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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
4ee5a9eb8a2ab92f814b0e0ea609d1be9b739784 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/analysis/special_functions/trigonometric/deriv.lean | 29a599126d297ed144ea93a4995b80f8f8898900 | [
"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 | 37,954 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-/
import order.monotone.odd
import analysis.special_functions.exp_deriv
import analysis.special_functions... |
c502d52a4833c670e440d1f4067cb442166b3282 | b074a51e20fdb737b2d4c635dd292fc54685e010 | /src/category_theory/monad/adjunction.lean | 02e235566989f9828cc439df16950e4555caa3ff | [
"Apache-2.0"
] | permissive | minchaowu/mathlib | 2daf6ffdb5a56eeca403e894af88bcaaf65aec5e | 879da1cf04c2baa9eaa7bd2472100bc0335e5c73 | refs/heads/master | 1,609,628,676,768 | 1,564,310,105,000 | 1,564,310,105,000 | 99,461,307 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,180 | 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 `... |
da8613faa88e0dc15234a6b604599afff64245da | bb31430994044506fa42fd667e2d556327e18dfe | /src/data/set/intervals/group.lean | ad8805380b283cef3b3827fd91cffec308ded657 | [
"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 | 4,556 | 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, Rémy Degenne
-/
import data.set.intervals.basic
import algebra.order.group.abs
/-! ### Lemmas about arithmetic operati... |
c68c66581707620e30b8e18c9a454c6efc27d064 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/data/dfinsupp/basic.lean | bfb3adf4aab1106e708b24bb340843a4406ddb61 | [
"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 | 80,847 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau
-/
import algebra.module.pi
import algebra.module.linear_map
import algebra.big_operators.basic
import data.set.finite
import group_theory.submonoid.membership
imp... |
f24189a14d0293d77473b0ddeb29739a2e808cff | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/group_theory/group_action/sub_mul_action.lean | 1527c908ef04ef3bf1055756adff52457bc1ef06 | [
"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 | 5,789 | lean | /-
Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import algebra.group_action_hom
import algebra.module.basic
import data.set_like.basic
import group_theory.group_action.basic
/-!
# Sets invariant to a `mul_action`
In th... |
e5b5ba399059f09c26a0028cb4832a763f38722d | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/algebra/ring/basic.lean | 3b89acf8f793397e1a4bd77f30c82c49b2618ccf | [
"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 | 47,621 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Amelia Livingston, Yury Kudryashov,
Neil Strickland
-/
import algebra.divisibility
import algebra.regular.basic
import data.set.basic... |
04c3c0786f4f29e9cc251fe2b2912084bc205724 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/order/group/prod.lean | 4a255df846e42b21aff79ccc79b8c8f03f667f69 | [
"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 | 590 | 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.order.group.instances
import algebra.order.monoid.prod
/-!
# Products of ordered commutative groups.
... |
12b828b36c61035f07fda0ade4e6dfc0f397fbdd | 92b50235facfbc08dfe7f334827d47281471333b | /library/data/subtype.lean | 14a807e59fe2e2506aee2e87d790b4dd93fa4b81 | [
"Apache-2.0"
] | permissive | htzh/lean | 24f6ed7510ab637379ec31af406d12584d31792c | d70c79f4e30aafecdfc4a60b5d3512199200ab6e | refs/heads/master | 1,607,677,731,270 | 1,437,089,952,000 | 1,437,089,952,000 | 37,078,816 | 0 | 0 | null | 1,433,780,956,000 | 1,433,780,955,000 | null | UTF-8 | Lean | false | false | 1,267 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura, Jeremy Avigad
-/
open decidable
set_option structure.proj_mk_thm true
structure subtype {A : Type} (P : A → Prop) :=
tag :: (elt_of : A) (has_property : P el... |
eb9c483a756c4e498a38a9c227efe5590dcea6d1 | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/order/filter/extr.lean | b6ed8ead9ee1ca76001934b5ca196942c5710f9a | [
"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 | 21,047 | lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import order.filter.basic
/-!
# Minimum and maximum w.r.t. a filter and on a aet
## Main Definitions
This file defines six predicates of the form `is_A_B`, where... |
c6c8787542473edc1c92f79c7713fab8de3bbe6b | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/topology/locally_constant/basic.lean | 28783cf6146496ec0924c786c15b177c4d8c8ad3 | [
"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 | 16,306 | 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 topology.subset_properties
import topology.connected
import topology.algebra.monoid
import topology.continuous_function.basic
import tactic.tfae
import tactic.... |
56c80d1679543d3cf872831e43f6c6a3ef765cf5 | 5c5878e769950eabe897ad08485b3ba1a619cea9 | /src/categories/heterogeneous_identity.lean | 202962fc02dceb9250cabe971450b32727828fd3 | [
"Apache-2.0"
] | permissive | semorrison/lean-category-theory-pr | 39dc2077fcb41b438e61be1685e4cbca298767ed | 7adc8d91835e883db0fe75aa33661bc1480dbe55 | refs/heads/master | 1,583,748,682,010 | 1,535,111,040,000 | 1,535,111,040,000 | 128,731,071 | 1 | 2 | Apache-2.0 | 1,528,069,880,000 | 1,523,258,452,000 | Lean | UTF-8 | Lean | false | false | 1,105 | lean | -- Copyright (c) 2018 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Scott Morrison
import category_theory.functor
import .isomorphism
universes u v
namespace category_theory
section
variables {C : Type u} [𝒞 : category.{u v} C]
include 𝒞
d... |
625aedae6bf5cd8bbd10298e7eb0c90c615f9051 | c8b4b578b2fe61d500fbca7480e506f6603ea698 | /src/number_theory/cyclotomic/zeta_sub_one_prime.lean | b2ef4c1c2ba9b5fefcacdab3379529d700cc521d | [] | no_license | leanprover-community/flt-regular | aa7e564f2679dfd2e86015a5a9674a6e1197f7cc | 67fb3e176584bbc03616c221a7be6fa28c5ccd32 | refs/heads/master | 1,692,188,905,751 | 1,691,766,312,000 | 1,691,766,312,000 | 421,021,216 | 19 | 4 | null | 1,694,532,115,000 | 1,635,166,136,000 | Lean | UTF-8 | Lean | false | false | 1,810 | lean | import norm.norm_prime
import number_theory.cyclotomic.gal
import number_theory.cyclotomic.rat
variables {K : Type*} [field K] {ζ : K}
open_locale number_field
open polynomial algebra
local notation `R` := 𝓞 K
namespace is_cyclotomic_extension.rat
variables {p : ℕ+} {k : ℕ} [hp : fact (p : ℕ).prime] [char_zero K... |
36180a381bf215bdfafffe173ffec33b91e03fd7 | a9fe717b93ccfa4b2e64faeb24f96dfefb390240 | /term.lean | e26cf125c9af00840bb1720ef90be0e87b9cff9a | [] | 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 | 3,050 | lean | import .coeffs .int
def term : Type := int × coeffs
namespace term
def subscript_digit : char → char
| '0' := '₀'
| '1' := '₁'
| '2' := '₂'
| '3' := '₃'
| '4' := '₄'
| '5' := '₅'
| '6' := '₆'
| '7' := '₇'
| '8' := '₈'
| '9' := '₉'
| c := c
--
--def subscript_digits (ds : string) : string :=
--⟨ds.data.map subscri... |
c20cf28bac40a9b1898ee30682f58de74b867cc2 | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /tests/lean/parserPrio.lean | 34e7be1fd744e01a7ea6453ed93b0dc004237e69 | [
"Apache-2.0"
] | permissive | collares/lean4 | 861a9269c4592bce49b71059e232ff0bfe4594cc | 52a4f535d853a2c7c7eea5fee8a4fa04c682c1ee | refs/heads/master | 1,691,419,031,324 | 1,618,678,138,000 | 1,618,678,138,000 | 358,989,750 | 0 | 0 | Apache-2.0 | 1,618,696,333,000 | 1,618,696,333,000 | null | UTF-8 | Lean | false | false | 905 | lean | --
-- New notation that overlaps with existing notation
syntax (name := myPair) (priority := high) "(" term "," term ")" : term
macro_rules[myPair]
| `(($a, $b)) => `([$a, $b])
#eval (1, 2) -- not ambiguous since myPair parser has higher priority
theorem ex1 : (1, 2) = [1, 2] :=
rfl
-- Define macro for expanding t... |
61c51b1c052cf70e1075854386b6fb483dadf878 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/group_theory/subgroup/basic.lean | 1163576cc90a15b0271eaf24066e1835950d763d | [
"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 | 128,919 | 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 group_theory.submonoid.pointwise
import group_theory.submonoid.membership
import group_theory.submonoid.centralizer
import algebra.group.conj
import algebra.module.b... |
d8668a6d6048aa79ccae4e6a35f72350cf178ced | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /stage0/src/Lean/Elab/MutualDef.lean | 2d6cfe66d78b06dd7bd6da7eb0bdf84af9dcef7f | [
"Apache-2.0"
] | permissive | williamdemeo/lean4 | 72161c58fe65c3ad955d6a3050bb7d37c04c0d54 | 6d00fcf1d6d873e195f9220c668ef9c58e9c4a35 | refs/heads/master | 1,678,305,356,877 | 1,614,708,995,000 | 1,614,708,995,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 28,988 | 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.Term
import Lean.Meta.Closure
import Lean.Meta.Check
import Lean.Elab.Command
import Lean.Elab.DefView
import Lean.Elab.PreDefinition
imp... |
a0877beda0649f419cbd4f50c32078d1d33f476a | d450724ba99f5b50b57d244eb41fef9f6789db81 | /src/mywork/Homework/Homework_4_inclass.lean | 31431a13fde582f6492d45ceb6cebb5b7606619e | [] | 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 | 1,155 | lean | -- 1
example : 0 ≠ 1 :=
begin
-- ¬ (0 = 1)
-- (0 = 1) → false
assume h,
cases h,
-- cases works because case analysis that there
-- are 0 ways to build a proof of 0 = 1.
