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values | src_encoding stringclasses 2
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class | is_generated bool 1
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values | content stringlengths 3 6.12M |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
d042e235e2ade58466768b1e72551a4b5bf402e8 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /06_Inductive_Types.org.22.lean | fbfee5d618f5dc85d4a078cecf028965bea64a64 | [] | 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 | 296 | lean | /- page 84 -/
import standard
namespace hide
-- BEGIN
inductive false : Prop
inductive true : Prop :=
intro : true
inductive and (a b : Prop) : Prop :=
intro : a → b → and a b
inductive or (a b : Prop) : Prop :=
| intro_left : a → or a b
| intro_right : b → or a b
-- END
end hide
|
2caf41d9036aa3067eabdd99bc62789c75d144d8 | d642a6b1261b2cbe691e53561ac777b924751b63 | /src/analysis/complex/exponential.lean | 479985c5b192828587a0427c225c7a1fe62f5966 | [
"Apache-2.0"
] | permissive | cipher1024/mathlib | fee56b9954e969721715e45fea8bcb95f9dc03fe | d077887141000fefa5a264e30fa57520e9f03522 | refs/heads/master | 1,651,806,490,504 | 1,573,508,694,000 | 1,573,508,694,000 | 107,216,176 | 0 | 0 | Apache-2.0 | 1,647,363,136,000 | 1,508,213,014,000 | Lean | UTF-8 | Lean | false | false | 74,176 | 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
-/
import topology.instances.complex tactic.linarith data.complex.exponential
group_theory.quotient_group topology.metr... |
4157d920b45c0f4d2a92fa638425e43d1637cd3a | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/normed_space/complemented.lean | 7c71577bec79bfb6960e13305774231ef63a361b | [
"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 | 5,932 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import analysis.normed_space.banach
import analysis.normed_space.finite_dimension
/-!
# Complemented subspaces of normed vector spaces
> THIS FILE IS SYNCHRONIZED... |
106dca7f79e8b94fbc64d0a8bc6bc68d7f07c1c3 | 7b02c598aa57070b4cf4fbfe2416d0479220187f | /algebra/module_exact_couple.hlean | bde504c98a53d40f51f1956958cc0d81f7d9c6ae | [
"Apache-2.0"
] | permissive | jdchristensen/Spectral | 50d4f0ddaea1484d215ef74be951da6549de221d | 6ded2b94d7ae07c4098d96a68f80a9cd3d433eb8 | refs/heads/master | 1,611,555,010,649 | 1,496,724,191,000 | 1,496,724,191,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 25,972 | hlean | /- Exact couples of graded (left-) R-modules. This file includes:
- Constructing exact couples from sequences of maps
- Deriving an exact couple
- The convergence theorem for exact couples -/
-- Author: Floris van Doorn
import .graded ..homotopy.spectrum .product_group
open algebra is_trunc left_module is_equi... |
004353862103857613fd545e731f30607357aa34 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/analysis/normed_space/finite_dimension.lean | 87caaba6ba994cba91e541d86b67c193579449df | [
"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 | 37,334 | 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.asymptotics.asymptotic_equivalent
import analysis.normed_space.add_torsor
import analysis.normed_space.affine_isometry
import analysis.normed_sp... |
577e68234d023a697e45dbf908d4eeeea6e1c13e | a7eef317ddec01b9fc6cfbb876fe7ac00f205ac7 | /src/geometry/manifold/charted_space.lean | 0b7e0c5302d9b84911a24d648666f5299eb86aa7 | [
"Apache-2.0"
] | permissive | kmill/mathlib | ea5a007b67ae4e9e18dd50d31d8aa60f650425ee | 1a419a9fea7b959317eddd556e1bb9639f4dcc05 | refs/heads/master | 1,668,578,197,719 | 1,593,629,163,000 | 1,593,629,163,000 | 276,482,939 | 0 | 0 | null | 1,593,637,960,000 | 1,593,637,959,000 | null | UTF-8 | Lean | false | false | 34,173 | 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 topology.local_homeomorph
/-!
# Charted spaces
A smooth manifold is a topological space `M` locally modelled on a euclidean space (or a euclidean
half-... |
bf57316ca1818da7f3aee3393a4f54dda4a52e29 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/lake/examples/targets/src/Foo/Baz.lean | 1c6ad44c15ebfc410ecf0f06259ff583892c6324 | [
"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 | 24 | lean | def Foo.baz := "foobaz"
|
4e0cc8a230488f064d552d14596ed6c79523ae52 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/sufficies.lean | 99fd4b330eccf6e2b5e55bde78702af409fa3688 | [
"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 | 262 | lean | open nat
protected theorem one_le_bit0 (n : ℕ) : n ≠ 0 → 1 ≤ bit0 n :=
nat.cases_on n
(λ h, absurd rfl h)
(λ n h,
suffices 1 ≤ succ (succ (bit0 n)), from
eq.symm (nat.bit0_succ_eq n) ▸ this,
succ_le_succ (succ (bit0 n)).zero_le)
|
c65af3ba87b6f2104598b042151c83f82156a324 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/playground/fix.lean | 36385a422f79bf8bb14bfd248b61ecd620276272 | [
"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 | 205 | lean | partial def foo : Nat → Nat → Nat
| 0 a := a
| (n+1) a := foo n a + a + foo n (a+1)
def main (xs : List String) : IO UInt32 :=
let v := foo (xs.head.toNat) 10 in
IO.println (toString v) *>
pure 0
|
a2b754273b779d118eacfd8d4b674d04703f4e7f | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/tactic/doc_commands.lean | 60aef3d9d87e903d35daa22da867562d00e10478 | [
"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 | 17,316 | lean | /-
Copyright (c) 2020 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
-/
import tactic.fix_reflect_string
/-!
# Documentation commands
We generate html documentation from mathlib. It is convenient to collect lists of tactics, commands,... |
75e189792587cc30200e6095ca2ef4e323997c28 | f083c4ed5d443659f3ed9b43b1ca5bb037ddeb58 | /algebra/order.lean | 5eecea73a5f83342f8a87e5de8f96fbd897f8ac0 | [
"Apache-2.0"
] | permissive | semorrison/mathlib | 1be6f11086e0d24180fec4b9696d3ec58b439d10 | 20b4143976dad48e664c4847b75a85237dca0a89 | refs/heads/master | 1,583,799,212,170 | 1,535,634,130,000 | 1,535,730,505,000 | 129,076,205 | 0 | 0 | Apache-2.0 | 1,551,697,998,000 | 1,523,442,265,000 | Lean | UTF-8 | Lean | false | false | 4,935 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
universe u
variables {α : Type u}
lemma not_le_of_lt [preorder α] {a b : α} (h : a < b) : ¬ b ≤ a :=
(le_not_le_of_lt h).right
lemma not_lt_of_le [preorder α] {a b... |
11d6e8b1ba6228467f670747991c32d59a92a688 | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/number_theory/zsqrtd/gaussian_int.lean | 870b01b3cb519df8f23dd9e77ca0f495b91f378a | [
"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 | 12,543 | 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 number_theory.zsqrtd.basic
import data.complex.basic
import ring_theory.principal_ideal_domain
import number_theory.quadratic_reciprocity
/-!
