV... |
dbe9df7f8cb61d45eea1a0e457452f6c3f64f12f | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/blast_cc_heq8.lean | a90ad66722cc2b87fab471bd35ff8d186d01245e | [
"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 | 292 | lean | open nat subtype
definition f (x : nat) (y : {n : nat | n > x}) : nat :=
x + elt_of y
set_option blast.subst false
example (h : nat → nat) (a b c d : nat) (Ha : h c > h a) (Hb : h d > h b)
: h a = h b → c = d → f (h a) (tag (h c) Ha) = f (h b) (tag (h d) Hb) :=
by inst_simp
|
8217938e5ab8525b39af1dda959955c0eadb1908 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/elabissues/issues8.lean | 73bd4e19302b53480fb9c2ec735ba59e929ea566 | [
"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 | 763 | lean | def forceNat (a : Nat) := true
def forceInt (a : Int) := false
def f1 :=
/-
The following example works, but it adds a coercion at `forceInt i`.
The elaborated term is
```
fun (n i : Nat) => if n == i then forceNat n else forceInt (coe i)
```
-/
fun n i => if n == i then forceNat n else forceInt i -- works
def f2 :=
... |
2937ea88d1fc0ad5ca8829ec2c541ffb95b37fdf | e953c38599905267210b87fb5d82dcc3e52a4214 | /library/data/int/div.lean | d23eef5844e035c852de9b920bf3d94a7e09743c | [
"Apache-2.0"
] | permissive | c-cube/lean | 563c1020bff98441c4f8ba60111fef6f6b46e31b | 0fb52a9a139f720be418dafac35104468e293b66 | refs/heads/master | 1,610,753,294,113 | 1,440,451,356,000 | 1,440,499,588,000 | 41,748,334 | 0 | 0 | null | 1,441,122,656,000 | 1,441,122,656,000 | null | UTF-8 | Lean | false | false | 29,514 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
Definitions and properties of div and mod, following the SSReflect library.
Following SSReflect and the SMTlib standard, we define a mod b so that 0 ≤ a mod b < |b| when ... |
9c7a2495ea5a6858754b733a827417704daf43c2 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/order/with_bot.lean | 4ad53041d78d96da93192a8e47133c40581e1e24 | [
"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 | 39,167 | 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 order.bounded_order
import data.option.n_ary
/-!
# `with_bot`, `with_top`
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a cor... |
53a114cbbc6ef74e23b7510d39f9847caacca54a | 097294e9b80f0d9893ac160b9c7219aa135b51b9 | /instructor/types/list.lean | 568aefeb2c5383a3da6c40149171f90b3ab68889 | [] | no_license | AbigailCastro17/CS2102-Discrete-Math | cf296251be9418ce90206f5e66bde9163e21abf9 | d741e4d2d6a9b2e0c8380e51706218b8f608cee4 | refs/heads/main | 1,682,891,087,358 | 1,621,401,341,000 | 1,621,401,341,000 | 368,749,959 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,923 | lean | /-
A list abstract data type.
-/
namespace hidden
/-
A list is either empty (nil) or it is
"cons"tructed from an element, h, at
its "head" (h) and from a smaller list,
t, as its "tail".
-/
inductive list (α : Type) : Type
| nil {} : list
| cons (h : α) (t : list) : list
/-
Notes: α in final type is implicit, and
f... |
ac479bf6874767b04762a0e6ece93eb0de9bf6d0 | c777c32c8e484e195053731103c5e52af26a25d1 | /archive/imo/imo2006_q3.lean | c6506dbcda082d56da38ac7289dc56997390e7bb | [
"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 | 5,352 | lean | /-
Copyright (c) 2021 Tian Chen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tian Chen
-/
import analysis.special_functions.sqrt
/-!
# IMO 2006 Q3
Determine the least real number $M$ such that
$$
\left| ab(a^2 - b^2) + bc(b^2 - c^2) + ca(c^2 - a^2) \right|
≤ M (a... |
3e94203bbef3192e193a7d0c0176b0c00fedc0c2 | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /tests/lean/run/injective.lean | bf8841fb1005d9d2c1c8bf3eca48e333c8efad86 | [
"Apache-2.0"
] | permissive | collares/lean4 | 861a9269c4592bce49b71059e232ff0bfe4594cc | 52a4f535d853a2c7c7eea5fee8a4fa04c682c1ee | refs/heads/master | 1,691,419,031,324 | 1,618,678,138,000 | 1,618,678,138,000 | 358,989,750 | 0 | 0 | Apache-2.0 | 1,618,696,333,000 | 1,618,696,333,000 | null | UTF-8 | Lean | false | false | 813 | lean | universes u v
structure InjectiveFunction (α : Type u) (β : Type v) where
fn : α → β
inj : ∀ a b, fn a = fn b → a = b
def add1 : InjectiveFunction Nat Nat where
fn a := a + 1
inj a b h := by injection h; assumption
instance : CoeFun (InjectiveFunction α β) (fun _ => α → β) where
coe s := s.fn
#eval ... |
fcddb53c9ac10544f8fd6eb311486fb6f9ebd671 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/letPatIssue.lean | 2bd8681e58647eba8f7432e60155ad244b934bd9 | [
"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 | 408 | lean | example (x : Nat × Nat) : x.1 + x.2 ≥ 0 :=
let (a, b) := x
_
example (x : Nat × Nat) : x.1 + x.2 ≥ 0 :=
have (a, b) := x
_
example (x : Nat × Nat) : x.1 + x.2 ≥ 0 := by
let (a, b) := x
done
example (x : Nat × Nat) : x.1 + x.2 ≥ 0 := by
have (a, b) := x
done
def f : Nat × Nat → Nat
| (a, b) => a + ... |
43a95d0e134eb468bbb3f7308e83e6f78c7b48c2 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /13_More_Tactics.org.14.lean | b4bb91e6f168502307de527aefce36db1dda2ae7 | [] | 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 | 171 | lean | import standard
open tactic
theorem tst {A B : Prop} (H1 : A) (H2 : B) : A :=
by (trace "first"; state; now |
trace "second"; state; fail |
trace "third"; assumption)
|
