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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
2dcf872edcc623a89a05c133109a55a47c2a54af | 8c9f90127b78cbeb5bb17fd6b5db1db2ffa3cbc4 | /distributivity.lean | 73faf6fb2c353495e5c17935417a8b1bee1784f9 | [] | no_license | picrin/lean | 420f4d08bb3796b911d56d0938e4410e1da0e072 | 3d10c509c79704aa3a88ebfb24d08b30ce1137cc | refs/heads/master | 1,611,166,610,726 | 1,536,671,438,000 | 1,536,671,438,000 | 60,029,899 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 843 | lean | variables p q r : Prop
theorem distributivity : p ∧ (q ∨ r) → (p ∧ q) ∨ (p ∧ r) :=
assume LHS : p ∧ (q ∨ r),
have Pp : p, from and.elim_left(LHS),
have Pqor : (q ∨ r), from and.elim_right(LHS),
have Poe : (q → (p ∧ q) ∨ (p ∧ r)) → (r → (p ∧ q) ∨ (p ∧ r)) → (p ∧ q) ∨ (p ∧ r), from or.elim Pqor,
have... |
7163ec151da6fca73660ce5222cf2988a8a66e3a | b7f22e51856f4989b970961f794f1c435f9b8f78 | /library/algebra/ordered_group.lean | f8ec18b516c9c59a984d8057fad1fb8b4da7fd86 | [
"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 | 38,620 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
Partially ordered additive groups, modeled on Isabelle's library. These classes can be refined
if necessary.
-/
import logic.eq data.unit data.sigma data.prod
import alge... |
3471bd06a5522d44f4b944ef65298834685bab07 | f1a12d4db0f46eee317d703e3336d33950a2fe7e | /common/atom.lean | 4d6612987a1ded869c054395876c42cea42a8d84 | [
"Apache-2.0"
] | permissive | avigad/qelim | bce89b79c717b7649860d41a41a37e37c982624f | b7d22864f1f0a2d21adad0f4fb3fc7ba665f8e60 | refs/heads/master | 1,584,548,938,232 | 1,526,773,708,000 | 1,526,773,708,000 | 134,967,693 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,053 | lean | import .logic
class atom_type (α β : Type) :=
(val : list β → α → Prop)
(neg : α → fm α)
(neg_nqfree : ∀ (a : α), nqfree (neg a))
(neg_prsv : ∀ (a : α) (xs : list β), (interp val xs (neg a)) ↔ (interp val xs (¬' A' a)))
(dep0 : α → Prop)
(dec_dep0 : decidable_pred dep0)
(decr : α → α)
(decr_prsv : ∀ {a : α} {hd : ¬ (... |
22b057f447526b2c30456bb3ae0949aa321be15e | 02005f45e00c7ecf2c8ca5db60251bd1e9c860b5 | /src/field_theory/fixed.lean | 108598ab448012eb5a35b2d5c727a817045d3242 | [
"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 | 12,494 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import algebra.polynomial.group_ring_action
import deprecated.subfield
import field_theory.normal
import field_theory.separable
import field_theory.tower
import linear_algebra... |
7a9f08973e8c9fdcdef1e3f6089e5e89f4c130c5 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/analysis/complex/phragmen_lindelof.lean | afcff7594f5793fc1b625bf96e9826a1985ce6e6 | [
"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 | 49,510 | lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import analysis.complex.abs_max
import analysis.asymptotics.superpolynomial_decay
/-!
# Phragmen-Lindelöf principle
In this file we prove several versions of the ... |
40b886c48c4c9a962652b3e6c70a0f5f0378da2d | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/linear_algebra/matrix.lean | d11904e07cba32884a2b7df5922d71b79bcc2825 | [
"Apache-2.0"
] | permissive | ilitzroth/mathlib | ea647e67f1fdfd19a0f7bdc5504e8acec6180011 | 5254ef14e3465f6504306132fe3ba9cec9ffff16 | refs/heads/master | 1,680,086,661,182 | 1,617,715,647,000 | 1,617,715,647,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 64,433 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz
-/
import linear_algebra.finite_dimensional
import linear_algebra.nonsingular_inverse
import linear_algebra.multilinear
import linear_algebr... |
40174db67e94a2bdc5b50779e7f0c2d28d8510ba | f57570f33b51ef0271f8c366142363d5ae8fff45 | /src/plurimodal.lean | 1e5c8a56cfe42c52bcf037b90524b5690be1037e | [] | no_license | maxd13/lean-logic | 4083cb3fbb45b423befca7fda7268b8ba85ff3a6 | ddcab46b77adca91b120a5f37afbd48794da8b52 | refs/heads/master | 1,692,257,681,488 | 1,631,740,832,000 | 1,631,740,832,000 | 246,324,437 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,253 | lean | import tactic
section modal
-- 2 modal logics: alethic, grounding
-- alethic logic
parameter {box₁ : Prop → Prop}
variable K : ∀ φ ψ : Prop, box₁ (φ → ψ) → box₁ φ → box₁ ψ
variable T : ∀ φ : Prop, box₁ φ → φ
-- also known as axiom 4,
-- but lean doesnt let me use a number as an identifier
variable S4 : ∀ φ: Prop, box... |
3aa0f6b4c77cc477a52a0ffcc032081c8a926ae1 | 6ae186a0c6ab366b39397ec9250541c9d5aeb023 | /src/category_theory/filtered.lean | cdde1cf28a3127adcaec3c5286c45415f149cdb7 | [] | no_license | ThanhPhamPhuong/lean-category-theory | 0d5c4fe1137866b4fe29ec2753d99aa0d0667881 | 968a29fe7c0b20e10d8a27e120aca8ddc184e1ea | refs/heads/master | 1,587,206,682,489 | 1,544,045,056,000 | 1,544,045,056,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 921 | lean | import category_theory.limits
import order.filter
open category_theory.limits
namespace category_theory
universes u₁ v₁
variables α : Type u₁
class directed [preorder α] :=
(bound (x₁ x₂ : α) : α)
(i₁ (x₁ x₂ : α) : x₁ ≤ bound x₁ x₂)
(i₂ (x₁ x₂ : α) : x₂ ≤ bound x₁ x₂)
variables (C : Type u₁) [𝒞 : category.{u₁ v₁... |
0053639b67e8038166c415f4188cbdea1ac10ee5 | 5a8eb1c11f93715e070b588e85f2961065c3714d | /books/theorem-proving-in-lean/ch02-05.lean | bc54d54fdc05247b172dbb732c261424fc206741 | [
"MIT"
] | permissive | luksamuk/study | 0e19bf99d33e0793127c3d3f8ad3936fbeb36505 | 6a9417e071a8624c4cd9db696c16a3abcc430219 | refs/heads/master | 1,677,960,533,266 | 1,676,234,529,000 | 1,676,234,529,000 | 151,009,060 | 4 | 1 | MIT | 1,676,234,531,000 | 1,538,343,224,000 | C++ | UTF-8 | Lean | false | false | 265 | lean | -- Replace every occurence of `y` in
-- `y * y` by `(2 + 2)`
#check let y := 2 + 2 in y * y
#reduce let y := 2 + 2 in y * y
def t (x : ℕ) : ℕ :=
let y := x + x
in y * y
#reduce t 2
#check t 2
def foo := let a := ℕ
in λ x : a, x + 2
#check foo
|
982492b44c66a76b75bd53138085ce3e002d836a | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/category_theory/monad/adjunction.lean | 3289ec03ae770975926e2a428268c6dd61751877 | [
"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 | 5,567 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.monad.algebra
import category_theory.adjunction.fully_faithful
namespace category_theory
open category
universes v₁ v₂ u₁ u₂ -- declare the `... |
f4b234d959c943b152e06f40ed2904c61aa06207 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/combinatorics/configuration.lean | c767e7bd0718ee205894ebaeaab09f44d2d712d3 | [
"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 | 23,340 | lean | /-
Copyright (c) 2021 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import algebra.big_operators.order
import combinatorics.hall.basic
import data.fintype.card
import set_theory.cardinal.finite
/-!
