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5bf55399cebf19012151e7180d1d0df46f72955a | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/topology/algebra/open_subgroup.lean | c2bec04ddf70fa9e748cc58e0da929a097c97d48 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 8,441 | lean | /-
Copyright (c) 2019 Johan Commelin All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import order.filter.lift
import topology.opens
import topology.algebra.ring
open topological_space
open_locale topological_space
set_option old_structure_cmd true
/... |
245edc439b8042ed43b702cd0b73f5cd8f5e0fe6 | ce6917c5bacabee346655160b74a307b4a5ab620 | /src/ch4/ex0505.lean | c0f64399ab5f17f068dbaa5c7863223b572b4dff | [] | 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 | 37 | lean | example (n : ℕ) : ℕ := ‹ℕ›
|
6f655db6c51e7c3410af467c2903d8cb29e02d42 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/group_theory/submonoid/center.lean | 08f6b5a7c815a58e59475ab2a48ead4ff040bf1c | [
"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 | 4,802 | lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import group_theory.submonoid.operations
import data.fintype.basic
/-!
# Centers of magmas and monoids
## Main definitions
* `set.center`: the center of a magma
* `submo... |
cf18693a2b058bbcaef255be8edc9db2197ec0bf | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/fintype/order.lean | 0a2de3b661247587e9e4230a18ecedb7cb542884 | [
"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 | 6,045 | lean | /-
Copyright (c) 2021 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson, Yaël Dillies
-/
import data.fintype.lattice
import data.finset.order
/-!
# Order structures on finite types
This file provides order instances on fintypes.
## Computable... |
9ace349e6da25812a3005bdd77a4756535ba3db1 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/analysis/normed/group/SemiNormedGroup.lean | 4c1ec7aa17b989acb4a81da421d4802f323087ce | [
"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 | 6,746 | lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Riccardo Brasca
-/
import analysis.normed.group.hom
import category_theory.limits.shapes.zero_morphisms
import category_theory.concrete_category.bundled_hom
import cate... |
7b5dbb0d28d72001f59e1274b08984e6da993889 | 80d0f8071ea62262937ab36f5887a61735adea09 | /src/certigrad/reparam.lean | c0afe47ec51222835e12511c6de98a29a1e0e56f | [
"Apache-2.0"
] | permissive | wudcscheme/certigrad | 94805fa6a61f993c69a824429a103c9613a65a48 | c9a06e93f1ec58196d6d3b8563b29868d916727f | refs/heads/master | 1,679,386,475,077 | 1,551,651,022,000 | 1,551,651,022,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,108 | lean | /-
Copyright (c) 2017 Daniel Selsam. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Daniel Selsam
Certified graph transformation that "reparameterizes" a specific occurrence of a stochastic choice.
-/
import .util .tensor .tfacts .compute_grad .graph .tactics .ops .pre... |
81a8a10d19e7672d9bc033422c902d5a3c1a5fdd | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /tests/lean/run/dofun_prec.lean | 388a21e0cb4c88fe87cca56d22ecc442b81c49f4 | [
"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 | 179 | lean | new_frontend
def tst1 (x : Nat) : IO Unit :=
when (x > 0) do
IO.println "hello";
IO.println "world"
def tst2 (xs : List Nat) : IO Unit :=
xs.forM fun x => do
IO.println x
|
a83e0fae73a4423a8ceb6aac572f503036e84bb1 | a721fe7446524f18ba361625fc01033d9c8b7a78 | /elaborate/rev_concat_nat.lean | 9a125defe64b713add5781552524d1ffc721b0ee | [] | 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 | 10,617 | lean | λ {lst1 lst2 : mylist mynat},
mylist.rec
(eq.rec true.intro
(eq.rec (eq.refl (rev lst2 = rev lst2 ++ empty))
(eq.rec
(eq.rec (eq.refl (rev lst2 = rev lst2 ++ empty))
(eq.rec (eq.refl (rev lst2 ++ empty))
(mylist.rec
(eq.rec tru... |
43c4f5c7d3c1e62cf88f1f4df24bb43926c9c2b3 | ad0c7d243dc1bd563419e2767ed42fb323d7beea | /analysis/topology/continuity.lean | 184e2ab0504be3849c3fc8c719fb3d1a935f8f31 | [
"Apache-2.0"
] | permissive | sebzim4500/mathlib | e0b5a63b1655f910dee30badf09bd7e191d3cf30 | 6997cafbd3a7325af5cb318561768c316ceb7757 | refs/heads/master | 1,585,549,958,618 | 1,538,221,723,000 | 1,538,221,723,000 | 150,869,076 | 0 | 0 | Apache-2.0 | 1,538,229,323,000 | 1,538,229,323,000 | null | UTF-8 | Lean | false | false | 52,444 | 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
Continuous functions.
Parts of the formalization is based on the books:
N. Bourbaki: General Topology
I. M. James: Topologies and U... |
696a208b8d6677604e02bdc806bad121d712324e | 6e9cd8d58e550c481a3b45806bd34a3514c6b3e0 | /src/data/pnat/basic.lean | c8047021118d2834d89bc046da2311bd1ac0bcb5 | [
"Apache-2.0"
] | permissive | sflicht/mathlib | 220fd16e463928110e7b0a50bbed7b731979407f | 1b2048d7195314a7e34e06770948ee00f0ac3545 | refs/heads/master | 1,665,934,056,043 | 1,591,373,803,000 | 1,591,373,803,000 | 269,815,267 | 0 | 0 | Apache-2.0 | 1,591,402,068,000 | 1,591,402,067,000 | null | UTF-8 | Lean | false | false | 13,480 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro, Neil Strickland
-/
import data.nat.prime
/-- `ℕ+` is the type of positive natural numbers. It is defined as a subtype,
and the VM representation of `ℕ+` is the... |
a46f2d3e038e1140953366a593b1ff1000f44b5e | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/ring/pi.lean | 7b0ff31115171d9cabd259cb678e92d28a64cfde | [
"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 | 5,725 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot
-/
import tactic.pi_instances
import algebra.group.pi
import algebra.ring.basic
/-!
# Pi instances for ring
This file defines instances for ring, semiring an... |
187eb07efb4f05bfffbd312b802dc7659810a9db | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/algebra/group_action_hom.lean | a689d75d654baf5db6887190a5033432cc5937d2 | [
"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 | 10,470 | 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.group_ring_action
/-!
# Equivariant homomorphisms
## Main definitions
* `mul_action_hom M X Y`, the type of equivariant functions from `X` to `Y`, where `M` i... |
f057c0485bf3ac5a3a84a8b11656237e782cfd85 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/combinatorics/simple_graph/basic_auto.lean | 531ac05916a32eac5fafb9ae837bb33f1d9e63c5 | [] | 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 | 17,348 | lean | /-
Copyright (c) 2020 Aaron Anderson, Jalex Stark, Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Aaron Anderson, Jalex Stark, Kyle Miller, Alena Gusakov
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.fintype.basic
import... |
8e207d8691617bcf4aecf2acb0d9041b0e4d657a | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/category_theory/full_subcategory.lean | 13c62f3ce0eaccefb415bf243ce8352ab3b1c28a | [
"Apache-2.0"
] | permissive | ayush1801/mathlib | 78949b9f789f488148142221606bf15c02b960d2 | ce164e28f262acbb3de6281b3b03660a9f744e3c | refs/heads/master | 1,692,886,907,941 | 1,635,270,866,000 | 1,635,270,866,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,703 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Reid Barton
-/
import category_theory.fully_faithful
namespace category_theory
universes v u₁ u₂ -- morphism levels before object levels. See note [category_theory un... |
92cfe6363c5a4306a7f2457e844b6ac9abf5e9fc | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /tests/lean/slow/list_elab2.lean | 632e862b6620f68df3b399ee1127acf9908b41b9 | [
"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 | 6,584 | lean | ----------------------------------------------------------------------------------------------------
--- Copyright (c) 2014 Parikshit Khanna. All rights reserved.
