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7b332c1534158ce678316b9baefe38cf89aad56e | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/natural_transformation.lean | 872826db90422e7ad0762fbb1f00cbf04c22ead4 | [
"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 | 3,670 | 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.basic
/-!
# Natural transformations
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any c... |
73e955414c9cdd6cacb705e79ef70f148de64574 | 4950bf76e5ae40ba9f8491647d0b6f228ddce173 | /src/logic/embedding.lean | 2809830e9cc8980b310c49d65e353555cb1777fc | [
"Apache-2.0"
] | permissive | ntzwq/mathlib | ca50b21079b0a7c6781c34b62199a396dd00cee2 | 36eec1a98f22df82eaccd354a758ef8576af2a7f | refs/heads/master | 1,675,193,391,478 | 1,607,822,996,000 | 1,607,822,996,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,487 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import data.equiv.basic
import data.sigma.basic
import algebra.group.defs
/-!
# Injective functions
-/
universes u v w x
namespace function
/-- `α... |
e407ec042fdf0b1ea2809e7221ebefcffe9e36bc | c777c32c8e484e195053731103c5e52af26a25d1 | /src/data/real/basic.lean | 4009cb9258435879928c54ea92bc1593f693d564 | [
"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 | 28,002 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Floris van Doorn
-/
import algebra.bounds
import algebra.order.archimedean
import algebra.star.basic
import data.real.cau_seq_completion
/-!
# Real numbers from Cauchy... |
0e2adcdba25439547f22e4c95e6f9abb942b2df3 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/data/polynomial/taylor.lean | 9f068792c86d8eb52126bc686adf75ffb472fbdd | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 4,555 | lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import data.polynomial.hasse_deriv
/-!
# Taylor expansions of polynomials
## Main declarations
* `polynomial.taylor`: the Taylor expansion of the polynomial `f` a... |
be8910d7a5b682e3c1832623e0ace0b0a788406e | 69bc7d0780be17e452d542a93f9599488f1c0c8e | /9-10-2019.lean | 1695d243bf1e9b06c12aa747e3fbce08d09ad72b | [] | no_license | joek13/cs2102-notes | b7352285b1d1184fae25594f89f5926d74e6d7b4 | 25bb18788641b20af9cf3c429afe1da9b2f5eafb | refs/heads/master | 1,673,461,162,867 | 1,575,561,090,000 | 1,575,561,090,000 | 207,573,549 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,272 | lean | /-
LEAN operates in "higher-order predicate logic."
Expressions yield values.
-/
#eval 2
/-
Terms -
Literal terms -
We've evaluated this literal expression to yield a value of 2.
Expressions are more general than literals because they can do operations.
Expressions are a part of the language's syntax, while valu... |
f839c40a0349ff8150c963a4f099cad899d5f601 | aa5a655c05e5359a70646b7154e7cac59f0b4132 | /stage0/src/Lean/Elab/Match.lean | 3ffd894e9906bbcc2cad866c4ecdad8bb4e22fa2 | [
"Apache-2.0"
] | permissive | lambdaxymox/lean4 | ae943c960a42247e06eff25c35338268d07454cb | 278d47c77270664ef29715faab467feac8a0f446 | refs/heads/master | 1,677,891,867,340 | 1,612,500,005,000 | 1,612,500,005,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 39,583 | 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.Match.MatchPatternAttr
import Lean.Meta.Match.Match
import Lean.Elab.SyntheticMVars
import Lean.Elab.App
import Lean.Parser.Term
namespace... |
879e35be1f9b908bd8c24d893536d1e73df65689 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /tests/lean/ctor_layout.lean | 1ac357fc1b6ace749fcb69970e120e3ab5b26deb | [
"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 | 673 | lean | import Init.Lean.Compiler.IR
open Lean
open Lean.IR
def tst : IO Unit :=
do initSearchPath "Init=../../src/Init";
env ← importModules [{module := `Init.Lean.Compiler.IR.Basic}];
ctorLayout ← IO.ofExcept $ getCtorLayout env `Lean.IR.Expr.reuse;
ctorLayout.fieldInfo.forM $ fun finfo => IO.println (format finfo)... |
42e7f0b75e51c1317261218e5ab15e0a7187e7ee | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/linear_algebra/basis.lean | 39b274cabb72e791f52af03f4f89eda22883ac32 | [
"Apache-2.0"
] | permissive | waynemunro/mathlib | e3fd4ff49f4cb43d4a8ded59d17be407bc5ee552 | 065a70810b5480d584033f7bbf8e0409480c2118 | refs/heads/master | 1,693,417,182,397 | 1,634,644,781,000 | 1,634,644,781,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 45,429 | 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, Alexander Bentkamp
-/
import algebra.big_operators.finsupp
import algebra.big_operators.finprod
import data.fintype.card
import linear_algebra.finsupp
i... |
61b948843e2d6d8178c28ba497a78958b44ecda6 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/data/rat/basic.lean | 9e51ccffcf294168cfbe4ab51ad931b6dd9bf5c6 | [
"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 | 24,926 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import
data.nat.gcd
data.pnat.basic data.int.sqrt data.equiv.encodable
algebra.group algebra.ordered_group algebra.group_power
algebra.ordered... |
f11b44b11a47a7deb85478e55dcb0f6567b8f45d | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/cc_ac1.lean | ae31fd2b046c9ae2d7a795221fcdb5e2b8abe751 | [
"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 | 425 | lean | open tactic
instance aa : is_associative ℕ (+) := ⟨nat.add_assoc⟩
instance ac : is_commutative ℕ (+) := ⟨nat.add_comm⟩
instance ma : is_associative ℕ (*) := ⟨nat.mul_assoc⟩
instance mc : is_commutative ℕ (*) := ⟨nat.mul_comm⟩
example (a b c : nat) (f : nat → nat) : f (a + b + c) = f (c + b + a) :=
by cc
example (a b... |
0067fd4996d632a565bc45824dbfc36a96d67f16 | 22e97a5d648fc451e25a06c668dc03ac7ed7bc25 | /src/set_theory/cardinal.lean | 697a8f1cc52067b5ec04e14384de5c53c3409556 | [
"Apache-2.0"
] | permissive | keeferrowan/mathlib | f2818da875dbc7780830d09bd4c526b0764a4e50 | aad2dfc40e8e6a7e258287a7c1580318e865817e | refs/heads/master | 1,661,736,426,952 | 1,590,438,032,000 | 1,590,438,032,000 | 266,892,663 | 0 | 0 | Apache-2.0 | 1,590,445,835,000 | 1,590,445,835,000 | null | UTF-8 | Lean | false | false | 45,199 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl, Mario Carneiro
-/
import data.set.countable
import set_theory.schroeder_bernstein
import data.fintype.card
/-!
# Cardinal Numbers
We define cardinal numbers as a quoti... |
d07200e2ac82a7ee50e22148a22b527dad2fca54 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/data/option/basic.lean | d011a6d58fe939a293f2747986237a60778423ac | [
"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 | 8,238 | 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) : ... |
2f617e3f470ff80366725b8b5d2a9e6f8acd23e0 | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/algebra/group/prod.lean | 0de87e8041f658776e852397d811b3679aaf54fb | [
"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 | 9,487 | 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.group.hom
import data.equiv.mul_add
import data.prod
/-!