9883a20226301934dc50682bbfc908eec8b71911 | f07ebb00c1b0eed4d4e2df146b6ab5d8aa10802d | /ch3.lean | 574792d8b3c7e56e1d649048cc01e8b78dcfb51e | [] | no_license | jgarte/theorem-proving-in-lean | 7762e7339ef94269f04e2d8c89ccdcc77053204f | 4b7b62f3ca82d4463f6e607e0ef974c9577a5b7e | refs/heads/master | 1,650,893,202,520 | 1,587,934,185,000 | 1,587,934,185,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,158 | lean | -- Chapter 3
variables p q r s: Prop
-- #check p → q → p ∧ q
-- #check ¬p → p ↔ false
-- #check p ∨ q → q ∧ p
-- commutativity of ∧ and ∨
theorem and_comm_ : p ∧ q ↔ q ∧ p :=
iff.intro
(assume hpq : p ∧ q,
show q ∧ p, from ⟨(and.right hpq), (and.left hpq)⟩)
(assume hqp : q ∧ p,
show p ∧ q, from ⟨(and.rig... |
3315a727f06c4f7cc770ac81940c4a76414f8632 | e151e9053bfd6d71740066474fc500a087837323 | /src/hott/types/arrow.lean | 7e5ef7b8c4b7cc5e65849fc6e1e7033ad1ce3220 | [
"Apache-2.0"
] | permissive | daniel-carranza/hott3 | 15bac2d90589dbb952ef15e74b2837722491963d | 913811e8a1371d3a5751d7d32ff9dec8aa6815d9 | refs/heads/master | 1,610,091,349,670 | 1,596,222,336,000 | 1,596,222,336,000 | 241,957,822 | 0 | 0 | Apache-2.0 | 1,582,222,839,000 | 1,582,222,838,000 | null | UTF-8 | Lean | false | false | 8,851 | lean | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Floris van Doorn
Ported from Coq HoTT
Theorems about arrow types (function spaces)
-/
import hott.types.pi
universe u
hott_theory
namespace hott
open eq hott.equiv hott.is_equiv i... |
8b691b02a96d21aa3b3ee12735a5b5f42f56e2e0 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/ring_theory/ring_hom/finite_type.lean | 3d5d2f9b43b152189257aba78105d1dd7e4ad6d3 | [
"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 | 3,833 | lean | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import ring_theory.local_properties
import ring_theory.localization.inv_submonoid
/-!
# The meta properties of finite-type ring homomorphisms.
> THIS FILE IS SYNCHRONIZE... |
2061ff5c1016d134dc91e7ec2919c54f042cbd1f | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/data/nat/log.lean | 521281477045fd2919e6ae4785f09a017d9c413c | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 11,624 | lean | /-
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Yaël Dillies
-/
import data.nat.pow
import tactic.by_contra
/-!
# Natural number logarithms
This file defines two `ℕ`-valued analogs of the logarithm of `n` with base `b`:
... |
b0d9eaf63effdd328f9b5c90f40930336e2e0ad9 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/topology/algebra/polynomial.lean | 3ab14deb33b6b446fadd300e92d1c2f04ffe50dd | [
"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 | 2,043 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Robert Y. Lewis
Analytic facts about polynomials.
-/
import topology.algebra.ring data.polynomial data.real.cau_seq
open polynomial is_absolute_value
lemma polynomial.tendsto_infin... |
61526649785b6d4606cf6fa8957f0d51935ddfd6 | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /tests/lean/run/class7.lean | 4b6c248e723fcaf96f89f9b1637d8f7db847aa28 | [
"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 | 467 | lean | import logic
open tactic
inductive inh [class] (A : Type) : Type :=
intro : A -> inh A
theorem inh_bool [instance] : inh Prop
:= inh.intro true
set_option class.trace_instances true
theorem inh_fun [instance] {A B : Type} (H : inh B) : inh (A → B)
:= inh.rec (λ b, inh.intro (λ a : A, b)) H
theorem tst {A B : Type}... |
3da3f73063f3886f9892f72b6dc04e52fbeb1b04 | e9ac8fc7b80f2e90e26764c906f915cc016c920f | /colimit/pointed.hlean | ba293e311766bffac0ec5caa88a65f8bf044577c | [
"Apache-2.0"
] | permissive | sinhp/Spectral | bb7e02dbfd7213e05e1d5c5e2f156254bbaab8ef | 234d9a703c0854b6f8ec1f564e8e6311eea25121 | refs/heads/master | 1,643,018,677,958 | 1,562,821,654,000 | 1,562,821,654,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,919 | hlean | import .seq_colim types.fin homotopy.chain_complex types.pointed2
open seq_colim pointed algebra eq is_trunc nat is_equiv equiv sigma sigma.ops chain_complex fiber
namespace seq_colim
definition pseq_diagram [reducible] (A : ℕ → Type*) : Type := Πn, A n →* A (succ n)
definition pseq_colim [constructor] {X : ℕ → T... |
f161074e480758c05a2dcae686c657ee17946ae8 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/topology/metric_space/holder.lean | 33edbf0aa23f1bbe282bc76d4917eb47d46ac0c1 | [
"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 | 9,684 | lean | /-
Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import topology.metric_space.lipschitz
import analysis.special_functions.pow
/-!
# Hölder continuous functions
In this file we define Hölder continuity on a... |
4b88a0680c9e2780b4363409df08803a6cbaf198 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/rquote.lean | c419edc6535fc47b36008622d488607c477ae21b | [
"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 | 344 | lean | --
namespace foo
constant f : nat → nat
constant g : nat → nat
end foo
namespace boo
constant f : nat → nat
end boo
open foo boo
#check ``f
#check ``g
open nat
#check ``has_add.add
#check ``gcd
#check `f
#check `foo.f
namespace bla
section
parameter A : Type
definition ID : A → A := λ x, x
#check ``I... |
fa826517b0f0d5b8e08322d79c2f6f6b5281cc24 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/ring_theory/bezout.lean | bd35124d47e44c73b3a4c7e073a5ec1ad551c38a | [
"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 | 4,416 | 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 ring_theory.principal_ideal_domain
/-!