# Gaussian integers
... |
ec0a459cbfccb6e559d03107390bef0c6be687b4 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /stage0/src/Init/Lean/Util/RecDepth.lean | 95863631e6a91ad25b0d4a29f4d6a8241e0c4159 | [
"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 | 663 | 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
-/
prelude
import Init.Lean.Data.Options
namespace Lean
def defaultMaxRecDepth := 512
def getMaxRecDepth (opts : Options) : Nat :=
opts.getNat `maxRecDepth ... |
8462c865f3706397be2aa641d39c4f5724d8de9b | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/error_pos_bug2.lean | 7df40186318a333cfb93a8a90bd87540fb45db50 | [
"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 | 396 | lean | inductive fibrant [class] (T : Type) : Type :=
mk : fibrant T
inductive Fib : Type :=
mk : ΠA : Type, fibrant A → Fib
namespace Fib
definition type [coercion] (F : Fib) : Type := Fib.rec_on F (λA f, A)
definition is_fibrant [instance] (F : Fib) : fibrant (type F) := Fib.rec_on F (λA f, f)
end Fib
-- open Fib
-- Pa... |
caaa3820e7b1237d54ea1f8a0309445ab225fcd3 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/topology/metric_space/completion.lean | d2bf39ffa9822d9647720ce321404f467b7da6b5 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,642 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Sébastien Gouëzel
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.topology.uniform_space.completion
import Mathlib.topology.metric_space.isometry
import... |
a398a86f459245a9491ff108e20f647d2005f4f1 | 9dd3f3912f7321eb58ee9aa8f21778ad6221f87c | /tests/lean/run/nested_inductive.lean | 821ba4008c6d330525072fdcc79f1fd6312346f0 | [
"Apache-2.0"
] | permissive | bre7k30/lean | de893411bcfa7b3c5572e61b9e1c52951b310aa4 | 5a924699d076dab1bd5af23a8f910b433e598d7a | refs/heads/master | 1,610,900,145,817 | 1,488,006,845,000 | 1,488,006,845,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,721 | lean | set_option trace.inductive_compiler.nested.define.failure true
set_option max_memory 1000000
inductive {u} vec (A : Type u) : nat -> Type u
| vnil : vec 0
| vcons : Pi (n : nat), A -> vec n -> vec (n+1)
namespace X1
print "simple"
inductive foo : Type
| mk : list foo -> foo
end X1
namespace X2
print "with param"
in... |
e14c7cc24f6c9d138fa6e84fd9f7fc18cbc3d9d9 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/group_theory/free_product.lean | beb73b8706d7e536732d26419de2bef174a68328 | [
"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 | 33,851 | lean | /-
Copyright (c) 2021 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn, Joachim Breitner
-/
import algebra.free_monoid
import group_theory.congruence
import group_theory.is_free_group
import group_theory.subgroup.pointwise
import data.list.chain
im... |
d3a94568b61f7bdd2b5f90f6cf868eb688d64d79 | 57fdc8de88f5ea3bfde4325e6ecd13f93a274ab5 | /tests/examples.lean | 23697c662c6c08d53296b9a239ab5b98e1494d78 | [
"Apache-2.0"
] | permissive | louisanu/mathlib | 11f56f2d40dc792bc05ee2f78ea37d73e98ecbfe | 2bd5e2159d20a8f20d04fc4d382e65eea775ed39 | refs/heads/master | 1,617,706,993,439 | 1,523,163,654,000 | 1,523,163,654,000 | 124,519,997 | 0 | 0 | Apache-2.0 | 1,520,588,283,000 | 1,520,588,283,000 | null | UTF-8 | Lean | false | false | 1,696 | lean | 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
example (s t u : set ℕ) (h : s ⊆ t ∩ u) (h' : u ⊆ s) : u ⊆ s → true :=
begin
delta has_subset.subset has_inte... |
8d2d399c92571520a14aaec13ffeac24ea7fcbb2 | 130c49f47783503e462c16b2eff31933442be6ff | /src/Lean/Elab/Deriving/Basic.lean | 5b4b8c2b436c347dbd458ff42a02bbfc459d3291 | [
"Apache-2.0"
] | permissive | Hazel-Brown/lean4 | 8aa5860e282435ffc30dcdfccd34006c59d1d39c | 79e6732fc6bbf5af831b76f310f9c488d44e7a16 | refs/heads/master | 1,689,218,208,951 | 1,629,736,869,000 | 1,629,736,896,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,106 | 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, Wojciech Nawrocki
-/
import Lean.Elab.Command
namespace Lean.Elab
open Command
def DerivingHandler := (typeNames : Array Name) → (args? : Option Syntax) → C... |
664ba43bd15d9d049c5307ea962f634ef023d87e | 5ec8f5218a7c8e87dd0d70dc6b715b36d61a8d61 | /events.lean | 3dfcfefc83044118feda0abf3512f65424968430 | [] | no_license | mbrodersen/kremlin | f9f2f9dd77b9744fe0ffd5f70d9fa0f1f8bd8cec | d4665929ce9012e93a0b05fc7063b96256bab86f | refs/heads/master | 1,624,057,268,130 | 1,496,957,084,000 | 1,496,957,084,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 27,609 | lean |
/- Observable events, execution traces, and semantics of external calls. -/
import .globalenvs .memory
namespace events
open integers word floats ast globalenvs values memory
ast.typ memory.perm_kind
/- * Events and traces -/
/- The observable behaviour of programs is stated in terms of
input/output events,... |
ca2fd82c12ed1abc0993fc106d4fb3930d083356 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /archive/imo/imo2008_q2.lean | 15c17b9c81941e4eb11924625fd7217e7a0c0b68 | [
"Apache-2.0"
] | permissive | hikari0108/mathlib | b7ea2b7350497ab1a0b87a09d093ecc025a50dfa | a9e7d333b0cfd45f13a20f7b96b7d52e19fa2901 | refs/heads/master | 1,690,483,608,260 | 1,631,541,580,000 | 1,631,541,580,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,205 | lean | /-
Copyright (c) 2021 Manuel Candales. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Manuel Candales
-/
import data.real.basic
import data.set.basic
import data.set.finite
/-!
# IMO 2008 Q2
(a) Prove that
```
x^2 / (x-1)^2 + y^2 / (y-1)^2 + z^2 / ... |
57244b9c609a40939f3aa28b589cb138ed151903 | fe84e287c662151bb313504482b218a503b972f3 | /src/data/pos_list.lean | efc6c0a932a8365803292312bd8ee939001389fd | [] | 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 | 8,937 | lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Neil Strickland
Here we define an inductive type of nonempty lists, and subtypes
of lists with specified starting and ending points. These can be
used for paths in a graph, or a mo... |
9174c2066693c722787e68b3eba4bcde2788cd1d | 0147f2031b9326cd40515c0735bc7b3217048388 | /library/init/meta/expr.lean | 39eb1ad39f5e493d5d26db768edc43c5bf061e62 | [
"Apache-2.0"
] | permissive | fpvandoorn/lean | d69aa9b497e6b689d499720ec88c8875744e4e2f | d457329969c7a18854a3cefdb3837306f43c2355 | refs/heads/master | 1,608,866,639,885 | 1,596,723,870,000 | 1,596,723,870,000 | 285,647,903 | 0 | 0 | Apache-2.0 | 1,596,740,075,000 | 1,596,740,074,000 | null | UTF-8 | Lean | false | false | 22,716 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.meta.level init.control.monad init.meta.rb_map
universes u v
open native
/-- Column and line position in a Lean source file. -/
structur... |
ef65b3ede7aab7fd43eedd3ae035cb6a89342dfd | df561f413cfe0a88b1056655515399c546ff32a5 | /6-advanced-addition-world/l8.lean | 594790c66bf9f41bd729cf7414a3c07ed11ccc68 | [] | no_license | nicholaspun/natural-number-game-solutions | 31d5158415c6f582694680044c5c6469032c2a06 | 1e2aed86d2e76a3f4a275c6d99e795ad30cf6df0 | refs/heads/main | 1,675,123,625,012 | 1,607,633,548,000 | 1,607,633,548,000 | 318,933,860 | 3 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 204 | lean | lemma eq_zero_of_add_right_eq_self {a b : mynat} : a + b = a → b = 0 :=
begin
intro s,
rw ← add_zero a at s,
rw add_assoc a 0 b at s,
rw zero_add at s,
have f := add_left_cancel a b 0,
exact f(s),
end |
453977c2977e06973bb36094a691f1a011c0b9f6 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/qpf/multivariate/constructions/sigma.lean | 784910c7c95401e3dc4de562a2de2b0572f191ef | [
"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 | 3,009 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import data.pfunctor.multivariate.basic
import data.qpf.multivariate.basic
/-!