# Monoid, group etc structures on `M × N`
In this file we def... |
595f8ffcbb161614cb8e5e5e989ac06bb6320f57 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/specializeAttr.lean | 735a754d81dcc8088108d87deb2fd9febf70df4c | [
"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 | 537 | lean | @[specialize f g h]
def f1 (f : Nat → Nat) (g : Nat → Nat) (x : Nat) :=
f (f (g x))
@[specialize f 1 g]
def f2 (f : Nat → Nat) (g : Nat → Nat) (x : Nat) :=
f (f (g x))
@[specialize 1 f g]
def f3 (f : Nat → Nat) (g : Nat → Nat) (x : Nat) :=
f (f (g x))
@[specialize 0 g]
def f4 (f : Nat → Nat) (g : Nat → Nat) (x... |
ca69981137f3e384ed36506911bec71257748b5b | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /stage0/src/Init/Core.lean | 88299b463b770f81f03796ddfb96ae5177494a78 | [
"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 | 65,485 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
notation, basic datatypes and type classes
-/
prelude
import Init.Prelude
import Init.SizeOf
set_option linter.missingDocs true -- keep it documented
univers... |
d08bb6cfd90963bc19df76f8e929ed09657553c1 | a537b538f2bea3181e24409d8a52590603d1ddd9 | /src/tidy/lib/expr.lean | 76fc91505249d70131ee71bc799a670055705342 | [] | no_license | rwbarton/lean-tidy | 6134813ded72b275d19d4d32514dba80c21708e3 | fe1125d32adb60decda7a77d0f679614ba9f6fbb | refs/heads/master | 1,585,549,718,705 | 1,538,120,619,000 | 1,538,120,624,000 | 150,864,330 | 0 | 0 | null | 1,538,225,790,000 | 1,538,225,790,000 | null | UTF-8 | Lean | false | false | 3,459 | lean | import data.list
import .string
import .pretty_print
meta def binder_info.brackets : binder_info → string × string
| binder_info.default := ("(", ")")
| binder_info.implicit := ("{", "}")
| binder_info.inst_implicit := ("[", "]")
| bi := ("?", "?" ++ repr bi)
meta structure binder :=
(name : name)
(type : expr)
(bi... |
3cdda6b57ad9e8967165c6b0947b1e10ae44c68a | 7541ac8517945d0f903ff5397e13e2ccd7c10573 | /src/category_theory/rel.lean | 0153dc94976f2f442b5629ea3bf10c7dc40c0647 | [] | no_license | ramonfmir/lean-category-theory | 29b6bad9f62c2cdf7517a3135e5a12b340b4ed90 | be516bcbc2dc21b99df2bcb8dde0d1e8de79c9ad | refs/heads/master | 1,586,110,684,637 | 1,541,927,184,000 | 1,541,927,184,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 291 | lean | import category_theory.category
import category_theory.tactics.obviously
namespace category_theory
universe u
def Rel : large_category (Type u) :=
{ hom := λ X Y, X → Y → Prop,
id := λ X, λ x y, x = y,
comp := λ X Y Z f g x z, ∃ y, f x y ∧ g y z }
end category_theory |
4193c030cbe4d1871561401384a83eb7dc49571a | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/ring_theory/polynomial/pochhammer.lean | 6907ad181a46d602ac7f0f57066926b0c882fd66 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 6,787 | 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 tactic.abel
import data.polynomial.eval
/-!
# The Pochhammer polynomials
We define and prove some basic relations about
`pochhammer S n : S[X] := X * (X + 1)... |
6af1d72a35710a37fefef4c05b9fec4f18acd2fe | e07b1aca72e83a272dd59d24c6e0fa246034d774 | /src/surreal/game/pgame.lean | 20860ab4759c1a3f4cd7addb24af761c9770f0e6 | [] | 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 | 56,324 | lean | import logic.relation
import set_theory.game.pgame
import tactic
example : (0 : pgame) = pgame.mk pempty pempty pempty.elim pempty.elim := rfl
example : (1 : pgame) = pgame.mk punit pempty (λ star, 0) pempty.elim := rfl
example : -(0 : pgame) = 0 :=
pgame.neg_zero
lemma neg_one_mk : -(1 : pgame) = pgame.mk pempty pu... |
83aed71b946aa38669a1acfe624b982bfdad5777 | 46125763b4dbf50619e8846a1371029346f4c3db | /src/analysis/mean_inequalities.lean | 09dd49e98b10c4062cfc56c41d53a77723dc498d | [
"Apache-2.0"
] | permissive | thjread/mathlib | a9d97612cedc2c3101060737233df15abcdb9eb1 | 7cffe2520a5518bba19227a107078d83fa725ddc | refs/heads/master | 1,615,637,696,376 | 1,583,953,063,000 | 1,583,953,063,000 | 246,680,271 | 0 | 0 | Apache-2.0 | 1,583,960,875,000 | 1,583,960,875,000 | null | UTF-8 | Lean | false | false | 6,841 | 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 analysis.calculus.mean_value data.nat.parity analysis.complex.exponential
analysis.convex.specific_functions
/-!
# Mean value inequalities
In this file w... |
073fc9bb43bbc2ddbc395c89b7107302cc8b7d5c | 737dc4b96c97368cb66b925eeea3ab633ec3d702 | /stage0/src/Lean/Elab/InfoTree.lean | 00d9e99665205dd74239b42a49ead2eb5a3ad58b | [
"Apache-2.0"
] | permissive | Bioye97/lean4 | 1ace34638efd9913dc5991443777b01a08983289 | bc3900cbb9adda83eed7e6affeaade7cfd07716d | refs/heads/master | 1,690,589,820,211 | 1,631,051,000,000 | 1,631,067,598,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 15,250 | lean | /-
Copyright (c) 2020 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki, Leonardo de Moura, Sebastian Ullrich
-/
import Lean.Data.Position
import Lean.Expr
import Lean.Message
import Lean.Data.Json
import Lean.Meta.Basic
import Lean.M... |
d7bdcce31fa2021553270f489f10a9c00d779f6e | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/data/complex/basic.lean | 6f71760494720d7a417bba62faf63b067333a011 | [
"Apache-2.0"
] | permissive | waynemunro/mathlib | e3fd4ff49f4cb43d4a8ded59d17be407bc5ee552 | 065a70810b5480d584033f7bbf8e0409480c2118 | refs/heads/master | 1,693,417,182,397 | 1,634,644,781,000 | 1,634,644,781,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 26,159 | lean | /-
Copyright (c) 2017 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Mario Carneiro
-/
import data.real.sqrt
/-!
# The complex numbers
The complex numbers are modelled as ℝ^2 in the obvious way and it is shown that they form a field
of c... |
c656bb09e9867747281b0ee15df7d059179a9af6 | 28be2ab6091504b6ba250b367205fb94d50ab284 | /levels/my_solutions/world1_addition.lean | 1b0323e4d6ea350b8370fef2f4f83254ad16eb64 | [
"Apache-2.0"
] | permissive | postmasters/natural_number_game | 87304ac22e5e1c5ac2382d6e523d6914dd67a92d | 38a7adcdfdb18c49c87b37831736c8f15300d821 | refs/heads/master | 1,649,856,819,031 | 1,586,444,676,000 | 1,586,444,676,000 | 255,006,061 | 0 | 0 | Apache-2.0 | 1,586,664,599,000 | 1,586,664,598,000 | null | UTF-8 | Lean | false | false | 4,700 | lean | import mynat.definition -- Imports the natural numbers.
/- Here's what you get from the import:
1) The following data:
* a type called `mynat`
* a term `0 : mynat`, interpreted as the number zero.
* a function `succ : mynat → mynat`, with `succ n` interpreted as "the number after n".
* Usual numerical notatio... |
b7ea32cdd48dad133e5645a7d890944982f2ef1c | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/linear_algebra/matrix/to_linear_equiv.lean | 2357a1efc44f98bce6a772bdbc70076192f141c6 | [
"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 | 7,374 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-/
import linear_algebra.matrix.nondegenerate
import linear_algebra.matrix.nonsingular_inverse
import linear_algebra.matrix.to_... |
e812592c47706ab9773724df8938d1329dfda295 | 38a6d5def645a1887e1306ceb4da06ff71452096 | /_5_The_Physical_Layer/qubit_carriers/quantum_state.lean | 1787d05b3135de51cf2b58f68f4236ea8c6f8854 | [] | no_license | QTM3x/Quantum-Internet | bcc2d61e2ae7233bb2b369fedaed22a1feb6fba1 | f90e09fb6c03d35043654d8b1bec1c63d6012268 | refs/heads/master | 1,609,224,401,937 | 1,599,911,583,000 | 1,599,911,583,000 | 238,495,221 | 45 | 33 | null | 1,603,625,079,000 | 1,580,919,815,000 | Jupyter Notebook | UTF-8 | Lean | false | false | 3,741 | lean | import data.real.basic
import common.matrix_ops
-- variables {n m : ℕ}
variables (n m : ℕ)
---- STATES IN FINITE DIMENSIONAL HILBERT SPACE
/-
Definition (density operator): A quantum state/density operator is
a positive semi-definite matrix with trace 1.