# Bézout rings
A Bézout ring (Bezout ring) is a ring whose finitely generated ideals are principal.
Notible examples inclu... |
71e404b27690f7c536d2cf9fb236b4684120a8d3 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/ring_theory/henselian.lean | 7e98fab4e198adf3be0243747637f39f60f31759 | [
"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 | 11,756 | lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import data.polynomial.taylor
import ring_theory.ideal.local_ring
import linear_algebra.adic_completion
/-!
# Henselian rings
In this file we set up the basic theo... |
4232c507c304a89cbd30e9b47669dc412a376a69 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/ppSyntax.lean | cc020003519057b4df45978372ac31c791a6a3a0 | [
"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 | cipher1024/lean4 | 6e1f98bb58e7a92b28f5364eb38a14c8d0aae393 | 69114d3b50806264ef35b57394391c3e738a9822 | refs/heads/master | 1,642,227,983,603 | 1,642,011,696,000 | 1,642,011,696,000 | 228,607,691 | 0 | 0 | Apache-2.0 | 1,576,584,269,000 | 1,576,584,268,000 | null | UTF-8 | Lean | false | false | 180 | lean | import Lean
open Lean
def test (stx : Unhygienic Syntax) : MetaM Unit := do
IO.println (← PrettyPrinter.ppTerm stx.run)
-- test imported `ParserDescr`
#eval test `(s!"hi!")
|
67e55c72911bc8ef03353e0b42e091bd880ea254 | 9b9a16fa2cb737daee6b2785474678b6fa91d6d4 | /src/data/polynomial.lean | b389da14a7997f57b416c4092eb48e06281395ae | [
"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 | 90,786 | 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, Jens Wagemaker
Theory of univariate polynomials, represented as `ℕ →₀ α`, where α is a commutative semiring.
-/
import data.finsupp algebra.gcd_domain ring... |
78ab2b61c0967f7a0859b62d8dd7f449599c0251 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/limits/shapes/strict_initial.lean | bc90752e1b9b0f5a63fa04eea2fe968801f665db | [
"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 | 8,265 | lean | /-
Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import category_theory.limits.shapes.terminal
import category_theory.limits.shapes.binary_products
/-!
# Strict initial objects
This file sets up the basic theory of s... |
f5ec837577b53057155582d4609c78da827c357c | c8af905dcd8475f414868d303b2eb0e9d3eb32f9 | /examples/phosphorylation.lean | 48174236ba200bd30a4a281651881b8c99cc8d6b | [
"BSD-3-Clause"
] | permissive | continuouspi/lean-cpi | 81480a13842d67ff5f3698643210d8ed5dd08de4 | 443bf2cb236feadc45a01387099c236ab2b78237 | refs/heads/master | 1,650,307,316,582 | 1,587,033,364,000 | 1,587,033,364,000 | 207,499,661 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,528 | lean | import .common
open cpi
open cpi.species
open_locale normalise
def k_react : ℍ := fin_poly.X "k₁"
def k_degrade : ℍ := fin_poly.X "k₂"
def aff : affinity ℍ := affinity.mk_pair k_react
def ω : context := context.extend 0 (context.extend 0 (context.extend 0 context.nil))
def Γ : context := context.extend aff.arity c... |
e9ac22d2d98e0c5e02912142ae05d876fde43bf4 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/linear_algebra/affine_space/ordered.lean | 9d4bde8d5650a4b798b49bf0cbadce9d9fa64c29 | [
"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 | 15,936 | lean | /-
Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import algebra.order.module
import linear_algebra.affine_space.midpoint
import tactic.field_simp
/-!
# Ordered modules as affine spaces
In this file we defi... |
d15c83563cc06ccd29bbe72697f355481ef442cf | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/struct_bug1.lean | ce00ef133d962c689894d3fc93fc042faecfcd49 | [
"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 | 193 | lean | variable (A : Type*)
structure foo (a : A) :=
(eqpr : a = a)
section
parameter (B : Type*)
structure foo2 (b : B) :=
(eqpr : b = b)
check foo2
definition tst : B → Type := foo2
end
|
9451c21d21b0f4df6428f264dd60182982f21661 | 0845ae2ca02071debcfd4ac24be871236c01784f | /library/init/control/default.lean | 60f66c5331dff33ae75394837542b4d9270273ed | [
"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 | 453 | 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.control.applicative init.control.functor init.control.alternative
import init.control.monad init.control.lift
import init.control.state ... |
a663713255c4546f30b60cffd55d61f355e04cf1 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/pnat/defs.lean | f08cf158710d0a44aad1d3ee0683690548fae1d7 | [
"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 | 6,771 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Neil Strickland
-/
import order.basic
import algebra.ne_zero
/-!
# The positive natural numbers
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to thi... |
ec51a10aff2bfc4039269be9b5892ca8352cffee | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/analysis/convex/exposed.lean | f267ea4bba5b39b438281072cd8ec99b795f1f81 | [
"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 | 9,328 | 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
-/
import analysis.convex.extreme
import analysis.convex.function
import analysis.normed_space.ordered
/-!
# Exposed sets
This file defines exp... |
aa6231815092ba18b8be3cad7c5503a1cfec1163 | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/nat/digits.lean | 891a931616766f55b9c15104bf9a4e13407e20d8 | [
"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 | 21,792 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Shing Tak Lam, Mario Carneiro
-/
import data.int.modeq
import data.list.indexes
import tactic.interval_cases
import tactic.linarith
/-!