end
--2
example: 0 ≠ 0 → 2 = 3 :=
begin
assume h,
exact false.elim(h (eq.refl 0)),
-- apply false elimination rule to a proof o... |
118ac5a1696ed6fac3ed70534d8619f66ce4445e | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/data/list/lattice.lean | 0516f3df51664283672ec57616b69e961e13a859 | [
"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 | 11,460 | lean | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro,
Scott Morrison
-/
import data.list.basic
/-!
# Lattice structure of lists
This files prove bas... |
edfa4399ea9a9f77a9fe876099f301f47ba83e5e | 8b9f17008684d796c8022dab552e42f0cb6fb347 | /hott/init/types/sum.hlean | 231aacada234de4281cf52fc0ba6b37f79461572 | [
"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 | 484 | hlean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.types.sum
Author: Leonardo de Moura, Jeremy Avigad
-/
prelude
import init.datatypes init.reserved_notation
namespace sum
notation A ⊎ B := sum A B
notation A + B := s... |
11c07fd81c86c0aaa6f7cd867a840b41579fceea | f02b05b665ad2d2cd970e93758a98d57f310a822 | /src/tactic/tcache/default.lean | c0ba0ae46141ccf0f7b5d8a30592f3dccb33b6c3 | [] | no_license | khoek/leancache | b0ed5d2a9a2e87f58d4ad27343d957a9cd49ce5f | 5c8329f7b647b8d82966ab180c4473b20d1f249c | refs/heads/master | 1,585,344,140,717 | 1,549,094,327,000 | 1,549,094,327,000 | 147,138,187 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 15 | lean | import .command |
8f90fc8a8af659d5e2c9eb2dd2897852f323eebe | 618003631150032a5676f229d13a079ac875ff77 | /src/topology/algebra/polynomial.lean | a154c2ead650ff47609130cc44c24e72432f6094 | [
"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 | 2,056 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Robert Y. Lewis
Analytic facts about polynomials.
-/
import topology.algebra.ring
import data.polynomial
import data.real.cau_seq
open polynomial is_absolute_value
lemma polynomial.... |
e911359a0294234c558a025d7c33e4b6c4361eda | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/algebra/module.lean | 5f451f76adfa1a332405d01e716f204c79bb0c96 | [
"Apache-2.0"
] | permissive | vaibhavkarve/mathlib | a574aaf68c0a431a47fa82ce0637f0f769826bfe | 17f8340912468f49bdc30acdb9a9fa02eeb0473a | refs/heads/master | 1,621,263,802,637 | 1,585,399,588,000 | 1,585,399,588,000 | 250,833,447 | 0 | 0 | Apache-2.0 | 1,585,410,341,000 | 1,585,410,341,000 | null | UTF-8 | Lean | false | false | 24,432 | lean | /-
Copyright (c) 2015 Nathaniel Thomas. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nathaniel Thomas, Jeremy Avigad, Johannes Hölzl, Mario Carneiro
Modules over a ring.
## Implementation notes
Throughout the `linear_map` section implicit `{}` brackets are often ... |
93f7610329820ee4e9dc170075fa239e2dfdb188 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/finset/fold.lean | a7129f2592bc2e7cfabfae7106f000ab5235f3b7 | [] | 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 | 6,918 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.finset.basic
import Mathlib.data.multiset.fold
import Mathlib.PostPort
universes u_1 u... |
d71a26a019eb34897bf708341546a5787a56308f | 969dbdfed67fda40a6f5a2b4f8c4a3c7dc01e0fb | /src/category_theory/epi_mono.lean | 84c73d7f7a9a74df37a09fed7fb8ca6bd966ba02 | [
"Apache-2.0"
] | permissive | SAAluthwela/mathlib | 62044349d72dd63983a8500214736aa7779634d3 | 83a4b8b990907291421de54a78988c024dc8a552 | refs/heads/master | 1,679,433,873,417 | 1,615,998,031,000 | 1,615,998,031,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,275 | lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Scott Morrison
Facts about epimorphisms and monomorphisms.
The definitions of `epi` and `mono` are in `category_theory.category`,
since they are used by some lemmas for `is... |
85fce4861100a2e2a5fe9adb1769400be93ccd92 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/discrRefinement3.lean | da99cbb5056d1c33807eb27aaa59f5ab9dc06bbe | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 1,280 | lean | inductive Mem (a : α) : List α → Prop where
| head {as} : Mem a (a::as)
| tail {as} : Mem a as → Mem a (a'::as)
infix:50 (priority := high) " ∈ " => Mem
example (a b : Nat) (h : a ∈ [b]) : b = a :=
match h with
| Mem.head => rfl
example {as : List α} (h : a ∈ b :: as) : b = a ∨ a ∈ as :=
match h with
| M... |
c35b4c1a665b92ff25000b4645f4807a67ec5c3d | 4fa161becb8ce7378a709f5992a594764699e268 | /src/category_theory/limits/shapes/constructions/binary_products.lean | f3a1624cbfbd68567460d0d8e0a3de658827d2eb | [
"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 | 1,642 | 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.pullbacks
import category_theory.limits.shapes.binary_products
universes v u
/-!
# Constructing binary product from pullbacks and t... |
9a7b7b4bfa70e7c3917993268e8e5dd62cc9440a | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/tactic/push_neg.lean | 9ca09bac1d40a2ae5278139cf95f4e370bb9b224 | [
"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 | 7,978 | lean | /-
Copyright (c) 2019 Patrick Massot All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Simon Hudon
A tactic pushing negations into an expression
-/
import logic.basic
import algebra.order
open tactic expr
namespace push_neg
section
universe u
variable... |
ae405c3f1aa1fa4431a2dec7012c18667e5b8356 | 3ef5255cebe505e5ab251615d9fbf31a132f461d | /lean/old/test_algebra2.lean | b3941ab4e22693beea9d40689177c825beba1fea | [] | no_license | avigad/scratch | 42441a2ea94918049391e44d7adab304d3adea51 | 3fb9cef15bc5581c9602561427a7f295917990a2 | refs/heads/master | 1,608,917,412,424 | 1,473,078,921,000 | 1,473,078,921,000 | 17,224,172 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,267 | lean | ----------------------------------------------------------------------------------------------------
--
-- test_algebra2.lean
-- Jeremy Avigad
--
-- Trying to handle the algebraic hierarchy, with explicit casts.