-/
structure density_operator (n : ℕ) : Type :=
(dim : ℕ)
(M ... |
a8dc0166256d1c8b0314dc76efbe905c637c289f | cc060cf567f81c404a13ee79bf21f2e720fa6db0 | /lean/20180218-weird-nat-unfolding.lean | 5ea3b6af68c5f069cdf9385c2fb7379f8bebcdf7 | [
"Apache-2.0"
] | permissive | semorrison/proof | cf0a8c6957153bdb206fd5d5a762a75958a82bca | 5ee398aa239a379a431190edbb6022b1a0aa2c70 | refs/heads/master | 1,610,414,502,842 | 1,518,696,851,000 | 1,518,696,851,000 | 78,375,937 | 2 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 694 | lean | structure {u v} Category :=
( Obj : Type u )
( Hom : Obj → Obj → Type v )
( identity : Π X : Obj, Hom X X )
( compose : Π { X Y Z : Obj }, Hom X Y → Hom Y Z → Hom X Z )
( left_identity : ∀ { X Y : Obj } (f : Hom X Y), compose (identity X) f = f )
( right_identity : ∀ { X Y : Obj } (f : Hom X Y), compose ... |
8d40dec5ec8c0516a37dd51195df925544caf064 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/topology/continuous_map.lean | 48a19322fc2376d73d18a90ac01ee585b859d93c | [
"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 | 1,749 | lean | /-
Copyright © 2020 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Nicolò Cavalleri.
-/
import topology.subset_properties
import topology.tactic
/-!
# Continuous bundled map
In this file we define the type `continuous_map` of continuous bundled maps... |
cc101a51cdf861ec626c4854da741bb10736f5ba | 957a80ea22c5abb4f4670b250d55534d9db99108 | /library/init/meta/smt/congruence_closure.lean | 312cc2e7680bea32c7ef9a16ae631cbb6f2d370c | [
"Apache-2.0"
] | permissive | GaloisInc/lean | aa1e64d604051e602fcf4610061314b9a37ab8cd | f1ec117a24459b59c6ff9e56a1d09d9e9e60a6c0 | refs/heads/master | 1,592,202,909,807 | 1,504,624,387,000 | 1,504,624,387,000 | 75,319,626 | 2 | 1 | Apache-2.0 | 1,539,290,164,000 | 1,480,616,104,000 | C++ | UTF-8 | Lean | false | false | 5,358 | 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.interactive_base init.meta.tactic init.meta.set_get_option_tactics
structure cc_config :=
/- If tt, congruence closure will treat ... |
3674313d19a6025827c7c751772e1d8187ac1250 | 618003631150032a5676f229d13a079ac875ff77 | /test/where.lean | 6d6217a32121377154c8fd1a55782bb2ced088d3 | [
"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 | 8,402 | lean | import data.multiset
import tactic.where
-- First set up the testing framework...
section framework
-- Note that we cannot have any explicit `open`s, we are currently working around this bug:
-- https://leanprover.zulipchat.com/#narrow/stream/113488-general/topic/What's.20the.20deal.20with.20.60open.60
@[user_comma... |
60d0909d4167ec1136a427e560d13aaec13065a9 | 46125763b4dbf50619e8846a1371029346f4c3db | /archive/sensitivity.lean | f3b8a10255726f77a2c9a4c16b7874a6a8ab826c | [
"Apache-2.0"
] | permissive | thjread/mathlib | a9d97612cedc2c3101060737233df15abcdb9eb1 | 7cffe2520a5518bba19227a107078d83fa725ddc | refs/heads/master | 1,615,637,696,376 | 1,583,953,063,000 | 1,583,953,063,000 | 246,680,271 | 0 | 0 | Apache-2.0 | 1,583,960,875,000 | 1,583,960,875,000 | null | UTF-8 | Lean | false | false | 16,695 | lean | /-
Copyright (c) 2019 Reid Barton, Johan Commelin, Jesse Han, Chris Hughes, Robert Y. Lewis, and Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Johan Commelin, Jesse Han, Chris Hughes, Robert Y. Lewis, and Patrick Massot
-/
import tactic.f... |
aabcad04fc3f335059549cfa109a2fd928537f20 | 675b8263050a5d74b89ceab381ac81ce70535688 | /src/ring_theory/ideal/basic.lean | 7aa80abb0c0725fc61b343eec3e2437e0ef7fb4b | [
"Apache-2.0"
] | permissive | vozor/mathlib | 5921f55235ff60c05f4a48a90d616ea167068adf | f7e728ad8a6ebf90291df2a4d2f9255a6576b529 | refs/heads/master | 1,675,607,702,231 | 1,609,023,279,000 | 1,609,023,279,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 32,132 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Chris Hughes, Mario Carneiro
-/
import algebra.associated
import linear_algebra.basic
import order.zorn
/-!
# Ideals over a ring
This file defines `ideal R`, the type of ideals... |
e0302f89972cf3fe680cd67819c0d7fc4fbab924 | c3f2fcd060adfa2ca29f924839d2d925e8f2c685 | /library/data/int/order.lean | 6d0cd604d72ef24e2121e34add8601250221384b | [
"Apache-2.0"
] | permissive | respu/lean | 6582d19a2f2838a28ecd2b3c6f81c32d07b5341d | 8c76419c60b63d0d9f7bc04ebb0b99812d0ec654 | refs/heads/master | 1,610,882,451,231 | 1,427,747,084,000 | 1,427,747,429,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 33,009 | lean | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.int.order
Authors: Floris van Doorn, Jeremy Avigad
The order relation on the integers. We show that int is an instance of linear_comm_ordered_ring
and transfer the results.
-/
... |
834e0994940a5393ce21635bcf29939847a952a1 | 4bcaca5dc83d49803f72b7b5920b75b6e7d9de2d | /tests/lean/run/doNotation3.lean | f64703dcc7dd3837073cb251c5218c6bddf24402 | [
"Apache-2.0"
] | permissive | subfish-zhou/leanprover-zh_CN.github.io | 30b9fba9bd790720bd95764e61ae796697d2f603 | 8b2985d4a3d458ceda9361ac454c28168d920d3f | refs/heads/master | 1,689,709,967,820 | 1,632,503,056,000 | 1,632,503,056,000 | 409,962,097 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,652 | lean | theorem zero_lt_of_lt : {a b : Nat} → a < b → 0 < b
| 0, _, h => h
| a+1, b, h =>
have : a < b := Nat.lt_trans (Nat.lt_succ_self _) h
zero_lt_of_lt this
def fold {m α β} [Monad m] (as : Array α) (b : β) (f : α → β → m β) : m β := do
let rec loop : (i : Nat) → i ≤ as.size → β → m β
| 0, h, b => b
| i+1, h, ... |
9d61d4137621f894457368f5a0415348d1a90fba | c31182a012eec69da0a1f6c05f42b0f0717d212d | /src/facts/normed_group.lean | af840b1a4fd814ef302a8de7d2b0b05cb9b36f52 | [] | 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 | 200 | lean | import analysis.normed_space.basic
variables {V : Type*} [semi_normed_group V]
instance fact_nnnorm_add_le (v w : V) :
fact (∥v + w∥₊ ≤ ∥v∥₊ + ∥w∥₊) :=
⟨nnnorm_add_le _ _⟩
|
a56cce497bb611782711dbb7b3a99657fec48383 | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /tests/lean/run/e5.lean | 9634f54e7f915deccc73d7682e86812c140ba18c | [
"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 | 1,530 | lean | prelude
definition Prop := Type.{0}
definition false : Prop := ∀x : Prop, x
check false
theorem false.elim (C : Prop) (H : false) : C
:= H C
definition eq {A : Type} (a b : A)
:= ∀ P : A → Prop, P a → P b
check eq
infix `=`:50 := eq
theorem refl {A : Type} (a : A) : a = a
:= λ P H, H
definition true : Prop
:= fa... |
442f67ad20bfd5ae1257aae3b4ce4669a6b53d57 | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /stage0/src/Lean/Elab/Tactic/Generalize.lean | 7e8c48edb4b92b058df9abd25b85a4877224bc62 | [
"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 | 2,801 | 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, Sebastian Ullrich
-/
import Lean.Meta.Tactic.Generalize
import Lean.Meta.Check
import Lean.Meta.Tactic.Intro
import Lean.Elab.Tactic.ElabTerm
namespace Lean
... |
aafb59cf1d3d74ac9047f8fe1adf1b4b67f9e400 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/run/tryPureCoe.lean | 4aac1b5979b8c448e6c7b636b719b85f5073eeef | [
"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 | 981 | lean | def m1 : IO Bool :=
pure true
def p (x : Nat) : Bool :=
x > 0
def tst1 : IO Bool :=
true <&&> m1
def tst2 (x : Nat) : IO Bool :=
x = 0 <&&> m1
def tst3 (x : Nat) : IO Unit := do
if ← (m1 <&&> x > 0) then
throw $ IO.userError "test"
def tst4 (x : Nat) : IO Unit := do
if x > 0 && (← m1) then
throw $ IO.userError... |
a4b18f3b9af3e36aff53cb07d89d1be1819cc28d | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/linear_algebra/contraction.lean | 29aa045beee4859c0880577c4f84b043c1c45377 | [
"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 | 12,259 | lean | /-
Copyright (c) 2020 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash, Antoine Labelle
-/
import linear_algebra.dual
import linear_algebra.matrix.to_lin
/-!
