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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
50a60b02d772c073deea3e62e0b3bac55c1f9745 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/data/real/cau_seq_completion.lean | dc4b759485a702744990a35bd17a30352d78a4f5 | [
"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 | 9,454 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Robert Y. Lewis
Generalizes the Cauchy completion of (β, abs) to the completion of a
commutative ring with absolute value.
-/
import data.real.cau_seq
namespace cau_... |
168b0e155e68e4ca26c39fa80ce34ba3b68c141d | 592ee40978ac7604005a4e0d35bbc4b467389241 | /Library/generated/mathscheme-lean/ModularLattice.lean | 3ebad548760a414289fbe4df3be288df183a833c | [] | no_license | ysharoda/Deriving-Definitions | 3e149e6641fae440badd35ac110a0bd705a49ad2 | dfecb27572022de3d4aa702cae8db19957523a59 | refs/heads/master | 1,679,127,857,700 | 1,615,939,007,000 | 1,615,939,007,000 | 229,785,731 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,377 | lean | import init.data.nat.basic
import init.data.fin.basic
import data.vector
import .Prelude
open Staged
open nat
open fin
open vector
section ModularLattice
structure ModularLattice (A : Type) : Type :=
(times : (A β (A β A)))
(plus : (A β (A β A)))
(commutative_times : (β {x y : A} , (times x ... |
927d708ec280a892cfc5faa95b9350cefe20318c | 2b2a05a7af89c79da194505bf88205a6c4e05d68 | /src/game/world_08_advanced_addition.lean | fa0b087867a3b1c9be62e4ec66eb4cebc8d564fe | [] | no_license | lacrosse/natural_number_game | 6401a11a8c965da3903ae6695f84586edf6fac85 | 400179cde1d3fcc9744901dabff98813ba2b544f | refs/heads/master | 1,677,566,006,582 | 1,612,576,917,000 | 1,612,576,917,000 | 335,655,947 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,079 | lean | import game.world_07_advanced_proposition
namespace mynat
theorem succ_inj' {a b : mynat} (hs : succ(a) = succ(b)) : a = b := begin[nat_num_game]
exact succ_inj hs,
end
theorem succ_succ_inj {a b : mynat} (h : succ(succ(a)) = succ(succ(b))) : a = b := begin[nat_num_game]
apply succ_inj β succ_inj,
exact h,
end... |
05fd77235a2c701df9110090e402a6b2c70e608a | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /stage0/src/Lean/ParserCompiler.lean | 5b42588338a06e6294a67d25fdff60f15222e9e1 | [
"Apache-2.0"
] | permissive | WojciechKarpiel/lean4 | 7f89706b8e3c1f942b83a2c91a3a00b05da0e65b | f6e1314fa08293dea66a329e05b6c196a0189163 | refs/heads/master | 1,686,633,402,214 | 1,625,821,189,000 | 1,625,821,258,000 | 384,640,886 | 0 | 0 | Apache-2.0 | 1,625,903,617,000 | 1,625,903,026,000 | null | UTF-8 | Lean | false | false | 7,395 | lean | /-
Copyright (c) 2020 Sebastian Ullrich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
-/
/-!
Gadgets for compiling parser declarations into other programs, such as pretty printers.
-/
import Lean.Util.ReplaceExpr
import Lean.Meta.Basic
import Lean... |
c659602610d4d860eb35672b5db76b88cba6f8e8 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/algebra/category/CommRing/colimits.lean | 89c8540efead3b1646a1fff4f1805328d0273fc3 | [
"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 | 11,903 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import algebra.category.CommRing.basic
import category_theory.limits.limits
/-!
# The category of commutative rings has all colimits.
This file uses a "pre-automate... |
08b4c248b8e39d5d7577dfeac1975bc1bf039805 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/def4.lean | 9e7e262ac85a19185b1969865130ab57c9be8561 | [
"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 | 265 | lean | universe variable u
section
parameter (A : Type u)
definition f : A β A :=
Ξ» x, x
check f
check f (0:nat) -- error
parameter {A}
definition g : A β A :=
Ξ» x, x
check g
check g (0:nat) -- error
end
check f
check f _ (0:nat)
check g 0
|
f3075526d4a93b051b6a57bf99fa3fd6b763adba | b7f22e51856f4989b970961f794f1c435f9b8f78 | /hott/homotopy/homotopy_group.hlean | d6953bfc1e1c8c72c2a403fbd4120e63bbd447bc | [
"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 | 11,659 | hlean | /-
Copyright (c) 2016 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Clive Newstead
-/
import .LES_of_homotopy_groups .sphere .complex_hopf
open eq is_trunc trunc_index pointed algebra trunc nat is_conn fiber pointed unit
namespa... |
a994c28c056f03fc9c2333b6eea40c20e1c6afc1 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/preadditive/generator.lean | c096257eed802aea754f2084b603bc08c5bb3911 | [
"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 | 3,551 | lean | /-
Copyright (c) 2022 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import category_theory.generator
import category_theory.preadditive.yoneda.basic
/-!
# Separators in preadditive categories
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.... |
9e11936ba752039ba82af9cc76df3eda372c4aeb | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/finset/preimage.lean | 9613410e4aa8a0d138ab03a338e01f347b3bbcf6 | [] | 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 | 7,638 | lean | /-
Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl, Mario Carneiro
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.set.finite
import Mathlib.algebra.big_operators.basic
import Mathlib.P... |
b2263ee2185329a91e31b5b29f0d3d7e6235fa0e | bb31430994044506fa42fd667e2d556327e18dfe | /src/data/finset/locally_finite.lean | 6e3cf7f7482239fabe3d37ee4a8fbcbbcc044c9b | [
"Apache-2.0"
] | permissive | sgouezel/mathlib | 0cb4e5335a2ba189fa7af96d83a377f83270e503 | 00638177efd1b2534fc5269363ebf42a7871df9a | refs/heads/master | 1,674,527,483,042 | 1,673,665,568,000 | 1,673,665,568,000 | 119,598,202 | 0 | 0 | null | 1,517,348,647,000 | 1,517,348,646,000 | null | UTF-8 | Lean | false | false | 30,010 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, YaΓ«l Dillies
-/
import order.locally_finite
import data.set.intervals.monoid
/-!
# Intervals as finsets
This file provides basic results about all the `finset.Ixx`, w... |
47ad68d72265922921ddafbd20b5bcfe62a2ada2 | 7fc0ec5c526f706107537a6e2e34ac4cdf88d232 | /src/linear_algebra/group_star_algebra.lean | fe548a01b0cd8b785440a51351d47bff7312acd3 | [
"Apache-2.0"
] | permissive | fpvandoorn/group-representations | 7440a81f2ac9e0d2defa44dc1643c3167f7a2d99 | bd9d72311749187d3bd4f542d5eab83e8341856c | refs/heads/master | 1,684,128,141,684 | 1,623,338,135,000 | 1,623,338,135,000 | 256,117,709 | 0 | 2 | null | null | null | null | UTF-8 | Lean | false | false | 6,130 | lean | /-
Group algebras considered as star algebras.
This is formally parallel to monoid_algebra, but instead of taking finite formal
combinations of the generators, we take L^1 combinations.
In this file we define `group_star_algebra k G := G ββ k`, and `add_monoid_star_algebra k G`
in the same way, and then define the ... |
08fb0dfc4669caff3d342e2ee6b980f6fa79dcfd | 01ae0d022f2e2fefdaaa898938c1ac1fbce3b3ab | /categories/universal/comparisons/equalizers.lean | 4214cf892c13062f12c82b50d00bc80427c1ba55 | [] | no_license | PatrickMassot/lean-category-theory | 0f56a83464396a253c28a42dece16c93baf8ad74 | ef239978e91f2e1c3b8e88b6e9c64c155dc56c99 | refs/heads/master | 1,629,739,187,316 | 1,512,422,659,000 | 1,512,422,659,000 | 113,098,786 | 0 | 0 | null | 1,512,424,022,000 | 1,512,424,022,000 | null | UTF-8 | Lean | false | false | 1,034 | lean | -- Copyright (c) 2017 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Stephen Morgan, Scott Morrison
import ...isomorphism
import ...natural_transformation
import ...equivalence
import ..comma_categories
import ..universal
open categories
open ca... |
d62ebbd961cd792ddfb24e2607a328318f67a9c9 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/tactic/abel.lean | 8f7581d983617b1a15c8d27ef973c7bdad363970 | [
"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 | 16,770 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import tactic.norm_num
/-!