--- Released under Apache 2.0 license as described in the file LICENSE.
--- Authors: Parikshit Khanna, Jeremy Avigad
----------------------------------------... |
00dabdb41d1d6fbe0c21c5c844c3a2d240b078ac | f7315930643edc12e76c229a742d5446dad77097 | /hott/types/pi.hlean | 3d69832e00ffac8ec9fd8139e6d247019ee849b5 | [
"Apache-2.0"
] | permissive | bmalehorn/lean | 8f77b762a76c59afff7b7403f9eb5fc2c3ce70c1 | 53653c352643751c4b62ff63ec5e555f11dae8eb | refs/heads/master | 1,610,945,684,489 | 1,429,681,220,000 | 1,429,681,449,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,406 | hlean | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: types.pi
Author: Floris van Doorn
Ported from Coq HoTT
Theorems about pi-types (dependent function spaces)
-/
import types.sigma
open eq equiv is_equiv funext
namespace pi
vari... |
93ce4a80a43678b51f659f0704219039f05e006c | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/ring_theory/ideal_operations.lean | 2922524c94f7f1ac200956fdf5df75f1a55aa311 | [
"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 | 24,790 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
More operations on modules and ideals.
-/
import ring_theory.ideals data.nat.choose order.zorn
import linear_algebra.tensor_product
import data.equiv.algebra
import ring_theory.... |
2e554eb789b044c8130d3abaa15fe9025231b933 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /test/solve_by_elim.lean | e738eb097828f415b5b13c7f783d0bd1724b4379 | [
"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 | 4,169 | 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.solve_by_elim
example {a b : Prop} (h₀ : a → b) (h₁ : a) : b :=
begin
apply_assumption,
apply_assumption,
end
example {X : Type} (x : X)... |
d234863b82ac0a787bda0c8c662d7e5aec0577fe | d5bef83c55d40cb88f9a01b755c882a93348a847 | /tests/lean/hole_issue2.lean | 3769da03823ad00624985a51b3ba933e185133bb | [
"Apache-2.0"
] | permissive | urkud/lean | 587d78216e1f0c7f651566e9e92cf8ade285d58d | 3526539070ea6268df5dd373deeb3ac8b9621952 | refs/heads/master | 1,660,171,634,921 | 1,657,873,466,000 | 1,657,873,466,000 | 249,789,456 | 0 | 0 | Apache-2.0 | 1,585,075,263,000 | 1,585,075,263,000 | null | UTF-8 | Lean | false | false | 1,821 | lean | constant bag_setoid : ∀ A, setoid (list A)
attribute [instance] bag_setoid
definition bag (A : Type) : Type :=
quotient (bag_setoid A)
constant subcount : ∀ {A}, list A → list A → bool
constant list.count : ∀ {A}, A → list A → nat
constant all_of_subcount_eq_tt : ∀ {A} {l₁ l₂ : list A}, subcount l₁ l₂ = tt → ∀ a, li... |
6055104b52b26b04b37026191be49b3c5a3e3682 | bb31430994044506fa42fd667e2d556327e18dfe | /src/algebra/big_operators/finprod.lean | 1f10a690f35a133f0143d031ded7d0aaf5491ddd | [
"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 | 47,691 | lean | /-
Copyright (c) 2020 Kexing Ying and Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying, Kevin Buzzard, Yury Kudryashov
-/
import algebra.big_operators.order
import algebra.indicator_function
/-!
# Finite products and sums over types and sets
... |
220e2ffcf40183ba1e12e71cdd7555eaed2daa2d | 3ed5a65c1ab3ce5d1a094edce8fa3287980f197b | /src/herstein/ex2_3/Q_02.lean | 8064c5218677091f65bcf1a5a456cee80e269d47 | [] | no_license | group-study-group/herstein | 35d32e77158efa2cc303c84e1ee5e3bc80831137 | f5a1a72eb56fa19c19ece0cb3ab6cf7ffd161f66 | refs/heads/master | 1,586,202,191,519 | 1,548,969,759,000 | 1,548,969,759,000 | 157,746,953 | 0 | 0 | null | 1,542,412,901,000 | 1,542,302,366,000 | Lean | UTF-8 | Lean | false | false | 769 | lean | import algebra.group algebra.group_power
variable A: Type*
theorem Q_02 (a b: A) [comm_group A]:
∀ n: ℕ, (a * b) ^ n = a ^ n * b ^ n
| 0 :=
calc (a * b) ^ 0
= 1 : by rw pow_zero
... = 1 * 1 : (mul_one 1).symm
... = (a ^ 0) * (b ^ 0) : by rw [pow_zero, pow_zero]
| (k + 1) :=
calc (a... |
d6656ce2798585468075ec03ba728fa844533b08 | d0f9af2b0ace5ce352570d61b09019c8ef4a3b96 | /hw9/induction.lean | d95482fee841baa3958fa60b6c0aceff888f4b08 | [] | no_license | jngo13/Discrete-Mathematics | 8671540ef2da7c75915d32332dd20c02f001474e | bf674a866e61f60e6e6d128df85fa73819091787 | refs/heads/master | 1,675,615,657,924 | 1,609,142,011,000 | 1,609,142,011,000 | 267,190,341 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,453 | lean | /-
Proof strategies.
- direct proof: use established facts
- by negation: to prove ¬ P, assume P;
show that this yields a contradiction,
from which a proof of false can then
be derived. This shows P → false, and
that is the definition of ¬ P.
- by contradiction : to prove P, assume
¬ P and show that t... |
25f2efcc666ee306997bd1eaa5cfa5b1a87ba7eb | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/algebraic_geometry/stalks.lean | 6c9e49f6a2a82233a1645dcc4b5e61df8574c93b | [
"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 | 2,094 | 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 algebraic_geometry.presheafed_space
import topology.sheaves.stalks
/-!
# Stalks for presheaved spaces
This file lifts constructions of stalks and pushforward... |
42bb01eeda530d804b05fcfb469402cff5697f6e | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/analysis/calculus/lhopital.lean | 7291cda2f3529d9bd4bcfeddbbc8363909bf2897 | [
"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 | 25,020 | lean | /-
Copyright (c) 2020 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
import analysis.calculus.mean_value
/-!
# L'Hôpital's rule for 0/0 indeterminate forms
In this file, we prove several forms of "L'Hopital's rule" for computing ... |
eb811efee6b7e57378d0a71759254e3f04a253f3 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/sum/interval.lean | e831e4564adfcb7879797ff23b01771a1dbebefe | [
"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 | 14,892 | lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import data.finset.sum
import data.sum.order
import order.locally_finite
/-!
# Finite intervals in a disjoint union
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any cha... |
3b93172f409fe950beb006e2efcc58561eebaaf9 | 0ce12e02063e04aa70b96c893caa58114f7abc87 | /leancrawler/crawler.lean | 0b8952ee3e5d81d82791d84a25add15e8a95b085 | [
"Apache-2.0"
] | permissive | leanprover-community/leancrawler | 9d027f9e06327a024aa6130d451cbc34e4e6dae1 | 951527886bcf22a1dcb823ce6b2d84f7f66ba25b | refs/heads/master | 1,664,420,201,941 | 1,663,091,473,000 | 1,663,096,065,000 | 146,176,705 | 16 | 4 | Apache-2.0 | 1,663,096,066,000 | 1,535,284,760,000 | Python | UTF-8 | Lean | false | false | 6,384 | lean |
import meta.expr
import system.io
open tactic declaration environment io io.fs (put_str_ln close)
-- The next instance is there to prevent PyYAML trying to be too smart
meta def my_name_to_string : has_to_string name :=
⟨λ n, "\"" ++ to_string n ++ "\""⟩
local attribute [instance] my_name_to_string
meta def expr.g... |
f8f77e26f71a61b98a21ff2105cc223bcebbf9ef | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/lie/quotient.lean | ad058650538188375b94d1fce07b2790a37fe64d | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 7,625 | 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.submodule
import algebra.lie.of_associative
import linear_algebra.isomorphisms
/-!