# Dependent product and sum of QPFs are QPFs
-/
universes u
namespace mvqpf
open_locale m... |
ff105ce95e9e21c3da08a83746046ac816876daa | a4673261e60b025e2c8c825dfa4ab9108246c32e | /src/Lean/Meta/Match/Match.lean | 4062bd78de2259feee4819d32d7d155db2dc1654 | [
"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 | 31,126 | 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.Util.CollectLevelParams
import Lean.Util.Recognizers
import Lean.Compiler.ExternAttr
import Lean.Meta.Check
import Lean.Meta.Closure
import Lean... |
8f724d37ae504e0cab4e66bb8cd8dca97a37fb28 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/algebra/periodic.lean | f7146dd723aaa8e5720fd9dafc1845005cae0390 | [
"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 | 20,237 | lean | /-
Copyright (c) 2021 Benjamin Davidson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Benjamin Davidson
-/
import algebra.field.opposite
import algebra.module.basic
import algebra.order.archimedean
import data.int.parity
import group_theory.coset
/-!
# Periodicity
... |
34ad2531686392b4be1ae6584bd164a7c9a81cf0 | fcf3ffa92a3847189ca669cb18b34ef6b2ec2859 | /src/world5/level8.lean | 3c537da164ff5a3ae18986e58a1c807635524db5 | [
"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 | 166 | lean | example (P Q : Type) : (P → Q) → ((Q → empty) → (P → empty)) :=
begin
intro pq,
intro qf,
intro p,
apply qf,
apply pq,
exact p,
end
|
a082444fdcbebcc3b975596f1a9bc0237bd35d29 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/category_theory/isomorphism.lean | b1e754b3286e1c50723ad64e429fb7b40218427d | [
"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 | 13,290 | 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.functor
/-!
# Isomorphisms
This file defines isomorphisms between objects of a category.
## M... |
dd1ccd5faa3f6c1e670919e7774e78efc3b67b97 | 36c7a18fd72e5b57229bd8ba36493daf536a19ce | /library/data/rat/order.lean | ba8bd015b4ef836fad435ed7f43b3c5847fc3d90 | [
"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 | 16,136 | lean | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
Adds the ordering, and instantiates the rationals as an ordered field.
-/
import data.int algebra.ordered_field algebra.group_power data.rat.basic
open quot eq.ops
open al... |
5e87a7af0ea063f69bbc4a0483509bf85ecc121b | 27a31d06bcfc7c5d379fd04a08a9f5ed3f5302d4 | /src/Lean/Elab/PreDefinition/Structural/Eqns.lean | 189298a2bc8f911f1b68ef6f16a3f704846cdfc9 | [
"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 | joehendrix/lean4 | 0d1486945f7ca9fe225070374338f4f7e74bab03 | 1221bdd3c7d5395baa451ce8fdd2c2f8a00cbc8f | refs/heads/master | 1,640,573,727,861 | 1,639,662,710,000 | 1,639,665,515,000 | 198,893,504 | 0 | 0 | Apache-2.0 | 1,564,084,645,000 | 1,564,084,644,000 | null | UTF-8 | Lean | false | false | 9,431 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.Eqns
import Lean.Meta.Tactic.Split
import Lean.Meta.Tactic.Apply
import Lean.Elab.PreDefinition.Basic
import Lean.Elab.PreDefinition.Struct... |
93181d3d8a8fd3ac82f8fb06100200952e67a27f | 94e33a31faa76775069b071adea97e86e218a8ee | /src/data/mv_polynomial/basic.lean | 379204a439a1cab8de7645792b9e780021ffd586 | [
"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 | 48,175 | 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 ring_theory.adjoin.basic
import data.finsupp.antidiagonal
import algebra.monoid_algebra.basic
import order.symm_diff
/-!
# Mu... |
41d56bfb93307238b1d2ff994e9a6cf9e9f93e2e | c777c32c8e484e195053731103c5e52af26a25d1 | /src/measure_theory/covering/one_dim.lean | 1df64bd0d094b8126185e6ac35b4f81c70dc8c70 | [
"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 | 2,333 | lean | /-
Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import measure_theory.covering.density_theorem
import measure_theory.measure.haar_lebesgue
/-!
# Covering theorems for Lebesgue measure in one dimension
We ha... |
4d9a49a7421f7a494774af199fe9995b897f8556 | 618003631150032a5676f229d13a079ac875ff77 | /src/analysis/normed_space/riesz_lemma.lean | 6e3d2de83bd341dfa7cfeb3b6d42e37deab43410 | [
"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 | 2,329 | lean | /-
Copyright (c) 2019 Jean Lo. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean Lo
-/
import topology.metric_space.hausdorff_distance
/-!
# Riesz's lemma
Riesz's lemma, stated for a normed space over a normed field: for any
closed proper subspace F of E, there is ... |
42f67b07ce09860bf5649b252d21520654a990fa | 969dbdfed67fda40a6f5a2b4f8c4a3c7dc01e0fb | /src/topology/algebra/monoid.lean | f95d6a378b99721dc918b7458833f1383ae8590b | [
"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 | 12,779 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import topology.continuous_on
import group_theory.submonoid.operations
import algebra.group.prod
import algebra.pointwise
/-!
# Theory of topological... |
f8defb73ac6a314f10cc9e85ff088f77147b9943 | d7189ea2ef694124821b033e533f18905b5e87ef | /galois/nat/div_lemmas.lean | 7f1fa263d908392a0e99f47e82f432d480d90bc7 | [
"Apache-2.0"
] | permissive | digama0/lean-protocol-support | eaa7e6f8b8e0d5bbfff1f7f52bfb79a3b11b0f59 | cabfa3abedbdd6fdca6e2da6fbbf91a13ed48dda | refs/heads/master | 1,625,421,450,627 | 1,506,035,462,000 | 1,506,035,462,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,225 | lean | import .simplify_le
namespace nat
theorem step_induction_on {C : ℕ → Prop} {c:ℕ} (c_pos:0 < c)
(base : ∀(m:ℕ), m < c → C m)
(step : ∀(m:ℕ), C m → C (m + c))
: ∀ (n:ℕ), C n :=
begin
intro n,
induction n using nat.strong_induction_on with n ind,
by_cases (n < c),
{
exact base n h,
},
{
have n_ge_c :... |
75a0c544008ba5b8c6376996cfe2c82d5d44ef20 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/simpAutoUnfold.lean | 999a1fa8ba97bbcb4e2bcc757b15aa57d5c670c3 | [
"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 | 984 | lean | def append (as bs : List α) : List α :=
match as with
| [] => bs
| a :: as => a :: append as bs
theorem append_nil (as : List α) : append as [] = as := by
induction as <;> simp_all!
theorem append_nil' (as : List α) : append as [] = as := by
induction as <;> simp! [*]
theorem append_assoc (as bs cs : List ... |
5c9dfeec85697870a57124f7ecdd03bb710e1f48 | b147e1312077cdcfea8e6756207b3fa538982e12 | /data/int/basic.lean | 2d7cf675d18b978cacdb821909f703ec8ad3aedd | [
"Apache-2.0"
] | permissive | SzJS/mathlib | 07836ee708ca27cd18347e1e11ce7dd5afb3e926 | 23a5591fca0d43ee5d49d89f6f0ee07a24a6ca29 | refs/heads/master | 1,584,980,332,064 | 1,532,063,841,000 | 1,532,063,841,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 42,545 | 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 integers, with addition, multiplication, and subtraction.
