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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
cd7acdad66f34b92f873356ed267b851049df198 | 6fca17f8d5025f89be1b2d9d15c9e0c4b4900cbf | /src/game/world8/level3.lean | c0cfb87ea611aaa40b3fca791c892ae688aa4aa5 | [
"Apache-2.0"
] | permissive | arolihas/natural_number_game | 4f0c93feefec93b8824b2b96adff8b702b8b43ce | 8e4f7b4b42888a3b77429f90cce16292bd288138 | refs/heads/master | 1,621,872,426,808 | 1,586,270,467,000 | 1,586,270,467,000 | 253,648,466 | 0 | 0 | null | 1,586,219,694,000 | 1,586,219,694,000 | null | UTF-8 | Lean | false | false | 613 | lean | import mynat.definition -- hide
import mynat.add -- hide
import game.world8.level2 -- hide
namespace mynat -- hide
/-
# Advanced Addition World
## Level 3: `succ_eq_succ_of_eq`.
-/
/-
We are going to prove something completely obvious: if $a=b$ then
$succ(a)=succ(b)$. This is *not* `succ_inj`!
This is trivial -- we... |
6dd57fc6dbb5cd530fc8469697677ab37f36a887 | 13133fade54057ee588bc056e4eaa14a24773d23 | /Proofs/binomial_isabelle.lean | 73f143c94cbf1c716403a470e17928d8e59c2982 | [] | no_license | lkloh/lean-project-15815 | 444cbdca1d1a2dfa258c76c41a6ff846392e13d1 | 2cb657c0e41baa318193f7dce85974ff37d80883 | refs/heads/master | 1,611,402,038,933 | 1,432,020,760,000 | 1,432,020,760,000 | 33,372,120 | 0 | 0 | null | 1,431,932,928,000 | 1,428,078,840,000 | Lean | UTF-8 | Lean | false | false | 1,034 | lean | import data.nat
open nat
-- These are taken from http://afp.sourceforge.net/browser_info/current/AFP/Girth_Chromatic/Binomial.html
-- ****************************************************************** --
definition binomial : nat → nat → nat
| binomial 0 0 := 1
| binomial 0 k := 0
| binomial(succ n) 0 := 1
| binomia... |
01652a3f624e4a40b9183c54afa2ed3532f1b7df | 94e33a31faa76775069b071adea97e86e218a8ee | /src/category_theory/limits/constructions/weakly_initial.lean | 8dc5249777940286a5cdd8b9a4e1d6b7377aa4e0 | [
"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 | 2,431 | lean | /-
Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import category_theory.limits.shapes.wide_equalizers
import category_theory.limits.shapes.products
import category_theory.limits.shapes.terminal
/-!
# Constructions rela... |
55393deb96888c96edd48646809dadbc8b68893a | a047a4718edfa935d17231e9e6ecec8c7b701e05 | /src/order/filter/basic.lean | 836c4e71870fb4de025662e5a777ef8ad17ce7a2 | [
"Apache-2.0"
] | permissive | utensil-contrib/mathlib | bae0c9fafe5e2bdb516efc89d6f8c1502ecc9767 | b91909e77e219098a2f8cc031f89d595fe274bd2 | refs/heads/master | 1,668,048,976,965 | 1,592,442,701,000 | 1,592,442,701,000 | 273,197,855 | 0 | 0 | null | 1,592,472,812,000 | 1,592,472,811,000 | null | UTF-8 | Lean | false | false | 85,422 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jeremy Avigad
-/
import order.zorn
import order.copy
import data.set.finite
/-!
# Theory of filters on sets
## Main definitions
* `filter` : filters on a set;
* `at_... |
6fcf5e1b245be6fe04383c0dd98883be1e260d03 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/tactic/lint/default.lean | cb2d52cb265200108380b674e7f9ec6ae154d9db | [
"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 | 3,928 | 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, Robert Y. Lewis, Gabriel Ebner
-/
import tactic.lint.frontend
tactic.lint.simp
tactic.lint.type_classes
tactic.lint.misc
open tactic
add_tactic_doc
{ name ... |
95f862e87c8a88c0b6a0c8a391257f6b5362849c | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/445.lean | db4293a5a76a984f272c7a49d6471db541907425 | [
"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 | 115 | lean | constants (A : Type) (a : A)
constants (B : Type) (b₁ b₂ : B) (H : b₁ = b₂)
#check a
#check b₁
#check H
|
327186c0d030561e86e1d802e6e43814b4d6fa1b | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/order/group/with_top.lean | 4a95ca79bbc1587e4e5b702f79b0d8fd5b1484d5 | [
"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 | 1,191 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl
-/
import algebra.order.group.instances
import algebra.order.monoid.with_top
/-!
# Adjoining a top element to a `linear... |
a3c8cc2da6c497c80439d7dbcb05a36fc82acecf | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/mllist.lean | 276f2c8dabf8c04001083c8b3922d7ddd37b0962 | [
"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 | 8,181 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Keeley Hoek, Simon Hudon, Scott Morrison
-/
import data.option.defs
/-! # Monadic lazy lists.
An alternative construction of lazy lists (see also `data.lazy_list`),
w... |
e168d532899eea64186c5c9142517b7fa60ea680 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /stage0/src/Init/Control/Option.lean | f0733d061f56bc5ee8d011cb80da9ee11dba371e | [
"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 | 2,204 | 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, Sebastian Ullrich
-/
prelude
import Init.Control.Alternative
import Init.Control.Lift
import Init.Control.Except
universes u v
def OptionT (m : Type u → Typ... |
11a72f1cb06a99de112c18f5938db92bdb339cbc | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/topology/basic.lean | ee11d73197e6ed8b2d10225cf1999bfe3d65da1b | [
"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 | 71,156 | 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, Jeremy Avigad
-/
import order.filter.ultrafilter
import order.filter.partial
import order.filter.small_sets
import algebra.support
/-!
# Basic theory o... |
50d82f2d7c8993d5ef6c24f5d5d6ba0c339048b3 | fe7174aadb02f3f5a6781c52facd5ebcbb35105c | /src/14.Inductive_Definitions/Data_Types/mybool.lean | 541deafc0eaa55c151887ba3544db939a4e6e075 | [] | no_license | tcmch/cs-dm-lean | 1ea180c6ff15e4e9a3ea78f2608506924e34e922 | 16ef75c7e68077e265441acc16cf5fe643db911b | refs/heads/master | 1,586,377,195,552 | 1,544,118,724,000 | 1,544,118,724,000 | 159,694,678 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,389 | lean | namespace my_bool
inductive mybool : Type
| mytt : mybool
| myff : mybool
#check mybool.mytt
/-
We declare mybool to be an
inductively defined type:
a value of type, Type.
The set of values of this
type that can be constructed
is defined by the available
constructors.
Here there are just two,
mytt and myff, ... |
5673044b9ef17343f20ff0ae451b3346207d0d88 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/topology/order.lean | abedffcea2a80848dece5624360959691f2552b8 | [
"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 | 28,234 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import topology.tactic
/-!
# Ordering on topologies and (co)induced topologies
Topologies on a fixed type `α` are ordered, by reverse inclusion.
Tha... |
749dd495ffb94e23f8f779d77c40f3744203b1ea | 94637389e03c919023691dcd05bd4411b1034aa5 | /src/zzz_junk/has_mul/has_mul_nat.lean | 1d6e6d5dc95d1002ed93d7628c23bbb97c5a3943 | [] | no_license | kevinsullivan/complogic-s21 | 7c4eef2105abad899e46502270d9829d913e8afc | 99039501b770248c8ceb39890be5dfe129dc1082 | refs/heads/master | 1,682,985,669,944 | 1,621,126,241,000 | 1,621,126,241,000 | 335,706,272 | 0 | 38 | null | 1,618,325,669,000 | 1,612,374,118,000 | Lean | UTF-8 | Lean | false | false | 741 | lean | import .has_mul
-- Overload has_mul_ident for nat
instance ident_nat : hidden.has_mul nat := ⟨ nat.mul ⟩
/-
Again this code would typically go in the module
that defines the nat type, as here we define an
implementation of ident_nat for this type.