# Quotients of Lie algebras and Lie modules
Given a Lie submodule of... |
0da331b59da15d6168c96469bf3e80b33a77c536 | 38ee9024fb5974f555fb578fcf5a5a7b71e669b5 | /Mathlib/Init/Data/Nat/Lemmas.lean | 8c30b38d989b4e240dd92f192858c660b6fcc327 | [
"Apache-2.0"
] | permissive | denayd/mathlib4 | 750e0dcd106554640a1ac701e51517501a574715 | 7f40a5c514066801ab3c6d431e9f405baa9b9c58 | refs/heads/master | 1,693,743,991,894 | 1,636,618,048,000 | 1,636,618,048,000 | 373,926,241 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 37,217 | 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.Init.Data.Nat.Basic
import Mathlib.Init.Algebra.Functions
universe u
namespace Nat
lemma succ_ne_self : ∀ n : ℕ, succ n ≠ n... |
9551198bc87ed384e58aa528f9645a7bf28bcaf9 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/limits/lattice.lean | 96a6dced81d5e10698d79cfc0cca7e953fa47e9d | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,775 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.limits.shapes.finite_limits
import Mathlib.order.complete_lattice
import Ma... |
39be58b85c0775a1ee987f8eacc25029f26ded7b | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /stage0/src/Lean/Compiler/LCNF/Simp/SimpM.lean | 57324d00bf7e8c26605d1f4f464fc435cc5e2f21 | [
"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 | 11,830 | 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.ImplementedByAttr
import Lean.Compiler.LCNF.Renaming
import Lean.Compiler.LCNF.ElimDead
import Lean.Compiler.LCNF.AlphaEqv
import Lean.... |
f11d6db98b7e2caf7ed5bf3109db592b18847cd0 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/ring/fin.lean | c465c67f7a78e13d4ccf4511b7e8bc080470bcd8 | [
"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 | 762 | 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 logic.equiv.fin
import algebra.ring.equiv
import algebra.group.prod
/-!
# Rings and `fin`
This file collects some basic results involving rings and the `fin` type
... |
c7bac4458e26938527297d08d0f660c241b7a33a | a46270e2f76a375564f3b3e9c1bf7b635edc1f2c | /5.8.2.lean | b6cd689b7804fb9a1013df81e7c500efe573e84b | [
"CC0-1.0"
] | permissive | wudcscheme/lean-exercise | 88ea2506714eac343de2a294d1132ee8ee6d3a20 | 5b23b9be3d361fff5e981d5be3a0a1175504b9f6 | refs/heads/master | 1,678,958,930,293 | 1,583,197,205,000 | 1,583,197,205,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 171 | lean | example (p q r : Prop) (hp : p) :
(p ∨ q ∨ r) ∧ (q ∨ p ∨ r) ∧ (q ∨ r ∨ p) :=
by split; try{split}; repeat {{left, assumption} <|> right <|> assumption}
|
180d53eaf1b46247fac8c5c7765a0c73ec95d98e | 4f065978c49388d188224610d9984673079f7d91 | /localization_alt.lean | c448bcf7cdcb802626726deb0a88310c87c3b1b0 | [] | no_license | kckennylau/Lean | b323103f52706304907adcfaee6f5cb8095d4a33 | 907d0a4d2bd8f23785abd6142ad53d308c54fdcb | refs/heads/master | 1,624,623,720,653 | 1,563,901,820,000 | 1,563,901,820,000 | 109,506,702 | 3 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 9,294 | lean | import algebra.ring group_theory.submonoid ring_theory.ideal_operations linear_algebra.basic
namespace localization_alt
universes u v w
variables {A : Type u} {B : Type v} {C : Type w}
variables [comm_ring A] [comm_ring B] [comm_ring C]
variables (S : set A) [is_submonoid S] (f : A → B) [is_ring_hom f]
/- This is e... |
f4974b06fd5011ace7532d36f274e8821ee25d25 | 3dd1b66af77106badae6edb1c4dea91a146ead30 | /tests/lean/run/tactic17.lean | a34a03069c783de7573ead20321d4803e48b99f1 | [
"Apache-2.0"
] | permissive | silky/lean | 79c20c15c93feef47bb659a2cc139b26f3614642 | df8b88dca2f8da1a422cb618cd476ef5be730546 | refs/heads/master | 1,610,737,587,697 | 1,406,574,534,000 | 1,406,574,534,000 | 22,362,176 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 228 | lean | import standard
using tactic
variable A : Type.{1}
variable f : A → A → A
theorem tst {a b c : A} (H1 : a = b) (H2 : b = c) : f a b = f b c
:= by apply (@congr A A (f a) (f b));
apply (congr2 f);
!assumption
|
864c8dbda39554fac02e2892c89e3cc0fe6cc7f2 | e030b0259b777fedcdf73dd966f3f1556d392178 | /library/init/algebra/functions.lean | 9c4fb5f616e768ed81d41e2e74b4387e1be3adad | [
"Apache-2.0"
] | permissive | fgdorais/lean | 17b46a095b70b21fa0790ce74876658dc5faca06 | c3b7c54d7cca7aaa25328f0a5660b6b75fe26055 | refs/heads/master | 1,611,523,590,686 | 1,484,412,902,000 | 1,484,412,902,000 | 38,489,734 | 0 | 0 | null | 1,435,923,380,000 | 1,435,923,379,000 | null | UTF-8 | Lean | false | false | 17,261 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
-/
prelude
import init.algebra.ordered_field
universe variables u
definition min {α : Type u} [decidable_linear_order α] (a b : α) : α := if a... |
16d7397215f4f92df981f5c03f2856ee45166cc0 | e151e9053bfd6d71740066474fc500a087837323 | /src/hott/init/equiv.lean | 08b269a3a897df0a905a67809dd4518439d32e6c | [
"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 | 20,136 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad, Jakob von Raumer, Floris van Doorn
Ported from Coq HoTT
-/
import .path .meta.rewrite
universes u v w
hott_theory
namespace hott
open function
/- Equivalences ... |
f4f75f389afa88cc96992a95ff31f4652608fb52 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/concrete_category/bundled_auto.lean | 0c0b518d643f68531b99ace7c83bcd141d19c41a | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,571 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Johannes Hölzl, Reid Barton, Sean Leather
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.category.default
import Mathlib.... |
0ab70adbdf6c8c4bc74e10eb5eb8f5c5a4c4bef9 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/ring_theory/polynomial/chebyshev/basic_auto.lean | cb9b492b89fd4817456014061f06efc8dff78631 | [] | 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 | 3,345 | 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.ring_theory.polynomial.chebyshev.defs
import Mathlib.analysis.special_functions.trigonometr... |
9eb8c8d9e33a39cd7d7d52dc291d8bb05ef5e240 | 02fbe05a45fda5abde7583464416db4366eedfbf | /tests/lean/run/term_app2.lean | 506df05a977762cfc9136099a3e698bb3518601d | [
"Apache-2.0"
] | permissive | jasonrute/lean | cc12807e11f9ac6b01b8951a8bfb9c2eb35a0154 | 4be962c167ca442a0ec5e84472d7ff9f5302788f | refs/heads/master | 1,672,036,664,637 | 1,601,642,826,000 | 1,601,642,826,000 | 260,777,966 | 0 | 0 | Apache-2.0 | 1,588,454,819,000 | 1,588,454,818,000 | null | UTF-8 | Lean | false | false | 2,267 | lean | local attribute [simp] nat.add_comm nat.add_left_comm
lemma nat.lt_add_of_lt {a b c : nat} : a < b → a < c + b :=
begin
intro h,
have aux₁ := nat.le_add_right b c,
have aux₂ := lt_of_lt_of_le h aux₁,
rwa [nat.add_comm] at aux₂
end
lemma nat.lt_one_add_of_lt {a b : nat} : a < b → a < 1 + b :=
begin
intro h,
... |
a6e9381b60f470403e633eab2de80673fcead387 | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /stage0/src/Lean/Parser/Basic.lean | 6683bcb56848e51988fe58c231b37b59fe745bf4 | [
"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 | 76,164 | 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
-/
/-!
