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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
fe4d3c13dca883c2d54706ceb98fba20a6bf986c | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /stage0/src/Lean/Elab/Do.lean | 710114f9a8db1acb5efef26356ee83c65cc4c1d3 | [
"Apache-2.0"
] | permissive | dupuisf/lean4 | d082d13b01243e1de29ae680eefb476961221eef | 6a39c65bd28eb0e28c3870188f348c8914502718 | refs/heads/master | 1,676,948,755,391 | 1,610,665,114,000 | 1,610,665,114,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 66,457 | 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.Elab.Term
import Lean.Elab.Binders
import Lean.Elab.Match
import Lean.Elab.Quotation.Util
import Lean.Parser.Do
namespace Lean.Elab.Term
open L... |
64323e2c6f7d301679f44db720cdc17c973d463e | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /tests/lean/docStr.lean | c452c2fbacd4271bcd5bf70966f66915c6098bb6 | [
"Apache-2.0"
] | permissive | WojciechKarpiel/lean4 | 7f89706b8e3c1f942b83a2c91a3a00b05da0e65b | f6e1314fa08293dea66a329e05b6c196a0189163 | refs/heads/master | 1,686,633,402,214 | 1,625,821,189,000 | 1,625,821,258,000 | 384,640,886 | 0 | 0 | Apache-2.0 | 1,625,903,617,000 | 1,625,903,026,000 | null | UTF-8 | Lean | false | false | 2,575 | lean | import Lean
/-- Foo structure is just a test -/
structure Foo where
/-- main name -/ name : String := "hello"
/-- documentation for the second field -/ val : Nat := 0
/-- documenting test axiom -/
axiom myAxiom : Nat
structure Boo (α : Type) where
/-- Boo constructor has a custom name -/
makeBoo ::
/-- B... |
30103eab1602ec71ae3cce3d9a2f700dd3dfa6ea | bf532e3e865883a676110e756f800e0ddeb465be | /data/pfun.lean | ce28df652fee8e529b664311768758d5a626f8b1 | [
"Apache-2.0"
] | permissive | aqjune/mathlib | da42a97d9e6670d2efaa7d2aa53ed3585dafc289 | f7977ff5a6bcf7e5c54eec908364ceb40dafc795 | refs/heads/master | 1,631,213,225,595 | 1,521,089,840,000 | 1,521,089,840,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,055 | 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 data.set data.set.basic
universes u v w
/-- `roption α` is the type of "partial values" of type `α`. It
is similar to `option α` except the domain condition... |
1628aca3ef8379c51858e156516bf3b5caa062c1 | 38bf3fd2bb651ab70511408fcf70e2029e2ba310 | /src/category/basic.lean | e540924f6d9ba74b38c2e3f9400a952ddb740392 | [
"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 | 6,958 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Extends the theory on functors, applicatives and monads.
-/
universes u v w
variables {α β γ : Type u}
notation a ` $< `:1 f:1 := f a
section functor
variables {f : ... |
2ba1c4c7abd7d0bf820491d6cd261bcdc6b8c183 | 0845ae2ca02071debcfd4ac24be871236c01784f | /library/init/data/nat/div.lean | 10807a53168966e8f4d5da8cd367827eb8233ce4 | [
"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 | 4,129 | 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.wf init.data.nat.basic
namespace Nat
private def divRecLemma {x y : Nat} : 0 < y ∧ y ≤ x → x - y < x :=
fun h => And.rec (fun ypos ylex... |
8e21a17dd9cf23aa7353de8a036cc62093f0dee0 | 7490bf5d40d31857a58062614642bb5a41c36154 | /exam2.lean | c56ed0b1e757622c5f41bab176734887692d2ca4 | [] | no_license | reesegrayallen/Lean-Discrete-Mathematics | 9f1d6fe1c814cc9264ce868a67adcf5a82566e22 | 00c875284613ea12e0a729f519738aab8599456b | refs/heads/main | 1,674,181,372,629 | 1,606,801,004,000 | 1,606,801,004,000 | 317,387,970 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,519 | lean | /-
REESE ALLEN (rga2uz)
-/
import .satisfiability
import .rules_of_reasoning
/-
CS2102 Exam #2: Propositional Logic
-/
/-
#1. Define a predicate function, is_satisfiable: pExp → bool
that returns true iff the given proposition is satisfiable.
Hint: Model your answer on our definition of is_valid. You
may need to def... |
bf7c88a8f913cf0fe0be88b61103ac12c907d34e | 432d948a4d3d242fdfb44b81c9e1b1baacd58617 | /src/analysis/normed_space/finite_dimension.lean | 1b4ae0bbbb30cda95f6bc244474affc70f0e966c | [
"Apache-2.0"
] | permissive | JLimperg/aesop3 | 306cc6570c556568897ed2e508c8869667252e8a | a4a116f650cc7403428e72bd2e2c4cda300fe03f | refs/heads/master | 1,682,884,916,368 | 1,620,320,033,000 | 1,620,320,033,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 24,202 | 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.normed_space.operator_norm
import analysis.normed_space.add_torsor
import topology.bases
import linear_algebra.finite_dimensional
/-!
# Finite ... |
b72d5e3a4fe520884769b71ec0b0fab818072d48 | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/tactic/generalize_proofs.lean | a64bc5ef7b59fdcea04fb14885b97d4b5c882038 | [
"Apache-2.0"
] | permissive | fpvandoorn/mathlib | b21ab4068db079cbb8590b58fda9cc4bc1f35df4 | b3433a51ea8bc07c4159c1073838fc0ee9b8f227 | refs/heads/master | 1,624,791,089,608 | 1,556,715,231,000 | 1,556,715,231,000 | 165,722,980 | 5 | 0 | Apache-2.0 | 1,552,657,455,000 | 1,547,494,646,000 | Lean | UTF-8 | Lean | false | false | 2,013 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
namespace tactic
private meta def collect_proofs_in :
expr → list expr → list name × list expr → tactic (list name × list expr)
| e ctx (ns, hs) :=
let go (tac : ... |
e573350bfbdcced58f1582a5ff5778d3e3d9ef95 | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/mv_polynomial/equiv.lean | 995bfb347a9446655bbda941561479b6c7c72a3d | [
"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 | 13,068 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
-/
import data.mv_polynomial.rename
import data.equiv.fin
import data.polynomial.algebra_map
/-!
# Equivalences between polynomial ring... |
c22964a880ee2684e5b23449ba5fe6ccffdec246 | a4673261e60b025e2c8c825dfa4ab9108246c32e | /stage0/src/Init/Control/EState.lean | 972c46b2866f10596dba39966f85436e1e5fb652 | [
"Apache-2.0"
] | permissive | jcommelin/lean4 | c02dec0cc32c4bccab009285475f265f17d73228 | 2909313475588cc20ac0436e55548a4502050d0a | refs/heads/master | 1,674,129,550,893 | 1,606,415,348,000 | 1,606,415,348,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,895 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import Init.Control.State
import Init.Control.Except
universes u v
namespace EStateM
variables {ε σ α : Type u}
instance [ToString ε] [ToString α... |
5732be8f220b8c9fedaf95844b8ef5983948ad90 | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /test/examples.lean | 1a2df9f6e2daf9f8912a580d5e2bdfd3dda97265 | [
"Apache-2.0"
] | permissive | ChrisHughes24/mathlib | 98322577c460bc6b1fe5c21f42ce33ad1c3e5558 | a2a867e827c2a6702beb9efc2b9282bd801d5f9a | refs/heads/master | 1,583,848,251,477 | 1,565,164,247,000 | 1,565,164,247,000 | 129,409,993 | 0 | 1 | Apache-2.0 | 1,565,164,817,000 | 1,523,628,059,000 | Lean | UTF-8 | Lean | false | false | 4,800 | lean | import tactic data.stream.basic data.set.basic data.finset data.multiset
category.traversable.derive
open tactic
universe u
variable {α : Type}
example (s t u : set ℕ) (h : s ⊆ t ∩ u) (h' : u ⊆ s) : u ⊆ s → true :=
begin
dunfold has_subset.subset has_inter.inter at *,
-- trace_state,
intro1, triv
end
exa... |
866b08974e48e5d2ae097aff9c2a6a6f02b13e17 | c3f2fcd060adfa2ca29f924839d2d925e8f2c685 | /tests/lean/run/tactic25.lean | 2d06a5ac787f149437c6ead8248c0d5bfc73b928 | [
"Apache-2.0"
] | permissive | respu/lean | 6582d19a2f2838a28ecd2b3c6f81c32d07b5341d | 8c76419c60b63d0d9f7bc04ebb0b99812d0ec654 | refs/heads/master | 1,610,882,451,231 | 1,427,747,084,000 | 1,427,747,429,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 532 | lean | import logic
open tactic
definition my_tac1 := apply @eq.refl
definition my_tac2 := repeat (apply @and.intro; assumption)
tactic_hint my_tac1
tactic_hint my_tac2
theorem T1 {A : Type.{2}} (a : A) : a = a
theorem T2 {a b c : Prop} (Ha : a) (Hb : b) (Hc : c) : a ∧ b ∧ c
definition my_tac3 := fixpoint (λ f, [apply @o... |
00fb9c7d166307a7f0fa961a2a07c92799a489c0 | 43390109ab88557e6090f3245c47479c123ee500 | /src/finite_dimensional_vector_spaces/basic.lean | a4547b460e8daa3922b110af72c120d37bc02597 | [
"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 | 5,471 | lean | /-
Copyright (c) 2018 Blair Shi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Kevin Buzzard, Blair Shi
This file is followed Linear Algebra Done Right and inspired by Johannes Hölzl's
implementation of linear algebra in mathlib.