-/
import data.nat.basic algebra.char_zero algebra.order_functions
open nat
namespace int
instance : inhab... |
d2f562c8b9fdaf841b36da9172461d3544abd95b | e37bb385769d6f4ac9931236fd07b708397e086b | /src/exercises/src_40_sequences.lean | beb50325df0adaaed9684d747c50a614c394c8f9 | [] | no_license | gihanmarasingha/ems_reals | 5f5d5b9d9dfb5a10da465046336d74995132dff6 | 9df527742db69d0a389add44b506538fdb4d0800 | refs/heads/master | 1,675,327,747,064 | 1,608,036,820,000 | 1,608,036,820,000 | 315,825,726 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,598 | lean | import data.real.basic
import data.set.basic
import tactic
namespace mth1001
/-
We'll only deal with real-valued sequences. Such a sequence is merely a function from `ℕ` to `ℝ`
We'll use the Lean built-in real number type rather than the type we've constructed.
-/
section convergence
-- `convergesto f a` means
def ... |
70ee0e031da99f1ee341301431704758512ee1ae | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/field_theory/separable.lean | 6ba14bbcdd1ea6f33af6c430d85db430085eaad3 | [
"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 | 21,122 | 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.squarefree
import data.polynomial.expand
import data.polynomial.splits
import field_theory.minpoly.field
import ring_theory.power_basis
/-!
# Separable polyno... |
70b626b7962408b3dc57cd337ad2fa7e61420be1 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/topology/continuous_on.lean | fca9e2b733088dbd7d7383c8f76277fe0b4c4b14 | [] | 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 | 40,673 | lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.topology.constructions
import Mathlib.PostPort
universes u_1 u_2 u_3 u_4
namespace Mathl... |
cebc9ba90b2bf16e827b98c07bc457c4659a9ae6 | b815abf92ce063fe0d1fabf5b42da483552aa3e8 | /library/init/data/option/basic.lean | 357d85cfdad6f80627b91705e4bdfccac70d5686 | [
"Apache-2.0"
] | permissive | yodalee/lean | a368d842df12c63e9f79414ed7bbee805b9001ef | 317989bf9ef6ae1dec7488c2363dbfcdc16e0756 | refs/heads/master | 1,610,551,176,860 | 1,481,430,138,000 | 1,481,646,441,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,015 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.logic init.category
open decidable
universe variables u v
instance (α : Type u) : inhabited (option α) :=
⟨none⟩
instance {α : Type u... |
e3d677edb7c6b1d1d4ff8d51d3eb8b3ca7927445 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/mv_polynomial/pderiv.lean | a00ea6a389635b8d204a1f10579c67ef14b699fe | [
"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 | 5,394 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shing Tak Lam
-/
import data.mv_polynomial.variables
import algebra.module.basic
import tactic.ring
/-!
# Partial derivatives of polynomials
This file defines the notion of the form... |
9ed046f4f3cacb92947a520e47476e203b562c74 | 41e069072396dcd54bd9fdadb27cfd35fd07016a | /src/apps/topological_semantics.lean | 84ab58a3dc50e17aad512c4055f7a03f80aadb8d | [
"MIT"
] | permissive | semorrison/ModalTab | 438ad601bd2631ab9cfe1e61f0d1337a36e2367e | cc94099194a2b69f84eb7a770b7aac711825179f | refs/heads/master | 1,585,939,884,891 | 1,540,961,947,000 | 1,540,961,947,000 | 155,500,181 | 0 | 0 | MIT | 1,540,961,175,000 | 1,540,961,175,000 | null | UTF-8 | Lean | false | false | 1,065 | lean | import defs analysis.topology.topological_space
open nnf
structure topo_model (α : Type) extends topological_space α :=
(v : ℕ → set α)
(is_alex : ∀s, (∀t∈s, is_open t) → is_open (⋂₀ s))
@[simp] def topo_force {α : Type} (tm : topo_model α) : α → nnf → Prop
| s (var n) := tm.v n s
| s (neg n) := ¬ tm.v n s
| s... |
1021a6ece17652d2fd899d11d50889902c6b11c3 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/topology/metric_space/gromov_hausdorff_realized.lean | f82894ad72d4547bfadb57b7458ff1dba60516fc | [
"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) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import topology.metric_space.gluing
import topology.metric_space.hausdorff_distance
import topology.continuous_function.bounded
/-!
# The Gromov-Hausdorff dist... |
9fdeee1b31048cfb1d3ed9183e72d555a9f86493 | bb31430994044506fa42fd667e2d556327e18dfe | /src/order/filter/ennreal.lean | 580c082a1d442ec0766660e50ac709239b8c0335 | [
"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 | 4,913 | 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 data.real.ennreal
import order.filter.countable_Inter
import order.liminf_limsup
/-!
# Order properties of extended non-negative reals
This file compiles filter... |
a2e40fc6c4da638009a341b29b0ac5133696290e | 54d7e71c3616d331b2ec3845d31deb08f3ff1dea | /library/tools/mini_crush/nano_crush.lean | 65b39f4bae8225bed71d6055c0652f64b90f97a3 | [
"Apache-2.0"
] | permissive | pachugupta/lean | 6f3305c4292288311cc4ab4550060b17d49ffb1d | 0d02136a09ac4cf27b5c88361750e38e1f485a1a | refs/heads/master | 1,611,110,653,606 | 1,493,130,117,000 | 1,493,167,649,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,863 | 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
We implement a crush-like strategy using simplifier,
SMT gadgets, and robust simplifier.
This is just a demo.
-/
namespace nano_crush
open tactic
meta def s... |
ac6557695c660a998d62901071a57145a4a614f5 | 9dd3f3912f7321eb58ee9aa8f21778ad6221f87c | /tests/lean/eta_tac.lean | ac57f4b1b58498e2dc55e5ad7f27689418250326 | [
"Apache-2.0"
] | permissive | bre7k30/lean | de893411bcfa7b3c5572e61b9e1c52951b310aa4 | 5a924699d076dab1bd5af23a8f910b433e598d7a | refs/heads/master | 1,610,900,145,817 | 1,488,006,845,000 | 1,488,006,845,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 445 | lean | open tactic
set_option pp.binder_types true
set_option pp.implicit true
set_option pp.notation false
example (a : nat) : true :=
by do
mk_const `add >>= eta_expand >>= trace,
mk_const `nat.succ >>= eta_expand >>= trace,
to_expr `(add a) >>= eta_expand >>= trace,
to_expr `(λ x : nat, add x) >>= eta_expand >>= ... |
55967ad005e90966c781151988abaffc3221e083 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/ring_theory/polynomial/cyclotomic/eval.lean | 1c1fd60e0196d2a53c36f3f412e1169aa8549ed8 | [
"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 | 15,811 | lean | /-
Copyright (c) 2021 Eric Rodriguez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Rodriguez
-/
import ring_theory.polynomial.cyclotomic.basic
import tactic.by_contra
import topology.algebra.polynomial
import number_theory.padics.padic_val
import analysis.compl... |
a7fa1a233208cdc0bcdaa046197a96923cc8d35e | 1446f520c1db37e157b631385707cc28a17a595e | /stage0/src/Init/Lean/Elab/Command.lean | 2ee265916016a50606aeb069495c8222a1d0601f | [
"Apache-2.0"
] | permissive | bdbabiak/lean4 | cab06b8a2606d99a168dd279efdd404edb4e825a | 3f4d0d78b2ce3ef541cb643bbe21496bd6b057ac | refs/heads/master | 1,615,045,275,530 | 1,583,793,696,000 | 1,583,793,696,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 27,658 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import Init.Lean.Elab.Alias
import Init.Lean.Elab.Log
import Init.Lean.Elab.ResolveName
import Init.Lean.Elab.Term
import Init.Lean.Elab.Binders
imp... |
a5ac910b3316c82ccecd513b9fa606a0fd4994cc | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/limits/lattice_auto.lean | 1dcf89a4515adf22b54b5f1e59116faaea7d076a | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,904 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.limits.shapes.finite_limits
import Mathlib.order.complete_lattice
import Ma... |
483e94f3b992893f90b1fe6540d844da7d59fada | 94e33a31faa76775069b071adea97e86e218a8ee | /src/category_theory/limits/preserves/shapes/biproducts.lean | 2092a52bfd35959b2e541643e3dd635d4fdb903a | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 19,203 | lean | /-
Copyright (c) 2022 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import category_theory.limits.shapes.biproducts
import category_theory.limits.preserves.shapes.zero
/-!