# Basic Lean parser infrastructure
The Lean parser was developed with the following primary goals in mind:
* flexibility: Lean's g... |
4a9821eeeeda6705bb25f91f43475e90c097a19b | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/category_theory/monoidal/natural_transformation.lean | 1b9787e64a5b6974ad5a15a64babaeb15a1220bb | [
"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 | 5,036 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.monoidal.functor
import category_theory.full_subcategory
/-!
# Monoidal natural transformations
Natural transformations between (lax) monoida... |
45ef9086f177127b122e015f38b39abde64a2a5e | b3fced0f3ff82d577384fe81653e47df68bb2fa1 | /src/algebraic_geometry/presheafed_space.lean | ecde18812d14440a9f44e7fdb28eae90b6f0683f | [
"Apache-2.0"
] | permissive | ratmice/mathlib | 93b251ef5df08b6fd55074650ff47fdcc41a4c75 | 3a948a6a4cd5968d60e15ed914b1ad2f4423af8d | refs/heads/master | 1,599,240,104,318 | 1,572,981,183,000 | 1,572,981,183,000 | 219,830,178 | 0 | 0 | Apache-2.0 | 1,572,980,897,000 | 1,572,980,896,000 | null | UTF-8 | Lean | false | false | 7,611 | 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 topology.sheaves.presheaf
/-!
# Presheafed spaces
Introduces the category of topological spaces equipped with a presheaf (taking values in an
arbitrary targe... |
7bb86a8cce469be52f0b0d2d6c7efe4f9e826cf8 | 500f65bb93c499cd35c3254d894d762208cae042 | /src/tactic/basic.lean | 0d1ab73395a61838cb30cb73b2df70364096fe17 | [
"Apache-2.0"
] | permissive | PatrickMassot/mathlib | c39dc0ff18bbde42f1c93a1642f6e429adad538c | 45df75b3c9da159fe3192fa7f769dfbec0bd6bda | refs/heads/master | 1,623,168,646,390 | 1,566,940,765,000 | 1,566,940,765,000 | 115,220,590 | 0 | 1 | null | 1,514,061,524,000 | 1,514,061,524,000 | null | UTF-8 | Lean | false | false | 392 | lean | import
tactic.alias
tactic.cache
tactic.converter.interactive
tactic.core
tactic.doc_blame
tactic.ext
tactic.generalize_proofs
tactic.interactive
tactic.library_search
tactic.lift
tactic.mk_iff_of_inductive_prop
tactic.push_neg
tactic.rcases
tactic.replacer
tactic.restate_axiom
tactic.re... |
428cad15fb9f19f3185ac20894d782daaf1588bd | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/linear_algebra/tensor_product_basis.lean | b25b27a330581e4acb093ceb55ace53d269858ff | [
"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 | 1,493 | lean | /-
Copyright (c) 2021 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer
-/
import linear_algebra.direct_sum.finsupp
import linear_algebra.finsupp_vector_space
/-!
# Bases and dimensionality of tensor products of modules
These can not g... |
f38f716f7c1c6b5f3648ae5020d320e359568f92 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /03_Propositions_and_Proofs.org.27.lean | e4cc920073490d65c0e7c11c0b34b1de4dcd3561 | [] | 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 | 118 | lean | /- page 41 -/
import standard
variables p q : Prop
-- BEGIN
example (Hp : p) (Hnp : ¬p) : q := absurd Hp Hnp
-- END
|
11aef50c1ca47f0e59063d6233b75b9ee387b9de | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/topology/metric_space/baire.lean | 6b9127f042a52650caabf46ffc0c3ee41088676d | [
"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 | 14,045 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import analysis.specific_limits
import order.filter.countable_Inter
import topology.G_delta
/-!
# Baire theorem
In a complete metric space, a countable inters... |
ce286a232548c5729263d790bbab6e6512e3cedb | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/equiv/ring_aut.lean | 6abad08abb8fff4ec7f8aaf1a4a5657f030d2b2f | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,199 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Callum Sutton, Yury Kudryashov
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.equiv.ring
import Mathlib.data.equiv.mul_add_aut
impor... |
8c92674371e617c7ee07d925b8b8d408d5a11d0d | 367134ba5a65885e863bdc4507601606690974c1 | /src/order/filter/interval.lean | 73b46af8609a88582f6a846fbe65490a7e3a6c8f | [
"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 | 9,978 | lean | /-
Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Yury G. Kudryashov
-/
import data.set.intervals.ord_connected
import order.filter.lift
import order.filter.at_top_bot
/-!
# Convergence of intervals
If both `a` and `b` tend to so... |
882fe12865ee337ebff3364d674a624be0ebfa3b | 9dd3f3912f7321eb58ee9aa8f21778ad6221f87c | /library/init/meta/lean/parser.lean | d18526a29c1501fac14aa34aeecfb23ca9e992f6 | [
"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 | 2,243 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
-/
prelude
import init.data.option.basic init.category.monad init.category.alternative
import init.meta.pexpr init.meta.interaction_monad
namespace lean
-- T... |
a1d609871ef0bfefdc5363bdff4633b8e7bcc151 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/bornology/constructions.lean | 3b9212fa47b0fddc455aa586f1e4f80109576d87 | [
"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 | 6,245 | lean | /-
Copyright (c) 2022 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import topology.bornology.basic
/-!
# Bornology structure on products and subtypes
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file req... |
02a70a005c046f8905c379f8063814a439e65b86 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/algebra/homology/differential_object.lean | e2d2410ae4fd722b6fdf0822268d16aa671fb23b | [
"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 | 4,964 | 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 algebra.homology.homological_complex
import category_theory.differential_object
/-!
# Homological complexes are differential graded objects.
We verify that a... |
b1daa107a4bb8603fd8c201657b04a8c93256145 | c3de33d4701e6113627153fe1103b255e752ed7d | /algebra/lattice/zorn.lean | e3deb8a71796560d452a37bc4e2f326247965cfc | [] | no_license | jroesch/library_dev | 77d2b246ff47ab05d55cb9706a37d3de97038388 | 4faa0a45c6aa7eee6e661113c2072b8840bff79b | refs/heads/master | 1,611,281,606,352 | 1,495,661,644,000 | 1,495,661,644,000 | 92,340,430 | 0 | 0 | null | 1,495,663,344,000 | 1,495,663,344,000 | null | UTF-8 | Lean | false | false | 9,478 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Zorn's lemmas.
Ported from Isabelle/HOL (written by Jacques D. Fleuriot, Tobias Nipkow, and Christian Sternagel).