# Contractions
Given modules $M, N$ over a commutative ring $R$, this file defines the... |
c8f831345f3d48b692835d45d71e3ad3eb6dd6d9 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/meta/exceptional_auto.lean | a26318cf9f1f6a896a14bba6ab0de81b493d4403 | [] | 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 | 563 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.control.monad
import Mathlib.Lean3Lib.init.meta.format
import Mathlib.Lean3Lib.init.util
namespace Math... |
9fde6c86e2a5c80ea6c258dfbd98fb771979d10d | 4950bf76e5ae40ba9f8491647d0b6f228ddce173 | /src/order/filter/filter_product.lean | 4070898614e1b51909e139dbe1d94d25db2fb04b | [
"Apache-2.0"
] | permissive | ntzwq/mathlib | ca50b21079b0a7c6781c34b62199a396dd00cee2 | 36eec1a98f22df82eaccd354a758ef8576af2a7f | refs/heads/master | 1,675,193,391,478 | 1,607,822,996,000 | 1,607,822,996,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,056 | lean | /-
Copyright (c) 2019 Abhimanyu Pallavi Sudhir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Abhimanyu Pallavi Sudhir, Yury Kudryashov
-/
import order.filter.ultrafilter
import order.filter.germ
/-!
# Ultraproducts
If `φ` is an ultrafilter, then the space of germs ... |
fa65a3c7d83aa2c9271572d837c8137b78076afb | e42ba0bcfa11e5be053e2ce1ce1f49f027680525 | /src/separation/program.lean | 9f8b206b1ccfe58a156c22419f87a475fc7c0193 | [] | no_license | unitb/separation-logic | 8e17c5b466f86caa143265f4c04c78eec9d3c3b8 | bdde6fc8f16fd43932aea9827d6c63cadd91c2e8 | refs/heads/master | 1,540,936,751,653 | 1,535,050,181,000 | 1,535,056,425,000 | 109,461,809 | 6 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 6,999 | lean |
import data.bitvec
import data.dlist
import util.meta.tactic
import util.logic
import util.control.applicative
import util.control.monad.non_termination
import separation.heap
universes u v w w'
open nat list function
namespace separation
structure hstate :=
(heap : heap)
(next : ℕ)
(free : ∀ p, next ≤ p → h... |
7e755197cc8372f09ab03e10d04bbfa2afee92ca | 7cdf3413c097e5d36492d12cdd07030eb991d394 | /src/game/world3/level6.lean | f2c7d179e59f25bb2eeeb489ea7e7c317dcccefa | [] | no_license | alreadydone/natural_number_game | 3135b9385a9f43e74cfbf79513fc37e69b99e0b3 | 1a39e693df4f4e871eb449890d3c7715a25c2ec9 | refs/heads/master | 1,599,387,390,105 | 1,573,200,587,000 | 1,573,200,691,000 | 220,397,084 | 0 | 0 | null | 1,573,192,734,000 | 1,573,192,733,000 | null | UTF-8 | Lean | false | false | 1,481 | lean | import game.world3.level5 -- hide
import mynat.mul -- hide
namespace mynat -- hide
/-
# Multiplication World
## Level 6: `succ_mul`
We now begin our journey to `mul_comm`, the proof that `a * b = b * a`.
We'll get there in level 8. Until we're there, it is frustrating
but true that we cannot assume commutativity. W... |
a6cb4908c11fd82a091dfa83d42674c343a0ff8a | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/order/filter/ennreal.lean | 19dfe62332c373708a8762233b1c4279abc2e468 | [] | 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 | 1,507 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.real.ennreal
import Mathlib.order.filter.countable_Inter
import Mathlib.order.liminf_limsu... |
083b28f993333e953e63956fa967b77f7d3517f2 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/measure_theory/function/ae_eq_fun.lean | d522110d67adcf823d1a80a3eae6a07bfec79563 | [
"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 | 31,779 | lean | /-
Copyright (c) 2019 Johannes Hölzl, Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Zhouhang Zhou
-/
import measure_theory.integral.lebesgue
import order.filter.germ
import topology.continuous_function.algebra
import measure_theory.funct... |
331128e34cb65a758bffe5eeb8b89e2a64b05876 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/1863.lean | 73e4afff829e9ea6521423ac96d1523af6648cf8 | [
"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 | 544 | lean | constant T : Type → Type
variables {α : Type}
def f : α → α := sorry
variables [decidable_eq α] {x y : T α}
axiom foo : true → f x = x
example : f x = x := by simp only [foo true.intro]
example : f x = x := by simp only [foo _]
example : f x = x := by simp [foo true.intro]
example : f x = x := by simp [foo _]
def g : ... |
47b712e0aa47f3a379599a4fe00dc4f46c3a2c4d | b328e8ebb2ba923140e5137c83f09fa59516b793 | /src/Lean/MetavarContext.lean | 8bd8f9ab98dc68db18eaad89882d869f5bfe0512 | [
"Apache-2.0"
] | permissive | DrMaxis/lean4 | a781bcc095511687c56ab060e816fd948553e162 | 5a02c4facc0658aad627cfdcc3db203eac0cb544 | refs/heads/master | 1,677,051,517,055 | 1,611,876,226,000 | 1,611,876,226,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 53,243 | 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.MonadCache
import Lean.LocalContext
namespace Lean
/-
The metavariable context stores metavariable declarations and their
assignments. It... |
4ab4d824b696ed88af0bc819e7929fe0c4408e90 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/algebra/order/module.lean | f4b75426245d9787e2d983f63aee8f764bccf4bc | [
"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 | 8,351 | lean | /-
Copyright (c) 2020 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis, Yaël Dillies
-/
import algebra.order.smul
/-!
# Ordered module
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to m... |
de3a06a27e9da1d471e2a125ea69390ab088cc02 | 02005f45e00c7ecf2c8ca5db60251bd1e9c860b5 | /src/category_theory/adjunction/limits.lean | f3c18edc1f52d8d764dfe8c37a20f56cc3e315af | [
"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 | 10,967 | lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Johan Commelin
-/
import category_theory.adjunction.basic
import category_theory.limits.creates
open opposite
namespace category_theory.adjunction
open category_theory
open... |
972c343f2454cdd3eb772fba014e8122fbae2e6b | 4da0c8e61fcd6ec3f3be47ee14a038850c03d0c3 | /src/s5/consistency.lean | e2f978e89380f25ddeb0a7f8910a2cdd94a42a49 | [
"Apache-2.0"
] | permissive | bbentzen/mpl | fcbea60204bc8fd64667e0f76a5cebf4b67fb6ca | bb5066ec51fa11a4b66f440c4f6c9a3d8fb2e0de | refs/heads/master | 1,625,175,849,308 | 1,624,207,634,000 | 1,624,207,634,000 | 142,774,375 | 9 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,266 | lean | /-
Copyright (c) 2018 Bruno Bentzen. All rights reserved.
Released under the Apache License 2.0 (see "License");
Author: Bruno Bentzen
-/
import .soundness
open prf classical
variables {σ : nat}
def is_consist (Γ : ctx σ) := Γ ⊬ₛ₅ ⊥
lemma consist_not_of_not_prf {Γ : ctx σ} {p : form σ} :
(Γ ⊬ₛ₅ p)... |
6257397041f0835d79f9d07b79ee3bc3a277d50d | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/algebra/category/Group/basic.lean | 75c2dc0f5a70819b5e055b58f63e63014a09c114 | [
"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 | 9,886 | lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import algebra.category.Mon.basic
import category_theory.endomorphism
/-!