--
----------------------------------------------------------------------------------------------------
imp... |
5b6ca69730df93bda3e6a78e928cd0b158fea4f8 | 947b78d97130d56365ae2ec264df196ce769371a | /tests/lean/run/CoeNew.lean | e23f909cf05a3c9a6ff28aa5959e69a9ace03aea | [
"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 | 750 | lean | new_frontend
universes u v w
instance boolToNat : Coe Bool Nat :=
{ coe := fun b => cond b 1 0 }
instance natToBool : Coe Nat Bool :=
{ coe := fun n => match n with
| 0 => false
| _ => true }
structure ConstantFunction (α β : Type) :=
(f : α → β)
(h : ∀ a₁ a₂, f a₁ = f a₂)
instance constantFunctionCoe {α β : T... |
7c848be9378bb7a7f0186c3028738db83d673052 | c5b07d17b3c9fb19e4b302465d237fd1d988c14f | /src/isos/fins.lean | f47adcb75b070fc2a33af458754bbbcb07bbb8a7 | [
"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 | 769 | lean | import isos.list
namespace fins
-- 0⁰ = 1
def one_iso : fin 0 → fin 0 ≃ 1 :=
⟨λ x, (),
λ x, fin.elim0,
λ x, funext (λ y, fin.elim0 (x y)),
λ x, by induction x; refl⟩
-- 0ⁿ⁺¹ = 0
def zero_iso {n} : fin (n + 1) → fin 0 ≃ 0 :=
⟨λ x, by have z : fin 0 := x 0; exact fin.elim0 z,
λ x, pempty.rec _ x,
λ x, funext (λ y,... |
d42f0ca32762375ba2efc0440cf4d6caa1494ea8 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/ring_theory/jacobson_auto.lean | 352bba2490e67ebc7cef29a9e6d0d09caec07017 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,583 | lean | /-
Copyright (c) 2020 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Devon Tuma
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.mv_polynomial.default
import Mathlib.ring_theory.ideal.over
import Mathlib.ring_theory.jacobso... |
99b18a39ca1826b78ff2a926db3723b8032b8b07 | f3849be5d845a1cb97680f0bbbe03b85518312f0 | /library/init/data/int/order.lean | 3c384ae95dbc79d5a400dc9c601ad538c85fdcdf | [
"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 | 8,795 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
The order relation on the integers.
-/
prelude
import init.data.int.basic
namespace int
private def nonneg (a : ℤ) : Prop := int.cases_on a (take n, true) (take n, fals... |
fc59c9792294842afe1a15630c1abdb672b9830a | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/algebra/is_prime_pow.lean | 6b57ede3c6afdb3209a2815124707215d2487886 | [
"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 | 4,707 | lean | /-
Copyright (c) 2022 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import algebra.associated
import number_theory.divisors
/-!
# Prime powers
This file deals with prime powers: numbers which are positive integer powers of a single prim... |
4407d7390633acf9726bc64097f01a9b988f0edf | 618003631150032a5676f229d13a079ac875ff77 | /src/data/polynomial.lean | 4996d3fca01111203e829f9b814b9eb36c53a16a | [
"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 | 108,312 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
-/
import data.monoid_algebra
import algebra.gcd_domain
import ring_theory.euclidean_domain
import ring_theory.multiplicity
i... |
e84b37b476812084c5b5e40786c2971b0083868d | 9c1ad797ec8a5eddb37d34806c543602d9a6bf70 | /monoidal_categories/monoidal_category.lean | 4c1fded4ee7abde4883b6c420f7e418953bddb8a | [] | no_license | timjb/lean-category-theory | 816eefc3a0582c22c05f4ee1c57ed04e57c0982f | 12916cce261d08bb8740bc85e0175b75fb2a60f4 | refs/heads/master | 1,611,078,926,765 | 1,492,080,000,000 | 1,492,080,000,000 | 88,348,246 | 0 | 0 | null | 1,492,262,499,000 | 1,492,262,498,000 | null | UTF-8 | Lean | false | false | 8,712 | lean | -- Copyright (c) 2017 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Stephen Morgan, Scott Morrison
import .tensor_product
open tqft.categories
open tqft.categories.functor
open tqft.categories.products
open tqft.categories.natural_transformation... |
2283dbab4c9fbbb7c59919ce4b43e8cf4fc83985 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/category/Group/images.lean | ed472bcd2383e6ddb997fd89a42e2bda270c099a | [] | 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 | 3,435 | 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.algebra.category.Group.abelian
import Mathlib.category_theory.limits.shapes.images
import M... |
5754ca8dca53386633dae77c83c9d5e4095de3ed | 77c5b91fae1b966ddd1db969ba37b6f0e4901e88 | /src/data/polynomial/field_division.lean | 83d80bc9bdeb0e3c8ee42170ca4b5d263e540ce3 | [
"Apache-2.0"
] | permissive | dexmagic/mathlib | ff48eefc56e2412429b31d4fddd41a976eb287ce | 7a5d15a955a92a90e1d398b2281916b9c41270b2 | refs/heads/master | 1,693,481,322,046 | 1,633,360,193,000 | 1,633,360,193,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 19,892 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
-/
import algebra.gcd_monoid.basic
import data.polynomial.derivative
import data.polynomial.ring_division
import data.set.pai... |
b49b73010a3ac5ce92edab15f94d3f525a089636 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/deprecated/subfield.lean | 15c0d3278020b2f68bd750851229ff911216a93a | [
"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 | 5,773 | 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 deprecated.subring
import algebra.group_with_zero.power
/-
# Unbundled subfields
This file introduces the predicate `is_subfield` on `S : set F` where `F... |
2490decd66f3a3fb6b076288ead000c8230c88df | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/ring_theory/nakayama.lean | b5fe642599314838f4bc0f0fd74c5be2ab034471 | [
"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 | 4,540 | lean | /-
Copyright (c) 2021 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import ring_theory.jacobson_ideal
/-!
# Nakayama's lemma
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
... |
43f61029115b303bdff39f89980a60384dd4a143 | 9631e35ca5dd719ccc7d3a57ec322fd93d6a0776 | /src/gcd_maze/level.lean | 073189299787671f1b1923e3a0b8667c96f115c6 | [] | no_license | kbuzzard/maze-game | 123fa47e0262edb6d147178d239a345d847ff147 | 362ab394ae5218c43b24232aaeef08efc0067eab | refs/heads/master | 1,670,131,466,823 | 1,598,546,702,000 | 1,598,546,702,000 | 290,744,081 | 5 | 1 | null | 1,598,546,703,000 | 1,598,523,538,000 | Lean | UTF-8 | Lean | false | false | 952 | lean | -- import the definition of the example maze
import gcd_maze.definition
import data.int.gcd
/-!
# Non-euclidean maze.
You are in a maze of integers, all distinct.