The thing we improved is this file ... |
dd19ff4b8d814cd54851478ebc415a3f42d4c0d6 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/finset/fold.lean | 84b5b476395bb833d4a17b1890e640288a40bf4f | [
"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 | 6,324 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.finset.basic
import data.multiset.fold
/-!
# The fold operation for a commutative associative operation over a finset.
-/
namespace finset
open multiset... |
bafb1940d947e5d7e0b4620d2bc862d9da4eb1d1 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/algebra/lie/solvable.lean | 4dfacb432f908502f95833dba49aa2cfaa85e94f | [
"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 | 13,823 | lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import algebra.lie.abelian
import algebra.lie.ideal_operations
import order.hom.basic
/-!
# Solvable Lie algebras
Like groups, Lie algebras admit a natural concept of sol... |
63112b04dd62875230074b1c35ab16c82fd34f6f | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /11_Tactic-Style_Proofs.org.15.lean | ea304b17c12d86eedae26db650ae3a82b0a7eaf7 | [] | 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 | 131 | lean | import standard
import data.nat
open nat
example : ∃ a : ℕ, a = a :=
begin
fapply exists.intro,
exact nat.zero,
apply rfl
end
|
bdc0826aae39e616afb412c87622349e4da147f4 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/topology/continuous_function/algebra.lean | 745996653cf1a6363c014423c73e3cd77b6e0f28 | [
"Apache-2.0"
] | permissive | abentkamp/mathlib | d9a75d291ec09f4637b0f30cc3880ffb07549ee5 | 5360e476391508e092b5a1e5210bd0ed22dc0755 | refs/heads/master | 1,682,382,954,948 | 1,622,106,077,000 | 1,622,106,077,000 | 149,285,665 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 23,807 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Nicolò Cavalleri
-/
import topology.algebra.module
import topology.continuous_function.basic
import algebra.algebra.subalgebra
/-!
# Algebraic structures over continuo... |
24734394e90c9fac2f18e633e9447fb8f91755e5 | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/group_theory/perm/cycles.lean | 3956ddd5a70873649bda21f2fc2cb952d79d1966 | [
"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 | 19,385 | lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import group_theory.perm.sign
/-!
# Cyclic permutations
## Main definitions
In the following, `f : equiv.perm β`.
* `equiv.perm.is_cycle`: `f.is_cycle` when two nonfix... |
1bfc34876ef7f47e669d4f8d223ef3d43d84c526 | 9d2e3d5a2e2342a283affd97eead310c3b528a24 | /src/exercises_sources/thursday/afternoon/category_theory/exercise4.lean | 8bb61d434493029eb341621b0ea0c121965a5c03 | [] | permissive | Vtec234/lftcm2020 | ad2610ab614beefe44acc5622bb4a7fff9a5ea46 | bbbd4c8162f8c2ef602300ab8fdeca231886375d | refs/heads/master | 1,668,808,098,623 | 1,594,989,081,000 | 1,594,990,079,000 | 280,423,039 | 0 | 0 | MIT | 1,594,990,209,000 | 1,594,990,209,000 | null | UTF-8 | Lean | false | false | 1,213 | lean | import algebra.category.CommRing
import category_theory.yoneda
open category_theory
open opposite
open polynomial
noncomputable theory
/-!
We show that the forgetful functor `CommRing ⥤ Type` is (co)representable.
There are a sequence of hints available in
`hints/thursday/afternoon/category_theory/hintX.lean`, for ... |
b25a2157e877d1559764aa2be08abc415e14e99b | dbd2d342e674b01c9097c761d49e297e3ce18292 | /src/leanpkg/toml.lean | 56d57789ae37638d5d7db1df8fa128798dfed71d | [] | no_license | cipher1024/lean-depot | b4c3b096fb2d9b669d171fe9b2395f0822821dbe | 4b2b879f429eac70dc4e9fa210a3d92f1db2b7f5 | refs/heads/master | 1,599,422,553,618 | 1,574,715,661,000 | 1,574,715,661,000 | 220,534,909 | 1 | 0 | null | 1,574,715,992,000 | 1,573,241,547,000 | Lean | UTF-8 | Lean | false | false | 4,340 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Gabriel Ebner
-/
import data.buffer.parser
-- I'd like to contribute a new naming convention:
-- CamelCase for non-terminals.
def join (sep : string) : list string → string
| [... |
fb5cd05f758bab387e88a61561221d91466fd339 | 367134ba5a65885e863bdc4507601606690974c1 | /src/measure_theory/pi.lean | cf603a02b8cbef77a689750efc6438a07b8bfea6 | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 21,438 | lean | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import measure_theory.prod
/-!
# Product measures
In this file we define and prove properties about finite products of measures
(and at some point, countable pr... |
b2b2407edecf93601791abd0fbf198b431bbdffa | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /tests/lean/run/ind3.lean | 499b242570049a9a2eaca2029386755ef9df27d7 | [
"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 | 427 | lean | inductive tree (A : Type) : Type :=
node : A → forest A → tree A
with forest : Type :=
nil : forest A,
cons : tree A → forest A → forest A
check tree.{1}
check forest.{1}
check tree.rec.{1 1}
check forest.rec.{1 1}
print "==============="
inductive group : Type :=
mk_group : Π (carrier : Type) (mul : carrier → car... |
ff4ff48d36c81f1882274014b077e26dbdb77930 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/tactic/ext.lean | 4701da0e00f6ee2fed98532309cb4b326c56638f | [
"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 | 19,996 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Jesse Michael Han
-/
import tactic.rcases
import logic.function.basic
universes u₁ u₂
open interactive interactive.types
section ext
open lean.parser nat tactic
declare_tr... |
60a6bfad88fd48eef36e0e823cae1a5690b524f5 | 30b012bb72d640ec30c8fdd4c45fdfa67beb012c | /order/basic.lean | a693ec2ea3d06983e3c196f9493f60a7e3db5fce | [
"Apache-2.0"
] | permissive | kckennylau/mathlib | 21fb810b701b10d6606d9002a4004f7672262e83 | 47b3477e20ffb5a06588dd3abb01fe0fe3205646 | refs/heads/master | 1,634,976,409,281 | 1,542,042,832,000 | 1,542,319,733,000 | 109,560,458 | 0 | 0 | Apache-2.0 | 1,542,369,208,000 | 1,509,867,494,000 | Lean | UTF-8 | Lean | false | false | 19,956 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Mario Carneiro
-/
import tactic.interactive logic.basic data.sum data.set.basic algebra.order
open function
/- TODO: automatic construction of dual definitions / theorem... |
5b26aaa3242ba04a88def68a119ebae2a6659dc9 | 0dbd5f7001f62ee8d54ed48bada66bfeaf55e550 | /src/data/nat/exactly_divides.lean | b780569837b0704cae2d078057dab9508acd5dcc | [] | no_license | rwbarton/lean-elementary-number-theory | 667203b08501792eef48217759539f6c1e2da25a | fabef0737fd2486e3f24f9e04652db4c182d5425 | refs/heads/master | 1,670,605,651,029 | 1,599,565,470,000 | 1,599,565,470,000 | 293,792,043 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,443 | lean | import data.nat.prime
open nat
-- local attribute [trans] dvd_trans
-- Definition
def exactly_divides (p : ℕ) (r : ℕ) (n : ℕ) := p^r ∣ n ∧ ¬(p^(succ r) ∣ n)
notation p`^`r `∣∣`:50 n:50 := exactly_divides p r n
section
variable {p : ℕ}
-- Equivalent definitions
lemma exactly_divides' {r : ℕ} {n : ℕ} : p^r ∣∣ n ↔ (... |
7a6776c8c4c33f3e68a12010552b330ce1056b88 | 968e2f50b755d3048175f176376eff7139e9df70 | /examples/prop_logic_theory/unnamed_2252.lean | c5a3078446fc65c9f818e08a016db7a939e1af03 | [] | no_license | gihanmarasingha/mth1001_sphinx | 190a003269ba5e54717b448302a27ca26e31d491 | 05126586cbf5786e521be1ea2ef5b4ba3c44e74a | refs/heads/master | 1,672,913,933,677 | 1,604,516,583,000 | 1,604,516,583,000 | 309,245,750 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 391 | lean | import tactic.rcases
variables {p q : Prop}
-- BEGIN
theorem not_or_of_not_and_not : ¬p ∧ ¬q → ¬(p ∨ q) :=
begin
rintro ⟨h₃, h₄⟩ (h₆ | h₇),
{ exact h₃ h₆, }, -- The goal in the first case is closed by false introduction on `h₃` and `h₆`.