# Digits of a natural number
T... |
c137a61b16538315c1bc218aa701a57319142c4d | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /src/Lean/Data/Json/Printer.lean | 053d337b02ce774a14f7b5370a331c778b1331ef | [
"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 | 2,810 | lean | /-
Copyright (c) 2019 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner, Marc Huisinga
-/
import Lean.Data.Format
import Lean.Data.Json.Basic
namespace Lean
namespace Json
private def escapeAux (acc : String) (c : Char) : String :=
-- esca... |
a4458b194ea2e9a42adf7797a7982cbd928b3f72 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/data/nat/modeq.lean | fbdeb93fe72474476222bd47d00535194bd51e5f | [
"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 | 12,787 | 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 data.int.gcd
import tactic.abel
import data.list.rotate
/-
# Congruences modulo a natural number
This file defines the equivalence relation `a ≡ b [MOD n]` on... |
78d6e151236f3ae604d4d8a7f8d242f79cb86f7e | 947b78d97130d56365ae2ec264df196ce769371a | /tests/lean/run/kernel1.lean | a5d8f12bdc56c11bbc8fa1248d8fd4f7b2e7435d | [
"Apache-2.0"
] | permissive | shyamalschandra/lean4 | 27044812be8698f0c79147615b1d5090b9f4b037 | 6e7a883b21eaf62831e8111b251dc9b18f40e604 | refs/heads/master | 1,671,417,126,371 | 1,601,859,995,000 | 1,601,860,020,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 782 | lean | import Lean
new_frontend
open Lean
def checkDefEq (a b : Name) : CoreM Unit := do
let env ← getEnv;
let a := mkConst a;
let b := mkConst b;
let r := Kernel.isDefEq env {} a b;
IO.println (toString a ++ " =?= " ++ toString b ++ " := " ++ toString r)
def a1 := 100 + 100
def a2 := 200
def a3 := 20
#eval checkDefEq `a1... |
3b1c1eaf7d5cceb72fdc8f0be630a56ee9027fa9 | 43390109ab88557e6090f3245c47479c123ee500 | /src/M3P14/Arithmetic_functions/phi.lean | 5d6ac9718fbdcd94f62c4ebd9d3b77155f2d134c | [
"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 | 2,550 | lean | import chris_hughes_various.zmod data.fintype data.nat.prime data.nat.gcd data.nat.modeq algebra.ring M3P14.order_zmodn_kmb
open nat
open fintype
--defining the phi function
definition phi (n : ℕ) := ((finset.range n).filter (nat.coprime n)).card
local notation `φ` := phi
-- theorems
theorem phi_n (n : ℕ) [pos_... |
ac4cd11e529be3a97331c479f4fdc842a7ed32d6 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/algebra/punit_instances.lean | 82bb667218f82c4429f1a54b3f98be647ed519f7 | [
"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 | 4,729 | 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
import algebra.gcd_monoid.basic
import algebra.group_ring_action
import group_theory.group_action.defs
/-!
# Instances on punit
This file collect... |
468f45790e8866d4eb5b97f7b87d8ea6d5433860 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/topology/sheaves/forget.lean | 56b03eeeeee7d0eb22c98b4ed281667bab60db2f | [
"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 | 8,019 | 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 topology.sheaves.sheaf
import category_theory.limits.preserves.shapes.products
import category_theory.limits.types
/-!
# Checking the sheaf condition on the u... |
1263d001b9e7691428556e19ed0a4c892b836656 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/format_thunk1.lean | 52564f290cc28a4603186a425de5c2ad07b69544 | [
"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 | 130 | lean | open tactic
example : true :=
by do
str ← to_expr `(string),
one ← to_expr `(1),
definev `H str one,
constructor
|
ec201c500c5f2f6652f4993b5d37b37a3e2523b6 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/data/nat/lemmas.lean | c4f9fab2092927f6ba11739f5e8d973e9377d511 | [] | 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 | 37,484 | 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, Jeremy Avigad
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.data.nat.basic
import Mathlib.Lean3Lib.init.data.nat.div
import Mathlib.Lean3Lib.init.met... |
555030cdcd6f342e6449ffb8c375cea13cebb815 | 30b012bb72d640ec30c8fdd4c45fdfa67beb012c | /ring_theory/unique_factorization_domain.lean | 574a4ff1c19a5898764a7e7641589b2ea8bdf22a | [
"Apache-2.0"
] | permissive | kckennylau/mathlib | 21fb810b701b10d6606d9002a4004f7672262e83 | 47b3477e20ffb5a06588dd3abb01fe0fe3205646 | refs/heads/master | 1,634,976,409,281 | 1,542,042,832,000 | 1,542,319,733,000 | 109,560,458 | 0 | 0 | Apache-2.0 | 1,542,369,208,000 | 1,509,867,494,000 | Lean | UTF-8 | Lean | false | false | 12,184 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker
Theory of unique factorization domains.
@TODO: setup the complete lattice structure on `factor_set`.
-/
import ring_theory.associated algebra.gcd_domai... |
8772001d45d80309818f60b3b9aa136189c7eab1 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/W/cardinal.lean | 3088bd1c239eb1ba8ed9e3ed408957975c83d7b8 | [
"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 | 2,835 | lean | /-
Copyright (c) 2021 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import set_theory.cardinal_ordinal
import data.W.basic
/-!
# Cardinality of W-types
This file proves some theorems about the cardinality of W-types. The main result is
`... |
c40636a13f3c113cb2c22a8456d9de4d9451ac54 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/control/traversable/equiv.lean | d90514c8633a936c362ddb7fb1a6d3940a14e76a | [
"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 | 4,454 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
Transferring `traversable` instances using isomorphisms.
-/
import data.equiv.basic
import control.traversable.lemmas
universes u
namespace equiv
section functor
parameter... |
311fc4f09c43da1b34ad21cdff0524aaced1783b | 92b50235facfbc08dfe7f334827d47281471333b | /library/data/int/div.lean | 6f533b05431f3403b9a7c1311c48058f67e25851 | [
"Apache-2.0"
] | permissive | htzh/lean | 24f6ed7510ab637379ec31af406d12584d31792c | d70c79f4e30aafecdfc4a60b5d3512199200ab6e | refs/heads/master | 1,607,677,731,270 | 1,437,089,952,000 | 1,437,089,952,000 | 37,078,816 | 0 | 0 | null | 1,433,780,956,000 | 1,433,780,955,000 | null | UTF-8 | Lean | false | false | 28,666 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
Definitions and properties of div and mod, following the SSReflect library.