You can go north, south east or west.
north adds 8 to your integer, south subtracts 8
east adds 3 to your integer, west subtrascts 3
When you're at th... |
be1cbd887e5e542522ddbdb26e5d7031950af5b6 | 618003631150032a5676f229d13a079ac875ff77 | /test/tactics.lean | 41d57209a62435ad7df1d0eabecaebf0dc8a736f | [
"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 | 16,018 | 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.interactive
import tactic.finish
import tactic.ext
import tactic.lift
import tactic.apply
import tactic.reassoc_axiom
import tactic.tfae
impo... |
faf11e216ee0002aeb61cc8bd7d881fc84084bbb | c777c32c8e484e195053731103c5e52af26a25d1 | /src/analysis/complex/open_mapping.lean | 9e347d273ff1a3e8e7c54508c692187ffe6fe6d9 | [
"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 | 11,295 | lean | /-
Copyright (c) 2022 Vincent Beffara. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Vincent Beffara
-/
import analysis.analytic.isolated_zeros
import analysis.complex.cauchy_integral
import analysis.complex.abs_max
/-!
# The open mapping theorem for holomorphic func... |
efb8cd5f39caaef0ed84fa4a0a07a1358b71cc1a | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/lcnf1.lean | e487ca8c4f072c25275c6368744ba871e13e37a2 | [
"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 | 2,558 | lean | import Lean
open Lean
#eval Compiler.compile #[``List.map]
#eval Compiler.compile #[``Lean.Elab.Term.synthesizeInstMVarCore]
#eval Compiler.compile #[``Eq.ndrec]
def g1 (x : Nat) (h : Nat = Int) : Int :=
(h ▸ x) + 1
#eval Compiler.compile #[``g1]
def f (h : False) (x : Nat) : Nat :=
(h.rec : Nat → Nat) x
#e... |
a2c40507f376971f831e13a8c0eb68240892859a | fd71e7836e9a5d14548f6d3291653cbb6c608dbe | /src/test/random.lean | c21a47acc100c366738b465632597dda3dfce513 | [] | no_license | cipher1024/slim_check | 382c80a98aed105a97eeac84f590a06dca4d8c7d | 5969b7f72e01fdd46f2502ed0cbf69c0699061d4 | refs/heads/master | 1,625,514,334,828 | 1,574,118,572,000 | 1,574,118,572,000 | 101,538,155 | 2 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 18,031 | lean | import data.bitvec
import data.stream
import util.data.list
import util.data.fin
import util.meta.tactic
import tactic.norm_num
import algebra.group_power
import test.slim_check.liftable
import system.io
import system.random
open list io applicative
universes u v w
-- instance {g : Type v} [random_gen g] : random_... |
cbe4e9e8016313e8a8c6b269e1a16e754804a147 | ee8cdbabf07f77e7be63a449b8483ce308d37218 | /lean/src/valid/mathd-algebra-214.lean | 85280abdbefb9c2e7df76011a63fae417a1ce84a | [
"MIT",
"Apache-2.0"
] | permissive | zeta1999/miniF2F | 6d66c75d1c18152e224d07d5eed57624f731d4b7 | c1ba9629559c5273c92ec226894baa0c1ce27861 | refs/heads/main | 1,681,897,460,642 | 1,620,646,361,000 | 1,620,646,361,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 297 | lean | /-
Copyright (c) 2021 OpenAI. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kunhao Zheng
-/
import data.real.basic
example (a : ℝ) (f : ℝ → ℝ) (h₀ : ∀ x, f x = a * ( x - 2 ) ^ 2 + 3) (h₁ : f 4 = 4) : f 6 = 7 :=
begin
sorry
end
|
98405d05ee7c92e617f11f920b28ed3f67b5cf25 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/essential_image_auto.lean | cbac16f71787d06fa9d09366831a0dd7509b0339 | [] | 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 | 6,222 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.natural_isomorphism
import Mathlib.category_theory.full_subcategory
import Math... |
b963c9f38d9eab3ec4d73e67ca8658beaec1df27 | 022547453607c6244552158ff25ab3bf17361760 | /src/analysis/normed_space/basic.lean | 44118f5f77140e665a1be7c42b51bb5677d17c0c | [
"Apache-2.0"
] | permissive | 1293045656/mathlib | 5f81741a7c1ff1873440ec680b3680bfb6b7b048 | 4709e61525a60189733e72a50e564c58d534bed8 | refs/heads/master | 1,687,010,200,553 | 1,626,245,646,000 | 1,626,245,646,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 83,477 | 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 algebra.punit_instances
import topology.instances.nnreal
import topology.algebra.module
import topology.algebra.algebra
import topology.algebra... |
74c06a3cd2df0c57bb239d36494b9149cf03438e | 75c54c8946bb4203e0aaf196f918424a17b0de99 | /old/conservative_extension.lean | a7249cf4d00d155f4fe938c3eb8ed1d137953ff2 | [
"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 | 8,369 | 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 .language_extension .completeness .zfc
local notation h :: t := dvector.cons h t
local notation `[` l:(foldr `, ` (h t, dvector.cons... |
658c60b0d57ff5742e055716614f106433354c4b | f313d4982feee650661f61ed73f0cb6635326350 | /Mathlib/Data/UInt.lean | 66f7af5eeae82494019e4f037ea003c393f9f9e1 | [
"Apache-2.0"
] | permissive | shingtaklam1324/mathlib4 | 38c6e172eec1385944db5a70a3b5545c924980ee | 50610c343b7065e8eec056d641f859ceed608e69 | refs/heads/master | 1,683,032,333,313 | 1,621,942,699,000 | 1,621,942,699,000 | 371,130,608 | 0 | 0 | Apache-2.0 | 1,622,053,166,000 | 1,622,053,166,000 | null | UTF-8 | Lean | false | false | 1,092 | lean |
theorem Fin.val_eq_of_lt : a < n.succ → (@Fin.ofNat n a).val = a := Nat.mod_eq_of_lt
theorem UInt32.val_eq_of_lt : a < UInt32.size → (UInt32.ofNat a).val = a := Fin.val_eq_of_lt
namespace UInt8
/-- Is this an uppercase ASCII letter? -/
def isUpper (c : UInt8) : Bool :=
c ≥ 65 && c ≤ 90
/-- Is this a lowercase AS... |
5dcae687750be6cc4ae7423dc3f43c670302da7b | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/list/forall2.lean | 335a7149238ab380e15ebc15339a933c86de242b | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 13,239 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl
-/
import data.list.infix
/-!
# Double universal quantification on a list
This file provides an API for `list.forall₂` (definition in `data.list.defs`)... |
b52e54679c62b1db4a6786385371b51624dd7366 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/analysis/calculus/mean_value.lean | 6edda971ad86e558e194dee8e7ae87c8a0881a4f | [
"Apache-2.0"
] | permissive | agjftucker/mathlib | d634cd0d5256b6325e3c55bb7fb2403548371707 | 87fe50de17b00af533f72a102d0adefe4a2285e8 | refs/heads/master | 1,625,378,131,941 | 1,599,166,526,000 | 1,599,166,526,000 | 160,748,509 | 0 | 0 | Apache-2.0 | 1,544,141,789,000 | 1,544,141,789,000 | null | UTF-8 | Lean | false | false | 50,111 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Yury Kudryashov
-/
import analysis.calculus.local_extr
import analysis.convex.topology
/-!