-/
/-
Now anywhere else in a code base that we need a nat,
we can use... |
541cdff40ce1ba2fd398a11714b215fceefc8b38 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/assert_fail.lean | 7471f495802b9a90d3fbf7bd690148e1eccaa096 | [
"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 | 148 | lean | example (a b : Prop) (H : b ∧ a) : a ∧ b :=
begin
assert H : a
end
example (a : Prop) (Ha : a) : a :=
begin
exact Ha,
assert H : a
end
|
7344e74669309199c1ab4bf920e09b03e2538724 | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/real/liouville.lean | a7a3b92cee886c066272a4bf49b2241ce591bc81 | [
"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 | 12,350 | lean | /-
Copyright (c) 2020 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
import analysis.calculus.mean_value
import data.polynomial.denoms_clearable
import data.real.irrational
import ring_theory.algebraic
import topology.algebra.polynomial
/-... |
c139746b49d538ebebe3e894ecda8a78d828a810 | 94637389e03c919023691dcd05bd4411b1034aa5 | /src/inClassNotes/type_library/prod_test.lean | 9ed3540870a0ac348285ff6b12bddeae47d76c37 | [] | no_license | kevinsullivan/complogic-s21 | 7c4eef2105abad899e46502270d9829d913e8afc | 99039501b770248c8ceb39890be5dfe129dc1082 | refs/heads/master | 1,682,985,669,944 | 1,621,126,241,000 | 1,621,126,241,000 | 335,706,272 | 0 | 38 | null | 1,618,325,669,000 | 1,612,374,118,000 | Lean | UTF-8 | Lean | false | false | 11 | lean | import .box |
453410e766beab5cb090e3f1261733a752ac7153 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/autoBoundImplicits1.lean | c512865a59126880f261dac69c70b15f4e801206 | [
"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 | 2,327 | lean | def myid (a : α) := a -- works
#check myid 10
#check myid true
theorem ex1 (a : α) : myid a = a := rfl
def cnst (b : β) : α → β := fun _ => b -- works
theorem ex2 (b : β) (a : α) : cnst b a = b := rfl
def Vec (α : Type) (n : Nat) := { a : Array α // a.size = n }
def mkVec : Vec α 0 := ⟨ #[], rfl ⟩
def Vec.map (x... |
d1c5939ba28c7f7c13453a6378c91ac23cea8b7a | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/group_theory/semidirect_product_auto.lean | ae82d18425144f2792e903b00ea3217709cd0448 | [] | 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 | 25,123 | lean | /-
Copyright (c) 2020 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.equiv.mul_add_aut
import Mathlib.logic.function.basic
import Mathlib.group_theory.subgroup... |
84e5684bb7d358ab4a8814dcf8284874c5adce84 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/analysis/special_functions/exp_deriv.lean | 8751ef9f6b49a7928464298e22b6e5c00be774ef | [
"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 | 10,145 | 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 analysis.calculus.inverse
import analysis.complex.real_deriv
import analysis.special_functions.exp
/-!
# Complex a... |
b0c4c6f071ea85e29271d2aaffd7a3e638e237f4 | c31182a012eec69da0a1f6c05f42b0f0717d212d | /src/system_of_complexes/basic.lean | e129662cc8405be6f8e0e49a2e6c9b7a24ed3ac4 | [] | no_license | Ja1941/lean-liquid | fbec3ffc7fc67df1b5ca95b7ee225685ab9ffbdc | 8e80ed0cbdf5145d6814e833a674eaf05a1495c1 | refs/heads/master | 1,689,437,983,362 | 1,628,362,719,000 | 1,628,362,719,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 17,250 | lean | import algebra.ordered_group
import category_theory.preadditive.functor_category
import algebra.homology.additive
import algebra.homology.homological_complex
import for_mathlib.SemiNormedGroup
import for_mathlib.SemiNormedGroup_Completion
import facts
import tactic.gptf
universe variables v u
noncomputable theory
o... |
db7bf8258b1abaced7ea0e00c981c0af44cf00ab | fffbc47930dc6615e66ece42324ce57a21d5b64b | /src/tactic/core.lean | cff9802a197d343a443c865303592c2a19e5a7e1 | [
"Apache-2.0"
] | permissive | skbaek/mathlib | 3caae8ae413c66862293a95fd2fbada3647b1228 | f25340175631cdc85ad768a262433f968d0d6450 | refs/heads/master | 1,588,130,123,636 | 1,558,287,609,000 | 1,558,287,609,000 | 160,935,713 | 0 | 0 | Apache-2.0 | 1,544,271,146,000 | 1,544,271,146,000 | null | UTF-8 | Lean | false | false | 35,371 | 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, Scott Morrison, Keeley Hoek
-/
import data.dlist.basic category.basic meta.expr meta.rb_map tactic.cache
namespace expr
open tactic
attribute [derive has... |
2c886bb411be201ae6381a4e99effea6bd94b5e5 | 947b78d97130d56365ae2ec264df196ce769371a | /src/Std/Data/RBTree.lean | b2a7f460e06443ff7c57545d41ee6a0d569b91a8 | [
"Apache-2.0"
] | permissive | shyamalschandra/lean4 | 27044812be8698f0c79147615b1d5090b9f4b037 | 6e7a883b21eaf62831e8111b251dc9b18f40e604 | refs/heads/master | 1,671,417,126,371 | 1,601,859,995,000 | 1,601,860,020,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,899 | 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
-/
import Std.Data.RBMap
namespace Std
universes u v w
def RBTree (α : Type u) (lt : α → α → Bool) : Type u :=
RBMap α Unit lt
@[inline] def mkRBTree (α : Ty... |
3d0f08c642e5fca9b030f12d18604d00c0cddf7c | 2f8bf12144551bc7d8087a6320990c4621741f3d | /library/init/lean/expander.lean | d00190c6b2b785d8cd7be2f5f53a2cae0db44a64 | [
"Apache-2.0"
] | permissive | jesse-michael-han/lean4 | eb63a12960e69823749edceb4f23fd33fa2253ce | fa16920a6a7700cabc567aa629ce4ae2478a2f40 | refs/heads/master | 1,589,935,810,594 | 1,557,177,860,000 | 1,557,177,860,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 23,488 | lean | /-
Copyright (c) 2018 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Sebastian Ullrich
Macro Expander for the Lean language, using a variant of the [sets of scopes](http://www.cs.utah.edu/plt/Scope-sets/) hygiene algorithm.
TODO(Sebastian): docu... |
a472af878b3224712aefad8b70cb0dfb5b24e3d7 | 3dd1b66af77106badae6edb1c4dea91a146ead30 | /tests/lean/run/bug6.lean | 530d40803a765057a2d228a2a8d35c4815638841 | [
"Apache-2.0"
] | permissive | silky/lean | 79c20c15c93feef47bb659a2cc139b26f3614642 | df8b88dca2f8da1a422cb618cd476ef5be730546 | refs/heads/master | 1,610,737,587,697 | 1,406,574,534,000 | 1,406,574,534,000 | 22,362,176 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 322 | lean | import standard
section
parameter {A : Type}
theorem T {a b : A} (H : a = b) : b = a
:= symm H
variables x y : A
axiom H : x = y
check T H
check T
end
section
parameter {A : Type}
theorem T2 ⦃a b : A⦄ (H : a = b) : b = a
:= symm H
variables x y : A
axiom H : x = y
check T2 H
check T2
end
|
6af8736bd9cea5f3037741b722900ba2c2a88aba | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /12_Axioms.org.25.lean | 0196865ae5550743a49cbb36b5057d9b5302c113 | [] | 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 | 1,075 | lean | import standard
import logic.eq
open classical eq.ops
section
parameter p : Prop
definition U (x : Prop) : Prop := x = true ∨ p
definition V (x : Prop) : Prop := x = false ∨ p
noncomputable definition u := epsilon U
noncomputable definition v := epsilon V
lemma u_def : U u :=
epsilon_spec (exists.intro true (or.in... |
7f5301dc55c431601f04902dcf2418b0a074b961 | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/linear_algebra/linear_independent.lean | 085f243ab5e4e84544369c5979f6d1a8e5ac59f6 | [
"Apache-2.0"
] | permissive | mcncm/mathlib | 8d25099344d9d2bee62822cb9ed43aa3e09fa05e | fde3d78cadeec5ef827b16ae55664ef115e66f57 | refs/heads/master | 1,672,743,316,277 | 1,602,618,514,000 | 1,602,618,514,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 39,772 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Alexander Bentkamp, Anne Baanen
-/
import linear_algebra.finsupp
import order.zorn
import data.finset.order
/-! Linear independence
This file defines lin... |
e924451b4ca380976c07eef8feb0efce12aa37c9 | c86b74188c4b7a462728b1abd659ab4e5828dd61 | /stage0/src/Lean/Server/InfoUtils.lean | 136e9f616776f8da63d50e6f123987a4f4e3a2b2 | [
"Apache-2.0"
] | permissive | cwb96/lean4 | 75e1f92f1ba98bbaa6b34da644b3dfab2ce7bf89 | b48831cda76e64f13dd1c0edde7ba5fb172ed57a | refs/heads/master | 1,686,347,881,407 | 1,624,483,842,000 | 1,624,483,842,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,947 | 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.Util.Sorry
protected structure String.Range where
start : String.Pos
stop : String.Pos
deri... |
f69293060ab30e9f037861eb1695e389487e1f6b | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/linear_algebra/unitary_group.lean | 8dca9c999e09cab55637a47f1669e064566e2d63 | [
"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 | 6,386 | lean | /-
Copyright (c) 2021 Shing Tak Lam. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shing Tak Lam
-/
import linear_algebra.matrix.nonsingular_inverse
import linear_algebra.matrix.to_lin
import data.complex.basic
/-!