# Preservation of biproducts
We define the image of a (binary)... |
904d1df198a40c9ff56a4e01a1fe4388a85c01db | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /stage0/src/Lean/Util/PPGoal.lean | bc497fc383fc9326f03656a7d382dbd209733ade | [
"Apache-2.0"
] | permissive | walterhu1015/lean4 | b2c71b688975177402758924eaa513475ed6ce72 | 2214d81e84646a905d0b20b032c89caf89c737ad | refs/heads/master | 1,671,342,096,906 | 1,599,695,985,000 | 1,599,695,985,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,226 | 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
-/
import Lean.Util.PPExt
namespace Lean
def ppGoal (env : Environment) (mctx : MetavarContext) (opts : Options) (mvarId : MVarId) : Format :=
match mctx.find... |
3dfdb9f6a482289681b57d49d479f32343a02a04 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/algebra/group/prod.lean | 9d5f674c68af6773269683830ccc0841d79d0c47 | [
"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 | 13,908 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot, Yury Kudryashov
-/
import algebra.opposites
/-!
# Monoid, group etc structures on `M × N`
In this file we define one-binop (`monoid`, `group` etc) struc... |
adbe91135365d29191c5e6bbb365147b62ba1f14 | 9a0b1b3a653ea926b03d1495fef64da1d14b3174 | /tidy/lib/default.lean | c9b133df59bed92db0520c1def194346aa220f6c | [
"Apache-2.0"
] | permissive | khoek/mathlib-tidy | 8623b27b4e04e7d598164e7eaf248610d58f768b | 866afa6ab597c47f1b72e8fe2b82b97fff5b980f | refs/heads/master | 1,585,598,975,772 | 1,538,659,544,000 | 1,538,659,544,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 94 | lean | import .num
import .utf8
import .list
import .array
import .table
import .env
import .tactic |
ec646bca515199d141bf8ca18c761197266b86eb | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /library/algebra/binary.lean | bb733c1470a11e0a62db520b34bdbb19a05e9a79 | [
"Apache-2.0"
] | permissive | davidmueller13/lean | 65a3ed141b4088cd0a268e4de80eb6778b21a0e9 | c626e2e3c6f3771e07c32e82ee5b9e030de5b050 | refs/heads/master | 1,611,278,313,401 | 1,444,021,177,000 | 1,444,021,177,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,292 | 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, Jeremy Avigad
General properties of binary operations.
-/
open eq.ops function
namespace binary
section
variable {A : Type}
variables (op₁ : A → A... |
61e4fe8535d0183b21fb3dfa838c902122c4a263 | de3bb37f178fdd10c6dc8c5de6cf51de10c1ba17 | /adj.lean | e7913a4099c557ad7eb93add4f83450cac65e070 | [] | no_license | RyanSandford/HOTT-adjoint-equivalences | e58b2be0cb2ebba260f45f46ff4668b14442df98 | 331a4e6085bc35ab19a59ef28a60f299dee4dc6d | refs/heads/master | 1,622,097,493,839 | 1,618,173,901,000 | 1,618,173,901,000 | 254,230,569 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,043 | lean | /-
Authors: Daniel Carranza, Jonathon Chang, Ryan Sandford
Under the supervision of Chris Kapulkin
Theorems about half-adjoint equivalences, including
a proof that the left half-adjoint type is a proposition
and is equivalent to the built-in equivalence type
Last updated: 2020-07-31
-/
import hott.init hott.typ... |
4ff04fc07d981fa955f193bc8c74b1f11416a425 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/number_theory/pell.lean | 0672046068332316c62051233998a5a4ab0a330a | [
"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 | 39,435 | 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.nat.modeq
import number_theory.zsqrtd.basic
/-!
# Pell's equation and Matiyasevic's theorem
This file solves Pell's equation, i.e. integer solutions to... |
18f83032cca1aebb9b107fd99c53f8b95b1f57c9 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/algebra/category/CommRing/colimits.lean | 17919c43b56d0e768a8ed744e1112640fe3c88c7 | [
"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 | 12,911 | 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.has_limits
import category_theory.limits.concrete_category
/-!
# The category of commutative rin... |
a09e004fb9b6d26c2d06720546643c3833b2a845 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/tactic/elide.lean | ebd16544b8b4bc6c065e0e8e9e1926f5293441f3 | [
"Apache-2.0"
] | permissive | gebner/mathlib | eab0150cc4f79ec45d2016a8c21750244a2e7ff0 | cc6a6edc397c55118df62831e23bfbd6e6c6b4ab | refs/heads/master | 1,625,574,853,976 | 1,586,712,827,000 | 1,586,712,827,000 | 99,101,412 | 1 | 0 | Apache-2.0 | 1,586,716,389,000 | 1,501,667,958,000 | Lean | UTF-8 | Lean | false | false | 3,034 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Simon Hudon
-/
import logic.basic tactic.core
namespace tactic
namespace elide
meta def replace : ℕ → expr → tactic expr
| 0 e := do
t ← infer_type e,
expr.sort ... |
9cf0d9f108e78567c78b55457244fb6fbdd5bf0e | 61ccc57f9d72048e493dd6969b56ebd7f0a8f9e8 | /src/topology/local_homeomorph.lean | a75172b345648ded76b1a91c107c7ee926c71d04 | [
"Apache-2.0"
] | permissive | jtristan/mathlib | 375b3c8682975df28f79f53efcb7c88840118467 | 8fa8f175271320d675277a672f59ec53abd62f10 | refs/heads/master | 1,651,072,765,551 | 1,588,255,641,000 | 1,588,255,641,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 28,920 | 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 data.equiv.local_equiv
import topology.homeomorph
/-!
# Local homeomorphisms
This file defines homeomorphisms between open subsets of topological space... |
7e34a22ba7ef0d4a10d246b76d077ea0a6734fe7 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /src/Lean/Widget/TaggedText.lean | b97e15348ba035b648b49f1691d6fb85317917dc | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | EdAyers/lean4 | 57ac632d6b0789cb91fab2170e8c9e40441221bd | 37ba0df5841bde51dbc2329da81ac23d4f6a4de4 | refs/heads/master | 1,676,463,245,298 | 1,660,619,433,000 | 1,660,619,433,000 | 183,433,437 | 1 | 0 | Apache-2.0 | 1,657,612,672,000 | 1,556,196,574,000 | Lean | UTF-8 | Lean | false | false | 4,303 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki
-/
import Lean.Data.Json.FromToJson
import Lean.Server.Rpc.Basic
namespace Lean.Widget
open Server
/-- The minimal structure needed to represent "string wit... |
3d150d365004b879a442038569ec729ab49624f7 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/mv_polynomial/invertible.lean | cbc346d250da1ac7ddcf39e6dcbba77fa1b0e90d | [] | 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 | 1,184 | lean | /-
Copyright (c) 2020 Johan Commelin and Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin and Robert Y. Lewis
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.mv_polynomial.basic
import Mathlib.ring_theory... |
8c2cc381246eb708e3fb5a6cfbfb9c691e7f7973 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/list/func.lean | 96224e56d8013ca3532a796d81716a3ed5ed6194 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 11,133 | lean | /-
Copyright (c) 2019 Seul Baek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Seul Baek
-/
import data.nat.order.basic
/-!