{ exact h₄ h₇, }, -- The goal in the second case is closed by false introdu... |
93a72cccbabf3468fb527f9c208456b5f4ca7a9f | 329788bf44a766cbceec47f6d3a91aeee20146cf | /src/elliptic_curve_nf.lean | f98c071d3d22339022908a7c11b61ed81131468a | [] | no_license | jamiebell2805/BSD-conjecture | ca69613bb4b0d7051575ff6a7528ccace1bf9c6b | 74aa51f13750868b7011e397576d6f8035d69360 | refs/heads/master | 1,685,937,124,285 | 1,624,744,421,000 | 1,624,744,421,000 | 364,047,425 | 7 | 0 | null | 1,624,482,924,000 | 1,620,072,330,000 | Lean | UTF-8 | Lean | false | false | 15,903 | lean | import data.nat.prime
import data.zmod.basic
import data.complex.basic
import analysis.special_functions.pow
import analysis.analytic.basic
import analysis.calculus.iterated_deriv
import tprod
import algebra.module.basic
import field_theory.tower
import fg_quotient
local attribute [semireducible] with_zero
open_local... |
e40ae27cf1369c0f3f25f159cffc5fc28d754afd | e0f9ba56b7fedc16ef8697f6caeef5898b435143 | /src/control/functor.lean | fcf70c7a8555bf0d372cc499fd33e631769112d8 | [
"Apache-2.0"
] | permissive | anrddh/mathlib | 6a374da53c7e3a35cb0298b0cd67824efef362b4 | a4266a01d2dcb10de19369307c986d038c7bb6a6 | refs/heads/master | 1,656,710,827,909 | 1,589,560,456,000 | 1,589,560,456,000 | 264,271,800 | 0 | 0 | Apache-2.0 | 1,589,568,062,000 | 1,589,568,061,000 | null | UTF-8 | Lean | false | false | 4,438 | lean | /-
Copyright (c) 2017 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Simon Hudon
Standard identity and composition functors
-/
import tactic.ext
import tactic.lint
universe variables u v w
section functor
variables {F : Type u → Type v}
variables {α β γ... |
8c37c4c4df7b1f9c3e3b9941ba196914580a7b18 | 968e2f50b755d3048175f176376eff7139e9df70 | /examples/prop_logic_theory/unnamed_1445.lean | 55649872a086ec36c4a7558c10548b698198ac53 | [] | no_license | gihanmarasingha/mth1001_sphinx | 190a003269ba5e54717b448302a27ca26e31d491 | 05126586cbf5786e521be1ea2ef5b4ba3c44e74a | refs/heads/master | 1,672,913,933,677 | 1,604,516,583,000 | 1,604,516,583,000 | 309,245,750 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 141 | lean | import data.nat.basic
variables x y z : ℕ
-- BEGIN
example : x * (y + z) = x * z + y * x :=
by rw [mul_add, add_comm, mul_comm x y]
-- END |
55862dcb65f9a881e29149284d802eb7f1e65697 | 432d948a4d3d242fdfb44b81c9e1b1baacd58617 | /src/field_theory/tower.lean | caaceb3005a62484959bd91bb702574a3fa25a8c | [
"Apache-2.0"
] | permissive | JLimperg/aesop3 | 306cc6570c556568897ed2e508c8869667252e8a | a4a116f650cc7403428e72bd2e2c4cda300fe03f | refs/heads/master | 1,682,884,916,368 | 1,620,320,033,000 | 1,620,320,033,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,171 | 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 ring_theory.algebra_tower
import linear_algebra.matrix
/-!
# Tower of field extensions
In this file we prove the tower law for arbitrary extensions and finite extensi... |
7b57902026bac5e096271cd052e15a0d65f0c334 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebraic_topology/fundamental_groupoid/product.lean | 6a9ecb69d9c066a352d96bb3ff598521b4ce5433 | [
"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 | 7,486 | lean | /-
Copyright (c) 2022 Praneeth Kolichala. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Praneeth Kolichala
-/
import category_theory.groupoid
import algebraic_topology.fundamental_groupoid.basic
import topology.category.Top.limits
import topology.homotopy.product
imp... |
a847abe8edda093d06d89652b64e01e7d5a4c1cc | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /stage0/src/Lean/MonadEnv.lean | acbaeb4886a015161bbc80e04cf92473245dde20 | [
"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 | 6,732 | 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.Environment
import Lean.Exception
import Lean.Declaration
import Lean.Util.FindExpr
import Lean.AuxRecursor
namespace Lean
def setEnv [MonadEn... |
ee2c5e8492eda9dd3c6b2a50bb2fbd8dfec40f0e | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/topology/algebra/order/floor.lean | 8825dc8d5baf1c0fa80fbc2f764416849b1d4902 | [
"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 | 9,551 | 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 algebra.order.floor
import topology.algebra.order.basic
/-!
# Topological facts about `int.floor`, `int.ceil` and `int.fract`
This file proves statements... |
bc3af62abeee9147f3bffb7cbb62689ea1d1f998 | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/ring_theory/algebra_tower.lean | be7916eb824357358888669e181b74f8f4a95d95 | [
"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 | 13,825 | 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.algebra.restrict_scalars
import algebra.algebra.tower
import algebra.invertible
import linear_algebra.basis
import ring_theory.adjoin.fg
import ring_theory.polyn... |
494d5657d8786dbe213d2a2b3987abbc072ed11d | 5a5e1bb8063d7934afac91f30aa17c715821040b | /lean3SOS/src/lib/poly.lean | 6f4ab1a3cc8849b6b1bd695035b0eeda55c3bd87 | [] | no_license | ramonfmir/leanSOS | 1883392d73710db5c6e291a2abd03a6c5b44a42b | 14b50713dc887f6d408b7b2bce1f8af5bb619958 | refs/heads/main | 1,683,348,826,105 | 1,622,056,982,000 | 1,622,056,982,000 | 341,232,766 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,133 | lean | /-
Results about multivariate polynomials.
-/
import data.mv_polynomial.basic
import data.matrix.basic
import lib.psd
open mv_polynomial matrix
variables {γ : Type*} [fintype γ]
variables {μ : Type*} [fintype μ]
variables {R : Type*} [linear_ordered_comm_ring R]
namespace poly
instance {σ R} [comm_semiring R] [h... |
f632c2b6cc4ea31ace13fef25e4c3cbecfb6ae40 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/ring_theory/polynomial/eisenstein.lean | 14f92adcb8e4c6ac0714e0fdcf803792f1bf0a18 | [
"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 | 27,355 | lean | /-
Copyright (c) 2022 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
import ring_theory.eisenstein_criterion
import ring_theory.integrally_closed
import ring_theory.norm
import ring_theory.polynomial.cyclotomic.basic
/-!
# Eisenste... |
fcd67afc486cdc5b0e80c97b502ee782fbb32a6b | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /archive/imo/imo2020_q2.lean | 54938a0afb1ec5b99eb477099091bf79d1c97380 | [
"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 | 2,312 | lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Yury Kudryashov
-/
import analysis.mean_inequalities
/-!