# The Unitary Group
This file defines elements of t... |
405f0f03d70eb37cbba543c1088f2e6de509bee7 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /library/data/set/filter.lean | 5923bc4c08c248b63549eb45f556d424fb2b8430 | [
"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 | 11,974 | lean | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
Filters, following Hölzl, Immler, and Huffman, "Type classes and filters for mathematical
analysis in Isabelle/HOL".
-/
import data.set.function logic.identities algebra.c... |
131530e23ea9fa8a465b6add530bdc58ad47f053 | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/tactic/push_neg.lean | 03210c68c66912dbc03b8c45d090d9f97d5273ed | [
"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 | 6,871 | lean | /-
Copyright (c) 2019 Patrick Massot All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Patrick Massot, Simon Hudon
A tactic pushing negations into an expression
-/
import tactic.interactive
import algebra.order
open tactic expr
namespace push_neg
section
universe u
... |
4ca31108281fa9256a95d5a44d3eb6f2f1c0a8d4 | 59aed81a2ce7741e690907fc374be338f4f88b6f | /src/math-688/lectures/lec-19.lean | 455715bc0ff78a3d3562e0a3f25c3427d337c09d | [] | no_license | agusakov/math-688-lean | c84d5e1423eb208a0281135f0214b91b30d0ef48 | 67dc27ebff55a74c6b5a1c469ba04e7981d2e550 | refs/heads/main | 1,679,699,340,788 | 1,616,602,782,000 | 1,616,602,782,000 | 332,894,454 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 50 | lean | /- 14 Oct 2019 -/
-- trees
-- TFAE
import walks
|
86353b3345f89145976febb76b3ce993828f2b5b | 4727251e0cd73359b15b664c3170e5d754078599 | /src/field_theory/subfield.lean | 4e17ecee1f717d0e29c7648f77db6a39a6655860 | [
"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 | 27,262 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import algebra.algebra.basic
/-!
# Subfields
Let `K` be a field. This file defines the "bundled" subfield type `subfield K`, a type
whose terms correspond to subfields o... |
09df3f19f296efce70318da16fabc4e71ab1a8db | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/1074b.lean | 4a3a15899d75583a82a80584c15a542e2c03cc8a | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 286 | lean | inductive Term
| id: Term -> Term
inductive Brx: Term -> Prop
| id: Brx z -> Brx (Term.id n)
def Brx.interp {a} (H: Brx a): Nat :=
match a with
| Term.id n => by
have ⟨Hn, Hz⟩: True ∧ Brx z
:= by cases H <;> exact ⟨by simp, by assumption⟩;
exact Hz.interp
|
500d0e11b657e942e61b1ecfb39f14e1e8a0c377 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/analysis/calculus/times_cont_diff.lean | e99a5f5ce20c1054ece5a147a529709493914a86 | [
"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 | 39,771 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import analysis.calculus.fderiv
/-!
# Higher differentiability
A function is `C^1` on a domain if it is differentiable there, and its derivative is continuou... |
ad0a9e82b5f5b26fb995f2bfeb4852653ab64f6e | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/linear_algebra/tensor_product_auto.lean | 5116afbb259dff617013c95b48138eaa8d52bd61 | [] | 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 | 54,789 | 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
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.group_theory.congruence
import Mathlib.linear_algebra.basic
import Mathlib.PostPort
... |
b008e3d172f9cd6371b5a1b7dcdace785628f957 | 2a70b774d16dbdf5a533432ee0ebab6838df0948 | /_target/deps/mathlib/src/algebra/group_with_zero/power.lean | edf5adcb17b61aec1da01b941f4ffa1834992695 | [
"Apache-2.0"
] | permissive | hjvromen/lewis | 40b035973df7c77ebf927afab7878c76d05ff758 | 105b675f73630f028ad5d890897a51b3c1146fb0 | refs/heads/master | 1,677,944,636,343 | 1,676,555,301,000 | 1,676,555,301,000 | 327,553,599 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,335 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import algebra.group_power
/-!
# Powers of elements of groups with an adjoined zero element
In this file we define integer power functions for groups with an adjoin... |
bf0c5788931dc2d16dbfe8b0bfe7b5e811476029 | e07b1aca72e83a272dd59d24c6e0fa246034d774 | /src/logic_and_proof/01_introduction.lean | 9b476585ce26011ecb03ef38961fd39863838b15 | [] | no_license | pedrominicz/learn | 637a343bd4f8669d76819ac660a2d2d3e0958710 | b79b802a9846c86c21d4b6f3e17af36e7382f0ef | refs/heads/master | 1,671,746,990,402 | 1,670,778,113,000 | 1,670,778,113,000 | 265,735,177 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,732 | lean | import data.int.parity
import data.real.irrational
open real
#print irrational
#check set.range (coe : ℚ → ℝ)
lemma eq_mul_div_of_nonneg {a b : ℝ} (h : b ≠ 0) : a = a / b * b :=
begin
calc
a = 1 * a : by ring
... = b / b * a : by rw ←div_self h
... = a / b * b : by exact div_mul_comm' b b a
end
#check... |
7c4d560caf73b5d0142a42df62a1283d6b0bec15 | 8d65764a9e5f0923a67fc435eb1a5a1d02fd80e3 | /src/analysis/convex/basic.lean | ed20d75ad852919871ce05c1416fadb833dcd5fe | [
"Apache-2.0"
] | permissive | troyjlee/mathlib | e18d4b8026e32062ab9e89bc3b003a5d1cfec3f5 | 45e7eb8447555247246e3fe91c87066506c14875 | refs/heads/master | 1,689,248,035,046 | 1,629,470,528,000 | 1,629,470,528,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 70,058 | lean | /-
Copyright (c) 2019 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, Yury Kudriashov
-/
import data.complex.module
import data.set.intervals.image_preimage
import linear_algebra.affine_space.affine_map
import order.closure
/-!