# The `abel` tactic
Evaluate expressions in the language of additive, commutative monoids and groups.
-/
namespace tactic
namespace ab... |
4afab67b27d28650b89f9098c89c2e6e58d54e0f | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/Fintype.lean | d19ae84779111728a3f93945a9e065586a6ddee0 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,658 | lean | /-
Copyright (c) 2020 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Adam Topaz
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.fintype.basic
import Mathlib.data.fin
import Mathlib.category_theory.concrete_ca... |
e0bebe591d1ed7d6ceaf450409e229a1483fedf5 | f3a5af2927397cf346ec0e24312bfff077f00425 | /src/game/world4/level8.lean | 2eddf2bf959430064de7261376c56a15e58039b4 | [
"Apache-2.0"
] | permissive | ImperialCollegeLondon/natural_number_game | 05c39e1586408cfb563d1a12e1085a90726ab655 | f29b6c2884299fc63fdfc81ae5d7daaa3219f9fd | refs/heads/master | 1,688,570,964,990 | 1,636,908,242,000 | 1,636,908,242,000 | 195,403,790 | 277 | 84 | Apache-2.0 | 1,694,547,955,000 | 1,562,328,792,000 | Lean | UTF-8 | Lean | false | false | 3,201 | lean | import game.world4.level7 -- hide
-- incantation for importing ring into framework -- hide
import tactic.ring -- hide
meta def nat_num_game.interactive.ring := tactic.interactive.ring -- hide
namespace mynat -- hide
def two_eq_succ_one : (2 : mynat) = succ 1 := rfl -- hide
/-
# Power World
-/
/-
## Level 8: `add_sq... |
53a33e108ddad619d02b636f85d624b5cec45f84 | 618003631150032a5676f229d13a079ac875ff77 | /src/geometry/manifold/manifold.lean | d11d6678861964bc78d6425c172a6daa5c04f002 | [
"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 | 27,180 | lean | /-
Copyright (c) 2019 SΓ©bastien GouΓ«zel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: SΓ©bastien GouΓ«zel
-/
import topology.local_homeomorph
/-!
# Manifolds
A manifold is a topological space M locally modelled on a model space H, i.e., the manifold is
covered by ope... |
6d753d9f389cfaa70d445a1fa651c66e90a02b9f | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/tactic/subtype_instance.lean | 2e67e74b1d7a3c2707d66049cae0ab79f125344e | [
"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 | 2,462 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
Provides a `subtype_instance` tactic which builds instances for algebraic substructures
(sub-groups, sub-rings...).
-/
import data.string.basic
open tactic expr name list
na... |
d893150cd4197904a40e1f5ddc5026a768cb5b19 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/category_theory/groupoid.lean | 1ada193dd2e32f7922b9a4b10edafc8864d0f757 | [
"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 | 2,170 | lean | /-
Copyright (c) 2018 Reid Barton All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Scott Morrison, David WΓ€rn
-/
import category_theory.epi_mono
namespace category_theory
universes v vβ u uβ -- declare the `v`'s first; see `category_theory.category` for an... |
53a93bdd10e4b64cd085344880bde4be496a82d9 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /test/noncomm_ring.lean | a53d395ca98bf530f92c38047099ba9e0601f59d | [
"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 | 2,803 | lean | import tactic.noncomm_ring
local notation `β
`a`,` b`β` := a * b - b * a
local infix ` β¬ `:70 := Ξ» a b, a * b + b * a
variables {R : Type*} [ring R]
variables (a b c : R)
example : 0 = 0 := by noncomm_ring
example : a = a := by noncomm_ring
example : (a + b) * c = a * c + b * c := by noncomm_ring
example : a * (b + ... |
67b49b73023c76bed89abbd4a1371651d3fc008b | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/eqTheoremForVec.lean | 56c8910a6d5801aeb91af9ab2d2d7e396e1efbb8 | [
"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 | 402 | lean | inductive Vector (Ξ± : Type u): Nat β Type u where
| nil : Vector Ξ± 0
| cons (head : Ξ±) (tail : Vector Ξ± n) : Vector Ξ± (n+1)
theorem Nat.lt_of_add_lt_add_right {a b c : Nat} (h : a + b < c + b) : a < c := sorry
def Vector.nth : β{n}, Vector Ξ± n β Fin n β Ξ±
| n+1, Vector.cons x xs, β¨ 0, _β© => x
| n+1, Vector.cons x xs... |
db9ad3459b31b3abb0f31a06ccde29c04a85fdd0 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/tactic/linarith.lean | e7852760effd5da18a7fd6d4717be961bc2a2197 | [
"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 | 33,039 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Robert Y. Lewis
-/
import tactic.ring data.nat.gcd data.list.basic meta.rb_map data.tree
/-!
A tactic for discharging linear arithmetic goals using Fourier-Motzkin elimination.
`li... |
61a8b63b1e1e60d9e993cd7413c45a595b79603e | d7189ea2ef694124821b033e533f18905b5e87ef | /galois/crypto/hmac.lean | 1470c78d30c76a7a0dee0dd8f094323c588f7525 | [
"Apache-2.0"
] | permissive | digama0/lean-protocol-support | eaa7e6f8b8e0d5bbfff1f7f52bfb79a3b11b0f59 | cabfa3abedbdd6fdca6e2da6fbbf91a13ed48dda | refs/heads/master | 1,625,421,450,627 | 1,506,035,462,000 | 1,506,035,462,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,410 | lean | /- This defines an hmac primitive.
-/
import galois.word
import galois.tactic.nat
import galois.bitvec.join
import galois.crypto.sha2
namespace crypto
definition hmac {olen : β} -- ^ Output length
(blen : β) -- ^ Block length
(hash : list byte β vector byte olen)
(key ... |
5e0ec39fa6aa6e44888db8796aeee729023cd95f | bdb33f8b7ea65f7705fc342a178508e2722eb851 | /analysis/complex.lean | 38c672ce64c7d96f1a4861118e7666c3ad1a6f15 | [
"Apache-2.0"
] | permissive | rwbarton/mathlib | 939ae09bf8d6eb1331fc2f7e067d39567e10e33d | c13c5ea701bb1eec057e0a242d9f480a079105e9 | refs/heads/master | 1,584,015,335,862 | 1,524,142,167,000 | 1,524,142,167,000 | 130,614,171 | 0 | 0 | Apache-2.0 | 1,548,902,667,000 | 1,524,437,371,000 | Lean | UTF-8 | Lean | false | false | 4,338 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
Topology of the complex numbers.
-/
import data.complex.basic analysis.metric_space
noncomputable theory
open filter
namespace complex
-- TODO(Mario): these proofs ar... |
d0bc59ba5bfab348ce25809628b9b882d1a0232c | 6f1049e897f569e5c47237de40321e62f0181948 | /src/solutions/09_limits_final.lean | 23599ad3df185e7308e6bea6d03156997f74869a | [
"Apache-2.0"
] | permissive | anrddh/tutorials | f654a0807b9523608544836d9a81939f8e1dceb8 | 3ba43804e7b632201c494cdaa8da5406f1a255f9 | refs/heads/master | 1,655,542,921,827 | 1,588,846,595,000 | 1,588,846,595,000 | 262,330,134 | 0 | 0 | null | 1,588,944,346,000 | 1,588,944,345,000 | null | UTF-8 | Lean | false | false | 12,805 | lean | import tuto_lib
set_option pp.beta true
set_option pp.coercions false
/-
This is the final file in this series. Here we use everything covered
in previous files to prove a couple of famous theorems from
elementary real analysis. Of course they all have more general versions
in mathlib.
As usual, keep in mind:
ab... |
0a34c368eddfe7df67502d2b35d9b18065a91d47 | 46125763b4dbf50619e8846a1371029346f4c3db | /src/data/list/sort.lean | d0aa67e02bc6ae6d7244f02c9a18e24d89459b4a | [
"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 | 11,136 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
Insertion sort and merge sort.