# The mean value inequality and equalities
In this file we prove the ... |
623747fabef92716bcc5f8d5da425a493ac82ba1 | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /tests/lean/run/ctx.lean | ce2499270bece3660a8bfdd24a7ce042e770b7de | [
"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 | 379 | lean | import data.nat logic.inhabited
open nat inhabited
constant N : Type.{1}
constant a : N
section s1
set_option pp.implicit true
definition f (a b : nat) := a
theorem nat_inhabited [instance] : inhabited nat :=
inhabited.mk zero
definition to_N [coercion] (n : nat) : N := a
infixl `$$`:65 := f
end s1
t... |
c599fd545a464dfab2fdacff88e85b58ff0d4c0d | fecda8e6b848337561d6467a1e30cf23176d6ad0 | /src/field_theory/splitting_field.lean | 19a89a4848863eb263f24034f8df03829b099b61 | [
"Apache-2.0"
] | permissive | spolu/mathlib | bacf18c3d2a561d00ecdc9413187729dd1f705ed | 480c92cdfe1cf3c2d083abded87e82162e8814f4 | refs/heads/master | 1,671,684,094,325 | 1,600,736,045,000 | 1,600,736,045,000 | 297,564,749 | 1 | 0 | null | 1,600,758,368,000 | 1,600,758,367,000 | null | UTF-8 | Lean | false | false | 31,199 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
Definition of splitting fields, and definition of homomorphism into any field that splits
-/
import ring_theory.adjoin_root
import ring_theory.algebra_tower
import ring_the... |
d7debba51674715898e9a3fc06333b550e9185fb | 36c7a18fd72e5b57229bd8ba36493daf536a19ce | /library/data/nat/examples/fib2.lean | f49002324e050e5047e9fe5c45602d391cf4fbdd | [
"Apache-2.0"
] | permissive | YHVHvx/lean | 732bf0fb7a298cd7fe0f15d82f8e248c11db49e9 | 038369533e0136dd395dc252084d3c1853accbf2 | refs/heads/master | 1,610,701,080,210 | 1,449,128,595,000 | 1,449,128,595,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,174 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
Show that tail recursive fib is equal to standard one.
-/
import data.nat
open nat algebra
definition fib : nat → nat
| 0 := 1
| 1 := 1
| (n+2) := fib... |
eed45e028d4e010791af552e82802a699323a17b | 4f9ca1935adf84f1bae9c5740ec1f2ad406716fa | /src/analysis/calculus/fderiv.lean | ba612db1cb8b781ff0bd71b35ffdafe4998c167c | [
"Apache-2.0"
] | permissive | matthew-hilty/mathlib | 36fd7db866365e9ee4a0ba1d6f8ad34d068cec6c | 585e107f9811719832c6656f49e1263a8eef5380 | refs/heads/master | 1,607,100,509,178 | 1,578,151,707,000 | 1,578,151,707,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 73,140 | lean | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Sébastien Gouëzel, Yury Kudryashov
-/
import analysis.asymptotics analysis.calculus.tangent_cone
/-!
# The Fréchet derivative
Let `E` and `F` be normed spaces, `f : E ... |
c349955cfade73a7cc27fcf0f13808bea73aa8d8 | 0845ae2ca02071debcfd4ac24be871236c01784f | /library/init/lean/kvmap.lean | 65f8c8df55aedebd9d0cc777e463001f817c296e | [
"Apache-2.0"
] | permissive | GaloisInc/lean4 | 74c267eb0e900bfaa23df8de86039483ecbd60b7 | 228ddd5fdcd98dd4e9c009f425284e86917938aa | refs/heads/master | 1,643,131,356,301 | 1,562,715,572,000 | 1,562,715,572,000 | 192,390,898 | 0 | 0 | null | 1,560,792,750,000 | 1,560,792,749,000 | null | UTF-8 | Lean | false | false | 4,537 | lean | /-
Copyright (c) 2018 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.lean.name init.data.option.basic init.data.int
namespace Lean
inductive DataValue
| ofString (v : String)
| ofBool (v : Bool)
| ofNa... |
a6b4a05b44bf5dba10c3ceb2994cbf63a2fdf344 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/decreasing_by.lean | 8cf1dde9ad5501128655e4b0e21a1bdb57b9deea | [
"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 | 738 | lean | mutual
inductive Even : Nat → Prop
| base : Even 0
| step : Odd n → Even (n+1)
inductive Odd : Nat → Prop
| step : Even n → Odd (n+1)
end
decreasing_by assumption
mutual
def f (n : Nat) :=
if n == 0 then 0 else f (n / 2) + 1
decreasing_by assumption
end
def g' (n : Nat) :=
match n with
| 0 =>... |
1916fad7a787b1e5ac9d93102c036a0eb5780723 | e5c11e5a7d990ce404047c2bd848eeafac3c0a85 | /src/principal_ideal_domain.lean | d23bc38f0f51d0d2acb60452442fb7c6d3f1daf8 | [
"LPPL-1.3c"
] | permissive | lean-forward/class-number | 9ec63c24845e46efc8fa8b15324d0815918292c7 | 4fccf36d5e0e16accae84c16df77a3839ad964e4 | refs/heads/main | 1,686,927,014,542 | 1,624,886,724,000 | 1,624,886,724,000 | 327,319,245 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,265 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Chris Hughes, Morenikeji Neri
-/
import ring_theory.noetherian
import ring_theory.unique_factorization_domain
/-!
# Principal ideal rings and principal ideal domains
A principal ideal ri... |
25dc43599012975b8d36387a12a8ac1d0156bf20 | 3446e92e64a5de7ed1f2109cfb024f83cd904c34 | /src/game/world2/level10.lean | 76fd9131e8a22d41964f1faedf7c969ac38f87ef | [] | no_license | kckennylau/natural_number_game | 019f4a5f419c9681e65234ecd124c564f9a0a246 | ad8c0adaa725975be8a9f978c8494a39311029be | refs/heads/master | 1,598,784,137,722 | 1,571,905,156,000 | 1,571,905,156,000 | 218,354,686 | 0 | 0 | null | 1,572,373,319,000 | 1,572,373,318,000 | null | UTF-8 | Lean | false | false | 1,428 | lean | import mynat.definition -- hide
import mynat.add -- hide
import game.world2.level9 -- hide
namespace mynat -- hide
/-
# World 2 -- Addition World
## Level 10 -- `add_right_cancel`
You have, amongst other things, these:
* `zero_ne_succ : ∀ (a : mynat), zero ≠ succ(a)`
* `succ_inj : ∀ a b : mynat, succ(a) = succ... |
2b8bbecd8d4092e411a069f8bb32b2d9b37c808a | bb31430994044506fa42fd667e2d556327e18dfe | /src/analysis/ODE/picard_lindelof.lean | a7bfe958abd542ddb46d28c88c30cd99d93a32af | [
"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 | 20,006 | lean | /-
Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov, Winston Yin
-/
import analysis.special_functions.integrals
import topology.metric_space.contracting
/-!
# Picard-Lindelöf (Cauchy-Lipschitz) Theorem
In this f... |
ccfc4f9e2a96a21c1378be378e487f6912808c87 | e1da55f4222dac91b940ca052928eaace09762da | /src/bounds.lean | 6c0f13bddaee410c4c90aec27257d734803ebaa2 | [] | no_license | b-mehta/regularity-lemma | c5826e22c280d0b073a4e62dba731f4dd3d1b69f | cf26082b0c88fa54276e6fdc3338c15e607c52c6 | refs/heads/master | 1,658,209,524,267 | 1,644,406,456,000 | 1,644,406,456,000 | 457,327,371 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,474 | lean | /-
Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import .mathlib
/-!
# Numerical bounds for Szemerédi Regularity Lemma
-/
open finset fintype
variables {α : Type*}
/-- Auxiliary function ... |
96a788180cc798cd8b08ef942fcd136cfb0f3c78 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/topology/instances/complex.lean | 720a0153f4e84e4a68d45b0e5d772783907832a8 | [
"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 | 6,084 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
Topology of the complex numbers.
-/
import data.complex.basic
import topology.instances.real
noncomputable theory
open filter metric
open_locale topological_space
name... |
cc74d86ee7c8b9b80a6df4844936b9ca01a48679 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/topology/local_homeomorph.lean | 64ab36280df56e84860e7b19af814d6f6742a865 | [
"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 | 54,493 | 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 logic.equiv.local_equiv
import topology.sets.opens
/-!
# Local homeomorphisms
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file req... |
35c30558c4297a4c1ed16c5bdd6d482d8d96bed7 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/field_theory/ratfunc.lean | e796b7f2ec61ee73d102f92bbe7ed4ae588a54a6 | [
"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 | 59,885 | lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import ring_theory.euclidean_domain
import ring_theory.laurent_series
import ring_theory.localization.fraction_ring
import ring_theory.polynomial.content
/-!