#... |
8f0e92a2849b17e91e0074ec5fa457dfbc97a7b1 | 271e26e338b0c14544a889c31c30b39c989f2e0f | /tests/lean/mvar1.lean | 85f9ec40dc1ded024a7c5f541c92bfbed6ebbe23 | [
"Apache-2.0"
] | permissive | dgorokho/lean4 | 805f99b0b60c545b64ac34ab8237a8504f89d7d4 | e949a052bad59b1c7b54a82d24d516a656487d8a | refs/heads/master | 1,607,061,363,851 | 1,578,006,086,000 | 1,578,006,086,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,074 | lean | import Init.Lean.MetavarContext
open Lean
def check (b : Bool) : IO Unit :=
unless b (throw "error")
def f := mkConst `f []
def g := mkConst `g []
def a := mkConst `a []
def b := mkConst `b []
def c := mkConst `c []
def b0 := mkBVar 0
def b1 := mkBVar 1
def b2 := mkBVar 2
def u := mkLevelParam `u
def typeE := mkSo... |
29e17291135436b6147b2b0a07af9f5dc7e05675 | e8d6a03af236c510516281c3b076aa984c212a1f | /lean4/ModelCount/ModelCount/Lib.lean | 4d65ab1231b1805afdbe6248ed4b71b2ff53d2fa | [
"MIT"
] | permissive | minsungc/model-counting | 9918a1afb2ef4cc91e6be906956b4ae2b82d10be | 02f650741bddb6a94a0729889dfeb8e9b0e8521a | refs/heads/main | 1,686,421,950,907 | 1,624,283,093,000 | 1,624,283,093,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,103 | lean | import Init
import Lean.Elab.Tactic
/- Facts about Nat -/
namespace Nat
theorem le_refl (a : Nat) : a ≤ a := sorry
theorem le_trans {a b c : Nat} : a ≤ b → b ≤ c → a ≤ c := sorry
theorem lt_trans {a b c : Nat} : a < b → b < c → a < c := sorry
theorem le_of_lt {a b : Nat} : a < b → a ≤ b := sorry
theorem not_le_of_lt... |
3dab2603cd9b7369881862dd34dae1633ffea208 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/tactic/explode.lean | 386e3724fb95cd7f5fcbeb7b822c1e2d7169a0c8 | [
"Apache-2.0"
] | permissive | Lix0120/mathlib | 0020745240315ed0e517cbf32e738d8f9811dd80 | e14c37827456fc6707f31b4d1d16f1f3a3205e91 | refs/heads/master | 1,673,102,855,024 | 1,604,151,044,000 | 1,604,151,044,000 | 308,930,245 | 0 | 0 | Apache-2.0 | 1,604,164,710,000 | 1,604,163,547,000 | null | UTF-8 | Lean | false | false | 8,809 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro, Minchao Wu
-/
import tactic.core
/-!
# `#explode` command
Displays a proof term in a line by line format somewhat akin to a Fitch style
proof or the Metamath proof styl... |
7e1e2fcebb857a64ca58c504600830077a30df3b | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/algebra/floor.lean | 76686a58d97c6fff5ccd4a324635c16ea796182f | [
"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 | 9,762 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kevin Kappelmann
-/
import data.int.basic
import tactic.linarith tactic.abel
/-!
# Floor and Ceil
## Summary
We define `floor`, `ceil`, and `nat_ceil` functions on li... |
2ed576e643be7575c370d84a7946eae38ebb53e2 | 9cb9db9d79fad57d80ca53543dc07efb7c4f3838 | /src/partition.lean | 7bb7661aabaf02cdb6648b36c101a048f0edfdbc | [] | no_license | mr-infty/lean-liquid | 3ff89d1f66244b434654c59bdbd6b77cb7de0109 | a8db559073d2101173775ccbd85729d3a4f1ed4d | refs/heads/master | 1,678,465,145,334 | 1,614,565,310,000 | 1,614,565,310,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 504 | lean | import data.real.nnreal
import topology.algebra.infinite_sum
open_locale nnreal
def mask_fun (f : ℕ → ℝ≥0) (mask : ℕ → Prop) [∀ n, decidable (mask n)] : ℕ → ℝ≥0 :=
λ n, if mask n then f n else 0
lemma exists_partition (N : ℕ) (hN : 0 < N) (f : ℕ → ℝ≥0) (hf : ∀ n, f n ≤ 1) :
∃ (mask : fin N → ℕ → Prop) [∀ i n, deci... |
0acb067e7c999e5285642beac1b22835f135f7bb | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/linear_algebra/quadratic_form.lean | 5666ebdcac2f40185866224669ccc3eff3b1e268 | [
"Apache-2.0"
] | permissive | dupuisf/mathlib | 62de4ec6544bf3b79086afd27b6529acfaf2c1bb | 8582b06b0a5d06c33ee07d0bdf7c646cae22cf36 | refs/heads/master | 1,669,494,854,016 | 1,595,692,409,000 | 1,595,692,409,000 | 272,046,630 | 0 | 0 | Apache-2.0 | 1,592,066,143,000 | 1,592,066,142,000 | null | UTF-8 | Lean | false | false | 20,466 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Anne Baanen
-/
import algebra.invertible
import linear_algebra.bilinear_form
import linear_algebra.determinant
import linear_algebra.special_linear_group
/-!
# Quadratic forms
This file... |
46835b7f7166fd65032dc9c8fd0b31cd2ddda8d5 | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/data/fin.lean | 2d18d330f754a9558150b1662888dd2a0bd26d72 | [
"Apache-2.0"
] | permissive | vaibhavkarve/mathlib | a574aaf68c0a431a47fa82ce0637f0f769826bfe | 17f8340912468f49bdc30acdb9a9fa02eeb0473a | refs/heads/master | 1,621,263,802,637 | 1,585,399,588,000 | 1,585,399,588,000 | 250,833,447 | 0 | 0 | Apache-2.0 | 1,585,410,341,000 | 1,585,410,341,000 | null | UTF-8 | Lean | false | false | 26,688 | lean | /-
Copyright (c) 2017 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Keeley Hoek
-/
import data.nat.basic
/-!
# The finite type with `n` elements
`fin n` is the type whose elements are natural numbers smaller than `n`.
This file expan... |
111b2de07f521ad308b172c98cb06a7a57b64a34 | acc85b4be2c618b11fc7cb3005521ae6858a8d07 | /data/hash_map.lean | 8cfa31354df4e77d3a08d4f3d84079085b3610fb | [
"Apache-2.0"
] | permissive | linpingchuan/mathlib | d49990b236574df2a45d9919ba43c923f693d341 | 5ad8020f67eb13896a41cc7691d072c9331b1f76 | refs/heads/master | 1,626,019,377,808 | 1,508,048,784,000 | 1,508,048,784,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 34,278 | 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, Mario Carneiro
-/
import data.list.basic data.pnat data.array.lemmas
universes u v w
def bucket_array (α : Type u) (β : α → Type v) (n : ℕ+) :=
array (list ... |
7bfc3a20bcd2edcff68140869c4743a392a1d19f | 5fbbd711f9bfc21ee168f46a4be146603ece8835 | /lean/natural_number_game/power/5.lean | 5198fd1e5362d7e2c1380f7cb83bdd083e92d3d9 | [
"LicenseRef-scancode-warranty-disclaimer"
] | no_license | goedel-gang/maths | 22596f71e3fde9c088e59931f128a3b5efb73a2c | a20a6f6a8ce800427afd595c598a5ad43da1408d | refs/heads/master | 1,623,055,941,960 | 1,621,599,441,000 | 1,621,599,441,000 | 169,335,840 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 186 | lean | lemma pow_add (a m n : mynat) : a ^ (m + n) = a ^ m * a ^ n :=
induction n with d hd,
rwa [add_zero, pow_zero, mul_one],
rw add_succ,
repeat {rw pow_succ},
rw hd,
simp,
end
|
359c4e5aabeec46333954e1bfa991f2da1d99f1b | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/bad_error2.lean | f0f6afa860c97bd65b25fb4cfbd9e21d3c99fb0c | [
"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 | 344 | lean | open nat
example {k n m : ℕ} (h : k + n ≤ k + m) : n ≤ m :=
match le.dest h with
| ⟨w, hw⟩ := @le.intro _ _ w
begin
-- hw is beta reduced after we added the equation compiler preprocessor.