-/
import ...data.set
noncomputable theory
open set ... |
f82cf32bc960074e64405d61187a68f898da1870 | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /tests/lean/run/level.lean | d246389ce9e35b1e9b0c814a88da8a43fb958eeb | [
"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 | 274 | lean | import Lean.Level
open Lean
#eval levelZero == levelZero
#eval levelZero == mkLevelSucc levelZero
#eval mkLevelMax (mkLevelSucc levelZero) levelZero == mkLevelSucc levelZero
#eval mkLevelMax (mkLevelSucc levelZero) levelZero == mkLevelMax (mkLevelSucc levelZero) levelZero
|
d057c34625bcf4539b1eefda5ca97ebf927f00f1 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/topology/algebra/continuous_functions.lean | ae5ae5e37b43f14cf628f77d9b7ffd64a8d92140 | [
"Apache-2.0"
] | permissive | rmitta/mathlib | 8d90aee30b4db2b013e01f62c33f297d7e64a43d | 883d974b608845bad30ae19e27e33c285200bf84 | refs/heads/master | 1,585,776,832,544 | 1,576,874,096,000 | 1,576,874,096,000 | 153,663,165 | 0 | 2 | Apache-2.0 | 1,544,806,490,000 | 1,539,884,365,000 | Lean | UTF-8 | Lean | false | false | 2,285 | 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 topology.basic
import topology.algebra.ring
import ring_theory.subring
universes u v
local attribute [elab_simple] continuous.comp
@[to_additive continuous_... |
e3e3988bead7a82378528ea282f35cf270ed7bcd | 1b8f093752ba748c5ca0083afef2959aaa7dace5 | /src/category_theory/Grothendieck_topology.lean | aa001f4f1219fee77b88537b1926cb5644a18523 | [] | no_license | khoek/lean-category-theory | 7ec4cda9cc64a5a4ffeb84712ac7d020dbbba386 | 63dcb598e9270a3e8b56d1769eb4f825a177cd95 | refs/heads/master | 1,585,251,725,759 | 1,539,344,445,000 | 1,539,344,445,000 | 145,281,070 | 0 | 0 | null | 1,534,662,376,000 | 1,534,662,376,000 | null | UTF-8 | Lean | false | false | 1,696 | lean | import category_theory.limits
import category_theory.over
open category_theory
open category_theory.limits
universes u₁ v₁
variables {C : Type u₁} [𝒞 : category.{u₁ v₁} C]
include 𝒞
variables {X Y : C}
structure cover (X : C) :=
(I : Type)
(U : I → C)
(π : Π i : I, U i ⟶ X)
def pullback_cover [has_pullbacks.{u₁... |
6cd43187f4dc7469d622a6abadd4d75ff306e574 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/linear_algebra/pi.lean | d6bb124ef56df74e8a20c90dc873183f1a9eb89c | [
"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 | 13,807 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov, Eric Wieser
-/
import linear_algebra.basic
/-!
# Pi types of modules
This file defines constructors for linear maps wh... |
c8aae2fad414682c84762696a199f680c34a7d09 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/topology/order.lean | a1377c4cfd675300af195cb2f4257f95a5a1df58 | [
"Apache-2.0"
] | permissive | ramonfmir/mathlib | c5dc8b33155473fab97c38bd3aa6723dc289beaa | 14c52e990c17f5a00c0cc9e09847af16fabbed25 | refs/heads/master | 1,661,979,343,526 | 1,660,830,384,000 | 1,660,830,384,000 | 182,072,989 | 0 | 0 | null | 1,555,585,876,000 | 1,555,585,876,000 | null | UTF-8 | Lean | false | false | 37,904 | 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
-/
import topology.tactic
/-!
# Ordering on topologies and (co)induced topologies
Topologies on a fixed type `α` are ordered, by reverse inclusion.
Tha... |
15107c0edf1edfeca7d975773a50bf82b3bc72f2 | d744d97b07fc1e61b0ebea192b2d624125898128 | /src/nat_util.lean | 3f150a60514e543a370d55bf84535afce3ffa83b | [
"MIT"
] | permissive | parkersullivan/leanstuff | 019c757848dd8f5db185e6973969141aee6fef7c | 3da132c44d365ecd933de64fa04ba66b9e620683 | refs/heads/master | 1,599,036,040,845 | 1,573,316,625,000 | 1,573,316,625,000 | 219,181,711 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 171 | lean | def ltb : ℕ → ℕ → bool
| 0 0 := ff
| 0 (m + 1) := tt
| (n + 1) 0 := ff
| (n + 1) (m + 1) := ltb n m
def my_max (n m : ℕ) : ℕ :=
if (ltb n m)
then m
else n
|
f9c4328370c5ea51e826331fa33c9d859cd818d0 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/special_functions/pow/real.lean | 26582880834d2d4df6fca940d3d6d3e1e4a0414e | [
"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 | 28,420 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Sébastien Gouëzel,
Rémy Degenne, David Loeffler
-/
import analysis.special_functions.pow.complex
/-! # Power function on ... |
46d46c235dab3b6b6e693b6c8e0f4174d96cfd47 | 7da5ceac20aaab989eeb795a4be9639982e7b35a | /src/group_theory/suzuki.lean | 6a4e78563180b49669185401970e91ef3916deb6 | [
"MIT"
] | permissive | formalabstracts/formalabstracts | 46c2f1b3a172e62ca6ffeb46fbbdf1705718af49 | b0173da1af45421239d44492eeecd54bf65ee0f6 | refs/heads/master | 1,606,896,370,374 | 1,572,988,776,000 | 1,572,988,776,000 | 96,763,004 | 165 | 28 | null | 1,555,709,319,000 | 1,499,680,948,000 | Lean | UTF-8 | Lean | false | false | 2,256 | lean | import ..data.dvector .presentation .monster
open category_theory (mk_ob)
local notation `⟪`:50 a `⟫`:50 := free_group.of a
local notation h :: t := dvector.cons h t
local notation `[` l:(foldr `, ` (h t, dvector.cons h t) dvector.nil `]`) := l
/- From the corresponding entry in the atlas (p. 128) Suz . 2 is a quoti... |
b7465bc23135eea9f1e538ab3d4e423d41daf607 | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/multiset/lattice.lean | 113a5abaf9a50b7a00cc90f87de7c1004f4f7671 | [
"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 | 3,609 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
-/
import data.multiset.finset_ops
import data.multiset.fold
/-!
# Lattice operations on multisets
-/
namespace multiset
variables {α : Type*}
/-! ### sup -/
section s... |
37f50d83c82d1e8fc12f6f1752ac91c677346c79 | a7eef317ddec01b9fc6cfbb876fe7ac00f205ac7 | /src/algebra/ordered_group.lean | 912ceb8eaf3dfeab7a4f76e95ea1829c98fabb11 | [
"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 | 65,976 | 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 algebra.group.units
import algebra.group.with_one
import algebra.group.type_tags
import order.bounded_lattice
... |
df8ef690ac354a8846af956616249e59c6cd0215 | bb31430994044506fa42fd667e2d556327e18dfe | /src/group_theory/perm/cycle/basic.lean | caa1530b9dcef9ee9d60f576dee0fb901989d2a8 | [
"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 | 68,347 | lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Yaël Dillies
-/
import data.finset.noncomm_prod
import data.fintype.perm
import data.int.modeq
import group_theory.perm.sign
import logic.equiv.fintype
/-!