# Configurations of Points and li... |
7697db9145fdb753c298c2be2aa83b4e996b1ce0 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/blast_backward_action_missing_normalize.lean | 6343c95ca042eadea3a7ee9ba2502f6d5647836e | [
"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 | 163 | lean | constants (P : ℕ → Prop) (R : Prop)
lemma foo [intro!] : (: P 0 :) → R := sorry
constants (P0 : P 0)
attribute P0 [intro!]
example : R :=
by grind -- fails
|
3f5ac3c2fc3bb72e3d9e0eb0e9e56bee7e09ac6f | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/topology/category/Top/limits.lean | 8ccd4b991d8540636fc0735719f1e95c6a7222c1 | [
"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 | 2,763 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Scott Morrison, Mario Carneiro
-/
import topology.category.Top.basic
import category_theory.limits.types
import category_theory.limits.preserves
open topological_space... |
ad6dfbf1ac89503124353183af293b6a7efed377 | 8b9f17008684d796c8022dab552e42f0cb6fb347 | /library/algebra/category/constructions.lean | ed0b7201005e91bb406c7c2ab0a7e4ea23c27a1c | [
"Apache-2.0"
] | permissive | chubbymaggie/lean | 0d06ae25f9dd396306fb02190e89422ea94afd7b | d2c7b5c31928c98f545b16420d37842c43b4ae9a | refs/heads/master | 1,611,313,622,901 | 1,430,266,839,000 | 1,430,267,083,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 15,973 | 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
-- This file contains basic constructions on categories, including common categories
import .natural_transformation
import data.unit data.sigma data.prod dat... |
0f9fab0d71c008e304f05edadfbea040aac151b8 | 2b2a05a7af89c79da194505bf88205a6c4e05d68 | /src/game/world_07_advanced_proposition.lean | c21a0432426e76b72596486eb4d0f01d62ba7863 | [] | no_license | lacrosse/natural_number_game | 6401a11a8c965da3903ae6695f84586edf6fac85 | 400179cde1d3fcc9744901dabff98813ba2b544f | refs/heads/master | 1,677,566,006,582 | 1,612,576,917,000 | 1,612,576,917,000 | 335,655,947 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,675 | lean | import game.world_06_proposition
namespace mynat
example (P Q : Prop) (p : P) (q : Q) : P ∧ Q := begin[nat_num_game]
split,
exact p,
exact q,
end
lemma and_symm (P Q : Prop) : P ∧ Q → Q ∧ P := begin[nat_num_game]
intro r, cases r,
split, exact r_right, exact r_left,
end
lemma and_trans (P Q R : Prop) : P ∧... |
24743a01bef111c1146c372c6f346dd64520f400 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/data/nat/bigops.lean | 9266b7e175b10c77f2488db688adf84ebe5f78f2 | [
"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 | 7,428 | lean | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
Finite sums and products over intervals of natural numbers.
-/
-- TODO(Leo): remove after refactoring
exit
import data.nat.order algebra.group_bigops algebra.interval
nam... |
30747c4d65381072488d0656ac8bdb50732eadef | dac4e6671410f506c880986cbb2212dd7f5b3dfd | /meta_data.lean | a9258dc7779fcd1b68eb9d73985d4cd612148ab8 | [
"CC-BY-4.0"
] | permissive | thalesant/formalabstracts-2018 | e6ddfe8b3ce5c6f055ddcccf345bf55c41f850c1 | d206dfa32a6b4a84aacc3a5500a144757e6d3454 | refs/heads/master | 1,642,678,879,231 | 1,561,648,713,000 | 1,561,648,713,000 | 97,608,420 | 1 | 0 | null | 1,564,063,995,000 | 1,500,388,250,000 | Lean | UTF-8 | Lean | false | false | 6,365 | lean | /- Each fabstract contains a list of results. The following type lists the
various kinds of results. You may read the values as follows:
* `Proof p` -- the paper contains the proof `p`
* `Construction c` -- the paper contains the construction `c`
* `Conjecture C` -- the paper contains the conjecture `C`
... |
216c4901b003f11a369eac53d076bb4a3c7b432b | bb31430994044506fa42fd667e2d556327e18dfe | /src/number_theory/ramification_inertia.lean | f9574236076280c49060b28140bbfb4aa5335d12 | [
"Apache-2.0"
] | permissive | sgouezel/mathlib | 0cb4e5335a2ba189fa7af96d83a377f83270e503 | 00638177efd1b2534fc5269363ebf42a7871df9a | refs/heads/master | 1,674,527,483,042 | 1,673,665,568,000 | 1,673,665,568,000 | 119,598,202 | 0 | 0 | null | 1,517,348,647,000 | 1,517,348,646,000 | null | UTF-8 | Lean | false | false | 39,103 | lean | /-
Copyright (c) 2022 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import linear_algebra.free_module.finite.rank
import ring_theory.dedekind_domain.ideal
/-!
# Ramification index and inertia degree
Given `P : ideal S` lying over `p : id... |
81b40dcd3aa42263ac7cc88f0610a9adc8d1bf53 | c8af905dcd8475f414868d303b2eb0e9d3eb32f9 | /src/data/cpi/concretion/basic.lean | 9ab1eb43eb998883ef11b5a67f1403fab584c438 | [
"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 | 4,673 | lean | import data.cpi.species
namespace cpi
/-- A concretion represents the potential for a species to interact with another.
-/
@[derive decidable_eq, nolint has_inhabited_instance]
inductive concretion (ℍ : Type) (ω : context) : context → ℕ → ℕ → Type
| apply {Γ} {b} (bs : vector (name Γ) b) (y : ℕ)
: species ℍ ω (... |
3daed1c161300aed7bd4d54f2185bb1f828e8e5f | 964a8bb66c2eb89b920fe65d0ec2f77eab0d5f65 | /src/testGames.lean | 8bbd1c76b751eeefe388a5d907475645933faa49 | [
"MIT"
] | permissive | SnobbyDragon/leanhanoi | 9990a7b586f1d843d39c3c7aab7ac0b5eefbe653 | a42811ce5ab55e0451880a8c111c75b082936d39 | refs/heads/master | 1,675,735,182,689 | 1,609,387,288,000 | 1,609,387,288,000 | 284,167,126 | 8 | 1 | MIT | 1,609,262,129,000 | 1,596,247,349,000 | Lean | UTF-8 | Lean | false | false | 473 | lean | import hanoi
import hanoiinteractive
open hanoi hanoi.tower
open hanoitactics
namespace testGames
/-
md a b = move disk from tower a to tower b
finish_game = check if you're done!
-/
example : game' 1 :=
begin [hanoi_tactic]
md a b,
md b c,
finish_game,
end
example : game' 3 :=
begin [hanoi_tactic]
md ... |
b5254ee303e4343fabc687b70600cc4d5cbd0c7d | 947b78d97130d56365ae2ec264df196ce769371a | /stage0/src/Lean/Compiler/ClosedTermCache.lean | 44fc98eb8dc62e72d5dcfe925d16f506581d469f | [
"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 | 1,097 | 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.Environment
namespace Lean
abbrev ClosedTermCache := SMap Expr Name
def mkClosedTermCacheExtension : IO (SimplePersistentEnvExtension (Expr ×... |
df83ee858e8ce8368c44629d8d4fd448eb215bb9 | 750acab0c635b67751bcfec43c5411aa3941c441 | /matrix.lean | 8ccd6e42b9c328053d3d5b15499963a0ccf04006 | [] | no_license | nthomas103/lean_work | 912f8e662cdd73ba97f5d3655ddb8a5d2cd204c9 | 7e9785cae2b60a77b41922fd5d5b159a1fae415c | refs/heads/master | 1,586,739,169,355 | 1,455,759,226,000 | 1,455,759,226,000 | 50,978,095 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 22,268 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Nathaniel Thomas, Leonardo de Moura
Matrices
NCT: translation of Coq Mathematical Components library into Lean
(https://github.com/math-comp/math-comp/blob/master/mathcomp/alge... |
4c14a89802ffe6bbb39cbee1ba2689889e96fc16 | 2c096fdfecf64e46ea7bc6ce5521f142b5926864 | /src/Lean/Elab/Structure.lean | 92e00137a6b96c135909f5f6c40a54da6b0aa93c | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | Kha/lean4 | 1005785d2c8797ae266a303968848e5f6ce2fe87 | b99e11346948023cd6c29d248cd8f3e3fb3474cf | refs/heads/master | 1,693,355,498,027 | 1,669,080,461,000 | 1,669,113,138,000 | 184,748,176 | 0 | 0 | Apache-2.0 | 1,665,995,520,000 | 1,556,884,930,000 | Lean | UTF-8 | Lean | false | false | 45,591 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Parser.Command
import Lean.Meta.Closure
import Lean.Meta.SizeOf
import Lean.Meta.Injective
import Lean.Meta.Structure
import Lean.Meta.AppBuilde... |
09bd6c6c4db2caf74ec5c1c9e199a6cf6909bb23 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/order/monoid/units.lean | 63ad4dd83958cf3908f75567c72da60c9776a385 | [
"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 | 1,673 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl
-/
import order.hom.basic
import order.min_max
import algebra.group.units
/-!