-- So, this test is not really relevant anymore.
rw [nat.add_assoc] at hw,
apply nat.add_left_cancel h... |
6f81315338655ddd5f50d523954f1a05f33e019b | 19cc34575500ee2e3d4586c15544632aa07a8e66 | /src/linear_algebra/linear_independent.lean | 97c2cb3223fb95e9ba243f44d0ca83e5707a22b2 | [
"Apache-2.0"
] | permissive | LibertasSpZ/mathlib | b9fcd46625eb940611adb5e719a4b554138dade6 | 33f7870a49d7cc06d2f3036e22543e6ec5046e68 | refs/heads/master | 1,672,066,539,347 | 1,602,429,158,000 | 1,602,429,158,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 40,007 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Alexander Bentkamp, Anne Baanen
-/
import linear_algebra.finsupp
import order.zorn
import data.finset.order
/-! Linear independence
This file defines lin... |
13b840af91e529d6eeb535bf2fc909d47867836f | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /library/logic/quantifiers.lean | 97b4de1160d9987dd760f697158d27ab0c0ace2d | [
"Apache-2.0"
] | permissive | codyroux/lean | 7f8dff750722c5382bdd0a9a9275dc4bb2c58dd3 | 0cca265db19f7296531e339192e9b9bae4a31f8b | refs/heads/master | 1,610,909,964,159 | 1,407,084,399,000 | 1,416,857,075,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,475 | 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
import logic.connectives logic.nonempty
open inhabited nonempty
inductive Exists {A : Type} (P : A → Prop) : Prop :=
intro : ∀ (a : A),... |
7495abcfc0d6af80dcfdaa16361d59accc0e10ec | e94d3f31e48d06d252ee7307fe71efe1d500f274 | /hott/init/tactic.hlean | ae66706282d000f2db08cdc8041af8fbf28fc1cc | [
"Apache-2.0"
] | permissive | GallagherCommaJack/lean | e4471240a069d82f97cb361d2bf1a029de3f4256 | 226f8bafeb9baaa5a2ac58000c83d6beb29991e2 | refs/heads/master | 1,610,725,100,482 | 1,459,194,829,000 | 1,459,195,377,000 | 55,377,224 | 0 | 0 | null | 1,459,731,701,000 | 1,459,731,700,000 | null | UTF-8 | Lean | false | false | 7,051 | hlean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
This is just a trick to embed the 'tactic language' as a Lean
expression. We should view 'tactic' as automation that when execute
produces a term. tactic.buil... |
2befabcb2d1550a385dc7170ef2fb630476749c9 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/interactive/goTo.lean | 910db5f838e89d5992267f8b8c97a8c37aa09212 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 2,360 | lean | import Lean.Elab
structure Bar where
structure Foo where
foo₁ : Nat
foo₂ : Nat
bar : Bar
def mkFoo₁ : Foo := {
--v textDocument/definition
foo₁ := 1
--^ textDocument/definition
--v textDocument/declaration
foo₂ := 2
--v textDocument/typeDefinition
bar := ⟨⟩
}
--v textDocument/definition
#c... |
f39dc6d5b0e56032e810654f50227aa5dd202967 | 8e6cad62ec62c6c348e5faaa3c3f2079012bdd69 | /src/topology/metric_space/hausdorff_distance.lean | b369e78d8b9112d404a206f8787e1343aaf7b965 | [
"Apache-2.0"
] | permissive | benjamindavidson/mathlib | 8cc81c865aa8e7cf4462245f58d35ae9a56b150d | fad44b9f670670d87c8e25ff9cdf63af87ad731e | refs/heads/master | 1,679,545,578,362 | 1,615,343,014,000 | 1,615,343,014,000 | 312,926,983 | 0 | 0 | Apache-2.0 | 1,615,360,301,000 | 1,605,399,418,000 | Lean | UTF-8 | Lean | false | false | 33,674 | 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 topology.metric_space.isometry
import topology.instances.ennreal
/-!
# Hausdorff distance
The Hausdorff distance on subsets of a metric (or emetric) spa... |
3a741e684f1e3ca315ba8c4a8e346fc610fa0480 | 1e3a43e8ba59c6fe1c66775b6e833e721eaf1675 | /src/data/padics/padic_norm.lean | 9ca0c1e64abdf13b3c03c2ffb8911982301eaf67 | [
"Apache-2.0"
] | permissive | Sterrs/mathlib | ea6910847b8dfd18500486de9ab0ee35704a3f52 | d9327e433804004aa1dc65091bbe0de1e5a08c5e | refs/heads/master | 1,650,769,884,257 | 1,587,808,694,000 | 1,587,808,694,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 17,057 | 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
-/
import data.rat
import algebra.gcd_domain
import algebra.field_power
import ring_theory.multiplicity
import data.real.cau_seq
/-!
# p-adic norm
This file defines ... |
a195705337a27253a6c9be380e570ee942bf8cb0 | 510e96af568b060ed5858226ad954c258549f143 | /topology/uniform_space.lean | fe53c541c17d0afdd2fbe9b1e4d45b84adf270d0 | [] | no_license | Shamrock-Frost/library_dev | cb6d1739237d81e17720118f72ba0a6db8a5906b | 0245c71e4931d3aceeacf0aea776454f6ee03c9c | refs/heads/master | 1,609,481,034,595 | 1,500,165,215,000 | 1,500,165,347,000 | 97,350,162 | 0 | 0 | null | 1,500,164,969,000 | 1,500,164,969,000 | null | UTF-8 | Lean | false | false | 52,901 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Theory of uniform spaces.
-/
import algebra.lattice.filter .topological_space .continuity
open set lattice filter
set_option eqn_compiler.zeta true
attribute [trans] ... |
554d4f4dacabaf98e5e4e28da5c3339c3580782e | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/suggest_auto.lean | 56b2e7ddfceb9b2cb477eae47cbcf85be67b4450 | [] | 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 | 9,849 | lean | /-
Copyright (c) 2019 Lucas Allen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lucas Allen and Scott Morrison
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.mllist
import Mathlib.tactic.solve_by_elim
import Mathlib.PostPort
unive... |
09b783a7dec62b6a287a4565915374b0e141bb9f | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/data/finsupp/basic.lean | 001b653dd16a18449f167b08e702df6eeb79d299 | [
"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 | 73,118 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Scott Morrison
-/
import algebra.big_operators.order
import algebra.module.basic
import data.fintype.card
import data.set.finite
import data.multiset.antidiagonal
/-!
... |
14350907b2691429600498348f98f557c7551e7c | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /tests/lean/run/trace.lean | df4294e833ba5951dafac8a5bced3670e3c38be8 | [
"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 | 1,387 | lean | import Lean.CoreM
open Lean
structure MyState :=
(traceState : TraceState := {})
(s : Nat := 0)
abbrev M := CoreM
def tst1 : M Unit :=
do trace! `module ("hello" ++ MessageData.nest 9 (Format.line ++ "world"));
trace! `module.aux "another message";
pure ()
def tst2 (b : Bool) : M Unit :=
traceCtx `mo... |
74fd36d4126792641160b7b45f3f531c5c920586 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/set_theory/game/impartial.lean | 09c7613ae1b70b64e9963c81d1283cae87367329 | [
"Apache-2.0"
] | permissive | Lix0120/mathlib | 0020745240315ed0e517cbf32e738d8f9811dd80 | e14c37827456fc6707f31b4d1d16f1f3a3205e91 | refs/heads/master | 1,673,102,855,024 | 1,604,151,044,000 | 1,604,151,044,000 | 308,930,245 | 0 | 0 | Apache-2.0 | 1,604,164,710,000 | 1,604,163,547,000 | null | UTF-8 | Lean | false | false | 6,901 | lean | /-
Copyright (c) 2020 Fox Thomson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fox Thomson
-/
import set_theory.game.winner
import tactic.nth_rewrite.default
import tactic.equiv_rw
universe u
/-!