Following SSReflect and the SMTlib standard, we define a mod b so that 0 ≤ a mod b < |b| when ... |
ff1374bd5bc7a2beff34ff0fd87ea353b1aef3f2 | 46125763b4dbf50619e8846a1371029346f4c3db | /src/category_theory/limits/shapes/images.lean | 710a59e38277f33d8ecfa57c6005b6d3a798b2d2 | [
"Apache-2.0"
] | permissive | thjread/mathlib | a9d97612cedc2c3101060737233df15abcdb9eb1 | 7cffe2520a5518bba19227a107078d83fa725ddc | refs/heads/master | 1,615,637,696,376 | 1,583,953,063,000 | 1,583,953,063,000 | 246,680,271 | 0 | 0 | Apache-2.0 | 1,583,960,875,000 | 1,583,960,875,000 | null | UTF-8 | Lean | false | false | 7,921 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Markus Himmel
-/
import category_theory.limits.shapes.equalizers
/-!
# Categorical images
We define the categorical image of `f` as a factorisation `f = e ≫ m` throug... |
d878e21aaa1d742a03734a8d92864ccf898f087e | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/structure_instance_bug.lean | a2fd48d279c47fc267bcf1e5d6176d604929993c | [
"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 | 220 | lean | structure weird (A : Type) :=
{B : Type} (op : A → B → A)
definition foo1 : weird nat :=
{ op := nat.add }
definition foo2 : weird nat :=
⟨ nat.add ⟩
definition foo3 : weird nat :=
{ B := nat, op := nat.add }
|
c797b1d1f2781850d7a9385deb36489e0bd53547 | ce6917c5bacabee346655160b74a307b4a5ab620 | /src/ch5/ex0303.lean | 696184d3d5868d9d48afcbbb49c21563f40d7446 | [] | 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 | 441 | lean | example (p q r : Prop) : p ∧ (q ∨ r) ↔ (p ∧ q) ∨ (p ∧ r) :=
begin
apply iff.intro,
intro h,
cases h with hp hqr,
cases hqr with hq hr,
left, constructor, exact hp, exact hq,
right, constructor, exact hp, exact hr,
intro h,
cases h with hpq hpr,
cases hpq with hp hq,
constru... |
d0ed8d829ee5e19642969a7eab6f25d72c597c66 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /07_Induction_and_Recursion.org.18.lean | c7f97cb76749b1051f3bbb3c1f1e26ad4f48c4d9 | [] | 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 | 658 | lean | /- page 106 -/
import standard
open nat option
definition f1 : nat → nat → nat
| f1 0 _ := 1
| f1 _ 0 := 2
| f1 _ _ := arbitrary nat -- the "incomplete" case
variables (a b : nat)
example : f1 0 0 = 1 := rfl
example : f1 0 (a+1) = 1 := rfl
example : f1 (a+1) 0 = 2 := rfl
example : f1 (a+1) (... |
6f226c00f853f9dff8a3e55457b853481fd1dd49 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/data/polynomial/coeff.lean | 07e0871b117d8712a264bb467eaa91de42bad6be | [
"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 | 4,915 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
-/
import data.polynomial.monomial
import data.finset.nat_antidiagonal
/-!
# Theory of univariate polynomials
The theorems ... |
93d9504f68665e8ade3651979af49a51b9ee3870 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/ring_theory/integral_closure.lean | 230d8cbd0aa29fc7eb13eaa80f7b5e15c82b3914 | [
"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 | 46,146 | lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import data.polynomial.expand
import linear_algebra.finite_dimensional
import linear_algebra.matrix.charpoly.linear_map
import ring_theory.adjoin.fg
import ring_theory.finite_t... |
9ba98bdb588a3632a08542571dedb92a47a47f2e | 367134ba5a65885e863bdc4507601606690974c1 | /src/category_theory/monad/equiv_mon.lean | 3c883dd2959abda95543e875e558c384779af9bb | [
"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 | 3,557 | lean | /-
Copyright (c) 2020 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import category_theory.monad.bundled
import category_theory.monoidal.End
import category_theory.monoidal.Mon_
import category_theory.category.Cat
/-!
# The equivalence betw... |
b6cef452186c4bb049b6ad9e8d5f304269906c68 | a721fe7446524f18ba361625fc01033d9c8b7a78 | /src/principia/mynat/le.lean | 2080882aa9974ed2eafac00da7404b75e8ac260b | [] | no_license | Sterrs/leaning | 8fd80d1f0a6117a220bb2e57ece639b9a63deadc | 3901cc953694b33adda86cb88ca30ba99594db31 | refs/heads/master | 1,627,023,822,744 | 1,616,515,221,000 | 1,616,515,221,000 | 245,512,190 | 2 | 0 | null | 1,616,429,050,000 | 1,583,527,118,000 | Lean | UTF-8 | Lean | false | false | 6,740 | lean | -- vim: ts=2 sw=0 sts=-1 et ai tw=70
import .basic
import ..tactic
namespace hidden
namespace mynat
def le (m n: mynat) := ∃ k: mynat, n = m + k
-- notation
instance: has_le mynat := ⟨le⟩
-- Given a proposition, we can say that if there are arbitrarily large
-- mynat satisfying it, then there are infinitely many ... |
cd05e8ed5671752f892f3e0cfe2a91a0791c9ac1 | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /stage0/src/Std/Data/BinomialHeap.lean | 6aa73215300f54944566df2ded21430241493f9f | [
"Apache-2.0"
] | permissive | dupuisf/lean4 | d082d13b01243e1de29ae680eefb476961221eef | 6a39c65bd28eb0e28c3870188f348c8914502718 | refs/heads/master | 1,676,948,755,391 | 1,610,665,114,000 | 1,610,665,114,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,314 | 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
-/
namespace Std
universes u
namespace BinomialHeapImp
structure HeapNodeAux (α : Type u) (h : Type u) where
val : α
rank : Nat
children : List h
induc... |
2b5f705ead50c1ddd7495fa4fa2b4174afd7e435 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/tactic/solve_by_elim.lean | b37fcd78123ba9b0d365cdb026033911caf6e1eb | [
"Apache-2.0"
] | permissive | waynemunro/mathlib | e3fd4ff49f4cb43d4a8ded59d17be407bc5ee552 | 065a70810b5480d584033f7bbf8e0409480c2118 | refs/heads/master | 1,693,417,182,397 | 1,634,644,781,000 | 1,634,644,781,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 15,249 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Scott Morrison
-/
import tactic.core
/-!