# Units in ordered monoids
> THIS FILE I... |
d85a6ac534a15c1218c5e70d57f7465fffd2284f | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/algebra/geom_sum.lean | b34d41e00e7fac6391831c3de4673f67effc7ddd | [
"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 | 7,834 | lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Neil Strickland
Sums of finite geometric series
-/
import algebra.group_with_zero_power
import algebra.big_operators.order
import algebra.big_operators.ring
import algebra.big_operat... |
4c6e4cfcf227afbc44fdf2ff9f45d0591ee62e77 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/linear_algebra/charpoly/basic.lean | 050109a3936fc4d22e78e1654fceb3ce3a9b1696 | [
"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 | 2,909 | lean | /-
Copyright (c) 2021 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
import linear_algebra.free_module.finite
import linear_algebra.matrix.charpoly.coeff
/-!
# Characteristic polynomial
We define the characteristic polynomial of ... |
68549afb8dfad20a436d64da09a90c54918b5249 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/monoidal/unitors.lean | f379d9cbae05f78f18b82c94ea292a8166b9273d | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,413 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.monoidal.category
import Mathlib.PostPort
universes v u
namespace Mathli... |
2eaa920afbedfcd96abb80d71d293f5e86e9cce9 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/dynamics/ergodic/ergodic.lean | a9a005f971042656ad6bfacdec716d2f43acb167 | [
"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 | 8,111 | lean | /-
Copyright (c) 2022 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import dynamics.ergodic.measure_preserving
/-!
# Ergodic maps and measures
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding P... |
71537dd2cb4b6c84fadd33601e1089761ade06b7 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/sites/canonical.lean | f92fdc076e0f186e1b58441ecb46d5c6963887b1 | [
"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 | 9,762 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import category_theory.sites.sheaf_of_types
/-!
# The canonical topology on a category
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a... |
d402b1f64afed6a33bc6d57084210ca1a471a091 | 28b6e1a13d35e9b450f65c001660f4ec4713aa10 | /Search/Generic/Heuristic.lean | 627f4c68277e6c68e31a3b658b9baf8b3b6e746a | [
"Apache-2.0"
] | permissive | dselsam/search | 14e3af3261a7a70f8e5885db9722b186f96fe1f5 | 67003b859d2228d291a3873af6279c1f61430c64 | refs/heads/master | 1,684,700,794,306 | 1,614,294,810,000 | 1,614,294,810,000 | 339,578,823 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,576 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Selsam
-/
import Search.Heuristic
import Search.Generic.CollectFns
import Search.Inspect.Basic
import Std.Data.HashMap
namespace Search
namespace Generic
open Lean
open... |
bed79f21536ef958cfafd520962117433d4ccaef | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/category_theory/elementwise.lean | 4760ba9160bf89247d5353d1a0bc59ee1ed395af | [
"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 | 739 | 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 tactic.elementwise
/-!
# Use the `elementwise` attribute to create applied versions of lemmas.
Usually we would use `@[elementwise]` at the point of definiti... |
b75f361c85014d6ece6bb004ef3e9056d2f9db68 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/geometry/manifold/times_cont_mdiff.lean | 11950b9a4007e3d94cf1345c2372356d78dc023e | [
"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 | 86,783 | 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 geometry.manifold.mfderiv
import geometry.manifold.local_invariant_properties
/-!
# Smooth functions between smooth manifolds
We define `Cⁿ` functions... |
616036b1938fdef0de9b0b29eff68fd38dc17435 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/run/mutwf3.lean | 71e1f003b7295ffe51ee9c8e7b335db57bad637a | [
"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 | 754 | lean | mutual
def f : Nat → α → α → α
| 0, a, b => a
| n, a, b => g a n b |>.1
def g : α → Nat → α → (α × α)
| a, 0, b => (a, b)
| a, n, b => (h a b n, a)
def h : α → α → Nat → α
| a, b, 0 => b
| a, b, n+1 => f n a b
end
termination_by
invImage
(fun
| Sum.inl ⟨_, n, _, _⟩ => (n, 2)
... |
81597b3195207e118a62887a721ae9fefe9b3ac2 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/nested_inductive.lean | 18eb412fe14b7d001fe3ebc8601030ade8ebaf3c | [
"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 | 2,439 | lean | set_option trace.inductive_compiler.nested.define.failure true
set_option max_memory 1000000
inductive vec (A : Type*) : nat -> Type*
| vnil : vec 0
| vcons : Pi (n : nat), A -> vec n -> vec (n+1)
namespace X1
print "simple"
inductive foo
| mk : list foo -> foo
end X1
namespace X2
print "with param"
inductive foo (... |
e50f990f04f4260f8501f8b1961d4df9d45f4fd8 | 02005f45e00c7ecf2c8ca5db60251bd1e9c860b5 | /src/category_theory/monoidal/of_chosen_finite_products.lean | 6b707693b482095723a4b145817d72680193d821 | [
"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 | 15,877 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Simon Hudon
-/
import category_theory.monoidal.braided
import category_theory.limits.shapes.binary_products
import category_theory.limits.shapes.terminal
import categor... |
461529deec989fbc1bfa92d1987b01be4d656345 | b561a44b48979a98df50ade0789a21c79ee31288 | /src/Lean/Syntax.lean | e1f6c3faea571e54eb14ee9768c7bf6de3328236 | [
"Apache-2.0"
] | permissive | 3401ijk/lean4 | 97659c475ebd33a034fed515cb83a85f75ccfb06 | a5b1b8de4f4b038ff752b9e607b721f15a9a4351 | refs/heads/master | 1,693,933,007,651 | 1,636,424,845,000 | 1,636,424,845,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 18,235 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Sebastian Ullrich, Leonardo de Moura
-/
import Lean.Data.Name
import Lean.Data.Format
namespace Lean
def SourceInfo.updateTrailing (trailing : Substring) : SourceInfo → SourceI... |
845e4141da1446ce2a9e536246938f78c77a5b3b | 9b0cdc31ceef59f5fbd4e20acad77a7a59044088 | /src/solutions/02_iff_if_and.lean | f012d803b6a8b8fc865227d15ab88ad96c5aa8dd | [
"Apache-2.0"
] | permissive | andrewparr/tutorials | 964ebb8b4eae2b658a946843f8f9fc5c69b79761 | 0fd6cefe7e62f0d4bfa12ebd115913f8ef4fbd62 | refs/heads/master | 1,687,573,595,883 | 1,626,653,659,000 | 1,626,653,659,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 15,473 | lean | import data.real.basic
/-
In the previous file, we saw how to rewrite using equalities.
The analogue operation with mathematical statements is rewriting using
equivalences. This is also done using the `rw` tactic.
Lean uses ↔ to denote equivalence instead of ⇔.
In the following exercises we will use the lemma:
su... |
3a4027996f381411dc1b4cd4e9f51cda19a9a6f8 | 11e28114d9553ecd984ac4819661ffce3068bafe | /src/examples/groups.lean | 878e2ca870c7d4a202510c7701c7c2dfc2df5c04 | [
"MIT"
] | permissive | EdAyers/lean-subtask | 9a26eb81f0c8576effed4ca94342ae1281445c59 | 04ac5a6c3bc3bfd190af4d6dcce444ddc8914e4b | refs/heads/master | 1,586,516,665,621 | 1,558,701,948,000 | 1,558,701,948,000 | 160,983,035 | 4 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 4,057 | lean | /- Author: E.W.Ayers © 2019 -/
import ..equate
open robot
universe u
attribute [equate] is_group_hom.mul
section additive_groups
variables {α : Type u} [add_comm_group α] {u v w x y z : α}
example : (x + y) + z = (z + x) + y :=
by equate
example : x + y + z = z + x + y :=
by equate
example : x... |
8038731bc12fbc499d3408229ab8fb8b7f416b93 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/depHd.lean | 393158ddc6596bff9326fc0faed66fcd9476ca9c | [
"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 | 303 | lean | def Hd : List α → Type
| [] => PUnit
| a :: _ => α
def hd : (as : List α) → Hd as
| [] => ()
| a :: l => a
theorem inj_hd (α : Type) : (a a': α) → (l l' : List α) → a :: l = a' :: l' → a = a' := by
intro a a' l l' h
show hd (a :: l) = hd (a' :: l')
cases h
rfl
|
562da5999cb7d651e509dbb5b59c9692f1aab186 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/group_power/basic.lean | 9910c50bcb1b9cfc7155471c815aa8461375de5c | [
"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 | 11,937 | 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
-/
import algebra.divisibility.basic
import algebra.group.commute
import algebra.group.type_tags
/-!