# Lists as Functions
Definitions for using lists as finite representations of finitely-supported functions with domain
ℕ.
These include point... |
0a08ecd2fb68d370ce695d1c16a562d06b2a1017 | 853df553b1d6ca524e3f0a79aedd32dde5d27ec3 | /src/analysis/calculus/local_extr.lean | 6f070a3a7718a925a9a4b86f31b187151e55fd86 | [
"Apache-2.0"
] | permissive | DanielFabian/mathlib | efc3a50b5dde303c59eeb6353ef4c35a345d7112 | f520d07eba0c852e96fe26da71d85bf6d40fcc2a | refs/heads/master | 1,668,739,922,971 | 1,595,201,756,000 | 1,595,201,756,000 | 279,469,476 | 0 | 0 | null | 1,594,696,604,000 | 1,594,696,604,000 | null | UTF-8 | Lean | false | false | 14,853 | 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 topology.local_extr
import analysis.calculus.deriv
/-!
# Local extrema of smooth functions
## Main definitions
In a real normed space `E` we define `pos_t... |
f1acf04f22577b09c0f53d669fed4c7dee83cb85 | 36938939954e91f23dec66a02728db08a7acfcf9 | /lean4/deps/galois_stdlib/src/Galois/Data/List.lean | c6a3e1c1f35dadf4ccfac23fe70b4b76f1b09e3b | [] | no_license | pnwamk/reopt-vcg | f8b56dd0279392a5e1c6aee721be8138e6b558d3 | c9f9f185fbefc25c36c4b506bbc85fd1a03c3b6d | refs/heads/master | 1,631,145,017,772 | 1,593,549,019,000 | 1,593,549,143,000 | 254,191,418 | 0 | 0 | null | 1,586,377,077,000 | 1,586,377,077,000 | null | UTF-8 | Lean | false | false | 196 | lean | namespace List
section
universes u v
variables {α : Type u} {β : Type v}
def joinMap (f : α → List β) : List α → List β
| [] => []
| a :: as => (f a) ++ joinMap as
end
end List
|
ef298f451ee8f47bd845a68fc62e599105e091d6 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/linear_algebra/finite_dimensional.lean | 276f3a3a096067f0b594df7deb679bd16b274192 | [
"Apache-2.0"
] | permissive | gebner/mathlib | eab0150cc4f79ec45d2016a8c21750244a2e7ff0 | cc6a6edc397c55118df62831e23bfbd6e6c6b4ab | refs/heads/master | 1,625,574,853,976 | 1,586,712,827,000 | 1,586,712,827,000 | 99,101,412 | 1 | 0 | Apache-2.0 | 1,586,716,389,000 | 1,501,667,958,000 | Lean | UTF-8 | Lean | false | false | 17,085 | 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 ring_theory.noetherian linear_algebra.dimension
import ring_theory.principal_ideal_domain
/-!
# Finite dimensional vector spaces
Definition and basic properties... |
2d328f589ac1f021f73bcbcba36f668d3dc346c0 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/pp_algebra_num_bug.lean | d59087ba65a5e87bbcc774766581d92a78fc6dbd | [
"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 | 271 | lean | import algebra.group
open algebra
variable {A : Type}
variable [s : group A]
variable (a : A)
check 1 * 1 * a
set_option pp.notation false
check 1 * a
variable [s2 : add_comm_group A]
set_option pp.notation true
check 0 + a
set_option pp.notation false
check 0 + a
|
141e52d0ab9967ae5b3ae08c8b83acf29de772e0 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/category_theory/category/default.lean | 3c74e1873336f4afb6e683f50f709028677db426 | [
"Apache-2.0"
] | permissive | rmitta/mathlib | 8d90aee30b4db2b013e01f62c33f297d7e64a43d | 883d974b608845bad30ae19e27e33c285200bf84 | refs/heads/master | 1,585,776,832,544 | 1,576,874,096,000 | 1,576,874,096,000 | 153,663,165 | 0 | 2 | Apache-2.0 | 1,544,806,490,000 | 1,539,884,365,000 | Lean | UTF-8 | Lean | false | false | 5,585 | 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
import tactic.tidy
/-!
# Categories
Defines a category, as a type class parametrised by the type o... |
d0b67bb9972d5de2d4242f9ddc0d5e15c8213b71 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/topology/uniform_space/separation.lean | f40b0c668bbea5d1a939f3c5beca5a0fb46ee1fb | [
"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 | 22,524 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot
-/
import topology.uniform_space.basic
import tactic.apply_fun
/-!
# Hausdorff properties of uniform spaces. Separation quotient.
This file studies un... |
6eef61bd4a88d577d659795399e1b71e16fe1b01 | 0c6b99c0daded009943e570c13367c8cc7d3bcae | /chapter14.lean | cef94ff30dd6013ca83acbd6a1dbc01dfc760561 | [] | no_license | TateKennington/logic-and-proof-exercises | e3c5c5b12b6238b47b0c5acf8717923bd471a535 | acca8882026e7b643453eb096d3021cd043005bd | refs/heads/main | 1,687,638,489,616 | 1,626,858,474,000 | 1,626,858,474,000 | 371,871,374 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,398 | lean | section
parameters {A : Type} {R : A → A → Prop}
parameter (irreflR : irreflexive R)
parameter (transR : transitive R)
local infix < := R
def R' (a b : A) : Prop := R a b ∨ a = b
local infix ≤ := R'
theorem reflR' (a : A) : a ≤ a :=
have a = a, from refl a,
show a ≤ a, from or.inr this
theor... |
0c7a8d7aee3d63f72e1ca53c0137104fe72e24d6 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /test/wlog.lean | 71a3917b6bcbf90b1f7efc7b7315e2df76f89f1c | [
"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 | 3,098 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import tactic.wlog
section wlog
example {x y : ℕ} (a : x = 1) : true :=
begin
suffices : false, trivial,
wlog h : x = y,
{ guard_target x = y ∨ y = x,
admit },
... |
dc1bf0c8f909c18ea66b8fea2a5b6ab44086545f | 94e33a31faa76775069b071adea97e86e218a8ee | /src/linear_algebra/invariant_basis_number.lean | 1d08b949b58ff7431028835b498dbeda87dc7112 | [
"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 | 12,029 | lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Scott Morrison
-/
import ring_theory.ideal.quotient
import ring_theory.principal_ideal_domain
/-!
# Invariant basis number property
We say that a ring `R` satisfies the... |
7dbdcf835a07538635ef3a114645e4368f2e56b9 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/logic/basic.lean | 30ebee865dd48c5df1dfb786b862f1cffb2b1763 | [
"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 | 45,448 | 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
-/
import tactic.doc_commands
/-!
# Basic logic properties
This file is one of the earliest imports in mathlib.
## Implementation notes
Theorems tha... |
14a57be4686bdca3e6981ebf1f6276b1702c63ca | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/int/basic_auto.lean | eee59906136f9d0d3f74232c37aed3019d9b9a1b | [] | 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 | 45,073 | 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 integers, with addition, multiplication, and subtraction.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.nat.basic
import Mathlib.... |
3d13c14b5f6e1389017a5c69ebba459ffa34f43f | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/ring_theory/noetherian.lean | ff91b08a69911f67e7982e9b1b234a899fe6ef74 | [
"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 | 34,691 | lean | /-
Copyright (c) 2018 Mario Carneiro, Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kevin Buzzard
-/
import data.multiset.finset_ops
import group_theory.finiteness
import linear_algebra.linear_independent
import order.compactly_generated... |
5ff70442fccbecc85cb8524fc955095e28687edc | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/category_theory/endomorphism.lean | 6e7fdb937828dfc6319fdac0d7544226fd7596b6 | [
"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 | 3,005 | lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Scott Morrison, Simon Hudon
Definition and basic properties of endomorphisms and automorphisms of an object in a category.