-/
import data.list.perm
open list.perm
namespace list
section sorted
universe variable uu
variables {Ξ± : Type uu} {r : Ξ± β Ξ± β Prop}
/--... |
7c6bcaa35327585b7ccd42a4556d6775ea034608 | 626e312b5c1cb2d88fca108f5933076012633192 | /src/analysis/calculus/fderiv_measurable.lean | 85f8769a1b81ef8fc4e79d788a5008331928c950 | [
"Apache-2.0"
] | permissive | Bioye97/mathlib | 9db2f9ee54418d29dd06996279ba9dc874fd6beb | 782a20a27ee83b523f801ff34efb1a9557085019 | refs/heads/master | 1,690,305,956,488 | 1,631,067,774,000 | 1,631,067,774,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 21,759 | lean | /-
Copyright (c) 2020 SΓ©bastien GouΓ«zel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: SΓ©bastien GouΓ«zel, Yury Kudryashov
-/
import analysis.calculus.deriv
import measure_theory.constructions.borel_space
/-!
# Derivative is measurable
In this file we prove that the ... |
7d300c0aaa371620224742e58b3858f86983f759 | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /src/Lean/Parser/Extension.lean | 87a299462e922fc80e3a794c9e84646f5a16ba9f | [
"Apache-2.0"
] | permissive | dupuisf/lean4 | d082d13b01243e1de29ae680eefb476961221eef | 6a39c65bd28eb0e28c3870188f348c8914502718 | refs/heads/master | 1,676,948,755,391 | 1,610,665,114,000 | 1,610,665,114,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 26,245 | 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.ScopedEnvExtension
import Lean.Parser.Basic
import Lean.Parser.StrInterpolation
import Lean.KeyedDeclsAttribute
/-! Extensib... |
494eb0636fe0eb4ce3a1796ad4af6329ff548a56 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/coe3.lean | f4c9c52f285972a9b7412caa4d4bc5d18ab6b938 | [
"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 | 759 | lean | import logic
namespace setoid
inductive setoid : Type :=
mk_setoid: Ξ (A : Type), (A β A β Prop) β setoid
definition carrier (s : setoid)
:= setoid.rec (Ξ» a eq, a) s
definition eqv {s : setoid} : carrier s β carrier s β Prop
:= setoid.rec (Ξ» a eqv, eqv) s
infix `β` := eqv
attribute carrier [coercio... |
75767cce13204976eb134fc4ac4b96a0f33a8f77 | a726f88081e44db9edfd14d32cfe9c4393ee56a4 | /src/game/world9/level4.lean | 26b33db835507ec1376fe301c77820d6a80c643c | [] | no_license | b-mehta/natural_number_game | 80451bf10277adc89a55dbe8581692c36d822462 | 9faf799d0ab48ecbc89b3d70babb65ba64beee3b | refs/heads/master | 1,598,525,389,186 | 1,573,516,674,000 | 1,573,516,674,000 | 217,339,684 | 0 | 0 | null | 1,571,933,100,000 | 1,571,933,099,000 | null | UTF-8 | Lean | false | false | 1,153 | lean | import game.world9.level3 -- hide
namespace mynat -- hide
/-
# Multiplication World
## Level 4: `mul_left_cancel`
This is the last of the bonus multiplication levels.
`mul_left_cancel` will be useful in inequality world.
-/
/- Theorem
If $a \neq 0$, $b$ and $c$ are natural numbers such that
$ ab = ac, $
then $b = c... |
3119980417c6f9ec7f8eed6e00e00a9577391462 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /test/induction.lean | ddd471dc6d49ec006195bb28435096e4c26da9a7 | [
"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 | 37,996 | lean | import tactic.induction
import tactic.linarith
universes u v w
--------------------------------------------------------------------------------
-- Setup: Some Inductive Types
--------------------------------------------------------------------------------
inductive le : β β β β Type
| zero {n} : le 0 n
| succ {n m} ... |
d8143342a49216aca8cbeb19aadbb36fee7cced2 | 34c1747a946aa0941114ffca77a3b7c1e4cfb686 | /src/sheaves/presheaf_on_basis.lean | 88bc4e7d5455601a9591aca08b9cc9aea08fe569 | [] | no_license | martrik/lean-scheme | 2b9edd63550c4579a451f793ab289af9fc79a16d | 033dc47192ba4c61e4e771701f5e29f8007e6332 | refs/heads/master | 1,588,866,287,405 | 1,554,922,682,000 | 1,554,922,682,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,529 | lean | /-
Presheaf (of types) on basis.
https://stacks.math.columbia.edu/tag/009I
-/
import topology.basic
import topology.opens
import sheaves.presheaf
universes u v
open topological_space
-- Presheaf of types where we only define sections on basis elements.
structure presheaf_on_basis (Ξ± : Type u) [T : topological... |
3531441d1394aeb63e6f773e363abb97e9280fef | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /11_Tactic-Style_Proofs.org.51.lean | b86135ecd7827f9397ced078c07a9bf585318345 | [] | 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 | 279 | lean | import standard
import data.list
open list
variable {A : Type}
theorem append_assoc : β (s t u : list A), s ++ t ++ u = s ++ (t ++ u)
| append_assoc nil t u := by apply rfl
| append_assoc (a :: l) t u :=
begin
rewrite βΈ a :: (l ++ t ++ u) = _,
rewrite append_assoc
end
|
28d4dd837126fb9d14d4b7e635b5364bfc4467bf | 95dcf8dea2baf2b4b0a60d438f27c35ae3dd3990 | /src/category_theory/limits/cones.lean | aa1275e12543dbc75b82c4dc070023c6fce30871 | [
"Apache-2.0"
] | permissive | uniformity1/mathlib | 829341bad9dfa6d6be9adaacb8086a8a492e85a4 | dd0e9bd8f2e5ec267f68e72336f6973311909105 | refs/heads/master | 1,588,592,015,670 | 1,554,219,842,000 | 1,554,219,842,000 | 179,110,702 | 0 | 0 | Apache-2.0 | 1,554,220,076,000 | 1,554,220,076,000 | null | UTF-8 | Lean | false | false | 11,111 | lean | -- Copyright (c) 2017 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Stephen Morgan, Scott Morrison
import category_theory.natural_isomorphism
import category_theory.whiskering
import category_theory.const
import category_theory.opposites
import ... |
1339e657a13a47be4c3b5c65a35d1fd84072009a | c31182a012eec69da0a1f6c05f42b0f0717d212d | /src/thm95/col_exact_prep.lean | 0e3af9cae80b0eb449d0a4c280481b61b1016734 | [] | 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 | 10,140 | lean | import pseudo_normed_group.FP
import system_of_complexes.basic
import prop819
import pseudo_normed_group.sum_hom
noncomputable theory
open_locale nnreal big_operators
open category_theory opposite simplex_category
local attribute [instance] type_pow
universe variables u uβ uβ
-- set_option pp.universes true
namesp... |
7766ec74b7ca77efbb6e850f232d844123872525 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/tactic/rewrite_all/congr.lean | 996dceb715ed78dfb7d77ab5920a7bf8c71e7db5 | [
"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 | 4,816 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Keeley Hoek
-/
import tactic.rewrite_all.basic
import tactic.core
namespace tactic
-- Sometimes `mk_congr_arg` fails, when the function is 'superficially dependent'.
... |
b8423fc48384b1f57f7b4e1eb8f6f2e2086b5091 | b00eb947a9c4141624aa8919e94ce6dcd249ed70 | /tests/lean/interactive/hover.lean | c02210f4599fa54f90ad75002eb8255b530017cf | [
"Apache-2.0"
] | permissive | gebner/lean4-old | a4129a041af2d4d12afb3a8d4deedabde727719b | ee51cdfaf63ee313c914d83264f91f414a0e3b6e | refs/heads/master | 1,683,628,606,745 | 1,622,651,300,000 | 1,622,654,405,000 | 142,608,821 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 245 | lean | example : True := by
apply True.intro
--^ textDocument/hover
example : True := by
simp [True.intro]
--^ textDocument/hover
example (n : Nat) : True := by
match n with
| Nat.zero => _
--^ textDocument/hover
| n + 1 => _
|
18fe27d4892e38998691c41d8cc2c86b7c4fbe98 | 137c667471a40116a7afd7261f030b30180468c2 | /src/linear_algebra/direct_sum_module.lean | dc0e040156d1a5125c5bb9a18383c31dcc08d9e8 | [
"Apache-2.0"
] | permissive | bragadeesh153/mathlib | 46bf814cfb1eecb34b5d1549b9117dc60f657792 | b577bb2cd1f96eb47031878256856020b76f73cd | refs/heads/master | 1,687,435,188,334 | 1,626,384,207,000 | 1,626,384,207,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,172 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
Direct sum of modules over commutative rings, indexed by a discrete type.