# solve_by_elim
A depth-first search backwards reasoner.
`solve_by_elim` takes a list of lemmas, and repeating tries to `apply` th... |
324daa86a6c5d3375067c4bc26af686ddb6a25b3 | 47181b4ef986292573c77e09fcb116584d37ea8a | /src/ostrowski/rationals/basic.lean | 8d6d2c81f4c71738be7836ddee86a62e10ef5fc7 | [
"MIT"
] | permissive | RaitoBezarius/berkovich-spaces | 87662a2bdb0ac0beed26e3338b221e3f12107b78 | 0a49f75a599bcb20333ec86b301f84411f04f7cf | refs/heads/main | 1,690,520,666,912 | 1,629,328,012,000 | 1,629,328,012,000 | 332,238,095 | 4 | 0 | MIT | 1,629,312,085,000 | 1,611,414,506,000 | Lean | UTF-8 | Lean | false | false | 3,621 | lean |
import data.nat.prime
import data.rat.basic
import data.real.basic
import analysis.special_functions.pow
import data.real.cau_seq
import number_theory.padics.padic_norm
import valuations.basic
import for_mathlib.hom
import for_mathlib.rat
open is_absolute_value
noncomputable theory
def trivial_abs : ℚ → ℝ := λ a,
... |
780811a60b65ca94d466536a6241c6cf92b3d7e8 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /src/Init/Lean/Compiler/IR/ElimDeadVars.lean | fe2e47f2668ec719f74c9c7ff8821cfe91f02023 | [
"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 | 1,689 | 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.Compiler.IR.Basic
import Init.Lean.Compiler.IR.FreeVars
namespace Lean
namespace IR
partial def reshapeWithoutDeadAux : Array FnB... |
afc8521e95236f8727bd8182e79f7bc82a21e869 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/analysis/calculus/specific_functions.lean | 8820b4018fe9073ffd894340989831b7f239f8cc | [
"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 | 22,979 | lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Floris van Doorn
-/
import analysis.calculus.iterated_deriv
import analysis.inner_product_space.euclidean_dist
import measure_theory.function.locally_integrable
i... |
23055d7c591de08e87670a153cfd127e19e33848 | 36c7a18fd72e5b57229bd8ba36493daf536a19ce | /library/init/default.lean | 87cde70ee0d54d2684c481823e30e440297500b9 | [
"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 | 434 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.datatypes init.reserved_notation init.tactic init.logic
import init.relation init.wf init.nat init.wf_k init.prod
import init.bool init.... |
b9dae2d9ec095b47b5b3a9908335f66469e61550 | a19a4fce1e5677f4d20cbfdf60c04b6386ab8210 | /hott/homotopy/wedge.hlean | 2eb6b95d46768b22daa4fa8a27a461f6ca1dcd88 | [
"Apache-2.0"
] | permissive | nthomas103/lean | 9c341a316e7d9faa00546462f90a8aa402e17eac | 04eaf184a92606a56e54d0d6c8d59437557263fc | refs/heads/master | 1,586,061,106,806 | 1,454,640,115,000 | 1,454,641,279,000 | 51,127,143 | 0 | 0 | null | 1,454,648,683,000 | 1,454,648,683,000 | null | UTF-8 | Lean | false | false | 2,731 | hlean | /-
Copyright (c) 2016 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer, Ulrik Buchholtz
The Wedge Sum of Two Pointed Types
-/
import hit.pointed_pushout .connectedness
open eq pushout pointed Pointed
definition Wedge (A B : Type*) : ... |
61fe1457b61b55c67abe0057a552c1d5bab10c0a | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/group/inj_surj_auto.lean | 5a9a402fdd3a599a7d525c7f22a9eec68f8e1f9f | [] | 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 | 12,356 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.group.defs
import Mathlib.logic.function.basic
import Mathlib.PostPort
universes u... |
b0bfbf6c0ffd5179c0f646782b54eb5eae56e5ce | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/tactic/wlog.lean | 67ad7fca1ce5b722ae4f12c35919fc01534a2cd7 | [
"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 | 9,427 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Without loss of generality tactic.
-/
import data.list.perm
open expr tactic lean lean.parser
local postfix `?`:9001 := optional
local postfix *:9001 := many
namespa... |
9ddbc4d4a27099f9c963088de858306bbb82ee85 | a7eef317ddec01b9fc6cfbb876fe7ac00f205ac7 | /src/ring_theory/valuation/basic.lean | 51c9191d394e7eddf246e268fc7c785cf09c2cdf | [
"Apache-2.0"
] | permissive | kmill/mathlib | ea5a007b67ae4e9e18dd50d31d8aa60f650425ee | 1a419a9fea7b959317eddd556e1bb9639f4dcc05 | refs/heads/master | 1,668,578,197,719 | 1,593,629,163,000 | 1,593,629,163,000 | 276,482,939 | 0 | 0 | null | 1,593,637,960,000 | 1,593,637,959,000 | null | UTF-8 | Lean | false | false | 14,530 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Johan Commelin, Patrick Massot
-/
import algebra.linear_ordered_comm_group_with_zero
import algebra.group_power
import ring_theory.ideal_operations
import ring_theory.s... |
415cfab47398226b7dc6f1db9ba3cbb663874b39 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/def_tac.lean | e0ecf8ca1eacdf29737ad10c4ee10952d0215198 | [
"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 | 928 | lean | infixl `;`:15 := tactic.and_then
section
open tactic
definition cases_refl (e : expr) : tactic :=
cases e expr_list.nil; apply rfl
definition cases_lst_refl : expr_list → tactic
| cases_lst_refl expr_list.nil := apply rfl
| cases_lst_refl (expr_list.cons a l) := cases a expr_list.nil; cases_lst_ref... |
75b0fba7372921fd59479c32af31aa97401fc721 | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/data/num/lemmas.lean | 5e65ef7a4b7fc56f068baa4ab46c265a3cb3731a | [
"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 | 49,235 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
Properties of the binary representation of integers.