# The field ... |
b1a684669f820b49c62dac29112c1edc87c21e81 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/ring/aut.lean | 2d77f91182fd252ed752296dffbd09b17d6ccb59 | [
"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 | 3,306 | 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 algebra.group_ring_action.basic
import algebra.hom.aut
import algebra.ring.equiv
/-!
# Ring automorphisms
This file defines t... |
657111dc324a839f92bd844105ccf54e372ca431 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /src/Lean/Compiler/ConstFolding.lean | bd886bb0a3ed118279b0ac484b70c7a601192845 | [
"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 | 7,246 | 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.Expr
import Lean.Compiler.Util
/- Constant folding for primitives that have special runtime support. -/
namespace Lean.Compiler
abbrev BinFol... |
1f5112d267c436c8a6b66b3b844f647609f15474 | 453dcd7c0d1ef170b0843a81d7d8caedc9741dce | /data/zmod.lean | f0af36fb9945231d2d6305639fd7fc1cc92d75af | [
"Apache-2.0"
] | permissive | amswerdlow/mathlib | 9af77a1f08486d8fa059448ae2d97795bd12ec0c | 27f96e30b9c9bf518341705c99d641c38638dfd0 | refs/heads/master | 1,585,200,953,598 | 1,534,275,532,000 | 1,534,275,532,000 | 144,564,700 | 0 | 0 | null | 1,534,156,197,000 | 1,534,156,197,000 | null | UTF-8 | Lean | false | false | 9,577 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Chris Hughes
-/
import data.int.modeq data.fintype data.nat.prime data.nat.gcd data.pnat
open nat nat.modeq int
def zmod (n : ℕ+) := fin n
namespace zmod
instance (n : ℕ+) : has_neg (... |
b540c83e3fef98990f315ff8ed4c6c3d80ca1155 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /counterexamples/phillips.lean | 67a4cb6a44874ef40691ac1a5cb080f7b9eaa3aa | [
"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 | 28,516 | lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import analysis.normed_space.hahn_banach
import measure_theory.lebesgue_measure
/-!
# A counterexample on Pettis integrability
There are several theories of i... |
21a69bd17dd7b03f4ab8b3c22cc903b03486982c | dd4e652c749fea9ac77e404005cb3470e5f75469 | /src/sdp.lean | 828fe1b2f55213111a1c457de44b0746522103ed | [] | no_license | skbaek/cvx | e32822ad5943541539966a37dee162b0a5495f55 | c50c790c9116f9fac8dfe742903a62bdd7292c15 | refs/heads/master | 1,623,803,010,339 | 1,618,058,958,000 | 1,618,058,958,000 | 176,293,135 | 3 | 2 | null | null | null | null | UTF-8 | Lean | false | false | 1,983 | lean | import .mat data.real.basic
-- To do : update using mat
#exit
open matrix
variables {k m n : nat}
namespace sdp
def S (n : nat) : Type := matrix real n n
structure primal (m n : nat) :=
(obf : S n)
(lhs : vector (S n) m)
(rhs : vector real m)
def primal.feasible (P : primal m n) (X : S n) : Prop :=
let ⟨C,A,... |
6904a9c901a326c2b134cf20170004603e8438b3 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/linear_algebra/matrix/orthogonal.lean | 561aa1d1c46ae297adee8d35fae04e0079412068 | [
"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 | 2,202 | lean | /-
Copyright (c) 2021 Lu-Ming Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lu-Ming Zhang
-/
import data.matrix.basic
/-!
# Orthogonal
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
This file con... |
4709a730cf0f103012b6994b9c016b18c8bdaea9 | a7dd8b83f933e72c40845fd168dde330f050b1c9 | /src/category_theory/equivalence.lean | 8dfc48b08f25bcbff8e8d01028b4935eaee18321 | [
"Apache-2.0"
] | permissive | NeilStrickland/mathlib | 10420e92ee5cb7aba1163c9a01dea2f04652ed67 | 3efbd6f6dff0fb9b0946849b43b39948560a1ffe | refs/heads/master | 1,589,043,046,346 | 1,558,938,706,000 | 1,558,938,706,000 | 181,285,984 | 0 | 0 | Apache-2.0 | 1,568,941,848,000 | 1,555,233,833,000 | Lean | UTF-8 | Lean | false | false | 14,487 | lean | -- Copyright (c) 2017 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Tim Baumann, Stephen Morgan, Scott Morrison, Floris van Doorn
import category_theory.fully_faithful
import category_theory.whiskering
import category_theory.natural_isomorphism
... |
57e451df54ec4e8ed6ba0bb16605ced814f9973a | fcf3ffa92a3847189ca669cb18b34ef6b2ec2859 | /src/world3/level7.lean | 744ef75aaf585eaf456559c8836163306c8aec10 | [
"Apache-2.0"
] | permissive | nomoid/lean-proofs | 4a80a97888699dee42b092b7b959b22d9aa0c066 | b9f03a24623d1a1d111d6c2bbf53c617e2596d6a | refs/heads/master | 1,674,955,317,080 | 1,607,475,706,000 | 1,607,475,706,000 | 314,104,281 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 517 | lean | import mynat.definition
import mynat.mul
import world2.level2
import world2.level5
import world2.level6
namespace mynat
lemma add_mul (a b c : mynat) : (a + b) * c = a * c + b * c :=
begin [nat_num_game]
induction c with d hd,
{
repeat {rw mul_zero},
rw add_zero,
refl,
},
{
... |
bcf47835d4a4075b4b64ab678453766d0e05be7e | 94e33a31faa76775069b071adea97e86e218a8ee | /src/linear_algebra/matrix/hermitian.lean | f5d464c0e47dc43cfb3045b3fd07a2ea55c4fa39 | [
"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 | 6,073 | lean | /-
Copyright (c) 2022 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp
-/
import analysis.inner_product_space.spectrum
/-! # Hermitian matrices
This file defines hermitian matrices and some basic results about them.
## Main defin... |
14060262d72fa6dedd6385adc791ef51b1200ac4 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/algebra/group/hom_instances.lean | 52b5264fd63d00adee1b875724501b489f22da6c | [
"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 | 9,598 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Kevin Buzzard, Scott Morrison, Johan Commelin, Chris Hughes,
Johannes Hölzl, Yury Kudryashov
-/
import algebra.group_power.basic
/-!
# Instances on spaces of monoid... |
95ff1780833986f59be964d34df54fe20b23c33a | aa5a655c05e5359a70646b7154e7cac59f0b4132 | /tests/lean/run/infoTree.lean | bb6b51b3f1774896359b5ac438c20dcded32e90c | [
"Apache-2.0"
] | permissive | lambdaxymox/lean4 | ae943c960a42247e06eff25c35338268d07454cb | 278d47c77270664ef29715faab467feac8a0f446 | refs/heads/master | 1,677,891,867,340 | 1,612,500,005,000 | 1,612,500,005,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 783 | lean | import Lean
open Lean.Elab
elab "enableInfo!" : command => enableInfoTree
elab "showInfoTrees!" : command => do
let trees ← getInfoTrees
trees.forM fun tree => do
logInfo f!"{← tree.format}"
structure A where
val : Nat → Nat
structure B where
pair : A × A
enableInfo!
def f (x : Nat) : Nat × Nat :=
... |
502fce2f86b35508be76ba495078f36bec6435f6 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/nat/prime.lean | 7a0f31731988373fabc74b9bf74ec14c71405783 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 46,427 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
import data.list.prime
import data.list.sort
import data.nat.gcd.basic
import data.nat.order.lemmas
import data.int.units
imp... |
eb13160d9bd84fc5af671d3cdeb4736e27a09c18 | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/combinatorics/simple_graph/degree_sum.lean | 153424afb42f2192ab470dc0aa7d1365463bd56f | [
"Apache-2.0"
] | permissive | hamdysalah1/mathlib | b915f86b2503feeae268de369f1b16932321f097 | 95454452f6b3569bf967d35aab8d852b1ddf8017 | refs/heads/master | 1,677,154,116,545 | 1,611,797,994,000 | 1,611,797,994,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,190 | lean | /-
Copyright (c) 2020 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Kyle Miller
-/
import combinatorics.simple_graph.basic
import algebra.big_operators.basic
import data.nat.parity
import data.zmod.parity
import tactic.omega
/-!