# IMO 2020 Q2
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR t... |
1a91fc35a0ec472bb2e2f752d04a69085feb3943 | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /tests/lean/run/discrRefinement2.lean | 996441117e8754ee4891530b58fe846a5ff3f349 | [
"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 | 950 | lean | theorem ex1 {α : Sort u} {a b : α} (h : a ≅ b) : a = b :=
match h with
| HEq.refl _ => rfl
theorem ex2 {α : Sort u2} {a : α} {motive : {β : Sort u2} → β → Sort u1} (m : motive a) {β : Sort u2} {b : β} (h : a ≅ b) : motive b :=
match h, m with
| HEq.refl _, m => m
theorem ex3 {α : Sort u} {a : α} {p : α → Sort... |
aa8945a040300525d7b056272fe3193238780f09 | 94b1d6e2f33c283a70415b9a58689f03be80f6df | /src/export_json.lean | f476297b9bf191ea781d8f76f0be74da7006fa19 | [
"Apache-2.0"
] | permissive | Julian/doc-gen | fbadbdc2d2f9365b50adf71e294f360fdd5cb6dd | 0ccd8bd2e2bdba537496350a26c505a55d28c258 | refs/heads/master | 1,671,263,423,675 | 1,601,073,044,000 | 1,601,073,044,000 | 298,692,003 | 0 | 0 | null | 1,601,072,937,000 | 1,601,072,936,000 | null | UTF-8 | Lean | false | false | 14,607 | lean | /-
Copyright (c) 2019 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Robert Y. Lewis
-/
import tactic.core system.io data.string.defs tactic.interactive data.list.sort
import all
/-!
Used to generate a json file for html docs.
The json file is a list... |
3cddfd34adad044601ad0f4d9679dea5cde06857 | bdb33f8b7ea65f7705fc342a178508e2722eb851 | /order/order_iso.lean | 653408e02c2ca94c2879632e0d2d5b2cd26f7afb | [
"Apache-2.0"
] | permissive | rwbarton/mathlib | 939ae09bf8d6eb1331fc2f7e067d39567e10e33d | c13c5ea701bb1eec057e0a242d9f480a079105e9 | refs/heads/master | 1,584,015,335,862 | 1,524,142,167,000 | 1,524,142,167,000 | 130,614,171 | 0 | 0 | Apache-2.0 | 1,548,902,667,000 | 1,524,437,371,000 | Lean | UTF-8 | Lean | false | false | 12,543 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import order.basic logic.embedding
open function
universes u v w
variables {α : Type*} {β : Type*} {γ : Type*}
{r : α → α → Prop} {s : β → β → Prop} {t : γ → γ → ... |
885ab863cbd8e74b23044a581de33daef3390a83 | 137c667471a40116a7afd7261f030b30180468c2 | /src/measure_theory/conditional_expectation.lean | 3ea640096b6ca1ef0b33941e6fde16d101847d61 | [
"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 | 16,111 | lean | /-
Copyright (c) 2021 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import measure_theory.l2_space
/-! # Conditional expectation
The conditional expectation will be defined for functions in `L²` by an orthogonal projection into
a compl... |
3bd720c87d74ffb59aba14f4657d33a7951b35fc | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/algebra/homology/flip.lean | 8963be0280c5dc4125e8e2060ead9f4ddd9bcd19 | [
"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 | 3,398 | 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
/-!
# Flip a complex of complexes
For now we don't have double complexes as a distinct thing,
but we can model them as c... |
976f8bde531db33a059aee4fcd6366a3d5ab1827 | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/order/zorn.lean | 01d863cedbab1bef41f885305ee65f8f3a3cfc9f | [
"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 | 13,825 | 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.lattice
noncomputable theory
univ... |
9a5c3a3b58f7ee72e58e358e93adafa629173d05 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /stage0/src/Lean/Server/InfoUtils.lean | f98799cfda5ea52063260e7c7e394ad9be719b4d | [
"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 | 9,846 | lean | /-
Copyright (c) 2021 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki
-/
import Lean.DocString
import Lean.Elab.InfoTree
import Lean.PrettyPrinter.Delaborator.Options
import Lean.Util.Sorry
protected structure String.Range where
... |
2f735dece9a19f3138f2e660e05e2eb330c38bb1 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/ring_theory/simple_module.lean | 9036f849b78858edb6cdcacef64d8e03af54854c | [
"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 | 5,357 | lean | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import linear_algebra.span
import order.atoms
/-!
# Simple Modules
## Main Definitions
* `is_simple_module` indicates that a module has no proper submodules
(t... |
fa887de6c642b5f1495c886b81cba28a55e886cd | 618003631150032a5676f229d13a079ac875ff77 | /src/geometry/euclidean.lean | 460756040d7927129fd2709f45014400e7bf86a6 | [
"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 | 942 | lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Joseph Myers.
-/
import analysis.normed_space.real_inner_product
import analysis.normed_space.add_torsor
noncomputable theory
/-!
# Euclidean spaces
This file defines Euclidean affine ... |
47a49ca2b0d460919a703d34451eb9027cca5879 | 97c8e5d8aca4afeebb5b335f26a492c53680efc8 | /ground_zero/types/eq.lean | 08de05c9fb5e6c849055167779a3caa5e26db5d1 | [] | no_license | jfrancese/lean | cf32f0d8d5520b6f0e9d3987deb95841c553c53c | 06e7efaecce4093d97fb5ecc75479df2ef1dbbdb | refs/heads/master | 1,587,915,151,351 | 1,551,012,140,000 | 1,551,012,140,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,217 | lean | import ground_zero.proto ground_zero.meta.hott_theory
namespace ground_zero.types
universes u v
theorem K {α : Sort u} {a b : α} (p q : a = b) : p = q :=
by trivial
inductive eq {α : Sort u} (a : α) : α → Sort u
| refl : eq a
attribute [refl] eq.refl
hott theory
notation a ` = ` b ` :> ` α := @eq α a b
/- fails!
... |
752996be681fb3221901c125ee211e115240390a | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/vm_eval1.lean | 6b37423aeb68bb72f617942d6f36d0e9dc2e23f3 | [
"Apache-2.0"
] | permissive | leanprover-community/lean | 12b87f69d92e614daea8bcc9d4de9a9ace089d0e | cce7990ea86a78bdb383e38ed7f9b5ba93c60ce0 | refs/heads/master | 1,687,508,156,644 | 1,684,951,104,000 | 1,684,951,104,000 | 169,960,991 | 457 | 107 | Apache-2.0 | 1,686,744,372,000 | 1,549,790,268,000 | C++ | UTF-8 | Lean | false | false | 776 | lean | open bool nat
-- set_option trace.compiler.code_gen true
attribute [reducible]
definition foo (b : bool) : Type :=
cond b nat (nat → nat)
definition bla (b : bool) : foo b → nat :=
bool.cases_on b (λ f, f 100) (λ n, n)
definition of_dec (p : Prop) [h : decidable p] : bool :=
decidable.cases_on h (λ h, ff) (λ h, tt)... |
a7f4105eead975db195186f60bb6300a04b44298 | 9b9a16fa2cb737daee6b2785474678b6fa91d6d4 | /src/algebra/group.lean | dd598aae12cbc9a71dc089daea487d3c3c911d5a | [
"Apache-2.0"
] | permissive | johoelzl/mathlib | 253f46daa30b644d011e8e119025b01ad69735c4 | 592e3c7a2dfbd5826919b4605559d35d4d75938f | refs/heads/master | 1,625,657,216,488 | 1,551,374,946,000 | 1,551,374,946,000 | 98,915,829 | 0 | 0 | Apache-2.0 | 1,522,917,267,000 | 1,501,524,499,000 | Lean | UTF-8 | Lean | false | false | 31,269 | 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
Various multiplicative and additive structures.