# Basic definitions about impartial (pre-)games
We will define an i... |
4a0d6df1f3d0ce2fe6e3e65476bfa1f373e21dd9 | e2fc96178628c7451e998a0db2b73877d0648be5 | /test/demo_unrestricted.lean | 0619289c868a26f2b8bbf5389e8985143f1dc9cb | [
"BSD-2-Clause"
] | permissive | madvorak/grammars | cd324ae19b28f7b8be9c3ad010ef7bf0fabe5df2 | 1447343a45fcb7821070f1e20b57288d437323a6 | refs/heads/main | 1,692,383,644,884 | 1,692,032,429,000 | 1,692,032,429,000 | 453,948,141 | 7 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 25,858 | lean | import classes.unrestricted.basics.toolbox
import utilities.list_utils
import utilities.written_by_others.trim_assoc
inductive alphabet
| _a : alphabet
| _b : alphabet
| _c : alphabet
inductive inner
| _S : inner
| _L : inner
| _R : inner
| _X : inner
| _B : inner
| _M : inner
| _E : inner
| _C : inner
| _K : inner
... |
e34bfa5a2dd5f2f66ee4233ef4b10f9bb09fa152 | a4673261e60b025e2c8c825dfa4ab9108246c32e | /src/Lean/Elab/MutualDef.lean | 462e16bcf7ef99c747bae9ba0c622b82655b4b0f | [
"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 | 28,375 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.Closure
import Lean.Meta.Check
import Lean.Elab.Command
import Lean.Elab.DefView
import Lean.Elab.PreDefinition
namespace Lean.Elab
/- De... |
a6b971eb52dfde62fec314f83a881d43376018b8 | 59a4b050600ed7b3d5826a8478db0a9bdc190252 | /src/category_theory/over.lean | 423200037d21ac3294336e4344173930d7fe923c | [] | no_license | rwbarton/lean-category-theory | f720268d800b62a25d69842ca7b5d27822f00652 | 00df814d463406b7a13a56f5dcda67758ba1b419 | refs/heads/master | 1,585,366,296,767 | 1,536,151,349,000 | 1,536,151,349,000 | 147,652,096 | 0 | 0 | null | 1,536,226,960,000 | 1,536,226,960,000 | null | UTF-8 | Lean | false | false | 461 | lean | import category_theory.category
import category_theory.tactics.obviously
universes u₁ v₁
namespace category_theory
variables {C : Type u₁} [𝒞 : category.{u₁ v₁} C]
include 𝒞
def over (Z : C) := Σ X : C, X ⟶ Z
instance {Z : C} : category (over Z) :=
{ hom := λ X Y, { f : X.1 ⟶ Y.1 // f ≫ Y.2 = X.2 },
id := λ X,... |
8c6c875615d1a8d4e2131d1bd8e4d0861730c050 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Elab/App.lean | 70eaf6ef21e40dc37569257f8a1fac1065da0980 | [
"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 | 70,730 | 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.FindMVar
import Lean.Parser.Term
import Lean.Meta.KAbstract
import Lean.Meta.Tactic.ElimInfo
import Lean.Elab.Term
import Lean.Elab.Binders... |
40e544e44302a030f690c598f9b10eed128cfd21 | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /src/Lean/Compiler/LCNF/Simp/Main.lean | 7db68a3e3cffd5de94445301e92a6a0b71d2926a | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | tobiasgrosser/lean4 | ce0fd9cca0feba1100656679bf41f0bffdbabb71 | ebdbdc10436a4d9d6b66acf78aae7a23f5bd073f | refs/heads/master | 1,673,103,412,948 | 1,664,930,501,000 | 1,664,930,501,000 | 186,870,185 | 0 | 0 | Apache-2.0 | 1,665,129,237,000 | 1,557,939,901,000 | Lean | UTF-8 | Lean | false | false | 11,834 | lean | /-
Copyright (c) 2022 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Compiler.ImplementedByAttr
import Lean.Compiler.LCNF.ElimDead
import Lean.Compiler.LCNF.AlphaEqv
import Lean.Compiler.LCNF.PrettyPrinter
import ... |
5f6125fd723e3a4c30b8c0f3844c94b1f211aef7 | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /tests/lean/run/tree.lean | caf4af0cbe51a96bc35571816024b35ae6020735 | [
"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 | 1,931 | lean | import logic data.prod
open eq.ops prod
inductive tree (A : Type) :=
leaf : A → tree A,
node : tree A → tree A → tree A
inductive one.{l} : Type.{max 1 l} :=
star : one
set_option pp.universes true
namespace tree
namespace manual
section
universe variables l₁ l₂
variable {A : Type.{l₁}}
variable (C : ... |
807ba6f9717f3b83d4bd0a368289b4f94a887a38 | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/option/basic.lean | c98373ee1e729289471f2191aa5d7d8ec328ff4d | [
"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 | 15,139 | 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 tactic.basic
namespace option
variables {α : Type*} {β : Type*} {γ : Type*}
lemma coe_def : (coe : α → option α) = some := rfl
lemma some_ne_none (x : α) : ... |
19ce5c1c1348a75ae8ca5dc73bc74b4d2d1c5386 | e61a235b8468b03aee0120bf26ec615c045005d2 | /stage0/src/Init/Lean/Elab/Util.lean | 9594f77402915e3c944df45cac5bab3d7469339a | [
"Apache-2.0"
] | permissive | SCKelemen/lean4 | 140dc63a80539f7c61c8e43e1c174d8500ec3230 | e10507e6615ddbef73d67b0b6c7f1e4cecdd82bc | refs/heads/master | 1,660,973,595,917 | 1,590,278,033,000 | 1,590,278,033,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,468 | 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.Util.Trace
import Init.Lean.Parser
import Init.Lean.KeyedDeclsAttribute
namespace Lean
def Syntax.prettyPrint (stx : Syntax) : Fo... |
97082a28b4c2c333c026c1dd1c54da2f7619a4ac | 78630e908e9624a892e24ebdd21260720d29cf55 | /src/logic_first_order/fol_21_22.lean | a392118752e72f5116cad57d88bfa9dfa303d48b | [
"CC0-1.0"
] | permissive | tomasz-lisowski/lean-logic-examples | 84e612466776be0a16c23a0439ff8ef6114ddbe1 | 2b2ccd467b49c3989bf6c92ec0358a8d6ee68c5d | refs/heads/master | 1,683,334,199,431 | 1,621,938,305,000 | 1,621,938,305,000 | 365,041,573 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,573 | lean | namespace fol_21_22
-- Proof of equivalence for:
-- ∃ x, A x ∧ ∀ y, (A y → y = x)
-- (∃ x, A x) ∧ (∀ y y', A y ∧ A y' → y = y')
variable U : Type
variable A : U → Prop
theorem fol_21 : (∃ x, A x ∧ ∀ y, (A y → y = x)) →
((∃ x, A x) ∧ (∀ y y', A y ∧ A y' → y = y')) :=
assume h1: (∃ x, A x ∧ (∀ y, A y → y = x)),
exis... |
51e9aaee28ffd7b5d9681591e8e60e420b393cbe | 618003631150032a5676f229d13a079ac875ff77 | /src/group_theory/presented_group.lean | d10560348eb3222c10df0501f9dbff3151b30028 | [
"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 | 2,846 | lean | /-
Copyright (c) 2019 Michael Howes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Howes
Defining a group given by generators and relations
-/
import group_theory.free_group
import group_theory.quotient_group
variables {α : Type}
/-- Given a set of relation... |
c8a939ec189e85456435562d5122e794108a3b87 | 9ad8d18fbe5f120c22b5e035bc240f711d2cbd7e | /src/group_theory/dihedral.lean | b59dfa55c7b8a910907c698200d60e4464bfef15 | [] | no_license | agusakov/lean_lib | c0e9cc29fc7d2518004e224376adeb5e69b5cc1a | f88d162da2f990b87c4d34f5f46bbca2bbc5948e | refs/heads/master | 1,642,141,461,087 | 1,557,395,798,000 | 1,557,395,798,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,259 | lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Neil Strickland
We define finite dihedral groups. We show that a pair of elements
`r,s ∈ G` satisfying appropriate relations gives rise to a
homomorphism `Dₙ → G`. (We have chose... |
604c943e4fc087092ff4894e33eb3cb06e51e280 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /10_Structures_and_Records.org.4.lean | 15977077c3be9316aafded58c13e101cd23d3859 | [] | 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 | 265 | lean | import standard
structure point (A : Type) :=
mk :: (x : A) (y : A)
-- BEGIN
eval point.x (point.mk 10 20)
eval point.y (point.mk 10 20)
open point
example (A : Type) (a b : A) : x (mk a b) = a :=
rfl
example (A : Type) (a b : A) : y (mk a b) = b :=
rfl
-- END
|
19cf7c717148f2ff39a0e3ee6f7e96c6b835a566 | 8f67b34bba98f894155dedf263bc8d61c31e89cd | /2ltt/fibrantlimits.lean | ed73c8ea44bcf2662832833103b223a30d4fd8f0 | [] | no_license | 5HT/two-level | 3b1523db242cba819681b862fbc8f490d9571a66 | 370f5a91311db3b463b10a31891370721e2476e2 | refs/heads/master | 1,648,254,367,420 | 1,576,269,550,000 | 1,576,269,550,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,491 | lean | import .fibrant .fibrantlimits_aux .matching .inverse algebra.category
.limit .pullbacks .finite
import data.fin
open invcat category functor matching_object Fib
sigma.ops fincat natural_transformation eq
open equiv equiv.ops
namespace fiblimits
universe variable u
variables {C : Category.{1 1}}
... |
bb534f72957a6fa7047038c05e9ac3f0abdddbdb | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/monad/coequalizer.lean | 3954e674ec514a6bc89e31f6eaa7c706483b37da | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 4,101 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import category_theory.limits.shapes.reflexive
import category_theory.limits.shapes.split_coequalizer
import category_theory.monad.algebra
/-!