# Power operations on monoids and groups
The power ... |
ce9dc6b20c1cc71b2173e164efa0f55fea0482c6 | a9fe717b93ccfa4b2e64faeb24f96dfefb390240 | /nat/neg_elim.lean | ed9182fbcd461de18b9e95b25e55f8f36faa2c78 | [] | no_license | skbaek/omega | ab1f4a6daadfc8c855f14c39d9459ab841527141 | 715e384ed14e8eb177a326700066e7c98269e078 | refs/heads/master | 1,588,000,876,352 | 1,552,645,917,000 | 1,552,645,917,000 | 174,442,914 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,358 | lean | import .form
namespace nat
@[omega] def push_neg : form → form
| (p ∨* q) := (push_neg p) ∧* (push_neg q)
| (p ∧* q) := (push_neg p) ∨* (push_neg q)
| (¬*p) := p
| p := ¬* p
lemma push_neg_equiv :
∀ {p}, form.equiv (push_neg p) (¬* p) :=
begin
form.induce `[intros v; try {refl}],
{ simp_omega [cla... |
905b863e991481dc0b7d7a266758229cee1ef23a | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /src/Lean/Compiler/LCNF/FixedArgs.lean | d34c103106d83c69476f5d5b4d5b1126201159ca | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | tobiasgrosser/lean4 | ce0fd9cca0feba1100656679bf41f0bffdbabb71 | ebdbdc10436a4d9d6b66acf78aae7a23f5bd073f | refs/heads/master | 1,673,103,412,948 | 1,664,930,501,000 | 1,664,930,501,000 | 186,870,185 | 0 | 0 | Apache-2.0 | 1,665,129,237,000 | 1,557,939,901,000 | Lean | UTF-8 | Lean | false | false | 2,274 | lean | /-
Copyright (c) 2022 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Compiler.LCNF.Basic
import Lean.Compiler.LCNF.Types
namespace Lean.Compiler.LCNF
private abbrev Visitor := NameMap (Array Bool) → NameMap (Arr... |
d9a0779152076febe01925b71bafdb5a3316245c | 76df16d6c3760cb415f1294caee997cc4736e09b | /lean/src/cs/fin.lean | f59ec6cb2f43664bebefe6d212cda2483b5d7744 | [
"MIT"
] | permissive | uw-unsat/leanette-popl22-artifact | 70409d9cbd8921d794d27b7992bf1d9a4087e9fe | 80fea2519e61b45a283fbf7903acdf6d5528dbe7 | refs/heads/master | 1,681,592,449,670 | 1,637,037,431,000 | 1,637,037,431,000 | 414,331,908 | 6 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 6,056 | lean | import tactic.basic
import tactic.split_ifs
import tactic.linarith
import tactic.apply_fun
import .svm
import .lib
namespace lang
-- A program is call free if it contains no calls.
def exp.call_free {D O : Type} : exp D O → bool
| (exp.call _ _) := ff
| (exp.let0 y x1 x2) := exp.call_free x1 ∧ exp.call_fre... |
ba2efc3130b190edc560bd5f0d0c0ee8855a99c9 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/data/multiset/antidiagonal.lean | 5dd03984059ff727b96b30b7cb2fbe5d2f190f71 | [
"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 | 3,076 | 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.multiset.powerset
/-!
# The antidiagonal on a multiset.
The antidiagonal of a multiset `s` consists of all pairs `(t₁, t₂)`
such that `t₁ + t₂ = s`. The... |
a2725999422472b6ed8526430f50df6bf88f6911 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/n5.lean | 9956924d541ef2ffd6c38fcee4fef1fb505ca102 | [
"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 | 434 | lean | prelude
constant N : Type.{1}
constant f : N → N → N → N
constant g : N → N → N
constant h : N → N → N → N
constant s : N → N → N → N → N
precedence `*`:75
precedence `|`:75
notation a * b:prev | c:prev := f a b c
notation a * b := g a b
notation a * b * c:prev := h a b c
notation a * b | c * d:prev := s a b c d
con... |
a88057d9f15da5a376edd7d2f1a49d81d2e3d430 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/string/basic.lean | b0fc9bf4e907f0982c1118368766cf66af46c4a6 | [
"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 | 4,501 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.list.lex
import data.char
/-!
# Strings
Supplementary theorems about the `string` type.
-/
namespace string
/-- `<` on string iterators. This coincide... |
ca545b8b9161c5535f0d44cb018e793f6c1599af | d450724ba99f5b50b57d244eb41fef9f6789db81 | /src/homework/hw4.lean | 808968b954ca16183f1ab71c0a74597b29eaaf4b | [] | no_license | jakekauff/CS2120F21 | 4f009adeb4ce4a148442b562196d66cc6c04530c | e69529ec6f5d47a554291c4241a3d8ec4fe8f5ad | refs/heads/main | 1,693,841,880,030 | 1,637,604,848,000 | 1,637,604,848,000 | 399,946,698 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,721 | lean | -- 1
example : 0 ≠ 1 :=
begin
-- ¬ (0 = 1)
-- (0 = 1) → false
assume h,
trivial,
end
-- 2
example : 0 ≠ 0 → 2 = 3 :=
begin
assume h,
have zeqz := eq.refl 0,
have f : false := h zeqz,
exact false.elim (f),
end
-- 3
example : ∀ (P : Prop), P → ¬¬P :=
begin
assume P,
assume (p : P),
-- ¬¬P
-- ¬P... |
96b8c04b4a482ea738cec0169e17558b61f5b480 | bb31430994044506fa42fd667e2d556327e18dfe | /src/data/int/dvd/basic.lean | 70b50fe2e31a92b85a8f531c1c89502c72f442d4 | [
"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 | 2,753 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
import data.int.order.basic
import data.nat.cast.basic
/-!
# Basic lemmas about the divisibility relation in `ℤ`.
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any cha... |
a82f6603104efadbe8bf7d61f511e3cd4179db82 | d436468d80b739ba7e06843c4d0d2070e43448e5 | /src/topology/metric_space/basic.lean | 8a3516e39fb1438d7de3c4200bc85388afee7755 | [
"Apache-2.0"
] | permissive | roro47/mathlib | 761fdc002aef92f77818f3fef06bf6ec6fc1a28e | 80aa7d52537571a2ca62a3fdf71c9533a09422cf | refs/heads/master | 1,599,656,410,625 | 1,573,649,488,000 | 1,573,649,488,000 | 221,452,951 | 0 | 0 | Apache-2.0 | 1,573,647,693,000 | 1,573,647,692,000 | null | UTF-8 | Lean | false | false | 62,758 | lean | /-
Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Metric spaces.
Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
Many definitions and theorems expected on metric spaces are already introduced o... |
40ce0de9c9d668428093ce7c558921ece232b895 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/dynamics/flow.lean | 149c1d405c7579f55e8b76d505c36b106571bb0c | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 6,144 | lean | /-
Copyright (c) 2020 Jean Lo. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean Lo
-/
import topology.algebra.group
import logic.function.iterate
/-!
# Flows and invariant sets
This file defines a flow on a topological space `α` by a topological
monoid `τ` as a c... |
effdef3c1292cffbc89982c0bec9d1e5e810bcf8 | 2861ebf54a4d4c5fc2c20af17ded71a38be55c7e | /src/kenimatics.lean | e915f67d8e8df241b6174794c6cebbc7e5d942f0 | [] | no_license | Nolrai/kenimatics | 098951b50bd4c7b20abaefbeb5de61958fb99ab7 | d2c80d8ca9cb8dc1445d534bd3d9d32cb883cdbd | refs/heads/master | 1,670,153,072,595 | 1,596,593,443,000 | 1,596,593,443,000 | 285,236,253 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,841 | lean | import analysis.calculus.deriv
section -- 'vectors' implemented as arrays.
open array
-- α ^^ n is a n-dim vector of 'α's implemented as an array.