-/
import tactic.interactive data.option.defs
section pending_1857
/- Transport multiplicative to add... |
7f9dde3290487496482ade8ee77d213d5dbe57d2 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/measure_theory/integral/interval_integral.lean | f330203708dfcef90afc73ebbec57ff0017c28aa | [
"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 | 124,694 | lean | /-
Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov, Patrick Massot, Sébastien Gouëzel
-/
import analysis.calculus.extend_deriv
import analysis.calculus.fderiv_measurable
import analysis.normed_space.dual
import m... |
4f3e7b412b0752d913c457074ee7012a12ab20a8 | 2cf781335f4a6706b7452ab07ce323201e2e101f | /decodex86/src/decodex86.lean | 7f62ffffa393e9800f255acea807c33fc75e0d19 | [] | no_license | simonjwinwood/reopt-vcg | 697cdd5e68366b5aa3298845eebc34fc97ccfbe2 | 6aca24e759bff4f2230bb58270bac6746c13665e | refs/heads/master | 1,586,353,878,347 | 1,549,667,148,000 | 1,549,667,148,000 | 159,409,828 | 0 | 0 | null | 1,543,358,444,000 | 1,543,358,444,000 | null | UTF-8 | Lean | false | false | 1,716 | lean |
import system.io
import .instruction
import .sexp -- debugging
namespace decodex86
/-
This function decodes the contents of input using the helper binary
located at path. The binary is expected to be llvm-tablegen-support
(from this same repo). The result of this function is a
decodex86.document, i.e. a list ... |
3169a081e523027a6976e8a86ed8c653caad3988 | 2c096fdfecf64e46ea7bc6ce5521f142b5926864 | /src/Init/Core.lean | bfb8f9d92b4b5b78ec13e48dde175b187018b8b7 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | Kha/lean4 | 1005785d2c8797ae266a303968848e5f6ce2fe87 | b99e11346948023cd6c29d248cd8f3e3fb3474cf | refs/heads/master | 1,693,355,498,027 | 1,669,080,461,000 | 1,669,113,138,000 | 184,748,176 | 0 | 0 | Apache-2.0 | 1,665,995,520,000 | 1,556,884,930,000 | Lean | UTF-8 | Lean | false | false | 65,826 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
notation, basic datatypes and type classes
-/
prelude
import Init.Prelude
import Init.SizeOf
set_option linter.missingDocs true -- keep it documented
univers... |
4d88cfec753823d1a57a2b8d6e75c6b28140a3b3 | a46270e2f76a375564f3b3e9c1bf7b635edc1f2c | /5.8.1-4.6.6.lean | 23237cff583603669e5a5346245ae633913c44e7 | [
"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 | 826 | lean | variables (real : Type) [ordered_ring real]
variables (log exp : real → real)
variable log_exp_eq : ∀ x, log (exp x) = x
variable exp_log_eq : ∀ {x}, x > 0 → exp (log x) = x
variable exp_pos : ∀ x, exp x > 0
variable exp_add : ∀ x y, exp (x + y) = exp x * exp y
-- this ensures the assumptions are avai... |
58187a60fdece25d4ade64b6764e4093b27e45d3 | 205f0fc16279a69ea36e9fd158e3a97b06834ce2 | /src/01_Equality/06_properties.lean | 8e1a798a6ca6309011964f251047c770a9f72fb7 | [] | no_license | kevinsullivan/cs-dm-lean | b21d3ca1a9b2a0751ba13fcb4e7b258010a5d124 | a06a94e98be77170ca1df486c8189338b16cf6c6 | refs/heads/master | 1,585,948,743,595 | 1,544,339,346,000 | 1,544,339,346,000 | 155,570,767 | 1 | 3 | null | 1,541,540,372,000 | 1,540,995,993,000 | Lean | UTF-8 | Lean | false | false | 4,770 | lean | /-
HOMEWORK: Read, complete, submit.
We've seen that equality is reflexive.
That is, everything is equal to itself.
It is also symmetric in the sense that
if any value, a, is equal to some other
value, b, i.e., if a = b, then b is also
equal to a, i.e., b = a.
What this means is we have an inference
rule that bot... |
72cc015c5bcfb1b6cb993c5de66bddc4994f360e | 94e33a31faa76775069b071adea97e86e218a8ee | /src/information_theory/hamming.lean | 6d0c9a16d68fcd01cf33daf06fa6d3e401f6b5e5 | [
"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 | 14,219 | lean | /-
Copyright (c) 2022 Wrenna Robson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wrenna Robson
-/
import analysis.normed_space.basic
/-!
# Hamming spaces
The Hamming metric counts the number of places two members of a (finite) Pi type
differ. The Hamming norm is ... |
6301d2d640aff2a35a24df964a0f597fc6cba79f | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/int/order/basic.lean | 2b426b0dd1aaac0c855a546d239e75545bc3dcfd | [
"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 | 25,901 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
import data.int.basic
import data.int.cast.basic
import algebra.ring.divisibility
import algebra.order.group.abs
import algebra.order.ring.char_zero
import tactic.asser... |
49e866682d85ba9f92a21cf28252c6d33c43c6f7 | 2cf781335f4a6706b7452ab07ce323201e2e101f | /decodex86/src/instruction.lean | 4196f55ff31180866be7faa5d59613b092fd4854 | [] | no_license | simonjwinwood/reopt-vcg | 697cdd5e68366b5aa3298845eebc34fc97ccfbe2 | 6aca24e759bff4f2230bb58270bac6746c13665e | refs/heads/master | 1,586,353,878,347 | 1,549,667,148,000 | 1,549,667,148,000 | 159,409,828 | 0 | 0 | null | 1,543,358,444,000 | 1,543,358,444,000 | null | UTF-8 | Lean | false | false | 9,149 | lean |
import .sexp
namespace decodex86
def regN := string
structure register :=
(top : regN)
(reg : regN)
(width : ℕ)
(offset : ℕ)
def register_to_string : register -> string := λr,
string.intercalate " " ["(", "R", r.top, r.reg, repr r.width, repr r.offset, ")"]
instance register_has_repr : has_repr registe... |
acb188f27187d4bad9150b30eb0a3ab0789a0e8f | 46125763b4dbf50619e8846a1371029346f4c3db | /src/tactic/interactive.lean | 52cd5b9fa3b06d8cde212260a9c8946262b16b2e | [
"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 | 33,711 | lean |
/-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Simon Hudon, Sebastien Gouezel, Scott Morrison
-/
import tactic.lint
open lean
open lean.parser
local postfix `?`:9001 := optional
local postfix *:9001 := many
name... |
fefd4e33173e81ca7141558200a51a3c85c94723 | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/order/galois_connection.lean | 4bb8db24f4ba5db8bbbd10c01b73f0659977509a | [
"Apache-2.0"
] | permissive | jumpy4/mathlib | d3829e75173012833e9f15ac16e481e17596de0f | af36f1a35f279f0e5b3c2a77647c6bf2cfd51a13 | refs/heads/master | 1,693,508,842,818 | 1,636,203,271,000 | 1,636,203,271,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 25,154 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import order.complete_lattice
import order.order_dual
/-!
# Galois connections, insertions and coinsertions
Galois connections are order theoretic adjoints, i.e. a p... |
e205cd815a0f1829016f3dd3b641160d90820cdd | fecda8e6b848337561d6467a1e30cf23176d6ad0 | /src/algebra/group_power/basic.lean | 87680b71bee917af3103b708d9a6144969f589ed | [
"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 | 4,926 | lean | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis
-/
import algebra.order_functions
import deprecated.group
/-!
# Power operations on monoids and groups
The power operation on monoids and groups.
We sep... |
8f0aef78ae28f92fc692bbf7f42092565bb64429 | 626e312b5c1cb2d88fca108f5933076012633192 | /src/group_theory/submonoid/operations.lean | 420abf54718acd5798b1e31e2a3c17db5bd9f96f | [
"Apache-2.0"
] | permissive | Bioye97/mathlib | 9db2f9ee54418d29dd06996279ba9dc874fd6beb | 782a20a27ee83b523f801ff34efb1a9557085019 | refs/heads/master | 1,690,305,956,488 | 1,631,067,774,000 | 1,631,067,774,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 34,820 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard,
Amelia Livingston, Yury Kudryashov
-/
import group_theory.submonoid.basic
import data.equiv.mul_add
import al... |
316b23622b7f549069d82999c034dfb7552b48f7 | 43dcf09a5df9dc4729cdc024e8680eeaacd05af3 | /facts.lean | 34bec341920c87568ff1e89eb79a275ac0306180 | [] | no_license | khoek/lmath | f9ea911aabee1eb276a5319e70a5e62e6bfe8fb1 | a4f35205e6b5a3f16926234bf8eb7f7b5f56e47f | refs/heads/master | 1,611,452,778,710 | 1,532,531,556,000 | 1,532,569,670,000 | 122,820,532 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 286 | lean | --facts which should be in the library but I haven't been bothered to find
lemma quotient_fact { β : Type } { α : setoid β } { a b : β } : (@setoid.r β α a b) → quot.mk α.r a = quot.mk α.r b := by admit
lemma leq_fact { a b : ℤ } : a ≤ b → b ≤ a → a = b := by admit |
e616101f6262f83845a2e05106c733b77bd4f8b6 | c055f4b7c29cf1aac2223bd8c1ac8d181a7c6447 | /src/categories/functor/default.lean | a4e424bda1b13b31a821f13f5e63d8c596c55bde | [
"Apache-2.0"
] | permissive | rwbarton/lean-category-theory-pr | 77207b6674eeec1e258ec85dea58f3bff8d27065 | 591847d70c6a11c4d5561cd0eaf69b1fe85a70ab | refs/heads/master | 1,584,595,111,303 | 1,528,029,041,000 | 1,528,029,041,000 | 135,919,126 | 0 | 0 | null | 1,528,041,805,000 | 1,528,041,805,000 | null | UTF-8 | Lean | false | false | 4,044 | 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
import ..category
import ..tactics
open categories
namespace categories.functor
universes u₁ v₁ u₂ v₂ u₃ v₃
structure Functor (C... |
81b0ffc6bfdb61cd2bdcb0684f7c90ec07f47887 | cf39355caa609c0f33405126beee2739aa3cb77e | /library/init/funext.lean | b14fb4b0bfd27943f8ca45c18b35bb38c8eb4df4 | [
"Apache-2.0"
] | permissive | leanprover-community/lean | 12b87f69d92e614daea8bcc9d4de9a9ace089d0e | cce7990ea86a78bdb383e38ed7f9b5ba93c60ce0 | refs/heads/master | 1,687,508,156,644 | 1,684,951,104,000 | 1,684,951,104,000 | 169,960,991 | 457 | 107 | Apache-2.0 | 1,686,744,372,000 | 1,549,790,268,000 | C++ | UTF-8 | Lean | false | false | 2,408 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
Extensional equality for functions, and a proof of function extensionality from quotients.