# Special coequalizers as... |
b13ae60b695570f2c0baa095fcbf68a9f91994c7 | ba4794a0deca1d2aaa68914cd285d77880907b5c | /src/game/world5/level3.lean | f9042ad4018f2faab2718ef874b6b3f11393a697 | [
"Apache-2.0"
] | permissive | ChrisHughes24/natural_number_game | c7c00aa1f6a95004286fd456ed13cf6e113159ce | 9d09925424da9f6275e6cfe427c8bcf12bb0944f | refs/heads/master | 1,600,715,773,528 | 1,573,910,462,000 | 1,573,910,462,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,784 | lean | /- Tactic : have
## Summary
`have h : P,` will create a new goal of creating a term of type `P`,
and will add `h : P` to the hypotheses for the goal you were working on.
## Details
If you want to name a term of some type (because you want it
in your local context for some reason), and if you have the
formula for th... |
c99cd580992daed4f1b479c2c6c90495194698f4 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/topology/continuous_function/algebra.lean | 5f242d44fcb96db1a05026f5d479decf55b940a6 | [
"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 | 25,499 | 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.basic
import topology.continuous_function.ordered
import topology.algebra.uniform_group
import topology.uniform_space... |
2fac3f33a00bc4cb6b52dc643984eb56330b5f1c | 08bd4ba4ca87dba1f09d2c96a26f5d65da81f4b4 | /src/Lean/Compiler/IR/EmitLLVM.lean | f7da43099815f58ff51b8892cd53d8cacf2f0df9 | [
"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",
"Apache-2.0",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | gebner/lean4 | d51c4922640a52a6f7426536ea669ef18a1d9af5 | 8cd9ce06843c9d42d6d6dc43d3e81e3b49dfc20f | refs/heads/master | 1,685,732,780,391 | 1,672,962,627,000 | 1,673,459,398,000 | 373,307,283 | 0 | 0 | Apache-2.0 | 1,691,316,730,000 | 1,622,669,271,000 | Lean | UTF-8 | Lean | false | false | 71,373 | lean | /-
Copyright (c) 2022 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Siddharth Bhat
-/
import Lean.Data.HashMap
import Lean.Runtime
import Lean.Compiler.NameMangling
import Lean.Compiler.ExportAttr
import Lean.Compiler.InitAttr
import Lean.Compi... |
0f7080200f0e00d980966724bbc444d143a4dc81 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /src/Lean/Elab/Import.lean | 18cab54e25b89f040b66e952422c1cae3b71c59b | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | cipher1024/lean4 | 6e1f98bb58e7a92b28f5364eb38a14c8d0aae393 | 69114d3b50806264ef35b57394391c3e738a9822 | refs/heads/master | 1,642,227,983,603 | 1,642,011,696,000 | 1,642,011,696,000 | 228,607,691 | 0 | 0 | Apache-2.0 | 1,576,584,269,000 | 1,576,584,268,000 | null | UTF-8 | Lean | false | false | 1,744 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
import Lean.Parser.Module
namespace Lean.Elab
def headerToImports (header : Syntax) : List Import :=
let imports := if header[0].isNon... |
4f741ce855971773ded27bc9a0e6486cf6afc6a2 | 38bf3fd2bb651ab70511408fcf70e2029e2ba310 | /src/category_theory/equivalence.lean | 55e90c90c92669ed3ad75e5bcc855cc59abccc26 | [
"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 | 14,238 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tim Baumann, Stephen Morgan, Scott Morrison, Floris van Doorn
-/
import category_theory.fully_faithful
import category_theory.whiskering
import category_theory.natural_isomorphism
impo... |
98b5cbcc4b88646ddb012207b73a2fa990a78a49 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Meta/Tactic/Revert.lean | 1c4da42e33f2b4cf3b1a9579ac1d66c95d69a00e | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 2,435 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.Tactic.Clear
namespace Lean.Meta
/--
Revert free variables `fvarIds` at goal `mvarId`.
-/
def _root_.Lean.MVarId.revert (mvarId : MVarId)... |
1bdb10520d9eb6cd9f61c3762d7f67888f32eecb | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Init/Data/Option/BasicAux.lean | 46298ca67e4ac1a40a001857d3a6e3c1e3041224 | [
"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 | 382 | 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.Data.Option.Basic
import Init.Util
universe u
namespace Option
@[inline] def get! {α : Type u} [Inhabited α] : Option α → α
| some ... |
d83c4a0027eaf2ee6587b271de7a4c7e6f139cd2 | 02005f45e00c7ecf2c8ca5db60251bd1e9c860b5 | /src/algebra/module/submodule.lean | e963afbeb2f71d9d8167c213c6ca934dafb5cbb0 | [
"Apache-2.0"
] | permissive | anthony2698/mathlib | 03cd69fe5c280b0916f6df2d07c614c8e1efe890 | 407615e05814e98b24b2ff322b14e8e3eb5e5d67 | refs/heads/master | 1,678,792,774,873 | 1,614,371,563,000 | 1,614,371,563,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,732 | lean | /-
Copyright (c) 2015 Nathaniel Thomas. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nathaniel Thomas, Jeremy Avigad, Johannes Hölzl, Mario Carneiro
-/
import algebra.module.linear_map
import group_theory.group_action.sub_mul_action
/-!
# Submodules of a module
In ... |
896e516b4bf24c18c3e2694f570bb2d7f05ee61a | 3863d2564418bccb1859e057bf5a4ef240e75fd7 | /hott/hit/pushout.hlean | 4efe06248f1c9c0e7923eca0efc00b63fa3b7965 | [
"Apache-2.0"
] | permissive | JacobGross/lean | 118bbb067ff4d4af48a266face2c7eb9868fa91c | eb26087df940c54337cb807b4bc6d345d1fc1085 | refs/heads/master | 1,582,735,011,532 | 1,462,557,826,000 | 1,462,557,826,000 | 46,451,196 | 0 | 0 | null | 1,462,557,826,000 | 1,447,885,161,000 | C++ | UTF-8 | Lean | false | false | 13,859 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
Declaration of the pushout
-/
import .quotient types.sigma types.arrow_2
open quotient eq sum equiv is_trunc
namespace pushout
section
parameters {TL BL TR : Ty... |
19342abf0f650b306b617de85304e57355d08393 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/decreasingTacticUpdatedEnvIssue.lean | 76d829809f91ac9eb57ab06c0b51e9814564d70d | [
"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 | 581 | lean | def g (x : Nat) (b : Bool) :=
if b then
x - 1
else
x + 1
theorem g_eq (x : Nat) (h : ¬ x = 0) : g x (x > 0) = x - 1 ∧ g x false = x + 1 := by
have : x > 0 := by match x with
| 0 => contradiction
| x+1 => apply Nat.zero_lt_succ
simp [g, this]
macro_rules
| `(tactic| decreasing_tactic) =>
`(tac... |
2b5ee401fb5d34e588bf33d041fb23d903e57a08 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/ring_theory/coprime/lemmas.lean | c6334f80f3d0c68cd051f547eb359bdaa86fb623 | [
"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 | 8,186 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Ken Lee, Chris Hughes
-/
import algebra.big_operators.ring
import data.fintype.basic
import data.int.gcd
import ring_theory.coprime.basic
/-!
# Additional lemmas about elements ... |
9d642dbb1243ab53342b4c39ba0f5eec3f5eb00e | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/ring_theory/polynomial/dickson.lean | b05aa0021c9de796678a08f565bf8ceac16b4119 | [
"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 | 10,482 | lean | /-
Copyright (c) 2021 Julian Kuelshammer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Kuelshammer
-/
import ring_theory.polynomial.chebyshev
import ring_theory.localization
import data.zmod.basic
import algebra.char_p.invertible
/-!