-- (not to be confused with the 'vector' type in core.init.data.vector)
notation a ` ^^ `:60 b := array b a
parameter {α : Type}
variables [nondiscrete_normed_field α] {n... |
84526598a7f93e3137ea97b5078842f0bc673234 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/data/finset/fin.lean | c4a89bad4813caf7ab81ffacc10cd2c199d8dfc4 | [
"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 | 1,766 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Scott Morrison, Johan Commelin
-/
import data.finset.card
/-!
# Finsets in `fin n`
A few constructions for finsets in `fin n`.
## Main declarations
* `finset.fin_range`... |
e37cf69a77a55d78b0a062dc5bb8d048152edaf7 | 4bcaca5dc83d49803f72b7b5920b75b6e7d9de2d | /src/Lean/Parser/Syntax.lean | 54dc9952e73b0dd92c8af27f2606f188a324cad9 | [
"Apache-2.0"
] | permissive | subfish-zhou/leanprover-zh_CN.github.io | 30b9fba9bd790720bd95764e61ae796697d2f603 | 8b2985d4a3d458ceda9361ac454c28168d920d3f | refs/heads/master | 1,689,709,967,820 | 1,632,503,056,000 | 1,632,503,056,000 | 409,962,097 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,058 | 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, Sebastian Ullrich
-/
import Lean.Parser.Command
import Lean.Parser.Tactic
namespace Lean
namespace Parser
builtin_initialize
registerBuiltinParserAttribut... |
91b007d4359e342c998685a0f3404e6bd84df028 | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /test/elementwise.lean | b0f9169425f631ea00eae5ad2ca6a881e1fe8fa6 | [
"Apache-2.0"
] | permissive | ilitzroth/mathlib | ea647e67f1fdfd19a0f7bdc5504e8acec6180011 | 5254ef14e3465f6504306132fe3ba9cec9ffff16 | refs/heads/master | 1,680,086,661,182 | 1,617,715,647,000 | 1,617,715,647,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,444 | lean | import algebra.category.Mon.basic
import tactic.elementwise
open category_theory
universes w v u
@[elementwise]
lemma foo {C : Type u} [category.{v} C]
{M N K : C} {f : M ⟶ N} {g : N ⟶ K} {h : M ⟶ K} (w : f ≫ g = h) : f ≫ 𝟙 N ≫ g = h :=
by simp [w]
@[elementwise]
lemma foo' {C : Type*} [category C]
{M N K : C}... |
cbbe21659f3c611e9fb03e15053965cd4c5396cd | 88892181780ff536a81e794003fe058062f06758 | /src/xena_challenge/challenge2.lean | afb112998d43c521f35274fa50be08c0a78fcd16 | [] | no_license | AtnNn/lean-sandbox | fe2c44280444e8bb8146ab8ac391c82b480c0a2e | 8c68afbdc09213173aef1be195da7a9a86060a97 | refs/heads/master | 1,623,004,395,876 | 1,579,969,507,000 | 1,579,969,507,000 | 146,666,368 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 876 | lean | import data.real.basic
import lib.attempt
namespace challenges
-- basic definitions
def upper_bounds (S : set ℝ) : set ℝ := { b | ∀s ∈ S, s ≤ b }
def lower_bounds (S : set ℝ) : set ℝ := { b | ∀s ∈ S, b ≤ s }
def is_least (S : set ℝ) (l : ℝ) : Prop := l ∈ S ∧ l ∈ lower_bounds S
def is_lub (S : set ℝ) (l : ℝ) : Prop :=... |
bae9bf24b5c6029122a779357f9b0a50b121f181 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/group_theory/subgroup_auto.lean | 57a6f9262b6d8979f68a7c882717bf3ed12a8a79 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 52,493 | lean | /-
Copyright (c) 2020 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.group_theory.submonoid.default
import Mathlib.algebra.group.conj
import Mathlib.order.modular_lat... |
1a34b7a60d997dd29dddf02e4731316a6e18866d | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/instance_cache_bug1.lean | bb7990da16d1b9d5f94c255d094767ad4fb4022a | [
"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 | 133 | lean | constant A : Type
constant a : A
constant A_has_add : has_add A
#check a + a -- ERROR
attribute [instance] A_has_add
#check a + a
|
cf36668e9988dd02ce365a53eece667e1e64e350 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/group_theory/quotient_group.lean | 9aeb88ef126d9e481f6bb0a2a7eb67f6b9d49e43 | [
"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 | 22,378 | lean | /-
Copyright (c) 2018 Kevin Buzzard, Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Patrick Massot
This file is to a certain extent based on `quotient_module.lean` by Johannes Hölzl.
-/
import group_theory.coset
import group_theory.congr... |
a3663324c8f65d7ab826d4365cb792518e052532 | a3db153d66921f9d5a199b60b52ab3c21cf0e023 | /src/util.lean | 5cf42fa9ea7b6ed9d9c20f7c49c4131ba285c8ca | [
"MIT"
] | permissive | metalogical/sia-lean | 3bd87a76b3ee6d910cbf182eb2a0e6d9eca3c056 | f8e354dd2ff6c09c4e001c1f80f6112c62da8592 | refs/heads/master | 1,629,775,811,523 | 1,512,684,874,000 | 1,512,684,874,000 | 106,763,566 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 375 | lean | universe u
notation `exists!` binders `, ` r:(scoped P, exists_unique P) := r
infix ` != `:50 := ne
namespace set -- set extensionality
variable {R : Type u}
@[reducible]
def eq (A : set R) (B : set R) := forall x : R, set.mem x A <-> set.mem x B
theorem ext {A : set R} {B : set R} (a_eq_b : eq A B)... |
9bdc3f545f7704c3e1407ceb711fb7d7b053af13 | a0a027e4a00cdb315527e8922122f2a4411fd01c | /9.7-bounded-quantification.lean | 871fb3bbf992a84f7cefedda872c72005c8b164f | [] | no_license | spl/lean-tutorial | 96a1ef321d06b9b28d044eeb6bf1ff9a86761a6e | 35c0250004d75d8ae58f6192b649744545116022 | refs/heads/master | 1,610,250,012,890 | 1,454,259,122,000 | 1,454,259,122,000 | 49,971,362 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 547 | lean | import data.nat
open nat decidable algebra
definition bex (n : nat) (P : nat → Prop) : Prop :=
∃ x : nat, x < n ∧ P x
definition not_bex_zero (P : nat → Prop) : ¬ bex 0 P :=
sorry
variables {n : nat} {P : nat → Prop}
definition bex_succ (H : bex n P) : bex (succ n) P :=
sorry
definition bex_succ_of_pred (H : P n)... |
9b8ea240f6a1a285a8097f62591b98cee42db44f | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/algebra/group/prod.lean | 6f31202a40b9d9b9c31abd1776f2ab34b0d99fd1 | [
"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 | 8,833 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot, Yury Kudryashov
-/
import algebra.group.hom
import data.prod
/-!
# Monoid, group etc structures on `M × N`
In this file we define one-binop (`monoid`, `... |
b8355e8989691d533c40e3fefb9668924140eff8 | eb586f8ae80b7045ba4ff08f1c7ba69403d61081 | /src/e_transcendental.lean | 77cd020506bf72d609fd8efdab7fd8de9b3767ec | [] | no_license | bryangingechen/transcendental | 926584f58c47d766b304d39d1aa6814284535394 | 3692ac5ebe85e49c5f65bc7f2ea4f873a973bac2 | refs/heads/master | 1,668,733,660,442 | 1,594,269,161,000 | 1,594,269,161,000 | 278,266,099 | 0 | 0 | null | 1,594,270,314,000 | 1,594,270,313,000 | null | UTF-8 | Lean | false | false | 87,073 | lean | import data.real.basic
import data.complex.exponential
import ring_theory.algebraic
import e_trans_helpers2
import data.int.basic
import data.polynomial
noncomputable theory
open_locale classical
open small_things
open_locale big_operators
def e : ℝ := real.exp 1
section e
private lemma nonneg_nat (i : ℕ) : (i : ℝ... |
40327d877fc1e44e6ef9cd7d0016e699af34b674 | 4fa161becb8ce7378a709f5992a594764699e268 | /src/order/lattice.lean | 3c3479855aab308f152b3856747176f27b15ea34 | [
"Apache-2.0"
] | permissive | laughinggas/mathlib | e4aa4565ae34e46e834434284cb26bd9d67bc373 | 86dcd5cda7a5017c8b3c8876c89a510a19d49aad | refs/heads/master | 1,669,496,232,688 | 1,592,831,995,000 | 1,592,831,995,000 | 274,155,979 | 0 | 0 | Apache-2.0 | 1,592,835,190,000 | 1,592,835,189,000 | null | UTF-8 | Lean | false | false | 18,857 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Defines the inf/sup (semi)-lattice with optionally top/bot type class hierarchy.