# Category instances for group, add_group, comm_group, and add_comm_group.
We introduce th... |
991b47a4912bfcf5781534d111bacdf03ae424da | b7fc5b86b12212bea5542eb2c9d9f0988fd78697 | /src/exercises_sources/thursday/category_theory/exercise2.lean | 0a156a45b6011107319c1f2a63e845d1daa50fab | [] | no_license | stjordanis/lftcm2020 | 3b16591aec853c8546d9c8b69c0bf3f5f3956fee | 1f3485e4dafdc587b451ec5144a1d8d3ec9b411e | refs/heads/master | 1,675,958,865,413 | 1,609,901,722,000 | 1,609,901,722,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,508 | lean | import algebra.category.CommRing.basic
import data.polynomial
/-!
Let's show that taking polynomials over a ring is functor `Ring ⥤ Ring`.
-/
noncomputable theory -- the default implementation of polynomials is noncomputable
-- Just ignore this for now: it's a hack that prevents an annoying problem,
-- and a cleaner... |
c28e9c99052516b908b173337f6b2e3994a2f146 | 737dc4b96c97368cb66b925eeea3ab633ec3d702 | /stage0/src/Lean/Elab/Extra.lean | 8a6aca48cbf3bb45a391092db968962d80045915 | [
"Apache-2.0"
] | permissive | Bioye97/lean4 | 1ace34638efd9913dc5991443777b01a08983289 | bc3900cbb9adda83eed7e6affeaade7cfd07716d | refs/heads/master | 1,690,589,820,211 | 1,631,051,000,000 | 1,631,067,598,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 12,968 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Elab.App
/-
Auxiliary elaboration functions: AKA custom elaborators
-/
namespace Lean.Elab.Term
open Meta
@[builtinTermElab binrel] def elabB... |
a06aa8c681b914f6034ebad139a63b646d0fc28b | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/arity1.lean | f55586b9b4d626b814d6ebe08d2b1f70d018ab52 | [
"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 | 405 | lean | open tactic decidable
definition foo (A B : Type) := A → B
definition boo (c : bool) :=
cond c nat bool
definition bla (a : nat) : boo (to_bool (a > 0)) → foo nat nat :=
λ v x, a + x
example : true :=
by do
bla ← mk_const `bla,
infer_type bla >>= trace,
n ← get_arity bla,
trace ("n arity: " ++ to_string n... |
417e757e3757f5f1119c7e759ef009e7e89777f6 | f083c4ed5d443659f3ed9b43b1ca5bb037ddeb58 | /analysis/real.lean | f146aa1db1cd083ed9292a8f5e0875e1f7fd8aa8 | [
"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 | 15,893 | 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
The real numbers ℝ.
They are constructed as the topological completion of ℚ. With the following steps:
(1) prove that ℚ forms a uniform space.
(2) subt... |
69c0fb026df629a443c9dffbd35c8b058f9a8a40 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/guard_names.lean | de82b840bb05efaa7216ac2780aa2177f5bce70e | [
"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 | 297 | lean | inductive tree (α : Type)
| leaf : tree
| node (left : tree) (val : α) (right : tree) : tree
constant foo {α : Type} : tree α → tree α
example {α : Type} (a b : tree α) : foo a = a :=
begin
with_cases { induction a },
{ admit },
case : l v r ih_l ih_r { trace_state, admit },
end
|
e43dcd9bea7656c7e48321655b781c29ff749a12 | aa2345b30d710f7e75f13157a35845ee6d48c017 | /data/padics/hensel.lean | e0618c6e30f4c3928b0ed84e836361fa3d48268e | [
"Apache-2.0"
] | permissive | CohenCyril/mathlib | 5241b20a3fd0ac0133e48e618a5fb7761ca7dcbe | a12d5a192f5923016752f638d19fc1a51610f163 | refs/heads/master | 1,586,031,957,957 | 1,541,432,824,000 | 1,541,432,824,000 | 156,246,337 | 0 | 0 | Apache-2.0 | 1,541,434,514,000 | 1,541,434,513,000 | null | UTF-8 | Lean | false | false | 20,799 | 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
A proof of Hensel's lemma on ℤ_p, roughly following Keith Conrad's writeup:
http://www.math.uconn.edu/~kconrad/blurbs/gradnumthy/hensel.pdf
-/
import data.padics.pad... |
6fc179f8aa9586c4a4a71ef4ead7a097c21214fd | f3849be5d845a1cb97680f0bbbe03b85518312f0 | /library/init/meta/smt/interactive.lean | 493a5abfe00b08baaae07ff1b9ceeb2319f70b01 | [
"Apache-2.0"
] | permissive | bjoeris/lean | 0ed95125d762b17bfcb54dad1f9721f953f92eeb | 4e496b78d5e73545fa4f9a807155113d8e6b0561 | refs/heads/master | 1,611,251,218,281 | 1,495,337,658,000 | 1,495,337,658,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,172 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.meta.smt.smt_tactic init.meta.interactive
import init.meta.smt.rsimp
namespace smt_tactic
meta def save_info (p : pos) : smt_tactic uni... |
8acda0aa8c971a139834648441c1212ea4151041 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/analysis/normed_space/basic.lean | 3e70aa5b481c383d31f62e1d5610b08a234f0d9b | [
"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 | 29,025 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
-/
import algebra.algebra.pi
import algebra.algebra.restrict_scalars
import analysis.normed.field.basic
import data.real.sqrt
import topology.algebra.mod... |
893d9b922042d8649311fce44e58e75fd0b79ed8 | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /tests/lean/run/meta6.lean | e23aa0f729bc596db161b5116480c3ddedaceb71 | [
"Apache-2.0"
] | permissive | collares/lean4 | 861a9269c4592bce49b71059e232ff0bfe4594cc | 52a4f535d853a2c7c7eea5fee8a4fa04c682c1ee | refs/heads/master | 1,691,419,031,324 | 1,618,678,138,000 | 1,618,678,138,000 | 358,989,750 | 0 | 0 | Apache-2.0 | 1,618,696,333,000 | 1,618,696,333,000 | null | UTF-8 | Lean | false | false | 2,520 | lean | import Lean.Meta
open Lean
open Lean.Meta
def print (msg : MessageData) : MetaM Unit :=
trace[Meta.debug] msg
def checkM (x : MetaM Bool) : MetaM Unit :=
unless (← x) do throwError "check failed"
def nat := mkConst `Nat
def boolE := mkConst `Bool
def succ := mkConst `Nat.succ
def zero := mkConst `Nat.zero
def a... |
3141f3e2d2140b053917d7fd4a629b3ed85137fd | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/quotient.lean | 73c3e1c6b819ab9f72e252e6e2e54a4f18a13e0e | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 2,163 | lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import tactic.basic
/-!
# Algebraic quotients
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
This file def... |
d35d9a2dde654490cbcdd75b9e1d777d2b7c0945 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/linarith/lemmas.lean | 6a27f9c586f5825e38e319762e2d73c802547070 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,544 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.ordered_ring
import Mathlib.data.int.basic
import Mathlib.tactic.norm_num
import ... |
da7f65452fd9d4710526762f19dd68d91e610c4c | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/order/filter/ultrafilter.lean | f0508c64b68f600ce271ec0919cf4a20f15864f5 | [
"Apache-2.0"
] | permissive | lacker/mathlib | f2439c743c4f8eb413ec589430c82d0f73b2d539 | ddf7563ac69d42cfa4a1bfe41db1fed521bd795f | refs/heads/master | 1,671,948,326,773 | 1,601,479,268,000 | 1,601,479,268,000 | 298,686,743 | 0 | 0 | Apache-2.0 | 1,601,070,794,000 | 1,601,070,794,000 | null | UTF-8 | Lean | false | false | 12,558 | 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.filter.cofinite
/-!
# Ultrafilters
An ultrafilter is a minimal (maximal in the set order) proper filter.
In this file we define
* `is_u... |
3f042c85cc08a0c817e2088fada1bcaa4fde708d | 4950bf76e5ae40ba9f8491647d0b6f228ddce173 | /src/ring_theory/witt_vector/truncated.lean | 9abf0efd3627369284ba88dba0e0665093855a6e | [
"Apache-2.0"
] | permissive | ntzwq/mathlib | ca50b21079b0a7c6781c34b62199a396dd00cee2 | 36eec1a98f22df82eaccd354a758ef8576af2a7f | refs/heads/master | 1,675,193,391,478 | 1,607,822,996,000 | 1,607,822,996,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,793 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-/
import ring_theory.witt_vector.init_tail
import tactic.equiv_rw
/-!