# Cyclic permuta... |
0d00fd7ca744a4d3c094d25b6413dcdf67e136a6 | 43390109ab88557e6090f3245c47479c123ee500 | /src/M1F/problem_bank/0505/Q0505.lean | 50e517141aee803828eee845730d924da6583943 | [
"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 | 201 | lean | import algebra.group_power tactic.norm_num algebra.big_operators
theorem Q5 : (¬ (∃ a b c : ℕ, 6*a+9*b+20*c = 43))
∧ ∀ m, m ≥ 44 → ∃ a b c : ℕ, 6*a+9*b+20*c = m := sorry
|
2c9c2173ff23dffbe146fbdb0eb52bbcde8b601c | 86f6f4f8d827a196a32bfc646234b73328aeb306 | /examples/basics/unnamed_1388.lean | a24924ce73600204197e3d3077ba55734c858f6d | [] | no_license | jamescheuk91/mathematics_in_lean | 09f1f87d2b0dce53464ff0cbe592c568ff59cf5e | 4452499264e2975bca2f42565c0925506ba5dda3 | refs/heads/master | 1,679,716,410,967 | 1,613,957,947,000 | 1,613,957,947,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 271 | lean | import data.real.basic tactic
variables a b : ℝ
-- BEGIN
example : 2*a*b ≤ a^2 + b^2 :=
begin
have h : 0 ≤ a^2 - 2*a*b + b^2,
calc
a^2 - 2*a*b + b^2 = (a - b)^2 : by ring
... ≥ 0 : by apply pow_two_nonneg,
linarith
end
-- END |
b8c289add948e2d77580a3d219790bcbab6ab85d | a7602958ab456501ff85db8cf5553f7bcab201d7 | /Notes/Logic_and_Proof/Chapter4/4.40.lean | f690c40fea2826cc718b6512254fda6523695cf2 | [] | no_license | enlauren/math-logic | 081e2e737c8afb28dbb337968df95ead47321ba0 | 086b6935543d1841f1db92d0e49add1124054c37 | refs/heads/master | 1,594,506,621,950 | 1,558,634,976,000 | 1,558,634,976,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 445 | lean | -- 4.40 Forward Reasoning
-- Lean provides the "have" command for forward reasoning.
variables A B C : Prop
variable h1: A -> B
variable h2: B -> C
-- Traditionally we might prove A -> C, as:
example: A -> C :=
assume h, -- Implicitly, |h| is a proof of |A|.
show C, from h2 (h1 h)
-- However we can use "have", like... |
dba6e8c670922790751e2da97f24c2b89073f74c | 09b3e1beaeff2641ac75019c9f735d79d508071d | /Mathlib/Set.lean | 913835940a256bd7971905b962d2b842a1aeab50 | [
"Apache-2.0"
] | permissive | abentkamp/mathlib4 | b819079cc46426b3c5c77413504b07541afacc19 | f8294a67548f8f3d1f5913677b070a2ef5bcf120 | refs/heads/master | 1,685,309,252,764 | 1,623,232,534,000 | 1,623,232,534,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,339 | 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
-/
import Mathlib.Mem
/-!
# Sets
This file sets up the theory of sets whose elements have a given type.
## Main definitions
Given a type `X` and a predicat... |
82871588c561028e34f5a6f29e10a61840cc1522 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/measure_theory/measure/outer_measure.lean | 39a686268f7f6646a422d0a55f98fdccc36e048a | [
"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 | 61,699 | 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
-/
import analysis.specific_limits
import measure_theory.pi_system
import data.matrix.notation
import topology.algebra.infinite_sum
/-!
# Outer Measures... |
38f3c44c8860074ab7c607c518343619335a3ed6 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/category_theory/preadditive/functor_category.lean | 1d6dc357ec7db6be3fcbec82b228b04b5e323de4 | [
"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 | 2,666 | 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 category_theory.preadditive.default
/-!
# Preadditive structure on functor categories
If `C` and `D` are categories and `D` is preadditive,
then `C ⥤ D` is ... |
eab9ffc244d016fccdb2c152045ac8c3ef660fa9 | 5749d8999a76f3a8fddceca1f6941981e33aaa96 | /src/order/bounded_lattice.lean | 7216fd293c430a86db018d9c15ff9832edbb36a7 | [
"Apache-2.0"
] | permissive | jdsalchow/mathlib | 13ab43ef0d0515a17e550b16d09bd14b76125276 | 497e692b946d93906900bb33a51fd243e7649406 | refs/heads/master | 1,585,819,143,348 | 1,580,072,892,000 | 1,580,072,892,000 | 154,287,128 | 0 | 0 | Apache-2.0 | 1,540,281,610,000 | 1,540,281,609,000 | null | UTF-8 | Lean | false | false | 29,628 | 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 bounded lattice type class hierarchy.
Includes the Prop and fun instances.
-/
import order.lattice data.option.basic
tactic.pi_instances
set_option ol... |
e34e9ab6f1128c0add6c31f93cde9f1d1eaf4ac3 | 137c667471a40116a7afd7261f030b30180468c2 | /src/algebra/big_operators/finprod.lean | be06afa68be1f30ab01b72ac228cc831ae343bf6 | [
"Apache-2.0"
] | permissive | bragadeesh153/mathlib | 46bf814cfb1eecb34b5d1549b9117dc60f657792 | b577bb2cd1f96eb47031878256856020b76f73cd | refs/heads/master | 1,687,435,188,334 | 1,626,384,207,000 | 1,626,384,207,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 36,792 | lean | /-
Copyright (c) 2020 Kexing Ying and Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying, Kevin Buzzard, Yury Kudryashov
-/
import data.set.finite
import data.set.disjointed
import algebra.big_operators
import algebra.indicator_function
/-!
# F... |
6a52e34cfe75ff70717234e8728eda7f51686949 | ff5230333a701471f46c57e8c115a073ebaaa448 | /tests/lean/run/injection_ginductive.lean | 38f2f8edc5ce64b79d4b915c8a85dcf1986c9625 | [
"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 | 402 | lean | inductive term
| const (n : string) : term
| app (fn : string) (args : list term) : term
constant p : Prop → Prop
axiom p_ax : ∀ x, p x = x
example (f₁ f₂ : string) (as₁ as₂ : list term) (h : term.app f₁ as₁ = term.app f₂ as₂) : p (as₁ = as₂) :=
begin
injection h,
trace_state,
guard_hyp h_1 := f₁ = f₂,
guard_... |
2ef019b015e7fa38133483d083d10b212909f0da | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /src/Lean/Elab/MacroRules.lean | 30110f74d68065a62ef90725d325407b48504099 | [
"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 | 3,340 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Elab.Syntax
import Lean.Elab.AuxDef
namespace Lean.Elab.Command
open Lean.Syntax
open Lean.Parser.Term hiding macroArg
open Lean.Parser.Command... |
515c6eadc56af01d156e89c178dbe11294681b12 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/run/ctorAutoParams.lean | 5207e4c089fa9add68d16d0e64c2ce21306918c9 | [
"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 | 1,526 | lean | structure State -- TODO
structure Expr -- TODO
def eval : State → Expr → Bool :=
fun _ _ => true
inductive Command where
| skip
| cond : Expr → Command → Command → Command
| while : Expr → Command → Command
| seq : Command → Command → Command
open Command
infix:10 ";;" => Command.seq
inductive Bigste... |
f3babac97c6b8859207899ce2aa8c4f4ac435768 | ea5678cc400c34ff95b661fa26d15024e27ea8cd | /presburger.lean | 65f38f563ff8c364734eb31d318196c4af1764da | [] | no_license | ChrisHughes24/leanstuff | dca0b5349c3ed893e8792ffbd98cbcadaff20411 | 9efa85f72efaccd1d540385952a6acc18fce8687 | refs/heads/master | 1,654,883,241,759 | 1,652,873,885,000 | 1,652,873,885,000 | 134,599,537 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 382 | lean | import data.set.basic
inductive presburger_equation : Type
|
inductive presburger : Π n, (set (fin n → ℕ)) → Prop
| empty (n : ℕ) : presburger n ∅
| union (n : ℕ) (s t : set (fin n → ℕ)) : presburger n s →
presburger n t → presburger n (s ∪ t)
| inter (n : ℕ) (s t : set (fin n → ℕ)) : presburger n s →
presburger... |
8983422e6d337ef7c502508088f7b88e90c3f591 | 367134ba5a65885e863bdc4507601606690974c1 | /src/combinatorics/hall.lean | c71809733c1d4b93859945f009931fab6e53f4b2 | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 14,769 | lean | /-
Copyright (c) 2021 Alena Gusakov, Bhavik Mehta, Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Alena Gusakov, Bhavik Mehta, Kyle Miller
-/
import data.fintype.basic
import data.rel
import data.set.finite
/-!