-/
prelude
import init.data.quot init.logic
open quotient
universes u ... |
623ba74b8816f27f970a5ecf0a770b7ee35cbf84 | 0b3933727d99a2f351f5dbe6e24716bb786a6649 | /src/sesh/types.lean | 83a49a7a26eda13ccaf851c448a07fad36c8f9bf | [] | no_license | Vtec234/lean-sesh | 1e770858215279f65aba92b4782b483ab4f09353 | d11d7bb0599406e27d3a4d26242aec13d639ecf7 | refs/heads/master | 1,587,497,515,696 | 1,558,362,223,000 | 1,558,362,223,000 | 169,809,439 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,494 | lean | /- Introduces types of Synchronous GV. -/
import metastuff
mutual inductive tp, sesh_tp
/- A, B, C -/
with tp: Type
| unit: tp
| fn: tp → tp → tp /- A⊸B -/
| sum: tp → tp → tp /- A+B -/
| prod: tp → tp → tp /- AxB -/
| sesh: sesh_tp → tp /- S -/
| hash: sesh_tp → tp /- S♯ -/
/- S, T -/
with sesh_tp: Type
| send: tp ... |
faf8c2edd17f5b64a5baf10b2cfcd67834c0de88 | 32da3d0f92cab08875472ef6cacc1931c2b3eafa | /src/measure_theory/measurable_space.lean | fb7e7f975ab2a359e29073871a514d9b32df2e90 | [
"Apache-2.0"
] | permissive | karthiknadig/mathlib | b6073c3748860bfc9a3e55da86afcddba62dc913 | 33a86cfff12d7f200d0010cd03b95e9b69a6c1a5 | refs/heads/master | 1,676,389,371,851 | 1,610,061,127,000 | 1,610,061,127,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 60,574 | 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 data.set.disjointed
import data.set.countable
import data.indicator_function
import data.equiv.encodable.lattice
import data.tprod
import order... |
d4c167c32f25cd65064f20445c713efeb59d4c8c | 48eee836fdb5c613d9a20741c17db44c8e12e61c | /src/algebra/theories/group.lean | b228e433f0983c8482f94741429c244497215920 | [
"Apache-2.0"
] | permissive | fgdorais/lean-universal | 06430443a4abe51e303e602684c2977d1f5c0834 | 9259b0f7fb3aa83a9e0a7a3eaa44c262e42cc9b1 | refs/heads/master | 1,592,479,744,136 | 1,589,473,399,000 | 1,589,473,399,000 | 196,287,552 | 1 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 5,439 | lean | -- Copyright © 2019 François G. Dorais. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
import .basic
import .monoid
import .loop
set_option default_priority 0
namespace algebra
signature group (α : Type*) :=
(op : α → α → α)
(inv : α → α)
(id : α)
namespace group_sig
va... |
97cd5bc7f018fe66532834481165f47370be532f | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/topology/algebra/ring.lean | bd3f9d6d539bf9eb938e0cfccbaca51c255203f7 | [
"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 | 13,175 | 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.ring.prod
import ring_theory.ideal.basic
import ring_theory.subring
import topology.algebra.group
/-!
# Topological (semi)rings
A to... |
d9c6c89dadcaa5b33d7b3f85fbb243ee144e831e | 432d948a4d3d242fdfb44b81c9e1b1baacd58617 | /src/ring_theory/localization.lean | ca561189c8258df89c014d097394ed67126498d1 | [
"Apache-2.0"
] | permissive | JLimperg/aesop3 | 306cc6570c556568897ed2e508c8869667252e8a | a4a116f650cc7403428e72bd2e2c4cda300fe03f | refs/heads/master | 1,682,884,916,368 | 1,620,320,033,000 | 1,620,320,033,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 69,503 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston
-/
import data.equiv.ring
import group_theory.monoid_localization
import ring_theory.ideal.operations
import ring_theory.algebr... |
9969a5b213ccd33ec86ef877e7d509fac07a083b | f3a5af2927397cf346ec0e24312bfff077f00425 | /src/game/world1/level4.lean | 9e4270e585e199896de6ac2990fea032b1b5ae80 | [
"Apache-2.0"
] | permissive | ImperialCollegeLondon/natural_number_game | 05c39e1586408cfb563d1a12e1085a90726ab655 | f29b6c2884299fc63fdfc81ae5d7daaa3219f9fd | refs/heads/master | 1,688,570,964,990 | 1,636,908,242,000 | 1,636,908,242,000 | 195,403,790 | 277 | 84 | Apache-2.0 | 1,694,547,955,000 | 1,562,328,792,000 | Lean | UTF-8 | Lean | false | false | 4,160 | lean | import mynat.add -- definition of addition
namespace mynat -- hide
/- Axiom : add_zero (a : mynat) :
a + 0 = a
-/
/- Axiom : add_succ (a b : mynat) :
a + succ(b) = succ(a + b)
-/
/-
# Tutorial world
## Level 4: addition
We have a new import -- the definition of addition.
Peano defined addition `a + b` by inductio... |
2783ea46ab9b89414881064305f1a04c7d434a6a | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /tests/lean/run/def13.lean | fd23a4565a569906c25593cda6d2e23448aaad90 | [
"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 | 594 | lean | variable {α} (p : α → Prop) [DecidablePred p]
def filter : List α → List α
| [] => []
| a::as => if p a then a :: filter as else filter as
theorem filter_nil : filter p [] = [] :=
rfl
theorem filter_cons (a : α) (as : List α) : filter p (a :: as) = if p a then a :: filter p as else filter p as :=
rfl
theorem fil... |
9ca91447a3206dad13883caec5314180875c8c71 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/group_theory/subgroup.lean | fac37514c82fdf5393e09ef3a7ef2fa38824f3cb | [
"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 | 80,832 | 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
import algebra.group.conj
import algebra.pointwise
import order.atoms
/-!
# Subgroups
This file defines multiplicative and additive subgroup... |
039702a7cedfb0045034f55816aa47a0e60278f8 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/data/set/countable.lean | 29bb573f252db3d29202df4366b4f6acec35a10d | [
"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 | 10,653 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import data.set.finite
import logic.equiv.list
/-!
# Countable sets
-/
noncomputable theory
open function set encodable
open classical (hiding some)
open_locale cl... |
3566739554eae9ec6898bf82c98245d8fef8f8f5 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/run/simp_zeta.lean | e3ebedb8db8f251d02ed04f393ad65eb77e3765f | [
"Apache-2.0"
] | permissive | GaloisInc/lean | aa1e64d604051e602fcf4610061314b9a37ab8cd | f1ec117a24459b59c6ff9e56a1d09d9e9e60a6c0 | refs/heads/master | 1,592,202,909,807 | 1,504,624,387,000 | 1,504,624,387,000 | 75,319,626 | 2 | 1 | Apache-2.0 | 1,539,290,164,000 | 1,480,616,104,000 | C++ | UTF-8 | Lean | false | false | 153 | lean | example (n : ℕ) : let m := 0 + n in m = n :=
begin
intro,
dsimp [m],
simp,
end
example (n : ℕ) : let m := 0 + n in m = n :=
begin
intro,
simp *,
end |
6b9abb18e446f5b4ccf0f302f84b448ecafd55d0 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/eqn_compiler_loop.lean | 823ab3f7d91b40e3774ac7f1630203edca431916 | [
"Apache-2.0"
] | permissive | leanprover-community/lean | 12b87f69d92e614daea8bcc9d4de9a9ace089d0e | cce7990ea86a78bdb383e38ed7f9b5ba93c60ce0 | refs/heads/master | 1,687,508,156,644 | 1,684,951,104,000 | 1,684,951,104,000 | 169,960,991 | 457 | 107 | Apache-2.0 | 1,686,744,372,000 | 1,549,790,268,000 | C++ | UTF-8 | Lean | false | false | 100 | lean | open nat
theorem succ_ne_self : ∀ (n : ℕ), succ n ≠ n
| 0 h := absurd h (nat.succ_ne_zero 0)
|
557acc74a4de2a9e721757647c4be378da6d6384 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/ring_theory/witt_vector/isocrystal.lean | 7323a6d8f3312aba2d12c4c2b6454110f57ca753 | [
"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 | 8,428 | lean | /-
Copyright (c) 2022 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import ring_theory.witt_vector.frobenius_fraction_field
/-!