-/
import order.basic
set_option old_structure_cmd true
universes u v w
variables {α... |
4a66e0911e0ba18dba13ac633c587ea06a74ee88 | 947b78d97130d56365ae2ec264df196ce769371a | /tests/lean/run/bigmul.lean | 52da5048cfd428e8ac768563007e45c29515669d | [
"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 | 242 | lean | new_frontend
@[noinline] def f (x : Nat) :=
1000000000000000000000000000000
@[noinline] def tst1 (n : Nat) : IO Unit := do
IO.println (n * f n)
@[noinline] def tst2 (n : Nat) : IO Unit := do
IO.println (f n * n)
#eval tst1 0
#eval tst2 0
|
aae35b9e4091b23eacf871940796f42b6c697f88 | a7eef317ddec01b9fc6cfbb876fe7ac00f205ac7 | /src/data/set/intervals/basic.lean | 62f712744e14a5f20363f25444252835644fd6ab | [
"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 | 30,525 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot, Yury Kudryashov
-/
import tactic.tauto
import algebra.order_functions
import algebra.ordered_field
/-!
# Intervals
In any preorder `α`... |
96905b5e42424eae244757af575df9296a68d1ed | ca1ad81c8733787aba30f7a8d63f418508e12812 | /clfrags/src/hilbert/wr/ki_bot.lean | fa9e18b0eced3a663d5933d0d0a8885307035637 | [] | no_license | greati/hilbert-classical-fragments | 5cdbe07851e979c8a03c621a5efd4d24bbfa333a | 18a21ac6b2e890060eb4ae65752fc0245394d226 | refs/heads/master | 1,591,973,117,184 | 1,573,822,710,000 | 1,573,822,710,000 | 194,334,439 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 277 | lean | import core.connectives
import hilbert.wr.ki
namespace clfrags
namespace hilbert
namespace wr
namespace ki_bot
axiom kib₁ : Π {a b c : Prop}, ki b a bot → ki b a c
end ki_bot
end wr
end hilbert
end clfrags
|
5440137e4ee07f6cd31fdc6338d3f53fb761ddfa | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/tactic/ring.lean | e2f222c520122d2593aa315b80b6b39c1ca411ac | [
"Apache-2.0"
] | permissive | abentkamp/mathlib | d9a75d291ec09f4637b0f30cc3880ffb07549ee5 | 5360e476391508e092b5a1e5210bd0ed22dc0755 | refs/heads/master | 1,682,382,954,948 | 1,622,106,077,000 | 1,622,106,077,000 | 149,285,665 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 29,965 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import tactic.norm_num
import data.int.range
/-!
# `ring`
Evaluate expressions in the language of commutative (semi)rings.
Based on <http://www.cs.ru.nl/~freek/cour... |
a8d57a1109b2ad36d3041d97888ae690c4ebf0e3 | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /tests/lean/run/coercion_bug2.lean | f23a05465e968e380baf1859409d17eed4da9f73 | [
"Apache-2.0"
] | permissive | codyroux/lean | 7f8dff750722c5382bdd0a9a9275dc4bb2c58dd3 | 0cca265db19f7296531e339192e9b9bae4a31f8b | refs/heads/master | 1,610,909,964,159 | 1,407,084,399,000 | 1,416,857,075,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 262 | lean | import data.nat
using nat
inductive list (T : Type) : Type :=
nil {} : list T,
cons : T → list T → list T
definition length {T : Type} : list T → nat := list.rec 0 (fun x l m, succ m)
theorem length_nil {T : Type} : length (@list.nil T) = 0
:= eq.refl _
|
2057c9d91ecb9730e5c4626764dbe1c2465c774c | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/mutual_parameter.lean | ce6640d19bd6e3cf9ba7c2c38c3ab4f0edf985a7 | [
"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 | 230 | lean | section
parameter (k : ℕ)
mutual def foo, bar
with foo : ℕ → ℕ
| 0 := k
| (n+1) := bar n
with bar : ℕ → ℕ
| 0 := k+10
| (n+1) := foo n
def baz : ℕ := foo 3
def foo' (n : ℕ) := k+n
def baz' : ℕ := foo' 3
end |
86f73c59cf6abbb3a38c750964f3184a172c61bb | d7189ea2ef694124821b033e533f18905b5e87ef | /galois/vector/rotate.lean | 1ccc92d294d47763d583f4ec5130833c855ed3ec | [
"Apache-2.0"
] | permissive | digama0/lean-protocol-support | eaa7e6f8b8e0d5bbfff1f7f52bfb79a3b11b0f59 | cabfa3abedbdd6fdca6e2da6fbbf91a13ed48dda | refs/heads/master | 1,625,421,450,627 | 1,506,035,462,000 | 1,506,035,462,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 455 | lean | import data.vector
import galois.list.rotate
namespace vector
variables {T : Type} {k : ℕ}
definition rol : vector T k → ℕ → vector T k
| ⟨ l, h ⟩ n := ⟨ list.rol l n, show list.length (list.rol l n) = k, from eq.trans (list.length_rol _ _) h ⟩
definition ror : vector T k → ℕ → vector T k
| ⟨ l, h ⟩ n := ... |
573e612ade950ce3109364fe1bc46a95e79a3f44 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/category_theory/limits/concrete_category.lean | 8ee91ef1f8b9a1af8f82a1f628738160c537f49c | [
"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 | 9,870 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Adam Topaz
-/
import category_theory.limits.preserves.basic
import category_theory.limits.types
import category_theory.limits.shapes.wide_pullbacks
import category_theo... |
97fcd3d72b3333c5cbfc61765f058158e67eead6 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/algebra/lie/tensor_product.lean | 9c1dd120212e18793ea6cca0ec564a1076cbda43 | [
"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 | 8,899 | lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import algebra.lie.abelian
/-!
# Tensor products of Lie modules
Tensor products of Lie modules carry natural Lie module structures.
## Tags
lie module, tensor product, ... |
ce501277208c439756d7e1ed5d3cd1aecf3b79ef | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/unfold_issue.lean | 2d3f4a0f2f4e87267045a3f4831e4075745d3f6f | [
"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 | 234 | lean | def f : nat → nat → nat
| 0 := λ x, x
| (n+1) := λ x, x + 1
meta def check_expr (p : pexpr) (t : expr) : tactic unit :=
do e ← tactic.to_expr p, guard (t = e)
example (n : nat): f (n+1) n = n + 1 :=
begin
unfold f
end
|
43f0e2f4d17da4dc7eeec47b2f62e72abe189981 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/limits/mono_coprod.lean | 76dd0b27804a1c16eb32c1b9c9f98cc1fd03d1bc | [
"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 | 4,021 | lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import category_theory.limits.shapes.regular_mono
import category_theory.limits.shapes.zero_morphisms
/-!