# Hall's Marriage Theorem
Given a list of fi... |
cb6bcaf7a8bdb0185c3533944a2b8be7f2be3f86 | f7c63613a4933f66368ef2802a50c417a46cddfc | /tests/lean/derive.lean | ff8c8dd59e11ea335d027b7e94c1c0dfbcfceae5 | [
"Apache-2.0"
] | permissive | avigad/lean | 28cef71cd8c4eae53f342c87f81ca78d7cc75874 | 5410178203ab5ae854b5804586ace074ffd63aae | refs/heads/master | 1,608,801,379,340 | 1,504,894,459,000 | 1,505,174,163,000 | 22,361,408 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 193 | lean | @[derive [decidable_eq, inhabited, has_sizeof]]
inductive foo (α β : Type*)
| bar : ℕ → foo
| baz : foo → α → foo
#check foo.decidable_eq
#check foo.inhabited
#check foo.has_sizeof
|
9dd58f15a8a878281295c2b99117a9f76a774925 | 618003631150032a5676f229d13a079ac875ff77 | /src/data/monoid_algebra.lean | 5f29eacb63bb392d50b664a0b2e36bb6f1254736 | [
"Apache-2.0"
] | permissive | awainverse/mathlib | 939b68c8486df66cfda64d327ad3d9165248c777 | ea76bd8f3ca0a8bf0a166a06a475b10663dec44a | refs/heads/master | 1,659,592,962,036 | 1,590,987,592,000 | 1,590,987,592,000 | 268,436,019 | 1 | 0 | Apache-2.0 | 1,590,990,500,000 | 1,590,990,500,000 | null | UTF-8 | Lean | false | false | 23,780 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury G. Kudryashov, Scott Morrison
-/
import data.finsupp
import ring_theory.algebra
/-!
# Monoid algebras
When the domain of a `finsupp` has a multiplicative or addi... |
8a77d7f0476bc2732d2fc499ef39ad1bd2b6349f | d1a52c3f208fa42c41df8278c3d280f075eb020c | /src/Lean/Elab/DeclarationRange.lean | 8d11137fd89fcfd31b9885e829c060020fb0811d | [
"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 | 2,514 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.DeclarationRange
import Lean.Elab.Log
import Lean.Data.Lsp.Utf16
namespace Lean.Elab
def getDeclarationRange [Monad m] [MonadFileMap m] (stx :... |
c49d873ac62f231b7c3e69d3b9cc2eaf3785f6df | 9bf90df35bb15a2f76571e35c48192142a328c40 | /src/ch6.lean | 90d25cbf38a059fb1242695270f75267350ca459 | [] | no_license | ehaskell1/set_theory | ed0726520e84990d5f3180bafa0a3674ed31fb5e | e6c829c4dd953d98c9cba08f9f79784cd91794fb | refs/heads/master | 1,693,282,405,362 | 1,636,928,916,000 | 1,636,928,916,000 | 428,055,746 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 30,069 | lean | import ch4
universe u
namespace Set
local attribute [irreducible] mem
reserve infix ` ≈ `:50
reserve infix ` ≉ `:50
reserve infix ` ≼ `:50
structure correspondence (A B f : Set) : Prop :=
(onto : f.onto_fun A B)
(oto : f.one_to_one)
lemma id_corr {A : Set} : A.correspondence A A.id :=
⟨id_onto, id_oto⟩
lemma empty... |
f72825a8f4bc731ac7316d3af610de36a1866df1 | 46125763b4dbf50619e8846a1371029346f4c3db | /src/topology/metric_space/emetric_space.lean | 80d5c1b8c27544c46b49b9eda46aabc5f936ef86 | [
"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 | 37,774 | lean | /-
Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
-/
import data.real.nnreal data.real.ennreal
import topology.uniform_space.separation topology.u... |
2962b949260469d69c5e4a761f3eebaed4f23514 | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/ring_theory/ideal/basic.lean | f7235863644b8f2303998f6e9ff91567fb4d6033 | [
"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 | 33,836 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Chris Hughes, Mario Carneiro
-/
import algebra.associated
import linear_algebra.basic
import order.zorn
import order.atoms
import order.compactly_generated
/-!
# Ideals over a r... |
8a1254cabb43d15a603515f5141e33363c039155 | 5d166a16ae129621cb54ca9dde86c275d7d2b483 | /library/init/meta/decl_cmds.lean | 92717a9e1ca93ff6d4c7e4838117d1e5720acc28 | [
"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 | 2,024 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.meta.tactic init.meta.rb_map
open tactic
private meta def apply_replacement (replacements : name_map name) (e : expr) : expr :=
e.repla... |
df2e97067b763db3ee3ba789e4849e7281441e37 | 798dd332c1ad790518589a09bc82459fb12e5156 | /algebra/big_operators.lean | 0a9c49296ba56ede2000dc016aa03f62b01f823a | [
"Apache-2.0"
] | permissive | tobiasgrosser/mathlib | b040b7eb42d5942206149371cf92c61404de3c31 | 120635628368ec261e031cefc6d30e0304088b03 | refs/heads/master | 1,644,803,442,937 | 1,536,663,752,000 | 1,536,663,907,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 19,123 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Some big operators for lists and finite sets.
-/
import data.list.basic data.list.perm data.finset
algebra.group algebra.ordered_group algebra.group_power
universes ... |
37aefd874c2286c9e40873110979575f05c5f2f7 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/topology/uniform_space/completion.lean | ae7133be2cc5694d9f45a976904a08fdc2f1ff55 | [
"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 | 24,487 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
-/
import topology.uniform_space.abstract_completion
/-!
# Hausdorff completions of uniform spaces
The goal is to construct a left-adjoint to the inclu... |
afab7cdc86298a4848ed4cb125765fa3f22af3ef | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/analysis/normed_space/is_R_or_C.lean | b8d83b44849ba4c7ec6df50042334470222433f3 | [
"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 | 4,146 | lean | /-
Copyright (c) 2021 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä
-/
import data.complex.is_R_or_C
import analysis.normed_space.operator_norm
import analysis.normed_space.pointwise
/-!
# Normed spaces over R or C
This file is about resul... |
f57e2f4c0b12c18767dd4a585df3bd96b48b9f37 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/algebra/tropical/basic.lean | 419b1fc1af7c0a85f3bed5ee507797d7aaf6d694 | [
"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 | 16,243 | 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 algebra.group_power.order
import algebra.smul_with_zero
/-!
# Tropical algebraic structures
This file defines algebraic structures of the (min-)tropical n... |
45a6f9dfb26dd5afd8ea48d451ae2ec42115d21f | 649957717d58c43b5d8d200da34bf374293fe739 | /src/topology/algebra/TopCommRing/basic.lean | 4b778b5b479e096050806c805f4e7ec322231b67 | [
"Apache-2.0"
] | permissive | Vtec234/mathlib | b50c7b21edea438df7497e5ed6a45f61527f0370 | fb1848bbbfce46152f58e219dc0712f3289d2b20 | refs/heads/master | 1,592,463,095,113 | 1,562,737,749,000 | 1,562,737,749,000 | 196,202,858 | 0 | 0 | Apache-2.0 | 1,562,762,338,000 | 1,562,762,337,000 | null | UTF-8 | Lean | false | false | 2,785 | 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 topology.Top.basic
import topology.instances.complex
universes u
open category_theory
structure TopCommRing :=
(α : Type u... |
111a6566f00c61606f53844dcc52cc872e5fd746 | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/linear_algebra/clifford_algebra/basic.lean | 13979cce70b16bbe77fa58e7c4e7fcea022fc0f2 | [
"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 | 7,491 | lean | /-
Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Utensil Song
-/
import algebra.ring_quot
import linear_algebra.tensor_algebra
import linear_algebra.exterior_algebra
import linear_algebra.quadratic_form
/-!