-/
import algebra.direct_sum
import linear_algebra.dfinsupp
/-!
# Direct sum of modules over commutativ... |
e57fece2dac0f50d261b4f87c6a51af1783a9fb2 | 618003631150032a5676f229d13a079ac875ff77 | /src/category_theory/limits/limits.lean | 9bcf401fcb92739f5a590cf22e3c03a2a539f577 | [
"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 | 42,800 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Mario Carneiro, Scott Morrison, Floris van Doorn
-/
import category_theory.limits.cones
import category_theory.adjunction.basic
open category_theory category_theory.categ... |
11983d0767237a6816ec1258862db10adb4b6410 | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/order/bounds.lean | 3ee7148f38c6423b20df963dfa3cc5c0b9c919cc | [
"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 | 29,277 | lean | /-
Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl, Yury Kudryashov
-/
import data.set.intervals.basic
import algebra.ordered_group
/-!
# Upper / lower bounds
In this file we define:
* `upper_bounds`, `lower_bounds` :... |
8cef40044ca852d771d280ecf47834db4ad18ac0 | 271e26e338b0c14544a889c31c30b39c989f2e0f | /src/Init/Lean/Environment.lean | 79abe699e07f04bae06ca625e0d01d106758a47f | [
"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 | 25,899 | 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.System.IO
import Init.Util
import Init.Data.ByteArray
import Init.Lean.Data.SMap
import Init.Lean.Util.Path
import Init.Lean.Declaration... |
6171cfd8baff2dab52ab70150e56c24b0afb3a02 | 845976968546725c9fa2976823b4102f4827056d | /src/problem_sheets/sheet_1/sht01Q01.lean | f803e080b0296f93934a4656d1f3870953838f89 | [
"Apache-2.0"
] | permissive | PatrickMassot/M1P1-lean | 37b2f56af7ce9765dbef1940062487914eb3b712 | 4000dc5f449020e4f1a4820fc807383a3df42d85 | refs/heads/master | 1,587,280,512,253 | 1,548,801,138,000 | 1,548,801,138,000 | 168,042,050 | 0 | 0 | null | 1,548,711,613,000 | 1,548,711,613,000 | null | UTF-8 | Lean | false | false | 1,757 | lean | -- This import gives us a working copy of the real numbers β,
-- and functions such as abs : β β β
import data.real.basic
-- This next import gives us several tactics of use to mathematicians:
-- (1) norm_num [to prove basic facts about reals like 2+2 = 4]
-- (2) ring [to prove basic algebra identities like (a+b)^2 =... |
c68f55aaeb2529f42fe01d54e39cddd470a13c89 | f083c4ed5d443659f3ed9b43b1ca5bb037ddeb58 | /group_theory/subgroup.lean | 80a5c25aef375fe81dda62e8458f7914ff776c07 | [
"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 | 15,211 | lean | /-
Copyright (c) 2018 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl, Mitchell Rowett, Scott Morrison, Johan Commelin, Mario Carneiro
-/
import group_theory.submonoid
open set function
variables {Ξ± : Type*} {Ξ² : Type*} {a aβ aβ b c: Ξ±}
... |
f2e044b8a0ce58c691ac0fca877ffd4345ef4b83 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/mv_polynomial/cardinal.lean | 2d1b7b0fbda670df20622e36d3df96b3f7e9639b | [
"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 | 4,380 | lean | /-
Copyright (c) 2021 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import data.W.cardinal
import data.mv_polynomial.basic
/-!
# Cardinality of Polynomial Ring
The main result in this file is `mv_polynomial.cardinal_mk_le_max`, which say... |
60ed8ea0fcbc842b9ca05a0fcc0502f8e3c58688 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/808.lean | 7d53c9751adc6088ef38e6dc5d77e25126a06b00 | [
"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 | 195 | lean | notation 1 := eq
postfix `x`:(max+1) := eq
postfix [priority 1] `y`:max := eq
definition foo [instance] [priority 1] : inhabited nat := inhabited.mk nat.zero
definition bar [unfold 1] := @eq
|
48b4e528f5b79bb6bcb2ff099e9b653ce422ddaf | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/trace.lean | 16c1701797e600683768e220d887c7ab3383a4b8 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 1,572 | lean | import Lean.CoreM
open Lean
structure MyState :=
(trace_state : TraceState := {})
(s : Nat := 0)
abbrev M := CoreM
def tst1 : M Unit :=
do trace[module] (m!"hello" ++ MessageData.nest 9 (m!"\n" ++ "world"));
trace[module.aux] "another message";
pure ()
def tst2 (b : Bool) : M Unit :=
withTraceNode `... |
f98c55a56de58fa74b46da92becfeb539228e67b | a7eef317ddec01b9fc6cfbb876fe7ac00f205ac7 | /src/category_theory/comma.lean | b14457530f44c421b0261be6ea339ee4c2abb1ee | [
"Apache-2.0"
] | permissive | kmill/mathlib | ea5a007b67ae4e9e18dd50d31d8aa60f650425ee | 1a419a9fea7b959317eddd556e1bb9639f4dcc05 | refs/heads/master | 1,668,578,197,719 | 1,593,629,163,000 | 1,593,629,163,000 | 276,482,939 | 0 | 0 | null | 1,593,637,960,000 | 1,593,637,959,000 | null | UTF-8 | Lean | false | false | 17,358 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Johan Commelin, Bhavik Mehta
-/
import category_theory.punit
import category_theory.reflect_isomorphisms
/-!
# Comma categories
A comma category is a construction in ... |
c8238d68e3ab60c5e5215d652967ffc1365f06c1 | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /src/Init/Control/Option.lean | af1dac4aa51844374aa564b7bc37252b99ef4771 | [
"Apache-2.0"
] | permissive | williamdemeo/lean4 | 72161c58fe65c3ad955d6a3050bb7d37c04c0d54 | 6d00fcf1d6d873e195f9220c668ef9c58e9c4a35 | refs/heads/master | 1,678,305,356,877 | 1,614,708,995,000 | 1,614,708,995,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,879 | 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.Data.Option.Basic
import Init.Control.Basic
import Init.Control.Except
universes u v
instance {Ξ±} : ToBool (Option ... |
2b839101eb9b6d6d28f162cb9bc44f7f0f641cb2 | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/data/real/cau_seq.lean | 11b8b99907912ae996695d195e93f029d58a5bc0 | [
"Apache-2.0"
] | permissive | jumpy4/mathlib | d3829e75173012833e9f15ac16e481e17596de0f | af36f1a35f279f0e5b3c2a77647c6bf2cfd51a13 | refs/heads/master | 1,693,508,842,818 | 1,636,203,271,000 | 1,636,203,271,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 23,703 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import algebra.order.absolute_value
import algebra.big_operators.order
/-!
# Cauchy sequences
A basic theory of Cauchy sequences, used in the construction of the re... |
a25093957edfdf2ef7621761f114cc185d165bab | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/data/polynomial/mirror.lean | a2cf132a655d232c21f5b913a0a876a2c0887848 | [
"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 | 7,486 | lean | /-
Copyright (c) 2020 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import data.polynomial.ring_division
/-!
# "Mirror" of a univariate polynomial
In this file we define `polynomial.mirror`, a variant of `polynomial.reverse`. The... |
5dc3b9eb035e5c96b9bf2cd0c8a3548905ed426e | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/unfold.lean | b152749677ab60a2afc37c87cba9c6526a599114 | [
"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 | 712 | lean | import data.nat
open nat algebra
definition f (a b : nat) := a + b
example (a b : nat) : f a b = 0 β f b a = 0 :=
begin
intro h,
unfold f at h,
state,
unfold f,
state,
rewrite [add.comm],
exact h
end
example (a b : nat) : f a b = 0 β f b a = 0 :=
begin
intro h,
unfold f at *,
state,
rewrite [ad... |
97f0e4f6cd3d272b520978966f8cbc185919d5b6 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/nat/even_odd_rec.lean | 4eb5627bf7d339b4e599183c22313655c698d387 | [
"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 | 1,996 | lean | /-
Copyright (c) 2022 Stuart Presnell. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stuart Presnell
-/
import data.nat.basic
/-! # A recursion principle based on even and odd numbers. -/
namespace nat
/-- Recursion principle on even and odd numbers: if we have `P... |
dcfec1161081329232e00f18ca2199fef7de7fbf | e151e9053bfd6d71740066474fc500a087837323 | /src/hott/hit/colimit.lean | 60e37c7b671d6848d5feb7d23d12244b7130a914 | [
"Apache-2.0"
] | permissive | daniel-carranza/hott3 | 15bac2d90589dbb952ef15e74b2837722491963d | 913811e8a1371d3a5751d7d32ff9dec8aa6815d9 | refs/heads/master | 1,610,091,349,670 | 1,596,222,336,000 | 1,596,222,336,000 | 241,957,822 | 0 | 0 | Apache-2.0 | 1,582,222,839,000 | 1,582,222,838,000 | null | UTF-8 | Lean | false | false | 8,364 | lean | /-
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
Definition of general colimits and sequential colimits.