-/
import category_theory.groupoid
import ... |
c9125074a281eb1bc6646e1f73f9a5e033f8ef4f | 4fa161becb8ce7378a709f5992a594764699e268 | /src/category_theory/monad/adjunction.lean | ed1fa1c62b4dbf79d7dbd8e94f367aa151cd62ba | [
"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 | 5,785 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.monad.algebra
import category_theory.adjunction.fully_faithful
namespace category_theory
open category
universes v₁ v₂ u₁ u₂ -- declare the `... |
9ddda60c90ac445034ac536b120d6f6f8b57f9d3 | bb31430994044506fa42fd667e2d556327e18dfe | /src/data/list/big_operators/basic.lean | 738d87ea3f9e650a6a351c2a615271c7c462f737 | [
"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 | 22,453 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Floris van Doorn, Sébastien Gouëzel, Alex J. Best
-/
import data.list.forall2
/-!
# Sums and products from lists
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any chan... |
52816b3fd8e453921323e5fea393079e613e4743 | 1dd482be3f611941db7801003235dc84147ec60a | /src/data/set/lattice.lean | b0f430e17ae56b3cc27309f7c4d868f7c0a59ce0 | [
"Apache-2.0"
] | permissive | sanderdahmen/mathlib | 479039302bd66434bb5672c2a4cecf8d69981458 | 8f0eae75cd2d8b7a083cf935666fcce4565df076 | refs/heads/master | 1,587,491,322,775 | 1,549,672,060,000 | 1,549,672,060,000 | 169,748,224 | 0 | 0 | Apache-2.0 | 1,549,636,694,000 | 1,549,636,694,000 | null | UTF-8 | Lean | false | false | 28,265 | 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, Johannes Hölzl, Mario Carneiro
-- QUESTION: can make the first argument in ∀ x ∈ a, ... implicit?
-/
import logic.basic data.set.basic data.equiv.basic... |
5f5da9184f029dc1aba956e398b9f65e9bed7b36 | 76c77df8a58af24dbf1d75c7012076a42244d728 | /tutorial_src/exercises/04_exists.lean | 56889f69afbefd31d77b12978cf1c6db52a1a887 | [] | no_license | kris-brown/theorem_proving_in_lean | 7a7a584ba2c657a35335dc895d49d991c997a0c9 | 774460c21bf857daff158210741bd88d1c8323cd | refs/heads/master | 1,668,278,123,743 | 1,593,445,161,000 | 1,593,445,161,000 | 265,748,924 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 3,068 | lean | import data.real.basic
import data.int.parity
/-
In this file, we learn how to handle the ∃ quantifier.
In order to prove `∃ x, P x`, we give some x₀ using tactic `use x₀` and
then prove `P x₀`. This x₀ can be an object from the local context
or a more complicated expression.
-/
example : ∃ n : ℕ, 8 = 2*n :=
begin
... |
9a5b552c15cec8587a87630f6c7718c1668fd10f | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /hott/types/sum.hlean | 270062c4d32df13cd6968307355c6f526387ba22 | [
"Apache-2.0"
] | permissive | soonhokong/lean-osx | 4a954262c780e404c1369d6c06516161d07fcb40 | 3670278342d2f4faa49d95b46d86642d7875b47c | refs/heads/master | 1,611,410,334,552 | 1,474,425,686,000 | 1,474,425,686,000 | 12,043,103 | 5 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 15,410 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Floris van Doorn
Theorems about sums/coproducts/disjoint unions
-/
import .pi .equiv logic
open lift eq is_equiv equiv prod prod.ops is_trunc sigma bool
namespace sum
universe v... |
a3bb89bcd92ed183dc31aa9785dbbd40878aabb4 | 2731214ea32f2a1a985300e281fb3117640a16c3 | /portmanteau_open_imp_cont.lean | 607469d050d519cfe67fda2521038bbdeb4c4b95 | [
"Apache-2.0"
] | permissive | kkytola/lean_portmanteau | 5d6a156db959974ebc4f5bed9118a7a2438a33fa | ac55eb4e24be43032cbc082e2b68d8fb8bd63f22 | refs/heads/main | 1,686,107,117,334 | 1,625,177,052,000 | 1,625,177,052,000 | 381,514,032 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 20,624 | lean | /-
Copyright (c) 2021 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä
-/
import portmanteau_definitions
import portmanteau_topological_lemmas
import portmanteau_proba_lemmas
import portmanteau_open_equiv_closed
import portmanteau_integrals
imp... |
011b07a7bc9c35ba2be38099970ff85bbd4945a1 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/gcd_monoid/basic.lean | 8a98908d5908f4e61e561466389cfe5e9ad0c818 | [
"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 | 50,990 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker
-/
import algebra.associated
import algebra.group_power.lemmas
import algebra.ring.regular
/-!
# Monoids with normalization functions, `gcd`, and `lcm`... |
f156d32b2aa87e70dc998aeeead88cda42302dbc | bb31430994044506fa42fd667e2d556327e18dfe | /src/data/zmod/basic.lean | 8c8957dd63ae9509a8ed12f4abb052bed4b4e393 | [
"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 | 37,389 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import algebra.char_p.basic
import data.nat.parity
import algebra.group.conj_finite
import tactic.fin_cases
/-!
# Integers mod `n`
Definition of the integers mod n, an... |
a6ac33ffcc2f876336aabcdc07d504c03a5ac874 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/data/finset/pi.lean | 7e00041ca144c81bfef1d52dcadd8dffb7fd4458 | [
"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 | 4,474 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
-/
import data.finset.basic
import data.multiset.pi
/-!
# The cartesian product of finsets
-/
namespace finset
open multiset
/-! ### pi -/
section pi
variables {α : Ty... |
04bcb33a9b1c29cacd42caa238d014b9649f72ce | d53312f14e4be505a8abcc1969b73308b038f020 | /06-formalizacija-dokazov/naravna.lean | 3fca82c4f999fd12103974fc48b8f237c5ee2313 | [] | no_license | lunar-starlight/teorija-programskih-jezikov | 18ccdfaa9200c10c2b1ec14624419532dd671d25 | bfdf69114a6b13b1ae5735e8749b543f722e5965 | refs/heads/master | 1,667,393,466,506 | 1,577,651,158,000 | 1,577,651,158,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,485 | lean | inductive naravno : Type -- type naravno =
| nic : naravno -- | Nic
| nasl : naravno -> naravno -- | Nasl of naravno
theorem niso_vsa_naravna_nic : ¬ (forall n, n = naravno.nic) :=
begin
apply not.intro,
intros,
have ena_je_nic : naravno.nasl (naravno.nic) = naravno.nic,
apply a (naravno.nasl... |
a956adc2ad3fc402aee56aa3040cc2a6c7d20d76 | 5d166a16ae129621cb54ca9dde86c275d7d2b483 | /tests/lean/defeq_simp4.lean | 59455d1a636140714cad9a8fe736c2cf1c70b383 | [
"Apache-2.0"
] | permissive | jcarlson23/lean | b00098763291397e0ac76b37a2dd96bc013bd247 | 8de88701247f54d325edd46c0eed57aeacb64baf | refs/heads/master | 1,611,571,813,719 | 1,497,020,963,000 | 1,497,021,515,000 | 93,882,536 | 1 | 0 | null | 1,497,029,896,000 | 1,497,029,896,000 | null | UTF-8 | Lean | false | false | 877 | lean | attribute [reducible]
definition nat_has_add2 : has_add nat :=
has_add.mk (λ x y : nat, x + y)
attribute [reducible]
definition nat_has_add3 : nat → has_add nat :=
λ n, has_add.mk (λ x y : nat, x + y)
open tactic
set_option pp.all true
-- Example where instance canonization does not work.