# Truncated Witt vectors
The ring of truncated Witt vectors (of length `n`) i... |
6d3412f062af683ce5c17d6f614371e4e94cf5de | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/analysis/convex/strict.lean | e04f33fa806b39562241b059247493c11a00cc00 | [
"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 | 16,255 | lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import analysis.convex.basic
import topology.algebra.mul_action
import topology.algebra.ordered.basic
/-!
# Strictly convex sets
This file defines strictly convex sets.... |
53e738c9c3e20404f0bd0172b9a19793ebb4e42f | c777c32c8e484e195053731103c5e52af26a25d1 | /src/analysis/mean_inequalities_pow.lean | 8292da30dfac056be4f95597fb9eeeba3f0d689c | [
"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 | 14,576 | lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne
-/
import analysis.convex.specific_functions
import tactic.positivity
/-!
# Mean value inequalities
In this file we prove several me... |
4ac49c11b76d15b28a9b7f7fa418f339aeeaa55c | ff5230333a701471f46c57e8c115a073ebaaa448 | /library/init/data/nat/lemmas.lean | 5d62f0478ead8b1fcac910969fd3b09ed2de69a0 | [
"Apache-2.0"
] | permissive | stanford-cs242/lean | f81721d2b5d00bc175f2e58c57b710d465e6c858 | 7bd861261f4a37326dcf8d7a17f1f1f330e4548c | refs/heads/master | 1,600,957,431,849 | 1,576,465,093,000 | 1,576,465,093,000 | 225,779,423 | 0 | 3 | Apache-2.0 | 1,575,433,936,000 | 1,575,433,935,000 | null | UTF-8 | Lean | false | false | 49,559 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad
-/
prelude
import init.data.nat.basic init.data.nat.div init.meta init.algebra.functions
universes u
namespace nat
attribute [pre_smt] nat_zero... |
4cece582442ee25c53c0046a0d0b5156ec1f65b6 | c09f5945267fd905e23a77be83d9a78580e04a4a | /src/topology/constructions.lean | 99238eb8bccf3ea00ef66ebbf8536a6a18386e49 | [
"Apache-2.0"
] | permissive | OHIHIYA20/mathlib | 023a6df35355b5b6eb931c404f7dd7535dccfa89 | 1ec0a1f49db97d45e8666a3bf33217ff79ca1d87 | refs/heads/master | 1,587,964,529,965 | 1,551,819,319,000 | 1,551,819,319,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 44,399 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot
Constructions of new topological spaces from old ones: product, sum, subtype, quotient, list, vector
-/
import topology.maps topology.su... |
02755bde7d5b246bd35ce1abb64eeda3c74461f0 | 4bcaca5dc83d49803f72b7b5920b75b6e7d9de2d | /stage0/src/Lean/Parser/Command.lean | 2e052188c896d7596cafce9fdec8852a41e871c0 | [
"Apache-2.0"
] | permissive | subfish-zhou/leanprover-zh_CN.github.io | 30b9fba9bd790720bd95764e61ae796697d2f603 | 8b2985d4a3d458ceda9361ac454c28168d920d3f | refs/heads/master | 1,689,709,967,820 | 1,632,503,056,000 | 1,632,503,056,000 | 409,962,097 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,533 | 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.Term
import Lean.Parser.Do
namespace Lean
namespace Parser
/--
Syntax quotation for terms and (lists of) commands.... |
03df54edc4bab9c45ce8b176cf0c04f862ebf629 | 82b86ba2ae0d5aed0f01f49c46db5afec0eb2bd7 | /stage0/src/Lean/Expr.lean | 5173758e7fe2323292148d204dccea59099cea28 | [
"Apache-2.0"
] | permissive | banksonian/lean4 | 3a2e6b0f1eb63aa56ff95b8d07b2f851072d54dc | 78da6b3aa2840693eea354a41e89fc5b212a5011 | refs/heads/master | 1,673,703,624,165 | 1,605,123,551,000 | 1,605,123,551,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 36,159 | lean | /-
Copyright (c) 2018 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Data.KVMap
import Lean.Level
namespace Lean
inductive Literal
| natVal (val : Nat)
| strVal (val : String)
instance : Inhabited Literal :... |
f8ffaae84f44893f447efce23482b84fddb1adc8 | 958488bc7f3c2044206e0358e56d7690b6ae696c | /lean/while/Soundness.lean | 7345128438cb776b4c37b7a42de7660683582c47 | [] | no_license | possientis/Prog | a08eec1c1b121c2fd6c70a8ae89e2fbef952adb4 | d4b3debc37610a88e0dac3ac5914903604fd1d1f | refs/heads/master | 1,692,263,717,723 | 1,691,757,179,000 | 1,691,757,179,000 | 40,361,602 | 3 | 0 | null | 1,679,896,438,000 | 1,438,953,859,000 | Coq | UTF-8 | Lean | false | false | 1,505 | lean | import HoareSyntax
import BigStep
open Hoare
lemma HoareSound : ∀ (p q:Pred) (e:Stmt) (s t:Env),
Hoare p e q → p s → BigStep e s t → q t :=
begin
intros p q e s t H1, revert s t,
induction H1
with p p x a p q r e₁ e₂ H1 H2 H3 H4 p q b e₁ e₂ H1 H2 H3 H4 p b e₁ H3 H4
p p' q q' e₁ H3 H4 H5 H6;
intro... |
d9b821d5bc1014356275bb7eb341d3bc0cc26f10 | ad0c7d243dc1bd563419e2767ed42fb323d7beea | /ring_theory/ideals.lean | 765cdee9cdfb310a849fbcbfe1f82937edbd4aab | [
"Apache-2.0"
] | permissive | sebzim4500/mathlib | e0b5a63b1655f910dee30badf09bd7e191d3cf30 | 6997cafbd3a7325af5cb318561768c316ceb7757 | refs/heads/master | 1,585,549,958,618 | 1,538,221,723,000 | 1,538,221,723,000 | 150,869,076 | 0 | 0 | Apache-2.0 | 1,538,229,323,000 | 1,538,229,323,000 | null | UTF-8 | Lean | false | false | 11,289 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Chris Hughes
-/
import algebra.module tactic.ring linear_algebra.quotient_module
universes u v
variables {α : Type u} {β : Type v} [comm_ring α] {a b : α}
open set function
loc... |
69198eb793877f5015b723edf2e42d2c5a3f55e4 | 36c7a18fd72e5b57229bd8ba36493daf536a19ce | /tests/lean/run/class8.lean | 522d42e2fba334d61a7a86c320fbdfa6ce52d245 | [
"Apache-2.0"
] | permissive | YHVHvx/lean | 732bf0fb7a298cd7fe0f15d82f8e248c11db49e9 | 038369533e0136dd395dc252084d3c1853accbf2 | refs/heads/master | 1,610,701,080,210 | 1,449,128,595,000 | 1,449,128,595,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,087 | lean | import logic data.prod
open tactic prod
inductive inh [class] (A : Type) : Prop :=
intro : A -> inh A
attribute inh.intro [instance]
theorem inh_elim {A : Type} {B : Prop} (H1 : inh A) (H2 : A → B) : B
:= inh.rec H2 H1
theorem inh_exists {A : Type} {P : A → Prop} (H : ∃x, P x) : inh A
:= obtain w Hw, from H, inh.in... |
1882297138acda33c0ceec812253bcb9adb169f5 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/category_theory/yoneda.lean | 471a078745bdcda5b5561216c88d2b61b36e0acf | [
"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 | 13,067 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.hom_functor
/-!