## F-isocrystals over a perfect field
When `k` is an integral domain, so is `𝕎 k`, and we can consi... |
dcddf3b824e2b957927b81fae891f90fec824e06 | 367134ba5a65885e863bdc4507601606690974c1 | /src/set_theory/cofinality.lean | eac11a290f3fb3ef4d035cd6aa957e685a599450 | [
"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 | 23,540 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Floris van Doorn
-/
import set_theory.cardinal_ordinal
/-!
# Cofinality
This file contains the definition of cofinality of a ordinal number and regular cardinals
## M... |
cd27dbbb53a9758fc355f015bee8918a3c5a7e63 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/combinatorics/additive/ruzsa_covering.lean | a7f65da9f18fac92277168b218a9971a5824c461 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 1,980 | 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.pointwise
/-!
# Ruzsa's covering lemma
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
... |
a8884ef7dd1a224653e473d49a1a2bf41d568718 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/field_theory/normal.lean | 7694d2e91e159197bd0d219d44578c6410cb1185 | [
"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 | 15,246 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Thomas Browning, Patrick Lutz
-/
import field_theory.adjoin
import field_theory.tower
import group_theory.solvable
import ring_theory.power_basis
/-!
# Normal field extensions
... |
4364fc8bece7e7791ca577d0509ba89319c69ddb | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/run/matchGenBug.lean | 8b77c53672a8e5551c23f22862c1201dfb39ef54 | [
"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 | 639 | lean | theorem foo (x : Nat) (h : x > 0) : x ≠ 0 :=
match x with
| 0 => sorry
| h+1 => sorry
inductive Mem : α → List α → Prop where
| head (a : α) (as : List α) : Mem a (a::as)
| tail (a b : α) (bs : List α) : Mem a bs → Mem a (b::bs)
infix:50 "∈" => Mem
theorem mem_split {a : α} {as : List α} (h : a ∈ as) : ∃ ... |
6f845a530abfcf3190d247dfd0b13c69680cf8c4 | e6b113af18eebb6e73c60e14d13ae096c05fe343 | /tutorial.lean | 4ccdb26293eb42668cbffbc66ebec0b176c1c391 | [] | no_license | bmsherman/lean-tutorial | 3889f1a4e7a16692759a6719c0e81c1cec9d603e | fe58a887b32e5f1e305e1e7a94766cd3585f01e2 | refs/heads/master | 1,621,098,141,939 | 1,508,513,676,000 | 1,508,513,676,000 | 107,567,061 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,111 | lean | /- This file is a tutorial for Coq users getting started
with Lean. They are quite similar systems, so picking
up Lean should not be too difficult.
I highly recommend consulting the Coq-Lean cheatsheet
that Joey Dodds and I made this summer:
https://jldodds.github.io/coq-lean-cheatsheet/
-/
import .tac... |
24e5baa54fd25f008f6182c8b883fb9e739ad08d | 56e5b79a7ab4f2c52e6eb94f76d8100a25273cf3 | /src/evaluation_step.lean | 360c3bf2ba9caea2807aec47331db5af1bbb49b6 | [
"Apache-2.0"
] | permissive | DyeKuu/lean-tpe-public | 3a9968f286ca182723ef7e7d97e155d8cb6b1e70 | 750ade767ab28037e80b7a80360d213a875038f8 | refs/heads/master | 1,682,842,633,115 | 1,621,330,793,000 | 1,621,330,793,000 | 368,475,816 | 0 | 0 | Apache-2.0 | 1,621,330,745,000 | 1,621,330,744,000 | null | UTF-8 | Lean | false | false | 2,560 | lean | import system.io
import .utils.util
import .utils.json
import all
import .evaluation
meta def evaluation_harness_from_decls_file
{search_state : Type}
[has_to_tactic_json search_state]
(search_core : state_t search_state tactic unit)
(decls_file : string)
(dest : string)
(global_timeout : ℕ) -- seconds
-... |
3a1dce5b1698b6f841235dbe35420aae908c6459 | 33340b3a23ca62ef3c8a7f6a2d4e14c07c6d3354 | /dlo/nnf.lean | cfa642aea0afd41c3250782948880dd88da54eb1 | [] | no_license | lclem/cooper | 79554e72ced343c64fed24b2d892d24bf9447dfe | 812afc6b158821f2e7dac9c91d3b6123c7a19faf | refs/heads/master | 1,607,554,257,488 | 1,578,694,133,000 | 1,578,694,133,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,828 | lean | import ..logic .qfree .remove_neg
-- Requires : nqfree arg
-- Ensures : nqfree ret
def push_neg : formula_dlo → formula_dlo
| ⊤' := ⊥'
| ⊥' := ⊤'
| (A' a) := remove_neg a
| (¬' p) := ⊥'
| (p ∨' q) := push_neg p ∧' push_neg q
| (p ∧' q) := push_neg p ∨' push_neg q
| (∃' p) := ⊥'
lemma nqfree_push_neg :
∀ {p : ... |
1e9c2d3c6f4de0b713a0dc4dc456e7e320549b3e | ca1ad81c8733787aba30f7a8d63f418508e12812 | /clfrags/src/hilbert/wr/proofs/dc.lean | ac91bd6915a90ca1aa5a64255ee1169676ae58d6 | [] | no_license | greati/hilbert-classical-fragments | 5cdbe07851e979c8a03c621a5efd4d24bbfa333a | 18a21ac6b2e890060eb4ae65752fc0245394d226 | refs/heads/master | 1,591,973,117,184 | 1,573,822,710,000 | 1,573,822,710,000 | 194,334,439 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,816 | lean | import hilbert.wr.dc
namespace clfrags
namespace hilbert
namespace wr
namespace dc
theorem dc₄' {a b c : Prop} (h₁ : dc a b c) : dc b a c :=
have h₂ : dc (dc b a c) (dc a b c) (dc a b c), from dc₃ h₁,
have h₃ : dc (dc a b c) (dc b a c) (d... |
e37d438bc1f464a08f6fc145f6dd9346da575f14 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /stage0/src/Init/Data/String/Extra.lean | 8b740ab1a2c0b7679d899162515a358d00f47a42 | [
"Apache-2.0"
] | permissive | mhuisi/lean4 | 28d35a4febc2e251c7f05492e13f3b05d6f9b7af | dda44bc47f3e5d024508060dac2bcb59fd12e4c0 | refs/heads/master | 1,621,225,489,283 | 1,585,142,689,000 | 1,585,142,689,000 | 250,590,438 | 0 | 2 | Apache-2.0 | 1,602,443,220,000 | 1,585,327,814,000 | C | UTF-8 | Lean | false | false | 351 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import Init.Util
namespace String
def toNat! (s : String) : Nat :=
if s.isNat then
s.foldl (fun n c => n*10 + (c.toNat - '0'.toNat)) 0
else
pan... |
9aed739cd3ee083a9a3e128df852f255cb88a038 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/topology/subset_properties.lean | a12720f02132c4fbc720008d367a343f285cf8a9 | [
"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 | 65,651 | 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, Yury Kudryashov
-/
import topology.bases
import data.finset.order
import data.set.accumulate
/-!
# Properties of subsets of topological spaces
In this... |
0da78dc1b4a1a992598aaa22e5205af97a54c4ec | 1963cb8789bf8cf695607cc2d4106d7fdd8fb9f2 | /homework2/solutions2.lean | 121c494c2996c586c1984ccac3473a90e3a0fe6d | [] | no_license | mtegene/homework-mtegene-master | ed43dd0b8cbcea936b6eec82c614842eca02a406 | 5f9b3623a46d2d3b98c54d8cbc82962d3fef49f5 | refs/heads/master | 1,610,605,612,607 | 1,488,481,866,000 | 1,488,481,866,000 | 81,875,687 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,324 | lean | /- Homework 2 -/
/- Part I: tactic proofs -/
/- Do five propositional logic proofs and three quantifier proofs, following the
same constraints as on the last assignment, but this time using tactics.
(You can prove the same theorems as on the last assignment!)