# Clifford Alg... |
eed46eb49308e5f547d90abc2753acddc0f704ab | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /test/induction.lean | 53587615dd6cc740f6a32f1b5c55b88a09e16d1e | [
"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 | 37,951 | lean | import tactic.induction
import tactic.linarith
universes u v w
--------------------------------------------------------------------------------
-- Setup: Some Inductive Types
--------------------------------------------------------------------------------
inductive le : ℕ → ℕ → Type
| zero {n} : le 0 n
| succ {n m} ... |
e4daf9ec67bdd03d8e4939ff2c3c8015b7259a09 | 037dba89703a79cd4a4aec5e959818147f97635d | /src/2020/relations/partition_challenge_official_solution.lean | 23a05395498064c1e16cb4a459ca87086089712e | [] | no_license | ImperialCollegeLondon/M40001_lean | 3a6a09298da395ab51bc220a535035d45bbe919b | 62a76fa92654c855af2b2fc2bef8e60acd16ccec | refs/heads/master | 1,666,750,403,259 | 1,665,771,117,000 | 1,665,771,117,000 | 209,141,835 | 115 | 12 | null | 1,640,270,596,000 | 1,568,749,174,000 | Lean | UTF-8 | Lean | false | false | 9,980 | lean | import tactic
/-!
# The partition challenge!
Prove that equivalence relations on α are the same as partitions of α.
Three sections:
1) partitions
2) equivalence classes
3) the challenge
Say `α` is a type, and `R` is a binary relation on `α`.
The following things are already in Lean:
reflexive R := ∀ (x : α), R... |
94720852ed41d58d50908416d2e365ace5f3cf48 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/group_theory/coset.lean | c9629e74782b101418ec8f86341a314a691fd9f2 | [
"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 | 16,693 | lean | /-
Copyright (c) 2018 Mitchell Rowett. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Rowett, Scott Morrison
-/
import group_theory.subgroup
/-!
# Cosets
This file develops the basic theory of left and right cosets.
## Main definitions
* `left_coset a s`:... |
e3fe301c8cf37abdc3d7c75efecd40aa7e581c7e | b7f22e51856f4989b970961f794f1c435f9b8f78 | /library/data/set/map.lean | f9e99a0244777395d8779f7d45aa168ff1dc456b | [
"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 | 6,179 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad, Andrew Zipperer
Functions between subsets of finite types, bundled with the domain and range.
-/
import data.set.function
open eq.ops
namespace set
record map {X Y : Ty... |
2f7674e7d8f60f0f7f6d3cae09cc719b6ba3edb7 | 6e9cd8d58e550c481a3b45806bd34a3514c6b3e0 | /src/data/rat/basic.lean | 09b8644a28420307433425d529381ba4d83e689d | [
"Apache-2.0"
] | permissive | sflicht/mathlib | 220fd16e463928110e7b0a50bbed7b731979407f | 1b2048d7195314a7e34e06770948ee00f0ac3545 | refs/heads/master | 1,665,934,056,043 | 1,591,373,803,000 | 1,591,373,803,000 | 269,815,267 | 0 | 0 | Apache-2.0 | 1,591,402,068,000 | 1,591,402,067,000 | null | UTF-8 | Lean | false | false | 25,329 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import data.int.sqrt
import data.equiv.encodable
import algebra.group
import algebra.euclidean_domain
import algebra.ordered_field
/-!
# Basics for t... |
eda1e9d4bcdc46a04f52e58651a8cb9292772f4c | a7eef317ddec01b9fc6cfbb876fe7ac00f205ac7 | /src/field_theory/subfield.lean | 59ef6bf636323a5ffcdaf0d87f89323771bb0c8f | [
"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 | 4,952 | lean | /-
Copyright (c) 2018 Andreas Swerdlow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andreas Swerdlow
-/
import ring_theory.subring
variables {F : Type*} [field F] (S : set F)
section prio
set_option default_priority 100 -- see Note [default priority]
class is_subf... |
108491ef67e42cbdb7ba90a42c1124b4a2bb8f79 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/list/sections.lean | eea26f06244f2b736e750b22873c92456aa0e314 | [
"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 | 1,458 | 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.forall2
/-!
# List sections
This file proves some stuff about `list.sections` (definition in `data.list.defs`). A section of a
list of lists `[l₁, ... |
459abce35d7ad767a11f92d3cb9591d8561ee18b | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/geometry/manifold/smooth_manifold_with_corners.lean | ec421d963876f04e5a0967acab0062dfd6144a10 | [
"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 | 33,096 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import analysis.calculus.times_cont_diff
import geometry.manifold.charted_space
/-!
# Smooth manifolds (possibly with boundary or corners)
A smooth manifold i... |
d7978b92acbcb97134fb330707da7a38f314819a | 75c54c8946bb4203e0aaf196f918424a17b0de99 | /old/reflection.lean | 06e7509c5ec3562ed901433f330270cc2bb53366 | [
"Apache-2.0"
] | permissive | urkud/flypitch | 261e2a45f1038130178575406df8aea78255ba77 | 2250f5eda14b6ef9fc3e4e1f4a9ac4005634de5c | refs/heads/master | 1,653,266,469,246 | 1,577,819,679,000 | 1,577,819,679,000 | 259,862,235 | 1 | 0 | Apache-2.0 | 1,588,147,244,000 | 1,588,147,244,000 | null | UTF-8 | Lean | false | false | 4,027 | lean | /-
Copyright (c) 2019 The Flypitch Project. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Han, Floris van Doorn
-/
import fol tactic.abel tactic.ring completeness abel
open fol
local notation h :: t := dvector.cons h t
local notation `[]` := dvector.nil
loca... |
2c3a5c561bb816e8f74d22ae27a4dbde4fd1db46 | 49ffcd4736fa3bdcc1cdbb546d4c855d67c0f28a | /library/init/data/fin/ops.lean | 0aff7950bd57b7b8f8fe8236673ad12c2e331020 | [
"Apache-2.0"
] | permissive | black13/lean | 979e24d09e17b2fdf8ec74aac160583000086bc8 | 1a80ea9c8e28902cadbfb612896bcd45ba4ce697 | refs/heads/master | 1,626,839,620,164 | 1,509,113,016,000 | 1,509,122,889,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,833 | lean | /-
Copyright (c) 2017 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.nat init.data.fin.basic
namespace fin
open nat
variable {n : nat}
protected def succ : fin n → fin (succ n)
| ⟨a, h⟩ := ⟨nat.succ ... |
4486d9e26289560e9a7bf1d827834dcefd2fed39 | ba4794a0deca1d2aaa68914cd285d77880907b5c | /src/game/world10/level7.lean | e6b768bdec6b5fb221f0b1e740748cfd9bd5c90e | [
"Apache-2.0"
] | permissive | ChrisHughes24/natural_number_game | c7c00aa1f6a95004286fd456ed13cf6e113159ce | 9d09925424da9f6275e6cfe427c8bcf12bb0944f | refs/heads/master | 1,600,715,773,528 | 1,573,910,462,000 | 1,573,910,462,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 493 | lean | import game.world10.level6 -- hide
namespace mynat -- hide
/-
# Inequality world
## Level 7: `le_zero`
We proved `add_right_eq_zero` back in advanced addition world.
Note that you can do things like `have h2 := add_right_eq_zero _ _ h1`
if `h1 : a + c = 0`.
-/
/- Lemma
For all naturals $a$, if $a\le 0$ then $a = 0$... |
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