# Categories where inclusions into coproducts are monomorphisms
> ... |
0ba9f0933546f9173d63e31322ef70216afe0642 | 07c6143268cfb72beccd1cc35735d424ebcb187b | /src/group_theory/submonoid.lean | 6bd07415e3726dd647f8049b6567d651cdb0e2e5 | [
"Apache-2.0"
] | permissive | khoek/mathlib | bc49a842910af13a3c372748310e86467d1dc766 | aa55f8b50354b3e11ba64792dcb06cccb2d8ee28 | refs/heads/master | 1,588,232,063,837 | 1,587,304,803,000 | 1,587,304,803,000 | 176,688,517 | 0 | 0 | Apache-2.0 | 1,553,070,585,000 | 1,553,070,585,000 | null | UTF-8 | Lean | false | false | 50,336 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard,
Amelia Livingston, Yury Kudryashov
-/
import algebra.big_operators
import algebra.free_monoid
import algebra.... |
1d6fb636b1d74bd447208836394bfb8789063b29 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/linearByRefl.lean | 5186187b30a5922c8775c78f57d7401e9e088ea6 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 2,375 | lean | open Nat.Linear
example (x₁ x₂ x₃ : Nat) : (x₁ + x₂) + (x₂ + x₃) = x₃ + 2*x₂ + x₁ :=
Expr.eq_of_toNormPoly [x₁, x₂, x₃]
(Expr.add (Expr.add (Expr.var 0) (Expr.var 1)) (Expr.add (Expr.var 1) (Expr.var 2)))
(Expr.add (Expr.add (Expr.var 2) (Expr.mulL 2 (Expr.var 1))) (Expr.var 0))
rfl
example (x₁ x₂ x₃ : Nat... |
8768604fa84fb01846716bffc846a533cdadcdc0 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/topology/sheaves/sheaf_condition/sites.lean | 815f909b024929434ebb89ab097097a1769de592 | [
"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 | 8,007 | lean | /-
Copyright (c) 2021 Justus Springer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Justus Springer
-/
import category_theory.sites.spaces
import topology.sheaves.sheaf
import category_theory.sites.dense_subsite
/-!
# Coverings and sieves; from sheaves on sites an... |
315c7f5b3d53b1f5ab9ad5abc19191f40e518c99 | 7d5ad87afb17e514aee234fcf0a24412eed6384f | /src/henkin.lean | 9b59f809e06c1b0a6908c16178a3c641fe1dc3f5 | [] | no_license | digama0/flypitch | 764f849eaef59c045dfbeca142a0f827973e70c1 | 2ec14b8da6a3964f09521d17e51f363d255b030f | refs/heads/master | 1,586,980,069,651 | 1,547,078,141,000 | 1,547,078,283,000 | 164,965,135 | 1 | 0 | null | 1,547,082,858,000 | 1,547,082,857,000 | null | UTF-8 | Lean | false | false | 52,282 | lean | import .completion .language_extension .colimit tactic.linarith
-- local attribute [instance, priority 0] classical.prop_decidable
open fol
universes u v
local infix ` →ᴸ `:10 := Lhom -- \^L
/- Temporarily putting this here because I can't get Lean to recognize Lhom in colimit.lean -/
namespace colimit
export dire... |
99660bd17991f418f751113ff8841f9d3f2524fc | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /tests/compiler/phashmap.lean | e745908a5173bd6f4f391c738a95427efeee317a | [
"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 | 2,061 | lean | import Std.Data.PersistentHashMap
import Lean.Data.Format
open Lean Std Std.PersistentHashMap
abbrev Map := PersistentHashMap Nat Nat
partial def formatMap : Node Nat Nat → Format
| Node.collision keys vals _ => Format.sbracket $
keys.size.fold
(fun i fmt =>
let k := keys.get! i;
let v := vals.ge... |
8744ad182179eb73527fd8944c8a25c3a02b89ea | f3849be5d845a1cb97680f0bbbe03b85518312f0 | /old_library/init/relation.lean | 8a4e7ba4a2819f26c9c6649e6f6ef3a6e42efd8d | [
"Apache-2.0"
] | permissive | bjoeris/lean | 0ed95125d762b17bfcb54dad1f9721f953f92eeb | 4e496b78d5e73545fa4f9a807155113d8e6b0561 | refs/heads/master | 1,611,251,218,281 | 1,495,337,658,000 | 1,495,337,658,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,731 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module init.relation
Authors: Leonardo de Moura
-/
prelude
import init.logic
-- TODO(Leo): remove duplication between this file and algebra/relation.lean
-- We need some of the followi... |
c42257bdf49924df9e554aadbd73068c90fff1e7 | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /stage0/src/Lean/Meta/Tactic/Assert.lean | 327c2340a8232bfe3ce24bfb2e063ad30a3147c9 | [
"Apache-2.0"
] | permissive | walterhu1015/lean4 | b2c71b688975177402758924eaa513475ed6ce72 | 2214d81e84646a905d0b20b032c89caf89c737ad | refs/heads/master | 1,671,342,096,906 | 1,599,695,985,000 | 1,599,695,985,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,030 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.Tactic.Util
namespace Lean
namespace Meta
/--
Convert the given goal `Ctx |- target` into `Ctx |- type -> target`.
It assumes `val` h... |
1c94e1b54725f62019e8af7bcd49db91a05a8c19 | e06332abb44b4720a102c91b393254505e242022 | /chapter2.hlean | 95a3408e2d3db257000a489989047922bc6532a9 | [
"Apache-2.0",
"LicenseRef-scancode-unknown-license-reference"
] | permissive | 11Kilobytes/hott-exercises-lean | 69501ee7fef64cb8669384d4356d43941c75a702 | a859755be688d3f22f14fbdfa35f5f5c32c438d3 | refs/heads/master | 1,611,265,681,636 | 1,455,643,818,000 | 1,455,643,818,000 | 48,048,788 | 1 | 1 | null | 1,455,643,819,000 | 1,450,190,626,000 | Lean | UTF-8 | Lean | false | false | 7,873 | hlean | import init.default types.pi types.sum types.arrow function_lemmas
open eq
section ex1
variables {A : Type} {x y z : A} (p : x = y) (q : y = z)
definition concat₁ : x = z := eq.rec' (λ a q, eq.rec' refl q) p q
definition concat₂ : x = z := eq.rec' (λ a q, q) p q
definition concat₃ : x = z := eq.rec' (λ a p,... |
0061b416834a1956e36ff0fa50841ce29bf8aede | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/973.lean | adfbbc553477ac21c3852202c304dda678f9cfde | [
"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 | 286 | lean | universe u
variable {α : Sort u} {p : α → Prop}
@[simp]
theorem Subtype.coe_mk (x : α) (h : p x) : (Subtype.mk x h).val = x :=
rfl
example (x : Nat) (h : x > 0) : (Subtype.mk x h).val = x := by
simp
set_option trace.Meta.Tactic.simp.discharge true
example : True := by simp
|
385a577588f2c521b0fafe3752b341353822fbc4 | 02005f45e00c7ecf2c8ca5db60251bd1e9c860b5 | /src/group_theory/submonoid/operations.lean | 5b6093b82fec533a8eb54704b8147c82e0f670c8 | [
"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 | 22,633 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard,
Amelia Livingston, Yury Kudryashov
-/
import group_theory.submonoid.basic
import data.equiv.mul_add
import al... |
d793335d95682e240632b2b93011a91e8294dc95 | 159fed64bfae88f3b6a6166836d6278f953bcbf9 | /Structure/TwoStructure.lean | 583a5b6b406a420cbb12341290a3444b3c2880fe | [
"MIT"
] | permissive | SReichelt/lean4-experiments | 3e56830c8b2fbe3814eda071c48e3c8810d254a8 | ff55357a01a34a91bf670d712637480089085ee4 | refs/heads/main | 1,683,977,454,907 | 1,622,991,121,000 | 1,622,991,121,000 | 340,765,677 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,805 | lean | -- An abstract formalization of "isomorphism is equality up to relabeling"
-- -------------------------------------------------------------------------
--
-- See `README.md` for more info.
--
-- A variant of `Structure` where equivalences are `Structure`s instead of setoids.