-/
import ..init
universes u v w
hott_theory
namespace hott
/- definition of a general colimit -/
open ho... |
71ef36e0ead48cf495acf7277b07089980f192d7 | 853df553b1d6ca524e3f0a79aedd32dde5d27ec3 | /src/category_theory/limits/shapes/pullbacks.lean | 250b56e05fef7b00a4fa533d709ce0808432b03c | [
"Apache-2.0"
] | permissive | DanielFabian/mathlib | efc3a50b5dde303c59eeb6353ef4c35a345d7112 | f520d07eba0c852e96fe26da71d85bf6d40fcc2a | refs/heads/master | 1,668,739,922,971 | 1,595,201,756,000 | 1,595,201,756,000 | 279,469,476 | 0 | 0 | null | 1,594,696,604,000 | 1,594,696,604,000 | null | UTF-8 | Lean | false | false | 25,061 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Markus Himmel, Bhavik Mehta
-/
import category_theory.limits.shapes.wide_pullbacks
import category_theory.limits.shapes.binary_products
/-!
# Pullbacks
We define a ca... |
4370bd822d7e69ecf28f4be1b828885052a2b847 | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /stage0/src/Init/Notation.lean | 6d6be5fe53ab1086ed5ac4334b60984e5f06e237 | [
"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 | 13,684 | 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
Notation for operators defined at Prelude.lean
-/
prelude
import Init.Prelude
-- DSL for specifying parser precedences and priorities
namespace Lean.Parser.... |
23b2e7f34e65548562328c045215cc4add150387 | 7b02c598aa57070b4cf4fbfe2416d0479220187f | /algebra/direct_sum.hlean | e5eaf82b3ecc9e906285ac158e1ad686cbc47df4 | [
"Apache-2.0"
] | permissive | jdchristensen/Spectral | 50d4f0ddaea1484d215ef74be951da6549de221d | 6ded2b94d7ae07c4098d96a68f80a9cd3d433eb8 | refs/heads/master | 1,611,555,010,649 | 1,496,724,191,000 | 1,496,724,191,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,823 | 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, Egbert Rijke
Constructions with groups
-/
import .quotient_group .free_commutative_group
open eq algebra is_trunc set_quotient relation sigma prod sum list trunc... |
49e7f9d936062bdc9b09d6c5699e6d460a41d506 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /archive/imo/imo1998_q2.lean | 65c26a8300a959a9e335df42aec0605588c07a62 | [
"Apache-2.0"
] | permissive | AntoineChambert-Loir/mathlib | 64aabb896129885f12296a799818061bc90da1ff | 07be904260ab6e36a5769680b6012f03a4727134 | refs/heads/master | 1,693,187,631,771 | 1,636,719,886,000 | 1,636,719,886,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,571 | lean | /-
Copyright (c) 2020 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import data.fintype.basic
import data.int.parity
import algebra.big_operators.order
import tactic.ring
import tactic.noncomm_ring
/-!
# IMO 1998 Q2
In a competition, there... |
54dea10cec210e8d7d22d5d69a9fdddf19c648bf | 4b264bd060cfaad29c2dca34fa94c34f88a4d619 | /colimit/move_to_lib.hlean | f7db1065be53f4f934105450c3c32c0918281c5f | [
"Apache-2.0"
] | permissive | UlrikBuchholtz/leansnippets | a0d2675f5173867a1b90c3b0e559af5152f2e96c | ee547e8b301c9364022937cdc4a1dbf2cb4b1162 | refs/heads/master | 1,611,460,071,315 | 1,441,903,237,000 | 1,441,903,237,000 | 41,886,729 | 0 | 0 | null | 1,441,319,113,000 | 1,441,319,113,000 | null | UTF-8 | Lean | false | false | 4,048 | 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, Egbert Rijke
-/
-- these definitions and theorems should be moved to the HoTT library
import types.nat
open eq
open nat
open is_trunc
open function
namespace my
... |
5dfc894c2c036e2823490ad502445c5171190310 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/category_theory/monoidal/rigid/functor_category.lean | ef3315f137b3d7cb36b59a9bde3e90c77f9f6db6 | [
"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 | 2,859 | lean | /-
Copyright (c) 2022 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.monoidal.rigid.basic
import category_theory.monoidal.functor_category
/-!
# Functors from a groupoid into a right/left rigid category form a r... |
94834eb77703d29023a33e5192579fa25a54c4f3 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/system/io_interface.lean | 834382a6f29b8619c8a13befabd50b03da4fe77a | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,980 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.Lean3Lib.data.buffer
import Mathlib.Lean3Lib.system.random
universes l
names... |
38eb2b7dcabdec662b093970dfff0af88af8f788 | aa5a655c05e5359a70646b7154e7cac59f0b4132 | /stage0/src/Lean/Meta/Match/MatcherInfo.lean | 013ba30c2053ff82d813914563f42ebd4f6c13b6 | [
"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 | 3,930 | 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.Basic
namespace Lean.Meta
namespace Match
/--
A "matcher" auxiliary declaration has the following structure:
- `numParams` parameters
- m... |
b6c15eba99cb923342dfe54850b59b8d5c686915 | 4fa161becb8ce7378a709f5992a594764699e268 | /src/data/equiv/encodable.lean | a5bc290d05c451f16fe26edf876bddb46652d186 | [
"Apache-2.0"
] | permissive | laughinggas/mathlib | e4aa4565ae34e46e834434284cb26bd9d67bc373 | 86dcd5cda7a5017c8b3c8876c89a510a19d49aad | refs/heads/master | 1,669,496,232,688 | 1,592,831,995,000 | 1,592,831,995,000 | 274,155,979 | 0 | 0 | Apache-2.0 | 1,592,835,190,000 | 1,592,835,189,000 | null | UTF-8 | Lean | false | false | 14,722 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura, Mario Carneiro
Type class for encodable Types.
Note that every encodable Type is countable.
-/
import data.equiv.nat
import order.order_iso
open option list n... |
2e811ef58dadc4dcd8f4b863d24e976150029029 | 798dd332c1ad790518589a09bc82459fb12e5156 | /analysis/topology/topological_space.lean | dcdd0da52a7be82e615e28a4ff3e4778c8026364 | [
"Apache-2.0"
] | permissive | tobiasgrosser/mathlib | b040b7eb42d5942206149371cf92c61404de3c31 | 120635628368ec261e031cefc6d30e0304088b03 | refs/heads/master | 1,644,803,442,937 | 1,536,663,752,000 | 1,536,663,907,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 58,054 | lean | /-
Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl, Mario Carneiro
Theory of topological spaces.