# The Yoneda embedding
The Yoneda embedding as a functor `yoneda : C ⥤ (Cᵒᵖ ⥤ Type v₁)`,
along with an instance that it is `f... |
547da5c0770058c72971d7904a8190aeceb9512b | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/pkg/frontend/Frontend/RegisterOption.lean | 8ec038226ff6e8719a498393e6c3d7f2628fd1bd | [
"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 | 83 | lean | import Lean
register_option option : Bool := {
defValue := true
descr := ""
}
|
b7bf70574768fdc0d145c1fa7f42f5c5f734c5a8 | 8d65764a9e5f0923a67fc435eb1a5a1d02fd80e3 | /src/algebra/category/Group/colimits.lean | 943c40f80757c3f6d9bb35eba970ca24e85e12e2 | [
"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 | 9,703 | 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.Group.preadditive
import group_theory.quotient_group
import category_theory.limits.concrete_category
import category_theory.limits.shapes.kern... |
2ffaaa0ee51688ea2d58e6133a179b67fec1de56 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/field_theory/separable.lean | ff0f15fed4dfd89e113a106401d9c1366f71bc74 | [
"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 | 28,600 | 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.polynomial.big_operators
import field_theory.minpoly
import field_theory.splitting_field
import field_theory.tower
import algebra.squarefree
/-!
# Separable p... |
7158dc63ec26de654d12ba2d709595eadccbe057 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/measure_theory/measurable_space.lean | 402bb3e26ab5849ae78a89176bb23b4d613fe672 | [
"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 | 44,706 | 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 measure_theory.measurable_space_def
import measure_theory.tactic
import data.tprod
/-!
# Measurable spaces and measurable functions
This fi... |
557d25a5aa82863d94d9abafe283ed9b06de1087 | 246309748072bf9f8da313401699689ebbecd94d | /src/data/monoid_algebra.lean | 6b610e3921215ee0c14da10eb53983574d57dc49 | [
"Apache-2.0"
] | permissive | YJMD/mathlib | b703a641e5f32a996f7842f7c0043bab2b462ee2 | 7310eab9fa8c1b1229dca42682f1fa6bfb7dbbf9 | refs/heads/master | 1,670,714,479,314 | 1,599,035,445,000 | 1,599,035,445,000 | 292,279,930 | 0 | 0 | null | 1,599,050,561,000 | 1,599,050,560,000 | null | UTF-8 | Lean | false | false | 27,182 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury G. Kudryashov, Scott Morrison
-/
import ring_theory.algebra
/-!
# Monoid algebras
When the domain of a `finsupp` has a multiplicative or additive structure, we c... |
490abcb86729055dc4dc297e9f7113168199ba7a | a1179fa077c09acc49e4fbc8d67084ba89ac4f4c | /tutorials/src/solutions/05_sequence_limits.lean | 052951dc4444cb91e27ce2e6552abb15b0c2fdc8 | [] | no_license | Seeram/Lean-proof-assistant | 11ca0ca0e0446bacdd1773c4c481a3653b2f1074 | e672d46e0e5f39d8de2933ad4f4cac095ca6094f | refs/heads/master | 1,682,754,224,366 | 1,620,959,431,000 | 1,620,959,431,000 | 299,000,950 | 0 | 1 | null | 1,620,680,462,000 | 1,601,200,258,000 | Lean | UTF-8 | Lean | false | false | 7,622 | lean | import data.real.basic
import algebra.group.pi
import tuto_lib
notation `|`x`|` := abs x
/-
In this file we manipulate the elementary definition of limits of
sequences of real numbers.
mathlib has a much more general definition of limits, but here
we want to practice using the logical operators and relations
covered... |
48d18faabf14f50d0d50acadb0b1e73774dc3500 | 1b8f093752ba748c5ca0083afef2959aaa7dace5 | /src/category_theory/projectives/default.lean | 65bd55315972e3ed72270103eb52415d572f56b9 | [] | no_license | khoek/lean-category-theory | 7ec4cda9cc64a5a4ffeb84712ac7d020dbbba386 | 63dcb598e9270a3e8b56d1769eb4f825a177cd95 | refs/heads/master | 1,585,251,725,759 | 1,539,344,445,000 | 1,539,344,445,000 | 145,281,070 | 0 | 0 | null | 1,534,662,376,000 | 1,534,662,376,000 | null | UTF-8 | Lean | false | false | 2,298 | lean | import ..abelian.abelian
import category_theory.universal.zero
open category_theory
open category_theory.limits
universes u v
class projective {C : Type u} [category.{u v} C] (P : C) :=
(lift : Π M N : C, Π f : M ⟶ N, Π w : epi f, Π g : P ⟶ N, P ⟶ M)
(factorisation : Π M N : C, Π f : M ⟶ N, Π w : epi f, Π g : P ⟶ N... |
d2864e941a019d90bf11a5b6532186292816fdf4 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/and_rec_code_gen_issue.lean | 8159b25458e2b07e3df28e6d93f5f7be0e376d7e | [
"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 | 3,211 | lean | import data.buffer
structure hoare_state (σ : Type) (α : Type) :=
(pre : σ → Prop)
(post : σ → α → σ → Prop)
(action : ∀ s : {s // pre s}, {as' : α × σ // post s.val as'.1 as'.2})
namespace hoare_state
protected def return (σ : Type) {α : Type} (a : α) : hoare_state σ α :=
{pre := λ s, true,
post := λ s a... |
7a3e05eb9d95f358e1e2e2ec7b6aab8fca8e9164 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebraic_topology/dold_kan/equivalence_pseudoabelian.lean | 4d6fff16434a8598eb5362599d669e24b6b99ad2 | [
"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 | 5,244 | lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import algebraic_topology.dold_kan.equivalence_additive
import algebraic_topology.dold_kan.compatibility
import category_theory.idempotents.simplicial_object
/-!
# The Dold-... |
f56c966d31e9b7ec9f2dc4f409b562ebbd129507 | 3b95ccbd4df78bd19a6aabdc7ecbd2c0816b137c | /stable_sort.lean | 4e67ba93c1d51c15874d3e1266830531c372da99 | [] | no_license | ClanokAEI/LeanStableInsert | 15f0b777aeb1d9f31d6e7a1fef9a0ff37a0f280f | ade28d67b0ed9bfabb1e7813ca5aeac773e9cfde | refs/heads/master | 1,631,221,768,994 | 1,521,482,539,000 | 1,521,482,539,000 | 125,899,276 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 43,772 | lean | section sort
theorem one_le_suc : ∀n, 1 ≤ nat.succ n :=
begin
intros n,
induction n,
reflexivity,
apply nat.less_than_or_equal.step,
unfold has_le.le at ih_1,
exact ih_1
end
def count_dec {α : Type} [decidable_eq α] : α → list α → ℕ
| _ [] := 0
| x (h :: t) := if x =... |
ae330c54449d831a1b0f1c1756482906dd8ffd9f | 584ec75a09b1d26439c98b908268399181646b41 | /logic_examples.lean | 24aadb16f8d0bb9ba7fad4449ab5d0a5d6d8ccf5 | [] | no_license | m-slee/lean-logic | da462203935eee4d0c3820728d2be786474a6854 | 9809f35bbfe96e5f70fceaa594b055bfbd9e64e3 | refs/heads/master | 1,683,921,863,186 | 1,604,026,451,000 | 1,604,026,451,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,065 | lean | variables A B C D : Prop
-- A ∧ (A → B) → B
example : A ∧ (A → B) → B :=
assume h : A ∧ (A → B),
show B, from and.right h (and.left h)
-- A → ¬ (¬ A ∧ B)
example : A → ¬ (¬ A ∧ B) :=
assume h1 : A,
assume h2 : ¬ A ∧ B,
show false, from and.left h2 h1
-- ¬ (A ∧ B) → (A → ¬ B)
example (A B : Prop):... |
289335b68c75d1194a6f38429566b91d5f4edabf | 0c1546a496eccfb56620165cad015f88d56190c5 | /library/tools/super/clausifier.lean | 58966dfb3eb704ddcbd7eb6c016492653c02b589 | [
"Apache-2.0"
] | permissive | Solertis/lean | 491e0939957486f664498fbfb02546e042699958 | 84188c5aa1673fdf37a082b2de8562dddf53df3f | refs/heads/master | 1,610,174,257,606 | 1,486,263,620,000 | 1,486,263,620,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,906 | lean | /-
Copyright (c) 2016 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner
-/
import .clause .clause_ops
import .prover_state .misc_preprocessing
open expr list tactic monad decidable
universe variable u
namespace super
meta def try_option {a ... |
6631aed093d1619d3fb5a2d717a4b2f938bf3421 | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/equiv/fin.lean | 5a63feb1f13b5702212445ec4646ce8159b0ac46 | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 9,460 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Kenny Lau
-/
import data.fin
import data.equiv.basic
/-!