-- Remark: we can "fix" it ... |
e7a15b1ee36d2c8b70f1c6912a020549683a5721 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/set/function.lean | 3f18ba12f2cf25e9547d4c323b484667294f641c | [
"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 | 41,793 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Andrew Zipperer, Haitao Zhang, Minchao Wu, Yury Kudryashov
-/
import data.set.basic
import logic.function.conjugate
/-!
# Functions over sets
## Main definitions
### P... |
9124afc663cf9f9cc2b859d1c025e31b46bd8a6c | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/big_operators/option.lean | a849bed837424c4e8c42404d5871a1dde40348de | [
"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 | 1,143 | lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import algebra.big_operators.basic
import data.finset.option
/-!
# Lemmas about products and sums over finite sets in `option α`
In this file we prove formulas f... |
247106a1df268bff2ad540a11f661e27024cff28 | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/let4.lean | b97e79608b4a2a9f86265fe2c9bcb6f617ee83fc | [
"Apache-2.0"
] | permissive | codyroux/lean0.1 | 1ce92751d664aacff0529e139083304a7bbc8a71 | 0dc6fb974aa85ed6f305a2f4b10a53a44ee5f0ef | refs/heads/master | 1,610,830,535,062 | 1,402,150,480,000 | 1,402,150,480,000 | 19,588,851 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 791 | lean | import Int.
print
let b := true,
a : Int := b
in a
variable vector : Type -> Nat -> Type
variable const {A : Type} (n : Nat) (a : A) : vector A n
check
let a := 10,
v1 := const a true,
v2 := v1
in v2
print
let a := 10,
v1 : vector Bool a := const a true,
v2 : vector Bool a := v1
in v2
check
l... |
81bebc6e9880e8106756b4d0d92e8c3804071ee3 | de91c42b87530c3bdcc2b138ef1a3c3d9bee0d41 | /old/embedded_spc_fm_demo/expressions_demo_current.lean | 977038517b9ba3f1b0d372cc4ac605f6c0ed7f75 | [] | no_license | kevinsullivan/lang | d3e526ba363dc1ddf5ff1c2f36607d7f891806a7 | e9d869bff94fb13ad9262222a6f3c4aafba82d5e | refs/heads/master | 1,687,840,064,795 | 1,628,047,969,000 | 1,628,047,969,000 | 282,210,749 | 0 | 1 | null | 1,608,153,830,000 | 1,595,592,637,000 | Lean | UTF-8 | Lean | false | false | 3,129 | lean | import ..expressions.time_expr_current
/-
Adapted from Dr Sullivan's phys/demo/demo.lean to highlight differences from phys and lang
-/
open lang.time
--Alias std time frame and space
def std_fr := time_std_frame ℚ --(std_frame ℚ TIME)
def std_sp := time_std_space ℚ --(std_space ℚ TIME)
/-
Define a time and durati... |
9db4f9b382fcd527f4d7f3a6db0ee14ef8941870 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /stage0/src/Init/Data/List/BasicAux.lean | 0f44deb1c4bac719e47c716d368d134a63f60e7e | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | cipher1024/lean4 | 6e1f98bb58e7a92b28f5364eb38a14c8d0aae393 | 69114d3b50806264ef35b57394391c3e738a9822 | refs/heads/master | 1,642,227,983,603 | 1,642,011,696,000 | 1,642,011,696,000 | 228,607,691 | 0 | 0 | Apache-2.0 | 1,576,584,269,000 | 1,576,584,268,000 | null | UTF-8 | Lean | false | false | 2,260 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import Init.Data.List.Basic
import Init.Util
universe u
namespace List
/- The following functions can't be defined at `Init.Data.List.Basic`, becau... |
c90f54ce3ed6fc6e56635653b52fd3f085bc7289 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/data/nat/pairing.lean | 365d0baaa34f4238aa4bd21ec2b95bcf8164a3da | [
"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 | 5,367 | 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, Mario Carneiro
-/
import data.nat.sqrt
import data.set.lattice
/-!
# Naturals pairing function
This file defines a pairing function for the naturals as fol... |
c93b9b17fac863ec0076db141799d5fc8f66c34a | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /tests/lean/run/reduce2.lean | e864beae7ffdf598ff010acb3c4321f80bc81518 | [
"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 | 141 | lean | #lang lean4
def fact : Nat → Nat
| 0 => 1
| (n+1) => (n+1)*fact n
def v1 := fact 10
theorem v1Eq : v1 = fact 10 :=
Eq.refl (fact 10)
|
f4d4f7255cfe1273645ae29ee57292a0acfaf439 | 26ac254ecb57ffcb886ff709cf018390161a9225 | /src/topology/algebra/monoid.lean | bdb8d33ae32fe553fa79303d24f2e44b73fee9f9 | [
"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 | 5,686 | 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
Theory of topological monoids.
TODO: generalize `topological_monoid` and `topological_add_monoid` to semigroups, or add a type class
`topological_opera... |
4c96166e0b0d491907eaf9aac7841ab135f041a6 | 97f752b44fd85ec3f635078a2dd125ddae7a82b6 | /tests/lean/defeq_simp_lemmas2.lean | a9e5ff29c95f19b7a46d8af23168ab82daa494cc | [
"Apache-2.0"
] | permissive | tectronics/lean | ab977ba6be0fcd46047ddbb3c8e16e7c26710701 | f38af35e0616f89c6e9d7e3eb1d48e47ee666efe | refs/heads/master | 1,532,358,526,384 | 1,456,276,623,000 | 1,456,276,623,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,272 | lean | universe l
constants (A : Type.{l})
definition q (x : A) := x
definition h (x : A) : A := q x
definition g (x y : A) := h y
definition f (x y z : A) := g (g x y) z
definition d (x y z w : A) := f (f x y z) (f y z w) (f x w z)
definition h.rfl [defeq] (x : A) : h x = x := rfl
definition g.rfl [defeq] (x y : A) : g x y... |
7a780850cf6ef010639df67d463d36cb07f94805 | 77c5b91fae1b966ddd1db969ba37b6f0e4901e88 | /src/tactic/push_neg.lean | 7a362c24182800ade91b0c3dee91b6b3c66b3568 | [
"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 | 7,992 | 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.basic
open tactic expr
namespace push_neg
section
universe u
va... |
966e1fbe1b53f2656e4cdb404944e32103dcafb2 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/category_theory/graded_object.lean | c5e9e498a4f5b981e5cdd21a567e860603492127 | [
"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 | 6,141 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.shift
import category_theory.concrete_category
import category_theory.pi.basic
import algebra.group.basic
/-!
# The category of graded objects... |
67f8d69b44c67421893cb5808b075237310ac825 | 1a61aba1b67cddccce19532a9596efe44be4285f | /library/logic/identities.lean | d5ba754faecd4e4ba192e6597edcd8b482b1a19b | [
"Apache-2.0"
] | permissive | eigengrau/lean | 07986a0f2548688c13ba36231f6cdbee82abf4c6 | f8a773be1112015e2d232661ce616d23f12874d0 | refs/heads/master | 1,610,939,198,566 | 1,441,352,386,000 | 1,441,352,494,000 | 41,903,576 | 0 | 0 | null | 1,441,352,210,000 | 1,441,352,210,000 | null | UTF-8 | Lean | false | false | 4,322 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
Useful logical identities. Since we are not using propositional extensionality, some of the
calculations use the type class support provided by... |
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