Parts of the formalization is based on the books:
N. Bourbaki: General Topology
I. M. James: Topologies and Uniformit... |
942f293cc6b73c1b242c51ecb40aa43ca0c5fd09 | 30b012bb72d640ec30c8fdd4c45fdfa67beb012c | /data/padics/hensel.lean | 17f58da8ba3b78d6c467d790b07a5e5fc70b000f | [
"Apache-2.0"
] | permissive | kckennylau/mathlib | 21fb810b701b10d6606d9002a4004f7672262e83 | 47b3477e20ffb5a06588dd3abb01fe0fe3205646 | refs/heads/master | 1,634,976,409,281 | 1,542,042,832,000 | 1,542,319,733,000 | 109,560,458 | 0 | 0 | Apache-2.0 | 1,542,369,208,000 | 1,509,867,494,000 | Lean | UTF-8 | Lean | false | false | 20,814 | 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 β€_p, roughly following Keith Conrad's writeup:
http://www.math.uconn.edu/~kconrad/blurbs/gradnumthy/hensel.pdf
-/
import data.padics.pad... |
e2e2496823355511ae880e16b1882a237100ed2a | 4727251e0cd73359b15b664c3170e5d754078599 | /src/linear_algebra/eigenspace.lean | b6ffa6d59f00724274d9d6fbea5b5d50b52d727d | [
"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 | 29,066 | lean | /-
Copyright (c) 2020 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp
-/
import linear_algebra.charpoly.basic
import linear_algebra.finsupp
import linear_algebra.matrix.to_lin
import algebra.algebra.spectrum
import order.hom.basic... |
a82549fcae2737b87e18f38272ae2b300be8581a | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/analysis/convex/strict_convex_space.lean | 39d0309c9d23d1a41e4ad666920f4fe0a97f40c9 | [
"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 | 14,185 | lean | /-
Copyright (c) 2022 YaΓ«l Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: YaΓ«l Dillies, Yury Kudryashov
-/
import analysis.convex.strict
import analysis.convex.topology
import analysis.normed.order.basic
import analysis.normed_space.add_torsor
import analysis.... |
aad3a6e60c4855e99a3282a5c661531cb4b8aa19 | ebb7367fa8ab324601b5abf705720fd4cc0e8598 | /homotopy/spectrum.hlean | 63dc0db23107963671b2f80419c119ded1f1a7f3 | [
"Apache-2.0"
] | permissive | radams78/Spectral | 3e34916d9bbd0939ee6a629e36744827ff27bfc2 | c8145341046cfa2b4960ef3cc5a1117d12c43f63 | refs/heads/master | 1,610,421,583,830 | 1,481,232,014,000 | 1,481,232,014,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 20,522 | hlean | /-
Copyright (c) 2016 Michael Shulman. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Shulman, Floris van Doorn
-/
import homotopy.LES_of_homotopy_groups .splice homotopy.susp ..move_to_lib ..colim
..pointed_pi
open eq nat int susp pointed pmap sigma i... |
00820389a8d001de33b7d90c2ed63e54f2599dab | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/order/filter/at_top_bot.lean | c22e04c66b6a54128d22a1e4294b0a735d727bed | [
"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 | 61,939 | lean | /-
Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl, Jeremy Avigad, Yury Kudryashov, Patrick Massot
-/
import order.filter.bases
import data.finset.preimage
/-!
# `at_top` and `at_bot` filters on preorded sets, monoids a... |
34bb34aef50f45d2903a5023c14ccf37ca2758cb | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/data/finset/lattice.lean | dad64260c9ef24ef16668c1c246c8f9fc99f2acb | [
"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 | 24,114 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
-/
import data.finset.fold
import data.multiset.lattice
/-!
# Lattice operations on finsets
-/
variables {Ξ± Ξ² Ξ³ : Type*}
namespace finset
open multiset
/-! ### sup -/... |
48b937e484137d8a4cc7bb6a751031d0a72bee07 | 4fa161becb8ce7378a709f5992a594764699e268 | /src/linear_algebra/basic.lean | 68c5b577bfd9672612a6ef036fcbc2829410ac0d | [
"Apache-2.0"
] | permissive | laughinggas/mathlib | e4aa4565ae34e46e834434284cb26bd9d67bc373 | 86dcd5cda7a5017c8b3c8876c89a510a19d49aad | refs/heads/master | 1,669,496,232,688 | 1,592,831,995,000 | 1,592,831,995,000 | 274,155,979 | 0 | 0 | Apache-2.0 | 1,592,835,190,000 | 1,592,835,189,000 | null | UTF-8 | Lean | false | false | 94,595 | lean | /-
Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov
-/
import algebra.pi_instances
import data.finsupp
/-!
# Linear algebra
This file defines the basics of linear algebra.... |
9ee3d3178576e308ccedf7f384f3604ebdce5e3d | f3a5af2927397cf346ec0e24312bfff077f00425 | /src/game/world6/level9.lean | ad720e40a06ba631a49ec40358b1aaa4948c1dce | [
"Apache-2.0"
] | permissive | ImperialCollegeLondon/natural_number_game | 05c39e1586408cfb563d1a12e1085a90726ab655 | f29b6c2884299fc63fdfc81ae5d7daaa3219f9fd | refs/heads/master | 1,688,570,964,990 | 1,636,908,242,000 | 1,636,908,242,000 | 195,403,790 | 277 | 84 | Apache-2.0 | 1,694,547,955,000 | 1,562,328,792,000 | Lean | UTF-8 | Lean | false | false | 1,316 | lean | /-
# Proposition world.
## Level 9: a big maze.
Lean's "congruence closure" tactic `cc` is good at mazes. You might want to try it now.
Perhaps I should have mentioned it earlier.
-/
/- Lemma : no-side-bar
There is a way through the following maze.
-/
example (A B C D E F G H I J K L : Prop)
(f1 : A β B) (f2 : B β... |
9aedd3c4aab3d853ce56577b174edec17622caae | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/abelian/functor_category.lean | 572d3f420b557ef214e899e89f5fedf6c46e67ff | [
"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 | 3,604 | lean | /-
Copyright (c) 2022 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.abelian.basic
import category_theory.preadditive.functor_category
import category_theory.limits.shapes.functor_category
import category_theory.... |
36a3527f96ca94c143757dc5063d657654e843b8 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /src/tests/shell/file2.lean | 26434a4a91520ede10ac632e84c4fce1c74f2f50 | [
"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 | 213 | lean | import data.nat
check nat
check nat.add_zero
check nat.zero_add
-- check finset
open nat
example (a b : nat) : a = 0 β b = 0 β a = b :=
assume h1 h2, eq.subst (eq.symm h1) (eq.subst (eq.symm h2) (eq.refl 0))
|
789033ff08f0278ec60663ce0e4ec5f95687a0d2 | c45b34bfd44d8607a2e8762c926e3cfaa7436201 | /uexp/src/uexp/rules/pushSemiJoinPastJoinRuleLeft.lean | 75c2c6135ddc72f04a2e9b32badc690c6e12e39f | [
"BSD-2-Clause"
] | permissive | Shamrock-Frost/Cosette | b477c442c07e45082348a145f19ebb35a7f29392 | 24cbc4adebf627f13f5eac878f04ffa20d1209af | refs/heads/master | 1,619,721,304,969 | 1,526,082,841,000 | 1,526,082,841,000 | 121,695,605 | 1 | 0 | null | 1,518,737,210,000 | 1,518,737,210,000 | null | UTF-8 | Lean | false | false | 1,869 | lean | import ..sql
import ..tactics
import ..u_semiring
import ..extra_constants
import ..ucongr
import ..TDP
open Expr
open Proj
open Pred
open SQL
open tree
notation `int` := datatypes.int
definition rule:
forall ( Ξ scm_dept scm_emp: Schema) (rel_dept: relation scm_dept) (rel_emp: relation scm_emp) (dept_deptno ... |
cba7805c7dfe74547b1a0439ba61f2e138129f93 | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/data/set/pairwise.lean | 23da1bf6d3fa9d18d57aa80840f62d004f17272f | [
"Apache-2.0"
] | permissive | ayush1801/mathlib | 78949b9f789f488148142221606bf15c02b960d2 | ce164e28f262acbb3de6281b3b03660a9f744e3c | refs/heads/master | 1,692,886,907,941 | 1,635,270,866,000 | 1,635,270,866,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,787 | lean | /-
Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl
-/
import data.set.lattice
import tactic.wlog
/-!
# Relations holding pairwise
This file defines pairwise relations and pairwise disjoint sets.
## Main declarations
... |
e2f04d5b7ab929d7760c4e882e80deb8faebc54a | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/order/boolean_algebra.lean | 5799ca91c3a9b6ff27f51b6bf9c60beb5a275c7e | [
"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 | 37,834 | lean | /-
Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl, Bryan Gin-ge Chen
-/
import order.bounded_order
/-!