# Equivalences for `fin n`
-/
universe variables u
variables {m n : ℕ}
/-- Equivalence between `fin 0` and `empty`. -/
def fin_ze... |
349570b947b331342166330d52d74abb4d4a2d97 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/nonrec.lean | 784fc9612acc69280dfb439d3a41f313fa28cd48 | [
"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 | 114 | lean | def Foo (n : Nat) : Prop := True
def aux := 1
nonrec def Foo.aux : Foo aux :=
have h : aux = 1 := rfl
trivial
|
a55f28989c43d67cf8eebf8037d4e00a9b8a8929 | c7e0fa0422da099d4b66b195c60455d87facee0d | /span.lean | fe0cdc0783f18b64bf1ca77383637e9048ed48fb | [] | no_license | viljamivirolainen/linear | 12d725a90a44ae2760f59e9a9d9dd12aae36300a | dcf28df05e06da1b4fc76bce61b8fa0741300dc8 | refs/heads/master | 1,678,895,327,362 | 1,516,045,398,000 | 1,516,045,398,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,538 | lean | import .vector_space .seq .subspace
universes u v
variables {V : Type u} {F : Type v} [field F] [vector_space V F]
-- Linear span of a finite list/seq of vectors
inductive span {n} (v : seq V n) : set V
-- span(v_1,...,v_n) = {sum a_iv_i | a_i ∈ F}
| intro (a : seq F n) : span (seq.sum (λ i, a i ⋅ v i))
theorem set.... |
94fb6e9b60635f8e6f47b513003b4c8ee0821192 | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/category_theory/monad/algebra.lean | 5524183878fff883b61c7de7d405513a86f714b9 | [
"Apache-2.0"
] | permissive | hamdysalah1/mathlib | b915f86b2503feeae268de369f1b16932321f097 | 95454452f6b3569bf967d35aab8d852b1ddf8017 | refs/heads/master | 1,677,154,116,545 | 1,611,797,994,000 | 1,611,797,994,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,225 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Bhavik Mehta
-/
import category_theory.monad.basic
import category_theory.adjunction.basic
import category_theory.reflects_isomorphisms
/-!
# Eilenberg-Moore (co)algeb... |
8a892ea95a2ea485d73b13d2931ea0e32d74ad66 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/measure_theory/integral/lebesgue.lean | c258dcbdac4c66513ac383eaf488fbbb2723fc79 | [
"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 | 102,947 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl
-/
import measure_theory.measure.measure_space
import measure_theory.constructions.borel_space
import algebra.indicator_function
import algebra.support
... |
7902921243de254a62eb34f649e747b7e0fb227d | a4673261e60b025e2c8c825dfa4ab9108246c32e | /stage0/src/Lean/Expr.lean | bf359d8aa59dfd86dcb5565361ad306703807213 | [
"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 | 36,234 | lean | /-
Copyright (c) 2018 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Data.KVMap
import Lean.Level
namespace Lean
inductive Literal :=
| natVal (val : Nat)
| strVal (val : String)
instance : Inhabited Litera... |
96ffe1c7512cef6806a3265dd0a6d7984b1814c1 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /library/init/meta/ref.lean | 5981ece7ec8069d80074c1c9ee29428ab0286985 | [
"Apache-2.0"
] | permissive | GaloisInc/lean | aa1e64d604051e602fcf4610061314b9a37ab8cd | f1ec117a24459b59c6ff9e56a1d09d9e9e60a6c0 | refs/heads/master | 1,592,202,909,807 | 1,504,624,387,000 | 1,504,624,387,000 | 75,319,626 | 2 | 1 | Apache-2.0 | 1,539,290,164,000 | 1,480,616,104,000 | C++ | UTF-8 | Lean | false | false | 716 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.meta.tactic
universes u v
namespace tactic
meta constant ref (α : Type u) : Type u
/-- Create a new reference `r` with initial value `a... |
29c5c955404e8df79075a43131781886c9c35ce7 | 1dd482be3f611941db7801003235dc84147ec60a | /src/data/list/sigma.lean | 22365b7e449df5b65c7272b862303f3315e098dc | [
"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 | 10,110 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Sean Leather
Functions on lists of sigma types.
-/
import data.list.perm
universes u v
namespace list
variables {α : Type u} {β : α → Type v}
/- nodupkeys -/
def n... |
5966d6fa74a9c6d816e7faca16a9a3a13bdaf953 | 9ad8d18fbe5f120c22b5e035bc240f711d2cbd7e | /src/undergraduate/MAS114/Semester 1/Q14.lean | 1eb98839edaf28165efa5e09847a3ba481f999b9 | [] | 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 | 2,826 | lean | import data.real.basic data.fintype algebra.big_operators data.nat.modeq
import tactic.find tactic.squeeze
namespace MAS114
namespace exercises_1
namespace Q14
def f : ℚ → ℚ := λ x, (x + 1) / (2 * x)
lemma f_step (x : ℚ) : x > 1 → (1 - 1 / (x ^ 2)) * f (x - 1) = f x :=
begin
intro x_big,
let d := 2 * (x - 1) * (... |
e32bca957fc6459b2f3e136d303f6331a568e7e7 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/data/list/big_operators.lean | 492101040a6f9d5366e180ad1a6b7e07deb8eae6 | [
"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 | 25,661 | 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 algebra.group_power
import data.list.forall2
/-!
# Sums and products from lists
This file provides basic r... |
45bd0bf85462aa2e07dc2a6f0e733a636ffaaa56 | 71c62298fd72620ddff9e4ed896ca29a77073a7c | /4.lean | 8c6cf1422b068dbe3603a1069c4081363bebecc0 | [] | no_license | BelegCuthalion/lean-exc | dcfe8e4c2293a661a830ce06f5fa032563901ec6 | 9143dc8b8aac62b9b2dcee85b619fe5c2e2a7144 | refs/heads/master | 1,688,507,036,780 | 1,627,883,419,000 | 1,627,883,419,000 | 335,643,688 | 3 | 2 | null | null | null | null | UTF-8 | Lean | false | false | 5,345 | lean | import init.data.nat.basic
variable A : Type*
variables P Q : A → Prop
variable R : Prop
-- 1
example : (∀ x, P x ∧ Q x) ↔ (∀ x, P x) ∧ (∀ x, Q x) :=
begin
split,
assume h, split,
assume x, from (h x).left,
assume x, from (h x).right,
assume h, assume x, split,
from h.left x,
from h.right x
end
... |
7533e47618f5a8243b3fda8de4072b4d3e6cac61 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/out_param_proj.lean | dfa9d641618e114f61d926f7be8784c09131217c | [
"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 | 331 | lean | universes u v
class ring (α : Type u) := (fld : α)
class add_comm_group (β : Type v) := (fld : β)
class module (α : out_param $ Type u) (β : Type v) [out_param $ ring α] extends add_comm_group β :=
(foo : β → nat)
-- both α and `ring α` should be implicit (_not_ instance implicit)
#print module.to_add_comm_group
|
2567c1b1a73605ba7739a8100c3ee07145a09dc8 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/linear_algebra/exterior_algebra.lean | b4df468eca13374a928aa2a41dc1897a025e7c3d | [
"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 | 12,145 | lean | /-
Copyright (c) 2020 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhangir Azerbayev, Adam Topaz, Eric Wieser
-/
import algebra.ring_quot
import linear_algebra.tensor_algebra
import linear_algebra.alternating
import group_theory.perm.sign
/-!
# Exterior... |
b755bfab2449cc2b2fb976b5237474e0c27b4def | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/scan_error3.lean | a45f48fe58e201eacf42c15e7899298d731f6c6f | [
"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 | 22 | lean | (* print("from lua") * |
fc2fac3d4cc8cca786d3c1fbb933a37e44f279be | ee8cdbabf07f77e7be63a449b8483ce308d37218 | /lean/src/test/mathd-numbertheory-66.lean | baf355868d1c8a86dfefde678f5b2e4bb302206a | [
"MIT",
"Apache-2.0"
] | permissive | zeta1999/miniF2F | 6d66c75d1c18152e224d07d5eed57624f731d4b7 | c1ba9629559c5273c92ec226894baa0c1ce27861 | refs/heads/main | 1,681,897,460,642 | 1,620,646,361,000 | 1,620,646,361,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 217 | lean | /-
Copyright (c) 2021 OpenAI. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kunhao Zheng
-/
import data.real.basic
example : 194 % 11 = 7 :=
begin
exact rfl,
end
|
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