# Dickson polynomials
... |
95b188a004ada2c8ed773d87516d02620373e365 | 947b78d97130d56365ae2ec264df196ce769371a | /src/Lean/Util/CollectMVars.lean | 5e5054791b12ee7202a09592cc1039dacafbefad | [
"Apache-2.0"
] | permissive | shyamalschandra/lean4 | 27044812be8698f0c79147615b1d5090b9f4b037 | 6e7a883b21eaf62831e8111b251dc9b18f40e604 | refs/heads/master | 1,671,417,126,371 | 1,601,859,995,000 | 1,601,860,020,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,208 | 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.Expr
namespace Lean
namespace CollectMVars
structure State :=
(visitedExpr : ExprSet := {})
(result : Array MVarId := #[])
insta... |
214e78652a9725b6e55257e5317c8e09847771c3 | 54c9ed381c63410c9b6af3b0a1722c41152f037f | /Lib4/Examples/Nullstellensatz.lean | 21cbf3a44870dbe529e5a8023fc7152150e8dae8 | [
"Apache-2.0"
] | permissive | dselsam/binport | 0233f1aa961a77c4fc96f0dccc780d958c5efc6c | aef374df0e169e2c3f1dc911de240c076315805c | refs/heads/master | 1,687,453,448,108 | 1,627,483,296,000 | 1,627,483,296,000 | 333,825,622 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,364 | lean | import Mathlib.ring_theory.jacobson
import Mathlib.field_theory.algebraic_closure
import Mathlib.field_theory.mv_polynomial
import Mathlib.algebraic_geometry.prime_spectrum
set_option synthInstance.maxHeartbeats 50000
namespace Mathlib
syntax "{ " ident (" : " term)? " | " term " }" : term
macro_rules
| `({ $x : ... |
4bbca16f084f1d7367fa482d9a78e2e7848e3335 | cf39355caa609c0f33405126beee2739aa3cb77e | /tmp/wf_ex.lean | 38db365ffbadbc2119be1e04f71487d24c1ebf07 | [
"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 | 6,232 | lean | open tactic
/- User spec
f 0 0 = some 1
f 0 m = f m 0
f (n+1) m = match f n m with
| some a := some (a+1)
| none := none
end
-/
/- Define f_aux using well-founded recursion -/
constant R : (nat × nat) → (nat × nat) → Prop
axioms R_wf : well_founded R
axiom Dec (p₂ p₁ :... |
7ee220873191fef7caaa1746d6dcdd524fe442f2 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/polynomial/div.lean | 39ef3af90ed4fcc4e91b0993df8c2db6176d8b23 | [
"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 | 24,913 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
-/
import data.polynomial.monic
import ring_theory.euclidean_domain
import ring_theory.multiplicity
/-!
# Division of univar... |
480adcbc899a8e563d4f6adc0d8644f3f1f741cd | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/tactic8.lean | e3c6503a9c68be5a42f8d2f2409cee5248962e18 | [
"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 | 150 | lean | (* import("tactic.lua") *)
theorem T (a b : Bool) : a \/ b → (not b) → a := _.
disj_hyp
exact
absurd
done
print environment 1. |
07952ecc982e06c94881b984e90979c8d9ed0fd7 | f5f7e6fae601a5fe3cac7cc3ed353ed781d62419 | /src/group_theory/free_group.lean | 05427bd7d002458ec74b0d91b147ffd5d5425fca | [
"Apache-2.0"
] | permissive | EdAyers/mathlib | 9ecfb2f14bd6caad748b64c9c131befbff0fb4e0 | ca5d4c1f16f9c451cf7170b10105d0051db79e1b | refs/heads/master | 1,626,189,395,845 | 1,555,284,396,000 | 1,555,284,396,000 | 144,004,030 | 0 | 0 | Apache-2.0 | 1,533,727,664,000 | 1,533,727,663,000 | null | UTF-8 | Lean | false | false | 30,843 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
Free groups as a quotient over the reduction relation `a * x * x⁻¹ * b = a * b`.
First we introduce the one step reduction relation
`free_group.red.step`: w * x * x⁻¹ * v ~... |
f4d7d7955081409c9e91e15c64ab155395d23118 | 022215fec0be87ac6243b0f4fa3cc2939361d7d0 | /src/algebraic_geometry/presheafed_space.lean | 949c5569397b9a53c936b473d5b16a4732d17c1f | [
"Apache-2.0"
] | permissive | PaulGustafson/mathlib | 4aa7bc81ca971fdd7b6e50bf3a245fade2978391 | c49ac06ff9fa1371e9b6050a121df618cfd3fb80 | refs/heads/master | 1,590,798,947,521 | 1,559,220,227,000 | 1,559,220,227,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,842 | 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.instances.Top.presheaf
universes v u
open category_theory
open category_theory.instances
open category_theory.instances.Top
open topologic... |
1f02afe9ebbe3a2cf0b5f3874bb7676906b503f0 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/eq2.lean | 266c3424d34bde5b5afbfa709c5ee69366c3f7e2 | [
"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 | 176 | lean |
definition symm {A : Type} : Π {a b : A}, a = b → b = a
| a .a rfl := rfl
definition trans {A : Type} : Π {a b c : A}, a = b → b = c → a = c
| a .a .a rfl rfl := rfl
|
c351b4341082227964825acbc82fad4f9d7303be | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/scan_error2.lean | 64b76bed6437e5bd7abee68779393c2181fc0807 | [
"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 | 20 | lean | (* print("from lua") |
4e62fb8fa24af808fa32001d3af6b47c6bb2ca54 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/inaccessible.lean | fb6a28ac2312600410c496eb83b7107cb7c2dcfc | [
"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 | 3,372 | lean | universe variables u v
inductive imf {A : Type u} {B : Type v} (f : A → B) : B → Type (max 1 u v)
| mk : ∀ (a : A), imf (f a)
definition inv_1 {A : Type u} {B : Type v} (f : A → B) : ∀ (b : B), imf f b → A
| .(f a) (imf.mk a) := a
definition inv_2 {A : Type u} {B : Type v} (f : A → B) : ∀ (b : B), imf f b → A
| ._ (... |
6e909b60a9b378c300accf1be14ba0008c830fa3 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/blast_ematch3.lean | 8147b1eee14486f066fce09773c67e1834024bc8 | [
"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 | 633 | lean | import algebra.ring data.nat
namespace foo
variables {A : Type}
section
variables [s : add_comm_monoid A]
include s
attribute add.comm [forward]
attribute add.assoc [forward]
set_option blast.strategy "ematch"
theorem add_comm_three (a b c : A) : a + b + c = c + b + a :=
by blast
theorem add.comm4 : ∀ (n m k l :... |
36c7c0037c78ee9ad1b7335b2468d3d42b36eaee | fe84e287c662151bb313504482b218a503b972f3 | /src/combinatorics/card_sign.lean | 39ffbbf972ed92ae5870be072ee772e35b33b03d | [] | 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 | 5,005 | lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Neil Strickland
If J is a finite set then the sum of (-1)^{|K|} over subsets K ⊆ J
is usually zero, except that the sum is one if J is empty.
We will prove two versions of this, ... |
c01c0e950440adc0d9ed6c8031a6448a975f21fd | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/topology/connected.lean | 427fdad0c380339993f0687fa1fc4abd3054fc27 | [
"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 | 61,884 | 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 data.int.succ_pred
import data.nat.succ_pred
import order.partial_sups
import order.succ_pred.relation
import topology.subset_... |
b88d5ee9f5d6c424c42f6a481d7453bb99c4d2da | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /04_Quantifiers_and_Equality.org.2.lean | d484735222c67779f23f4fc9363e60903ab6b9d2 | [] | 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 | 228 | lean | /- page 48 -/
import standard
variables (A : Type) (p q : A → Prop)
-- BEGIN
example : (∀ x : A, p x ∧ q x) → ∀ y : A, p y :=
assume H : ∀ x : A, p x ∧ q x,
take z : A,
show p z, from and.elim_left (H z)
-- END
|
96ce1444e909ab2262087308a9b97b8bce728da0 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/ring_theory/polynomial/eisenstein/is_integral.lean | ca3651eddda983109f0cfce0699ef36d1a2182dd | [
"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 | 20,383 | 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 data.nat.choose.dvd
import ring_theory.integrally_closed
import ring_theory.norm
import ring_theory.polynomial.cyclotomic.expand
/-!
# Eisenstein polynomial... |
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