# (Generalized) Boolean algebras
A Boolean algebra is a bounded distributive lattice with a complement operator. Bo... |
adfccffc82c29af0b428ee406a1e1eeaecf522ef | f7315930643edc12e76c229a742d5446dad77097 | /library/data/int/basic.lean | c393a6095cb7e40f3d787aedca94decbf6ff5f1f | [
"Apache-2.0"
] | permissive | bmalehorn/lean | 8f77b762a76c59afff7b7403f9eb5fc2c3ce70c1 | 53653c352643751c4b62ff63ec5e555f11dae8eb | refs/heads/master | 1,610,945,684,489 | 1,429,681,220,000 | 1,429,681,449,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 35,357 | lean | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: int.basic
Authors: Floris van Doorn, Jeremy Avigad
The integers, with addition, multiplication, and subtraction. The representation of the integers is
chosen to compute efficiently.... |
ac789ac0d366a5e3fdcfeb9db39ee95b8ef3a907 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/ring_theory/ore_localization/basic.lean | 0a968d6ae647e1410b2055ea2d12df1c862e6895 | [
"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 | 33,711 | lean | /-
Copyright (c) 2022 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer, Kevin Klinge
-/
import group_theory.monoid_localization
import ring_theory.non_zero_divisors
import ring_theory.ore_localization.ore_set
import tactic.noncomm_ring
... |
e524797fb2d0d0a10a4e2031a785447f077a624c | 4b846d8dabdc64e7ea03552bad8f7fa74763fc67 | /tests/lean/run/basic_monitor2.lean | 2970a109540e19cfb84a7a032840c3c02b4d35fa | [
"Apache-2.0"
] | permissive | pacchiano/lean | 9324b33f3ac3b5c5647285160f9f6ea8d0d767dc | fdadada3a970377a6df8afcd629a6f2eab6e84e8 | refs/heads/master | 1,611,357,380,399 | 1,489,870,101,000 | 1,489,870,101,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 878 | lean | meta def get_file (fn : name) : vm format :=
do {
d β vm.get_decl fn,
some n β return (vm_decl.olean d) | failure,
return (to_fmt n)
}
<|>
return (to_fmt "<curr file>")
meta def pos_info (fn : name) : vm format :=
do {
d β vm.get_decl fn,
some pos β return (vm_decl.pos d) | failure,
file β get_f... |
b3c693e005ca2ecfa1189fbdbbb9ee6feb3c17d7 | 26ac254ecb57ffcb886ff709cf018390161a9225 | /src/algebra/group/prod.lean | 3f51ede624513296899cb3cccd28430053246ee7 | [
"Apache-2.0"
] | permissive | eric-wieser/mathlib | 42842584f584359bbe1fc8b88b3ff937c8acd72d | d0df6b81cd0920ad569158c06a3fd5abb9e63301 | refs/heads/master | 1,669,546,404,255 | 1,595,254,668,000 | 1,595,254,668,000 | 281,173,504 | 0 | 0 | Apache-2.0 | 1,595,263,582,000 | 1,595,263,581,000 | null | UTF-8 | Lean | false | false | 8,949 | 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 algebra.group_with_zero
import data.prod
/-!
# Monoid, group etc structures on `M Γ N`
In this file w... |
8cb3e4173626afb2aca6cc13ab343e9b46fb9ecb | 6094e25ea0b7699e642463b48e51b2ead6ddc23f | /hott/init/logic.hlean | 3f28fff11c4b1ed5aedb9e24c96b605e3b7f9fd0 | [
"Apache-2.0"
] | permissive | gbaz/lean | a7835c4e3006fbbb079e8f8ffe18aacc45adebfb | a501c308be3acaa50a2c0610ce2e0d71becf8032 | refs/heads/master | 1,611,198,791,433 | 1,451,339,111,000 | 1,451,339,111,000 | 48,713,797 | 0 | 0 | null | 1,451,338,939,000 | 1,451,338,939,000 | null | UTF-8 | Lean | false | false | 24,238 | hlean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Floris van Doorn
-/
prelude
import init.reserved_notation
open unit
definition id [reducible] [unfold_full] {A : Type} (a : A) : A :=
a
/- not -/
definiti... |
b89423df4f2d1e0b4cb40008633a0026e63458f0 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/algebra/category/Group/biproducts.lean | f26c732b28e00773fc56a792a584f671b29639fd | [
"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 | 3,003 | 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 algebra.category.Group.basic
import algebra.category.Group.preadditive
import category_theory.limits.shapes.biproducts
import algebra.group.pi
/-!
# The categ... |
ad07f0c9b170737b91865cd1166e4a21a04126db | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/linear_algebra/coevaluation.lean | 31abc9c6cc8e8e24db612ab2890c7ab308445a97 | [
"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 | 4,267 | lean | /-
Copyright (c) 2021 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer
-/
import linear_algebra.contraction
import linear_algebra.finite_dimensional
import linear_algebra.dual
/-!
# The coevaluation map on finite dimensional vector spa... |
c6207bff0f50af118dbcb66ecdcf411094e43f6f | d1a52c3f208fa42c41df8278c3d280f075eb020c | /stage0/src/Init/Control/StateCps.lean | 6a1c39c8356ab7bb6a4743ece3b90ab09c39d82c | [
"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 | 3,670 | 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
-/
prelude
import Init.Control.Lawful
/-
The State monad transformer using CPS style.
-/
def StateCpsT (Ο : Type u) (m : Type u β Type v) (Ξ± : Type u) := (Ξ΄ ... |
7e46bbc9e32437fa97bed1189e355bd38da54e5d | d436468d80b739ba7e06843c4d0d2070e43448e5 | /src/group_theory/coset.lean | db393663f2eb73b6d5ae24113c53ca803f063eb3 | [
"Apache-2.0"
] | permissive | roro47/mathlib | 761fdc002aef92f77818f3fef06bf6ec6fc1a28e | 80aa7d52537571a2ca62a3fdf71c9533a09422cf | refs/heads/master | 1,599,656,410,625 | 1,573,649,488,000 | 1,573,649,488,000 | 221,452,951 | 0 | 0 | Apache-2.0 | 1,573,647,693,000 | 1,573,647,692,000 | null | UTF-8 | Lean | false | false | 9,159 | lean | /-
Copyright (c) 2018 Mitchell Rowett. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Rowett, Scott Morrison
-/
import group_theory.subgroup data.equiv.basic data.quot
open set function
variable {Ξ± : Type*}
@[to_additive left_add_coset]
def left_coset [has_m... |
7183d680461eefa4124347afe1ecdeaf0d12328d | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/category_theory/limits/constructions/limits_of_products_and_equalizers.lean | 246e4e9e5e4eadfe6a578155a71c98e69610a705 | [
"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 | 13,105 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Scott Morrison
-/
import category_theory.limits.shapes.equalizers
import category_theory.limits.shapes.finite_products
import category_theory.limits.preserves.shapes.produc... |
46b4533462b8d1b0716ec01034ea0960c8b369ab | a726f88081e44db9edfd14d32cfe9c4393ee56a4 | /src/game/world9/level2.lean | ff38d7739c83936b7d95c57ab3e05267971f9fc3 | [] | no_license | b-mehta/natural_number_game | 80451bf10277adc89a55dbe8581692c36d822462 | 9faf799d0ab48ecbc89b3d70babb65ba64beee3b | refs/heads/master | 1,598,525,389,186 | 1,573,516,674,000 | 1,573,516,674,000 | 217,339,684 | 0 | 0 | null | 1,571,933,100,000 | 1,571,933,099,000 | null | UTF-8 | Lean | false | false | 555 | lean | import game.world9.level1 -- hide
namespace mynat -- hide
/-
# Advanced Multiplication World
## Level 2: `eq_zero_or_eq_zero_of_mul_eq_zero`
A variant on the previous level.
-/
/- Theorem
If $a * b = 0$, then at least one of $a$ or $b$ is equal to zero.
-/
theorem eq_zero_or_eq_zero_of_mul_eq_zero (a b : mynat) (h ... |
a76c77c32f1461ccaf2af5a2a1f6d0f43f10d624 | e0f9ba56b7fedc16ef8697f6caeef5898b435143 | /src/tactic/linarith.lean | e1c1892d10ec886eb9d8f1aac3a06cb6f78fcb57 | [
"Apache-2.0"
] | permissive | anrddh/mathlib | 6a374da53c7e3a35cb0298b0cd67824efef362b4 | a4266a01d2dcb10de19369307c986d038c7bb6a6 | refs/heads/master | 1,656,710,827,909 | 1,589,560,456,000 | 1,589,560,456,000 | 264,271,800 | 0 | 0 | Apache-2.0 | 1,589,568,062,000 | 1,589,568,061,000 | null | UTF-8 | Lean | false | false | 35,448 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Robert Y. Lewis
-/
import tactic.ring
import data.tree
/-!
