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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
2478b63b9f4e6b5f9402df9f3f94f95b52a1ca9b | 367134ba5a65885e863bdc4507601606690974c1 | /src/ring_theory/subsemiring.lean | 2820b7c220d3b8154c428dc9c97aaed427c42bc5 | [
"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 | 27,013 | lean | /-
Copyright (c) 2020 Yury Kudryashov All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import algebra.ring.prod
import group_theory.submonoid
import data.equiv.ring
/-!
# Bundled subsemirings
We define bundled subsemirings and some standard construc... |
03a8bd3bbf4887a34558177fbb160e81c8a49f4f | 94637389e03c919023691dcd05bd4411b1034aa5 | /src/zzz_junk/has_monoid/monoid.lean | 6361cc1e2f878af9b913f88a8648bedca229fbf2 | [] | no_license | kevinsullivan/complogic-s21 | 7c4eef2105abad899e46502270d9829d913e8afc | 99039501b770248c8ceb39890be5dfe129dc1082 | refs/heads/master | 1,682,985,669,944 | 1,621,126,241,000 | 1,621,126,241,000 | 335,706,272 | 0 | 38 | null | 1,618,325,669,000 | 1,612,374,118,000 | Lean | UTF-8 | Lean | false | false | 664 | lean | import ..semigroup.semigroup
import ..has_mul.has_mul
import ..has_one.has_one
/-
A monoid is a semigroup
with an element 1
such that 1 * a = a * 1 = a.
-/
namespace hidden
universe u
@[class]
structure has_monoid (α : Type u) extends (hidden.semigroup α), (hidden.has_one α) : Type u
-- mul -- from se... |
025f917f26beada05dda5ae80b1ad28ece3a0251 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/topology/metric_space/algebra.lean | 3ed29eb490197a6b4baa81318c9809c4fba3022b | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 7,934 | lean | /-
Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import topology.algebra.mul_action
import topology.metric_space.lipschitz
/-!
# Compatibility of algebraic operations with metric space structures
In this file we... |
ce3aeadb21f04b44cf68901b3fafe4dbb211c239 | 98000ddc36f1ec26addea0df1853c69fa0e71d67 | /examples.lean | 2aa2f426dc48b6096b9f565f930ed2ce16946ed3 | [] | no_license | SCRK16/Intuitionism | 50b7b5ed780a75c4ff1339c3d36f1133b8acdfe3 | a3d9920ae056b39a66e37d1d0e03d246bca1e961 | refs/heads/master | 1,670,199,869,808 | 1,598,045,061,000 | 1,598,045,061,000 | 254,657,585 | 1 | 0 | null | 1,590,754,909,000 | 1,586,529,604,000 | Lean | UTF-8 | Lean | false | false | 1,408 | lean | import ..Intuitionism.reckless
example (P Q : Prop) : (P ∨ Q) → ¬(¬P ∧ ¬Q) :=
begin
intros h₁ h₂,
cases h₁ with hp hq,
{
exact h₂.elim_left hp,
},
{
exact h₂.elim_right hq,
}
end
lemma LEM_equiv_double_not : (∀ P : Prop, P ∨ ¬P) ↔ ∀ Q : Prop, ¬¬Q → Q :=
begin
split,
{
... |
a4d2853773dc559621523326e35e114fdfa703e8 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/analysis/calculus/taylor.lean | 0ad33d0d2830954829946f7e08c9c2666c3c160d | [
"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 | 18,587 | lean | /-
Copyright (c) 2022 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
import analysis.calculus.iterated_deriv
import analysis.calculus.mean_value
import data.polynomial.module
/-!
# Taylor's theorem
This file defines the Taylor polynomial o... |
6f813885a5863967a7cdc8f2c0870a2434bc038b | ba4794a0deca1d2aaa68914cd285d77880907b5c | /src/game/world6/level9.lean | c0ce2355c05368e019bbdc9185b9a1a74e7a82cc | [
"Apache-2.0"
] | permissive | ChrisHughes24/natural_number_game | c7c00aa1f6a95004286fd456ed13cf6e113159ce | 9d09925424da9f6275e6cfe427c8bcf12bb0944f | refs/heads/master | 1,600,715,773,528 | 1,573,910,462,000 | 1,573,910,462,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,007 | lean | /-