# Degree-sum formula and ha... |
6df5bffae543c4850c3fad602da40bc8184eb8d0 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /library/init/function.lean | 2454134533ff499a0c1715d4ac8e99b9409ab7d6 | [
"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 | 5,590 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura, Jeremy Avigad, Haitao Zhang
General operations on functions.
-/
prelude
import init.prod init.funext init.logic
namespace function
variables {A : Type} {B :... |
c1f404511a2753b227def1a01ffe8827b9511372 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/multiset/fintype.lean | 01ef958860e0102376eaed613f4fbb4ffe68d874 | [
"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 | 9,340 | lean | /-
Copyright (c) 2022 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import algebra.big_operators.basic
import data.fintype.card
import data.prod.lex
/-!
# Multiset coercion to type
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes ... |
a829521376e99e289f6b5aef2e2cfd5a9633f864 | a7dd8b83f933e72c40845fd168dde330f050b1c9 | /src/category_theory/instances/Top/basic.lean | 8d692f0b0f7753e9d75885e4a3ee521317c97290 | [
"Apache-2.0"
] | permissive | NeilStrickland/mathlib | 10420e92ee5cb7aba1163c9a01dea2f04652ed67 | 3efbd6f6dff0fb9b0946849b43b39948560a1ffe | refs/heads/master | 1,589,043,046,346 | 1,558,938,706,000 | 1,558,938,706,000 | 181,285,984 | 0 | 0 | Apache-2.0 | 1,568,941,848,000 | 1,555,233,833,000 | Lean | UTF-8 | Lean | false | false | 1,061 | 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 category_theory.concrete_category
import category_theory.full_subcategory
import topology.opens
open category_theory
open ... |
da6249fb7684bd38468fa243196b7a08731b85c2 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/rewrite_search/discovery_auto.lean | f6eb8e4805892a6eaafd07cce5997f7a44f3dd49 | [] | 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 | 708 | lean | /-
Copyright (c) 2020 Kevin Lacker, Keeley Hoek, Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker, Keeley Hoek, Scott Morrison
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.tactic.nth_rewrite.default
import Mat... |
ea289788f445ab6bbe7d45ca382a0116ef0f5c54 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/linear_algebra/affine_space/affine_map.lean | 308a2a1b28475d8a9e25ea3aa966bff4330da4b9 | [
"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 | 19,243 | lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import linear_algebra.affine_space.basic
import linear_algebra.tensor_product
import linear_algebra.prod
import linear_algebra.pi
import data.set.intervals.unordered_inte... |
d8b2e863e75ea8f1369f10b46c50d74ad2a4efa0 | 47181b4ef986292573c77e09fcb116584d37ea8a | /src/for_mathlib/multiplicity.lean | 03ea1550cfdd0df42289f2c988003b0b970b13b8 | [
"MIT"
] | permissive | RaitoBezarius/berkovich-spaces | 87662a2bdb0ac0beed26e3338b221e3f12107b78 | 0a49f75a599bcb20333ec86b301f84411f04f7cf | refs/heads/main | 1,690,520,666,912 | 1,629,328,012,000 | 1,629,328,012,000 | 332,238,095 | 4 | 0 | MIT | 1,629,312,085,000 | 1,611,414,506,000 | Lean | UTF-8 | Lean | false | false | 524 | lean | import algebra.associated
import ring_theory.multiplicity
lemma multiplicity.eq_of_associated {α} [comm_monoid_with_zero α]
[decidable_rel ((∣): α → α → Prop)]
{a b c: α} (h: associated b c): multiplicity a b = multiplicity a c :=
begin
have aux: ∀ a b c: α, associated b c → multiplicity a b ≤ multiplicity a c,
... |
14c2fb64870a202b18855496f00c9336e3e490ea | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/linear_algebra/dimension.lean | 007803dc5a3aa209e64ea9c19faec73319751e4c | [
"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 | 30,785 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen
-/
import linear_algebra.basis
import linear_algebra.std_basis
import set_theory.cardinal_ordinal
/-!
# Dimension of modules and vector s... |
4185416c8dd5192d989b2ccaac00b54a883d3760 | 217bb195841a8be2d1b4edd2084d6b69ccd62f50 | /library/init/lean/expander.lean | c53599ba702879fa72dc0ad40214cb224c4785c0 | [
"Apache-2.0"
] | permissive | frank-lesser/lean4 | 717f56c9bacd5bf3a67542d2f5cea721d4743a30 | 79e2abe33f73162f773ea731265e456dbfe822f9 | refs/heads/master | 1,589,741,267,933 | 1,556,424,200,000 | 1,556,424,281,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 23,490 | lean | /-
Copyright (c) 2018 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Sebastian Ullrich
Macro Expander for the Lean language, using a variant of the [sets of scopes](http://www.cs.utah.edu/plt/Scope-sets/) hygiene algorithm.
TODO(Sebastian): docu... |
ee43835ce7baa41194e99a5678c8809029a8119f | 76ce87faa6bc3c2aa9af5962009e01e04f2a074a | /01_Equality/01_equality.lean | 067bc10feee5afc531c63b77cba2741e4f3b45e2 | [] | no_license | Mnormansell/Discrete-Notes | db423dd9206bbe7080aecb84b4c2d275b758af97 | 61f13b98be590269fc4822be7b47924a6ddc1261 | refs/heads/master | 1,585,412,435,424 | 1,540,919,483,000 | 1,540,919,483,000 | 148,684,638 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,911 | lean | /- ** An inference rule for equality in general ** -/
/-
Intuitively you would suppose that the proposition,
0 = 0, should be true in any reasonable logical system.
There are two ways a logic could make this happen.
The first is that the logic could provide 0 = 0 as
an axiom, as we just discussed.
That'd be ok, ... |
e0ef818c3d214a91dace1ae21ed1b3c8b3dd24b4 | 38bf3fd2bb651ab70511408fcf70e2029e2ba310 | /src/algebra/category/CommRing/limits.lean | dd8df71d4244e25a8e0d3eda2bcb05ca2f2666c2 | [
"Apache-2.0"
] | permissive | JaredCorduan/mathlib | 130392594844f15dad65a9308c242551bae6cd2e | d5de80376088954d592a59326c14404f538050a1 | refs/heads/master | 1,595,862,206,333 | 1,570,816,457,000 | 1,570,816,457,000 | 209,134,499 | 0 | 0 | Apache-2.0 | 1,568,746,811,000 | 1,568,746,811,000 | null | UTF-8 | Lean | false | false | 4,628 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import algebra.category.CommRing.basic
import category_theory.limits.types
import category_theory.limits.preserves
import ring_theory.subring
import algebra.pi_instan... |
bbbf46827ee6bbada7459e1a94977f03aa767813 | 0845ae2ca02071debcfd4ac24be871236c01784f | /library/init/data/rbmap/basic.lean | 5193a3af49c841898d3fcc5cf69cb939141bc252 | [
"Apache-2.0"
] | permissive | GaloisInc/lean4 | 74c267eb0e900bfaa23df8de86039483ecbd60b7 | 228ddd5fdcd98dd4e9c009f425284e86917938aa | refs/heads/master | 1,643,131,356,301 | 1,562,715,572,000 | 1,562,715,572,000 | 192,390,898 | 0 | 0 | null | 1,560,792,750,000 | 1,560,792,749,000 | null | UTF-8 | Lean | false | false | 11,689 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.data.repr init.data.option.basic
universes u v w w'
inductive Rbcolor
| red | black
inductive RBNode (α : Type u) (β : α → Type v)
| ... |
a5744f33d5f2ea5fe74971b5268726291920fcbd | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/algebra/archimedean.lean | 48b584489be65d8f215f7f1dcb725a60826dacf2 | [
"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 | 13,958 | 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 algebra.field_power
import data.rat
import data.int.least_greatest
/-!