# `linarith`
A tactic for discharging linear arithmetic goals using Fourier-Motzkin elimination.
`linarith` is (in princip... |
bf6b5ce5ca910efba848166571b06b4bd63f12a3 | 205f0fc16279a69ea36e9fd158e3a97b06834ce2 | /src/01_Equality/04_propositions_as_types.lean | 5c322b7cf31b47d8075874093770cf25d0cd295e | [] | no_license | kevinsullivan/cs-dm-lean | b21d3ca1a9b2a0751ba13fcb4e7b258010a5d124 | a06a94e98be77170ca1df486c8189338b16cf6c6 | refs/heads/master | 1,585,948,743,595 | 1,544,339,346,000 | 1,544,339,346,000 | 155,570,767 | 1 | 3 | null | 1,541,540,372,000 | 1,540,995,993,000 | Lean | UTF-8 | Lean | false | false | 6,749 | lean | /-
Wait! Lean is telling us that: eq.refl 0 : 0 = 0.
Putting parenthesis in can make it easier to read:
(eq.refl 0) : (0 = 0). We've so far read this as
saying that (eq.refl 0) is a proof of 0 = 0. But
the observant reader will see that it looks just
like a type judgment as well. It looks like it's
saying that (eq.... |
cd64044c169a9d69d48dbf14d98aa558e6aeb97c | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/analysis/calculus/mean_value.lean | 3a9e0bc673cae6c880260ea90b2496cceb248600 | [
"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 | 74,763 | lean | /-
Copyright (c) 2019 SΓ©bastien GouΓ«zel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: SΓ©bastien GouΓ«zel, Yury Kudryashov
-/
import analysis.calculus.local_extr
import analysis.convex.slope
import analysis.convex.topology
import data.complex.is_R_or_C
/-!
# The mean ... |
4d17ac359513957e9d264a1f4c926caee7177832 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/808.lean | 0faaab79524a17923f13d4ba922b6a7b05828946 | [
"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 | 193 | lean | notation 1 := eq
postfix `x`:(max+1) := eq
postfix [priority 1] `y`:max := eq
attribute [instance, priority 1]
definition foo : inhabited nat := inhabited.mk nat.zero
definition bar := @eq
|
1e14d4a079cfdab1e6ba44fcc73caced1ce49b47 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/category_theory/limits/constructions/binary_products.lean | c9be3227021adad77c6bfe16bba6bbbada904080 | [
"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 | 6,588 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Andrew Yang
-/
import category_theory.limits.shapes.terminal
import category_theory.limits.shapes.pullbacks
import category_theory.limits.shapes.binary_products
/-!
# Cons... |
bd39cf51333521f04f1bfe0da32ff0b2181ebba3 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/omega/nat/sub_elim.lean | 165ac5f8b2461b6ad498bac63cbd91e33f670b94 | [] | 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 | 2,982 | lean | /-
Copyright (c) 2019 Seul Baek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Seul Baek
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.tactic.omega.nat.form
import Mathlib.PostPort
namespace Mathlib
/-
Subtraction elimination for linea... |
71cbbe6c373d3d3a517a6651aa1a54ecb71eb912 | e030b0259b777fedcdf73dd966f3f1556d392178 | /library/init/native/default.lean | 6a19fe0ac88ca74830580175ec3fe9fcb754e2c3 | [
"Apache-2.0"
] | permissive | fgdorais/lean | 17b46a095b70b21fa0790ce74876658dc5faca06 | c3b7c54d7cca7aaa25328f0a5660b6b75fe26055 | refs/heads/master | 1,611,523,590,686 | 1,484,412,902,000 | 1,484,412,902,000 | 38,489,734 | 0 | 0 | null | 1,435,923,380,000 | 1,435,923,379,000 | null | UTF-8 | Lean | false | false | 23,820 | lean | /-
Copyright (c) 2016 Jared Roesch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jared Roesch
-/
prelude
import init.meta.format
import init.meta.expr
import init.category.state
import init.data.string
import init.data.list.instances
import init.native.ir
import in... |
8344ccc102d007d3704548e1256fed42ea041e42 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/analysis/normed_space/dual.lean | a58102cd917d4ed462a30b119954059241883eb6 | [
"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 | 4,210 | lean | /-
Copyright (c) 2020 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import analysis.normed_space.hahn_banach
/-!
# The topological dual of a normed space
In this file we define the topological dual `normed_space.dual` of a normed ... |
603c18fd0ea6860791555864322bf9397972841f | b3c7090f393c11bd47c82d2f8bb4edf8213173f5 | /src/equivalence.lean | ed38d13a5cafa13c75fa8d9eb51c4512a5a89b30 | [] | no_license | ImperialCollegeLondon/lean-groups | 964b197478f0313d826073576a3e0ae8b166a584 | 9a82d2a66ef7f549107fcb4e1504d734c43ebb33 | refs/heads/master | 1,592,371,184,330 | 1,567,197,270,000 | 1,567,197,270,000 | 195,810,480 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,384 | lean | import data.quot -- equivalence relations and equivalence classes
import tactic.interactive -- for "choose" tactic
-- Sian's definition of an equivalence relation on X corresponding to a function f : X β Y
-- X and Y and f are fixed once and for all in this story, so let's make them parameters
-- in a section.
secti... |
eea58d8cdf0846a113b36896f36176fd93ddd3c0 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/multiset/sort.lean | 210190a1dae072cf8c6154e1aafbb1204b5616d1 | [] | 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 | 2,633 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.list.sort
import Mathlib.data.multiset.basic
import Mathlib.data.string.basic
import Ma... |
71a8ffd4acf95b032441ec19c43965b714c1980e | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/analysis/normed_space/completion.lean | 11b159a3fcf99ce747e2dfd7b08993beb00309f7 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 3,722 | lean | /-
Copyright (c) 2022 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import analysis.normed.group.completion
import analysis.normed_space.operator_norm
import topology.algebra.uniform_ring
/-!
# Normed space structure on the c... |
aeab3439dbc871ed55ebb39f07a6384252df440a | 7b9ff28673cd3dd7dd3dcfe2ab8449f9244fe05a | /src/rob/type_classes.lean | ebf5e8a26e1afff9be84815262ae49c432951cbb | [] | no_license | jesse-michael-han/hanoi-lean-2019 | ea2f0e04f81093373c48447065765a964ee82262 | a5a9f368e394d563bfcc13e3773863924505b1ce | refs/heads/master | 1,591,320,223,247 | 1,561,022,886,000 | 1,561,022,886,000 | 192,264,820 | 1 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 2,478 | lean | import topology.metric_space.basic
namespace playground
class my_add_semigroup (Ξ± : Type) :=
(add : Ξ± β Ξ± β Ξ±)
(add_assoc' : β a b c, add (add a b) c = add a (add b c))
(add_comm' : β a b, add a b = add b a)
section
open my_add_semigroup
theorem comm_assoc' {Ξ± : Type} [my_add_semigroup Ξ±] (a b c : Ξ±) :
add (add a... |
79276dca40cd8acff02b533a58e4be7fc8fb457a | 5412d79aa1dc0b521605c38bef9f0d4557b5a29d | /stage0/src/Lean/Compiler/IR/Basic.lean | 8b258f49b95bc960f98a92ebcafe91db326accd8 | [
"Apache-2.0"
] | permissive | smunix/lean4 | a450ec0927dc1c74816a1bf2818bf8600c9fc9bf | 3407202436c141e3243eafbecb4b8720599b970a | refs/heads/master | 1,676,334,875,188 | 1,610,128,510,000 | 1,610,128,521,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 25,751 | 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.Data.KVMap
import Lean.Data.Name
import Lean.Data.Format
import Lean.Compiler.ExternAttr
/-
Implements (extended) Ξ»Pure and Ξ»Rc proposed in the ... |
e2880a3fc207cba5fe5734130d860ee8798d321b | acc85b4be2c618b11fc7cb3005521ae6858a8d07 | /data/set/finite.lean | c307125247ed25f003e400f735c5e46a24c9a2c6 | [
"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 | 2,833 | lean | /-
Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl
Finite sets -- assuming a classical logic.
-/
import data.set.lattice data.set.prod data.nat.basic
noncomputable theory
universes u v w
variables {Ξ± : Type u} {Ξ² : Typ... |
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