-/
import data.num.basic data.num.bitwise algebra.ordered_ring
tactic.interactive data.int.basic data.... |
839e0384c4d6b7b6653b7a126b596ac9c2ab74e3 | a7eef317ddec01b9fc6cfbb876fe7ac00f205ac7 | /src/topology/metric_space/isometry.lean | c8571eaed8994b7a16757f2cb451ffd6e204162e | [
"Apache-2.0"
] | permissive | kmill/mathlib | ea5a007b67ae4e9e18dd50d31d8aa60f650425ee | 1a419a9fea7b959317eddd556e1bb9639f4dcc05 | refs/heads/master | 1,668,578,197,719 | 1,593,629,163,000 | 1,593,629,163,000 | 276,482,939 | 0 | 0 | null | 1,593,637,960,000 | 1,593,637,959,000 | null | UTF-8 | Lean | false | false | 16,804 | lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Isometries of emetric and metric spaces
Authors: Sébastien Gouëzel
-/
import topology.bounded_continuous_function
import topology.opens
/-!
# Isometries
We define isometries, i.e., maps be... |
16dd25e56befbd94350484c2e7989119b37b7e52 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/778.hlean | e32fd4034b053a1a497e2c75759ec56633f639c4 | [
"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 | 169 | hlean | open bool
definition is_equiv_bnot : is_equiv bnot :=
begin
fapply is_equiv.mk,
exact bnot,
all_goals (intro b;cases b),
state,
repeat reflexivity
end
|
4c8b04fa5e5d34a7687059e76d29c3c23a6e73be | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/algebra/lie/of_associative.lean | 9c91983d744b702fde7a0cab7dc9c3783b793c3f | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 9,358 | 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.basic
import algebra.lie.subalgebra
import algebra.algebra.subalgebra
/-!
# Lie algebras of associative algebras
This file defines the Lie algebra stru... |
b365a95befe95b90d0a489e8170fc3febd31ba46 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /12_Axioms.org.20.lean | 1fe811a2caf3ec2f2af82d8de3a4d28a7e2f4673 | [] | 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 | 949 | lean | import standard
open classical
section
variable A : Type
variable a : A
-- o.k.
example : ∃ x : A, x = x :=
have H1 : ∃ y, y = y, from exists.intro a rfl,
have H2 : some H1 = some H1, from some_spec H1,
exists.intro (some H1) H2
/-
-- invalid local context
example : ∃ x : A, x = x :=
have H1 : ∃ y, y = y, from exist... |
dca12fcace2fa1e114e30fb162e83ac3abf91970 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/brackets_parens.lean | c97a578bcd114156bc0648cd0e6a46eaeb99c278 | [
"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 | 424 | lean | variables {α : Type} [has_one α]
#check {(1 : α)}
#check {(1), (2), (3)}
#check ({(∘), (∘)} : set ((ℕ → ℕ) → (ℕ → ℕ) → (ℕ → ℕ)))
#check {(0) + (0)}
variables (a : α) [has_add α]
#check {(a)}
#check λ a, (by exact {(a)} : set α)
#check {(a + b) | b ∈ (∅ : set α)}
#check λ a, by exact {(a + b) | b ∈ (∅ : set α)}
#chec... |
7b50c64147926be5298ab261a817be6cf715bd20 | ff5230333a701471f46c57e8c115a073ebaaa448 | /library/data/rbtree/basic.lean | 5d8397ec53af58098a9f9b6555f5c44314d050fb | [
"Apache-2.0"
] | permissive | stanford-cs242/lean | f81721d2b5d00bc175f2e58c57b710d465e6c858 | 7bd861261f4a37326dcf8d7a17f1f1f330e4548c | refs/heads/master | 1,600,957,431,849 | 1,576,465,093,000 | 1,576,465,093,000 | 225,779,423 | 0 | 3 | Apache-2.0 | 1,575,433,936,000 | 1,575,433,935,000 | null | UTF-8 | Lean | false | false | 8,745 | 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
-/
universe u
meta def tactic.interactive.blast_disjs : tactic unit :=
`[cases_type* or]
namespace rbnode
variables {α : Type u}
open color nat
inductive i... |
1e83d90550762d2ec3e92e61b87ca46eb2e8f201 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /stage0/src/Lean/Linter/MissingDocs.lean | c5afc3b6aedca2f17ffaf60dc7cb2ec0b4de41c1 | [
"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 | 9,942 | lean | /-
Copyright (c) 2022 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Lean.Linter.Util
namespace Lean.Linter
open Elab.Command Parser.Command
open Parser.Term hiding «set_option»
register_builtin_option linter.missingDocs : Bo... |
bfcd4b40113e74003cf9dc3c91da9eb09f495b36 | fd7ca05aed4422fb0428e5a31bf6fa13221ee291 | /src/hats.lean | a58db95f8f2275cad7061539028cfba49ca5213c | [] | no_license | ericrbg/HatGames | f5712f2ab1b9bf1e681d9b57f17f51b3c010af24 | 33cfbf4d23d43c1f71b4aa2a6a0d60a2b2b2a984 | refs/heads/main | 1,692,247,407,481 | 1,632,194,504,000 | 1,632,194,504,000 | 354,602,607 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 15,441 | lean | import combinatorics.simple_graph.subgraph
import algebra.big_operators.order
import data.fintype.card
import .constructions
import tactic.ring_exp
open_locale big_operators
/-!