# Archimedean groups and fields.
This file defines the archimedean property for ordere... |
55c47216a4ea3638583d2db33df886983c2cc572 | 22e97a5d648fc451e25a06c668dc03ac7ed7bc25 | /src/topology/algebra/group_completion.lean | 6018b4c08ac22a573ce9fda2ec7d88923e50d2d4 | [
"Apache-2.0"
] | permissive | keeferrowan/mathlib | f2818da875dbc7780830d09bd4c526b0764a4e50 | aad2dfc40e8e6a7e258287a7c1580318e865817e | refs/heads/master | 1,661,736,426,952 | 1,590,438,032,000 | 1,590,438,032,000 | 266,892,663 | 0 | 0 | Apache-2.0 | 1,590,445,835,000 | 1,590,445,835,000 | null | UTF-8 | Lean | false | false | 4,118 | 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
Completion of topological groups:
-/
import topology.uniform_space.completion
import topology.algebra.uniform_group
noncomputable theory
section group
... |
bf840aefa0442df5cf9ad170889619814e5eb169 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/1342.lean | b3d98bb8dcb8a30cef5bc50061b6fb3eb07c6041 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 1,215 | lean | example (a b c : Nat) (h1 : a <= b) (h2 : b <= c) : a <= c :=
calc a
<= b := h1
_ <= c := h2
_ <= c := Nat.le_refl _
example (a b c : Nat) (h1 : a <= b) (h2 : b <= c) : a <= c :=
calc a
<= b := h1
_ <= c := h2
example (a b c : Nat) (h1 : a <= b) (h2 : b <= c) : a <= c :=
calc a <= b := h1
_... |
7942d8bb37c92e2e5d91abc16d585baeda3a6145 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/setoid/basic.lean | f986c93c71414d3f2de77d38db246281282a0128 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,994 | lean | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston, Bryan Gin-ge Chen
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.order.galois_connection
import Mathlib.PostPort
universes u_1 u_2... |
5fa4f8350addff987767dde11d006036e4c90486 | 947b78d97130d56365ae2ec264df196ce769371a | /tests/lean/run/tactic1.lean | 88717dcab49620b4826dd0e116b4bb57622f818b | [
"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 | 1,140 | lean | new_frontend
theorem ex1 (x : Nat) (y : { v // v > x }) (z : Nat) : Nat :=
by {
clear y x;
exact z
}
theorem ex2 (x : Nat) (y : { v // v > x }) (z : Nat) : Nat :=
by {
clear x y;
exact z
}
theorem ex3 (x y z : Nat) (h₁ : x = y) (h₂ : z = y) : x = z :=
by {
have y = z from h₂.symm;
apply Eq.trans;
exact... |
06aa3e857b5e18411af0050ab0ae4d1fd4374d09 | 592ee40978ac7604005a4e0d35bbc4b467389241 | /Library/generated/mathscheme-lean/DualDeMorgan.lean | 5b5bd76a5093837878483cebff1af4b3a5295d61 | [] | no_license | ysharoda/Deriving-Definitions | 3e149e6641fae440badd35ac110a0bd705a49ad2 | dfecb27572022de3d4aa702cae8db19957523a59 | refs/heads/master | 1,679,127,857,700 | 1,615,939,007,000 | 1,615,939,007,000 | 229,785,731 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,245 | lean | import init.data.nat.basic
import init.data.fin.basic
import data.vector
import .Prelude
open Staged
open nat
open fin
open vector
section DualDeMorgan
structure DualDeMorgan (A : Type) : Type :=
(times : (A → (A → A)))
(plus : (A → (A → A)))
(prim : (A → A))
(andDeMorgan_times_plus_p... |
e440d09c673abcf73fc651abf5b88492f41c22dc | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/functor_category_auto.lean | 5873f6d2880be035bbe4c256bf90fa334ee75edf | [] | 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 | 6,330 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tim Baumann, Stephen Morgan, Scott Morrison, Floris van Doorn
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.natural_transformation
impor... |
8076fee0f8e5d8a73e20246d75b632e5b5efe559 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/measure_theory/integral/torus_integral.lean | d13836f451806ade9b95934dd2f16c4826d69622 | [
"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 | 12,288 | lean | /-
Copyright (c) 2022 Cuma Kökmen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Cuma Kökmen, Yury Kudryashov
-/
import measure_theory.integral.circle_integral
/-!
# Integral over a torus in `ℂⁿ`
In this file we define the integral of a function `f : ℂⁿ → E` over a ... |
d9728a1731df1432962d1c23dd85677c40fa8c57 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/category_theory/category/default.lean | 185ce0b00252d31583f7c39070ce80319252b2b7 | [
"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 | 10,561 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stephen Morgan, Scott Morrison, Johannes Hölzl, Reid Barton
-/
import tactic.basic
/-!
# Categories
Defines a category, as a type class parametrised by the type of objects.
## Notat... |
adeab7a94341558d160b234d7523b42c34e499ab | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/analysis/hofer.lean | a06e3b053195b9068b9b7d7cfda47c976516d492 | [
"Apache-2.0"
] | permissive | Lix0120/mathlib | 0020745240315ed0e517cbf32e738d8f9811dd80 | e14c37827456fc6707f31b4d1d16f1f3a3205e91 | refs/heads/master | 1,673,102,855,024 | 1,604,151,044,000 | 1,604,151,044,000 | 308,930,245 | 0 | 0 | Apache-2.0 | 1,604,164,710,000 | 1,604,163,547,000 | null | UTF-8 | Lean | false | false | 4,557 | lean | /-
Copyright (c) 2020 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import analysis.specific_limits
/-!
# Hofer's lemma
This is an elementary lemma about complete metric spaces. It is motivated by an
application to the bubbling-off... |
40e0b63f9c8eddaa58552b57fed42731095b0755 | fe84e287c662151bb313504482b218a503b972f3 | /src/undergraduate/MAS114/fiber.lean | cbb09c54bafeee9b49ef82e7b0e3aa5264634964 | [] | no_license | NeilStrickland/lean_lib | 91e163f514b829c42fe75636407138b5c75cba83 | 6a9563de93748ace509d9db4302db6cd77d8f92c | refs/heads/master | 1,653,408,198,261 | 1,652,996,419,000 | 1,652,996,419,000 | 181,006,067 | 4 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 2,441 | lean | import data.fintype.basic data.fintype.card
import algebra.big_operators.basic algebra.big_operators.order
import tactic.squeeze
namespace MAS114
universes u v
variables {α : Type u} {β : Type v} (p : α → β)
variables [fintype α] [fintype β] [decidable_eq α] [decidable_eq β]
def fiber (b : β) : Type* := { a : α //... |
2e6caa467a3142d12f2b0e46ebc7f82e50846b4a | 42c01158c2730cc6ac3e058c1339c18cb90366e2 | /M1F/weird_unfold.lean | bc342f3e4a2040d59ce7fc1491b7428bec165198 | [] | no_license | ChrisHughes24/xena | c80d94355d0c2ae8deddda9d01e6d31bc21c30ae | 337a0d7c9f0e255e08d6d0a383e303c080c6ec0c | refs/heads/master | 1,631,059,898,392 | 1,511,200,551,000 | 1,511,200,551,000 | 111,468,589 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 867 | lean | import analysis.real
variable x : real
-- set_option pp.all true
example : x < (x+1) :=
begin
unfold has_lt.lt,
unfold preorder.lt,
unfold partial_order.lt,
unfold ordered_comm_monoid.lt,
unfold discrete_linear_ordered_field.lt,
unfold has_lt.lt,
unfold preorder.lt,
unfold partial_order.lt,
unfold lattice.semilattice_i... |
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