-/
section
open classical
variables p q r s : ... |
13642999a24c41e9133b1b9ac4b61e20be18646e | d1bbf1801b3dcb214451d48214589f511061da63 | /src/topology/subset_properties.lean | 7ed73252f81bff72ac31d2401a1403747057fba1 | [
"Apache-2.0"
] | permissive | cheraghchi/mathlib | 5c366f8c4f8e66973b60c37881889da8390cab86 | f29d1c3038422168fbbdb2526abf7c0ff13e86db | refs/heads/master | 1,676,577,831,283 | 1,610,894,638,000 | 1,610,894,638,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 67,823 | 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, Yury Kudryashov
-/
import topology.continuous_on
import data.finset.order
/-!
# Properties of subsets of topological spaces
In this file we define var... |
4b76869cc67fb6b0588d66a5f71a44fbbe884cf6 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/lake/Lake/Build/Info.lean | 46e5227c043eb77a1f6ad0dc422d18a54727b317 | [
"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 | 9,353 | lean | /-
Copyright (c) 2022 Mac Malone. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mac Malone
-/
import Lake.Config.LeanExe
import Lake.Config.ExternLib
import Lake.Build.Facets
import Lake.Util.EquipT
/-!
# Build Info
This module defines the Lake build info type and r... |
12014d7571dbc185613cb33e15c5e7a7cf4a5f5e | b66669ef1ec06ddbd9526fe3afe0a68566dfbad3 | /src/utils.lean | 59dcfb1be27d805095b488af6096e00e77e3f95e | [
"MIT"
] | permissive | FerdoSil/LatticesAndCellularAutomata | 40185a9099bb3cf1371c85f1ca33a17c2e26fecb | 2a69d2e74a231addf0e446dca86ef90d50d60218 | refs/heads/master | 1,587,683,992,072 | 1,586,018,471,000 | 1,586,018,471,000 | 171,533,028 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 43,135 | lean | -- Random assortment of utilities used throughout the project.
-- Integer (modulo) arithmetic properties.
-- Data structure properties.
-- Auxiliary algorithms and their poperties.
import data.int.basic data.list data.vector tactic.omega tactic.linarith
namespace utils
open int nat list
lemma gt_and_gt_of_mul_gt ... |
d3ec0cde1b6776f3b25bb4a56e82ca14cc54ddfa | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /02_Dependent_Type_Theory.org.34.lean | 7046d714ba591cf20a4d2a287fd13635559b6e6d | [] | 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 | 276 | lean | /- page 28 -/
import standard
import data.sigma data.prod
variable A : Type
variable B : A → Type
variable a : A
variable b : B a
variables C D : Type
variables (c : C) (d : D)
open sigma.ops
open prod.ops
eval (a, b).1
eval (a, b).2
eval ⟨c, d⟩.1
eval ⟨c, d⟩.2
|
a85fd5eff7d6184237fe24b9a00afaf41a2c1cb9 | 26ac254ecb57ffcb886ff709cf018390161a9225 | /src/ring_theory/multiplicity.lean | 1dbbaf4dbe8e1fd371c94f63184d09fca2c11c56 | [
"Apache-2.0"
] | permissive | eric-wieser/mathlib | 42842584f584359bbe1fc8b88b3ff937c8acd72d | d0df6b81cd0920ad569158c06a3fd5abb9e63301 | refs/heads/master | 1,669,546,404,255 | 1,595,254,668,000 | 1,595,254,668,000 | 281,173,504 | 0 | 0 | Apache-2.0 | 1,595,263,582,000 | 1,595,263,581,000 | null | UTF-8 | Lean | false | false | 17,312 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Chris Hughes
-/
import algebra.associated
import data.int.gcd
import algebra.big_operators
variables {α : Type*}
open nat roption
open_locale big_operators
theorem... |
2698880e3f69b8db22736b46a78ddc40e342cd8f | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/continued_fractions/translations.lean | ae7b5a8324b5d007d567b4356946ee7333316ecb | [
"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 | 5,498 | lean | /-
Copyright (c) 2019 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import algebra.continued_fractions.basic
/-!
# Basic Translation Lemmas Between Functions Defined for Continued Fractions
> THIS FILE IS SYNCHRONIZED WITH MATHLI... |
df90fa5632bc4ff1e357af9313205c9e5805da50 | b00eb947a9c4141624aa8919e94ce6dcd249ed70 | /src/Lean/Server/Snapshots.lean | 55a7d1cbc8b349cda40e618e083cfedd4240518d | [
"Apache-2.0"
] | permissive | gebner/lean4-old | a4129a041af2d4d12afb3a8d4deedabde727719b | ee51cdfaf63ee313c914d83264f91f414a0e3b6e | refs/heads/master | 1,683,628,606,745 | 1,622,651,300,000 | 1,622,654,405,000 | 142,608,821 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,431 | lean | /-
Copyright (c) 2020 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki
-/
import Init.System.IO
import Lean.Elab.Import
import Lean.Elab.Command
/-! One can think of this module as being a partial reimplementation
of Lean.Elab.Fron... |
1aa95aaf82c08be4caf7966acc5b9424140ab675 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/measure_theory/measure/content.lean | 638de3e349a3739396ea75ede0751b1290d5babd | [
"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 | 17,125 | lean | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import measure_theory.measure.measure_space
import measure_theory.measure.regular
import topology.opens
import topology.compacts
/-!
# Contents
In this file we ... |
2749e305e8bb4b2bc8fbf93b41ad89b0ca8a0058 | d29d82a0af640c937e499f6be79fc552eae0aa13 | /src/group_theory/complement.lean | bb65d3c1d49a4ccf7a08ee37cbc65a7bbc7f61e8 | [
"Apache-2.0"
] | permissive | AbdulMajeedkhurasani/mathlib | 835f8a5c5cf3075b250b3737172043ab4fa1edf6 | 79bc7323b164aebd000524ebafd198eb0e17f956 | refs/heads/master | 1,688,003,895,660 | 1,627,788,521,000 | 1,627,788,521,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 16,264 | lean | /-
Copyright (c) 2021 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import group_theory.group_action
import group_theory.order_of_element
import group_theory.quotient_group
/-!
# Complements
In this file we define the complement ... |
fe34cb5a810d85a3f0ff3b31c20d27f8c67366fd | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/data/finset/pi.lean | 06e4681d032e7e5ddc07b05c10cc2cc4224d9200 | [
"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 | 4,454 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import data.finset.basic
import data.multiset.pi
/-!
# The cartesian product of finsets
-/
namespace finset
open multiset
/-! ### pi -/
section pi
variables {α : T... |
ea4a252bebf93733d78a3d061f5b33627e6a83f8 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/ifcongr.lean | 06d4ac52d2f9107177242c840240055d65a907c0 | [
"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 | 552 | lean | --
@[simp] theorem andTrue (p : Prop) : (p ∧ True) = p :=
propext <| Iff.intro (fun ⟨h, _⟩ => h) (fun h => ⟨h, trivial⟩)
attribute [simp] Nat.add_comm
theorem ex1 (x : Nat) : (if x > 3 ∧ True then 1 else 2) = (if x > 3 then 1 else 2) :=
by simp
theorem ex2 (x : Nat) : (if x = 0 ∧ True then x + 1 else 2 + x) = (if ... |
f5e74dd41cc2749c3653a77915ff683b69520c6c | 7da5ceac20aaab989eeb795a4be9639982e7b35a | /src/group_theory/sporadic_group.lean | c00face43b792cc3f2989db809c4c3ef45f409ef | [
"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 | 14,718 | lean | import .basic .monster .presentation .suzuki .higman_sims .mclaughlin .conway_groups .mathieu_group
-- import tactic.metadata
noncomputable theory
open monster suzuki higman_sims mclaughlin conway_groups mathieu_group coxeter_vertices mul_action
open category_theory (mk_ob)
local infix ` ≅ `:60 := isomorphic
local not... |
09efad29d76bca43002a4069321a0eeffe406e1f | 4bcaca5dc83d49803f72b7b5920b75b6e7d9de2d | /stage0/src/Lean/Meta/Tactic/Util.lean | 78bb8cbcf49aa2fa11e6eab5fa5245bf817dcb3b | [
"Apache-2.0"
] | permissive | subfish-zhou/leanprover-zh_CN.github.io | 30b9fba9bd790720bd95764e61ae796697d2f603 | 8b2985d4a3d458ceda9361ac454c28168d920d3f | refs/heads/master | 1,689,709,967,820 | 1,632,503,056,000 | 1,632,503,056,000 | 409,962,097 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,125 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Util.ForEachExpr
import Lean.Meta.Basic
import Lean.Meta.AppBuilder
import Lean.Meta.LevelDefEq
import Lean.Meta.PPGoal
namespace Lean.Meta
/-... |
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