# Hat Games
This module defines the notion of a simple hat game played on an `α` `simple_graph`
with `β` colours, and proves bounds from th... |
5fe7cc0723d538b2126f7fda023c216b72593bfd | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/category_theory/eq_to_hom.lean | f8df79dad6d927540ddc551a099d318f53f577c3 | [
"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 | 2,839 | 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
import category_theory.opposites
universes v v' u u' -- declare the `v`'s fi... |
c4c149321ba7fe6268aea541955090754ca8ba1b | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/group_theory/perm/list.lean | 9e9f1834704cb0ad8042e2919c3a0bd97d5ce763 | [
"Apache-2.0"
] | permissive | stjordanis/mathlib | 51e286d19140e3788ef2c470bc7b953e4991f0c9 | 2568d41bca08f5d6bf39d915434c8447e21f42ee | refs/heads/master | 1,631,748,053,501 | 1,627,938,886,000 | 1,627,938,886,000 | 228,728,358 | 0 | 0 | Apache-2.0 | 1,576,630,588,000 | 1,576,630,587,000 | null | UTF-8 | Lean | false | false | 12,544 | lean | /-
Copyright (c) 2021 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
import data.list.rotate
import group_theory.perm.support
/-!
# Permutations from a list
A list `l : list α` can be interpreted as a `equiv.perm α` where each ele... |
ea0ca57314882903ae35e904645348e3a19d52cc | 8cb37a089cdb4af3af9d8bf1002b417e407a8e9e | /library/init/ite_simp.lean | ae94727dcb978b4f78656765f49717c554894576 | [
"Apache-2.0"
] | permissive | kbuzzard/lean | ae3c3db4bb462d750dbf7419b28bafb3ec983ef7 | ed1788fd674bb8991acffc8fca585ec746711928 | refs/heads/master | 1,620,983,366,617 | 1,618,937,600,000 | 1,618,937,600,000 | 359,886,396 | 1 | 0 | Apache-2.0 | 1,618,936,987,000 | 1,618,936,987,000 | null | UTF-8 | Lean | false | false | 898 | 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.bool
/-
Simplification lemmas for ite.
We don't prove them at logic.lean because it is easier to prove them using
the tactic fram... |
b9a43d7d36267bccc5a48c40a13056c6b17ab07c | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/blast_cc_heq4.lean | c42325d607035355bd4a2fb8a5acc2163b166f91 | [
"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 | 2,818 | lean | universes l1 l2 l3 l4 l5 l6
constants (A : Type.{l1}) (B : A → Type.{l2}) (C : ∀ (a : A) (ba : B a), Type.{l3})
(D : ∀ (a : A) (ba : B a) (cba : C a ba), Type.{l4})
(E : ∀ (a : A) (ba : B a) (cba : C a ba) (dcba : D a ba cba), Type.{l5})
(F : ∀ (a : A) (ba : B a) (cba : C a ba) (dcba : D a... |
32fbfc4d2e61954e54f21fb9f674f1981db49f48 | 7cdf3413c097e5d36492d12cdd07030eb991d394 | /world_experiments/world7/level6andahalf.lean | 821e78461e12e475ed94a74a3667d0380e02dc2a | [] | no_license | alreadydone/natural_number_game | 3135b9385a9f43e74cfbf79513fc37e69b99e0b3 | 1a39e693df4f4e871eb449890d3c7715a25c2ec9 | refs/heads/master | 1,599,387,390,105 | 1,573,200,587,000 | 1,573,200,691,000 | 220,397,084 | 0 | 0 | null | 1,573,192,734,000 | 1,573,192,733,000 | null | UTF-8 | Lean | false | false | 1,961 | lean | import mynat.definition -- hide
import mynat.add -- hide
import game.world2.level6 -- hide
namespace mynat -- hide
/-
# World 2 -- Addition World
## Level 6 and a half: -- `succ_inj`. A function.
If you're playing this level, you have decided against
collectible-hunting and are looking to learn something else.
Wh... |
01ac26dd88a23107871c4de0b0f819d950e5599b | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/monad/coequalizer.lean | 752f7fe14b20fa5f42126d13d8f328a40a85996a | [] | 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 | 5,241 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.limits.shapes.reflexive
import Mathlib.category_theory.limits.preserves.shapes.... |
4a9522643f4b849780e6970616405fc05f60468d | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/vector/mem.lean | 3a3d4503deb583aad7e4f963ef8c0a5609a4994e | [
"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 | 2,997 | lean | /-
Copyright (c) 2022 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Devon Tuma
-/
import data.vector.basic
/-!
# Theorems about membership of elements in vectors
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding... |
7202faed153878ff37b391b38b2c49e5ec525b1c | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/revert1.lean | d40e1ffc744e90d086418e9a9f256f3c971f2413 | [
"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 | 437 | lean |
theorem tst1 (x y z : Nat) : y = z → x = x → x = y → x = z :=
by {
intros h1 h2 h3;
revert h2;
intro h2;
exact Eq.trans h3 h1
}
theorem tst2 (x y z : Nat) : y = z → x = x → x = y → x = z :=
by {
intros h1 h2 h3;
revert y;
intros y hb ha;
exact Eq.trans ha hb
}
theorem tst3 (x y z : Nat) : y = z → x ... |
dd6fb6ffca30b33b9e75bf9557c1f32ce6f1a778 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/model_theory/encoding.lean | 131d479944f9c93b87b3d7a5e182fac0c2399523 | [
"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 | 14,119 | lean | /-
Copyright (c) 2022 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import computability.encoding
import model_theory.syntax
import set_theory.cardinal.ordinal
/-! # Encodings and Cardinality of First-Order Syntax
## Main Definitio... |
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