import Structure.Basic
open Morphisms... |
36a70c2ba1a5b31bc70c1b35853e857c858dd330 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /tests/lean/run/record10.lean | bc5232166d3d648f556851157d0de37708a95d5c | [
"Apache-2.0"
] | permissive | davidmueller13/lean | 65a3ed141b4088cd0a268e4de80eb6778b21a0e9 | c626e2e3c6f3771e07c32e82ee5b9e030de5b050 | refs/heads/master | 1,611,278,313,401 | 1,444,021,177,000 | 1,444,021,177,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 641 | lean | import logic
structure has_mul [class] (A : Type) :=
(mul : A → A → A)
structure semigroup [class] (A : Type) extends has_mul A :=
(assoc : ∀ a b c, mul (mul a b) c = mul a (mul b c))
print prefix semigroup
print "======================="
structure has_two_muls [class] (A : Type) extends has_mul A renaming mul→mul... |
88f044f41b2de88490b2e856c4433cacdcbe0cf7 | c5b07d17b3c9fb19e4b302465d237fd1d988c14f | /src/isos/option.lean | cc4b3ddf627b933070953fcef3d2a12b681c96f3 | [
"MIT"
] | permissive | skaslev/papers | acaec61602b28c33d6115e53913b2002136aa29b | f15b379f3c43bbd0a37ac7bb75f4278f7e901389 | refs/heads/master | 1,665,505,770,318 | 1,660,378,602,000 | 1,660,378,602,000 | 14,101,547 | 0 | 1 | MIT | 1,595,414,522,000 | 1,383,542,702,000 | Lean | UTF-8 | Lean | false | false | 1,213 | lean | import functors.generating
namespace option
-- option(x) = 1 + x
def def_iso {A} : option A ≃ 1 ⊕ A :=
⟨λ x, option.rec (sum.inl ()) sum.inr x,
λ x, sum.rec (λ _, option.none) option.some x,
λ x, by induction x; repeat { simp },
λ x, begin induction x, { induction x, simp }, simp end⟩
def cf (n : ℕ) : ℕ := ite (n ... |
c92f7ce89da59a103e218e4a8c41d2818606fd28 | f3849be5d845a1cb97680f0bbbe03b85518312f0 | /library/init/category/monad.lean | adb0b3112cee3b744e44f3fd0da647c67e23b6d8 | [
"Apache-2.0"
] | permissive | bjoeris/lean | 0ed95125d762b17bfcb54dad1f9721f953f92eeb | 4e496b78d5e73545fa4f9a807155113d8e6b0561 | refs/heads/master | 1,611,251,218,281 | 1,495,337,658,000 | 1,495,337,658,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,116 | lean | /-
Copyright (c) Luke Nelson and Jared Roesch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Luke Nelson, Jared Roesch, Sebastian Ullrich
-/
prelude
import init.category.applicative
universes u v
open function
class has_bind (m : Type u → Type v) ... |
38da0d12d342c033f72a4b230ce7e2b478c7c9fe | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/analysis/convex/topology.lean | 1efbd7ec8b029dad5e83afb33ee6ef233ffef9a0 | [
"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 | 19,308 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, Yury Kudryashov
-/
import analysis.convex.jensen
import analysis.normed.group.pointwise
import topology.algebra.module.finite_dimension
import analysis.normed_spac... |
874c8c3a11ffa68c27858c87df987d3628d609da | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/634b.lean | d841392ba95fe4bdccca710d4f3db432d25c3699 | [
"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 | 894 | lean | open nat
namespace foo
section
parameter (X : Type)
definition A {n : ℕ} : Type := X
definition B : Type := X
variable {n : ℕ}
check @A n
check foo.A nat
check foo.A (X × B)
check @foo.A (X × B) 10
check @foo.A (@foo.B (@A n)) n
check @foo.A (@foo.B (@foo.A X n)) n
check @foo.A (@foo.B (@foo.A nat... |
cbb7ad5a20ee59520651c3ac95fe395b54b6a290 | f00cc9c04d77f9621aa57d1406d35c522c3ff82c | /library/data/rbtree/basic.lean | 97f58c80a49b1558d2d901455cf20b07f4d64b00 | [
"Apache-2.0"
] | permissive | shonfeder/lean | 444c66a74676d74fb3ef682d88cd0f5c1bf928a5 | 24d5a1592d80cefe86552d96410c51bb07e6d411 | refs/heads/master | 1,619,338,440,905 | 1,512,842,340,000 | 1,512,842,340,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,746 | 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... |
6e37497fb29587c949e73ef395bf6f0ce8380e21 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/category_theory/limits/preserves/shapes/binary_products.lean | 32070a3d7366d5359489331afccc3adae7344eb1 | [
"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 | 6,417 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import category_theory.limits.shapes.binary_products
import category_theory.limits.preserves.basic
/-!
# Preserving binary products
Constructions to relate the notions ... |
7b04da819b551829e2ac52b4669b2d85e20a5354 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/tactic/delta_instance.lean | 58edf825e1b2c0c362ee7e1c3f3ccdd9bcf9426c | [
"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 | 3,073 | lean | /-
Copyright (c) 2019 Rob Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rob Lewis
-/
import tactic.simp_result
namespace tactic
/--
`delta_instance ids` tries to solve the goal by calling `apply_instance`,
first unfolding the definitions in `ids`.
-/
-- We ca... |
22b149cd98afb07a300c0d86299a24f234a3509c | d7189ea2ef694124821b033e533f18905b5e87ef | /galois/csp/csp.lean | fccbf702eb2a4bc7304b6acbb4999957a0bc4368 | [
"Apache-2.0"
] | permissive | digama0/lean-protocol-support | eaa7e6f8b8e0d5bbfff1f7f52bfb79a3b11b0f59 | cabfa3abedbdd6fdca6e2da6fbbf91a13ed48dda | refs/heads/master | 1,625,421,450,627 | 1,506,035,462,000 | 1,506,035,462,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,993 | lean | -- This defines a framework for defining communicating sequential
-- agents with asynchronous messages.
--
-- The key concepts are agents and messages. The type for agents is
-- defined by the framework, but message type is left as an abstract
-- parameter.
--
-- Each agent consists of existentially quantified state t... |
7fe39e08b768b79da74053d65d83169069899f05 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/logic/equiv/functor.lean | 54d3dfeed9eb3a2ded7e829ae62044436c0accb4 | [
"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 | 2,412 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Simon Hudon, Scott Morrison
-/
import control.bifunctor
import logic.equiv.defs
/-!
# Functor and bifunctors can be applied to `equiv`s.
> THIS FILE IS SYNCHRONIZED W... |
3e15b34d0399b6d6bf15ffda0bd26ad2fbeca81e | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/topology/homeomorph.lean | b6d30e127a36120e58c46298a6fb31199a52de99 | [
"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 | 7,230 | lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Sébastien Gouëzel, Zhouhang Zhou, Reid Barton
-/
import topology.subset_properties topology.dense_embedding
open set
variables {α : Type*} {β : Type*} {γ... |
7a9801d77a0449505b709dd1bd692de67882a51d | 9dd3f3912f7321eb58ee9aa8f21778ad6221f87c | /library/init/data/sigma/lex.lean | b01ac062f5073eaecf8c1d8067e4845d48e92428 | [
"Apache-2.0"
] | permissive | bre7k30/lean | de893411bcfa7b3c5572e61b9e1c52951b310aa4 | 5a924699d076dab1bd5af23a8f910b433e598d7a | refs/heads/master | 1,610,900,145,817 | 1,488,006,845,000 | 1,488,006,845,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,589 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import init.data.sigma.basic init.meta
universes u v
namespace sigma
section
variables {α : Type u} {β : α → Type v}
variable (r : α → α → Prop... |
db37848ad235bbf6c2b11fc51377a7e5f4b97e20 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/tactic/reassoc_axiom.lean | e119e647a14b3208529bd5a573f669f2d38b5538 | [
"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 | 8,043 | lean | /-
Copyright (c) 2019 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author(s): Simon Hudon
-/
import category_theory.category
/-!
# Tools to reformulate category-theoretic axioms in a more associativity-friendly way
## The `reassoc` attribute
The `reassoc` attr... |
149b51d14fcba3f2959fdcb4961467b7ed7282c2 | 958488bc7f3c2044206e0358e56d7690b6ae696c | /lean/exercise_7_10_2.lean | 1ed69510728a5d9333ff27c2df606972f9515c77 | [] | no_license | possientis/Prog | a08eec1c1b121c2fd6c70a8ae89e2fbef952adb4 | d4b3debc37610a88e0dac3ac5914903604fd1d1f | refs/heads/master | 1,692,263,717,723 | 1,691,757,179,000 | 1,691,757,179,000 | 40,361,602 | 3 | 0 | null | 1,679,896,438,000 | 1,438,953,859,000 | Coq | UTF-8 | Lean | false | false | 3,740 | lean | namespace hidden
open list
universe u
def length {α : Type u} (xs : list α) : ℕ :=
begin
induction xs with x xs n,
{exact 0},
{exact (n + 1)}
end
--#check @length
def reverse {α : Type u} (xs : list α) : list α :=
begin
induction xs with x xs rs,
{exact []},
{exact (rs ++ [x])... |
9c195c897fd47d92e5ac35767c6c563a6eead263 | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/j5.lean | f8876a89d23e35235c24643cac94eb2739a805d4 | [
"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 | 108 | lean | theorem or_imp2 (p q : Bool) : (p ∨ q) ↔ (¬ p → q)
:= subst (symm (imp_or (¬ p) q)) (not_not_eq p)
|
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