# Proposition world.
## Level 9: a big maze.
Lean's "congruence closure" tactic `cc` is good at mazes. 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 → B) (f2 : B → E) (f3 : E → D) (f4 : D → A) ... |
959f42359f9688f401f2cb98393bab4e8d9f5df0 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/lake/examples/reverse-ffi/lib/lakefile.lean | 8c56421b938f2f02316ff4ece500b759ba709cba | [
"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 | 128 | lean | import Lake
open System Lake DSL
package rffi
@[default_target]
lean_lib RFFI where
defaultFacets := #[LeanLib.sharedFacet]
|
881a1448d7ac5d46a427fb633a8aa471c41fb658 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/measure_theory/group/arithmetic.lean | a2ede97a8e05a29d5b25614cb2f3c5080d1b9b75 | [
"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 | 33,099 | lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import measure_theory.measure.ae_measurable
/-!
# Typeclasses for measurability of operations
In this file we define classes `has_measurable_mul` etc and prove do... |
d51aca746ec94841525730759c749f76c8f36cd0 | 0ec6b5eb2131429a4464b8e6c6f09897abba3de1 | /src/algebra_tensor.lean | 59e50183c4796218605ba93b184614e9bcdd00e5 | [] | no_license | kckennylau/local-langlands-abelian | ba1b86e9d956778cd28ac900ffec02b0f0ba172a | ee22666898357dab800a0432214a22c519ed26a9 | refs/heads/master | 1,584,671,060,846 | 1,545,151,246,000 | 1,545,151,246,000 | 137,111,892 | 8 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,086 | lean | import .algebra
noncomputable theory
set_option eqn_compiler.zeta true
universes u v w u₁ v₁ w₁
infix ` ⊗ `:100 := tensor_product
variables {R : Type u} {A : Type v} {B : Type w} {C : Type u₁} {D : Type v₁}
variables [comm_ring R] [comm_ring A] [comm_ring B] [comm_ring C] [comm_ring D]
variables (iA : al... |
4f4b55755cb2a65160bc82c9965fc4d8be4aa618 | bb31430994044506fa42fd667e2d556327e18dfe | /src/group_theory/submonoid/basic.lean | a503eca7573f67251c2948fd16a4350d1ba9aac6 | [
"Apache-2.0"
] | permissive | sgouezel/mathlib | 0cb4e5335a2ba189fa7af96d83a377f83270e503 | 00638177efd1b2534fc5269363ebf42a7871df9a | refs/heads/master | 1,674,527,483,042 | 1,673,665,568,000 | 1,673,665,568,000 | 119,598,202 | 0 | 0 | null | 1,517,348,647,000 | 1,517,348,646,000 | null | UTF-8 | Lean | false | false | 22,069 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard,
Amelia Livingston, Yury Kudryashov
-/
import algebra.hom.group -- Only needed for notation
import algebra.gro... |
333a796b0fb95fe8a294a17f6e81824cd6701ddf | 8e6cad62ec62c6c348e5faaa3c3f2079012bdd69 | /src/data/complex/is_R_or_C.lean | cbabb05343039a56443b16a4c33a4167d08ed23e | [
"Apache-2.0"
] | permissive | benjamindavidson/mathlib | 8cc81c865aa8e7cf4462245f58d35ae9a56b150d | fad44b9f670670d87c8e25ff9cdf63af87ad731e | refs/heads/master | 1,679,545,578,362 | 1,615,343,014,000 | 1,615,343,014,000 | 312,926,983 | 0 | 0 | Apache-2.0 | 1,615,360,301,000 | 1,605,399,418,000 | Lean | UTF-8 | Lean | false | false | 28,842 | lean | /-
Copyright (c) 2020 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import data.real.sqrt
import field_theory.tower
import analysis.normed_space.finite_dimension
/-!
# `is_R_or_C`: a typeclass for ℝ or ℂ
This file defines the type... |
596976dc55aca05070728af2db8ca73d1efebb39 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/group_theory/group_action/group.lean | 02971812f57845f0427542d10694697d01baba87 | [
"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 | 11,659 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import algebra.hom.aut
import group_theory.group_action.units
/-!
# Group actions applied to various types of group
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any cha... |
71846aba3615a0c6e94220328fe43b73e3c66ad4 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/W/cardinal.lean | 2d2db0f54efc2212588f24e58211eefffd07cb6c | [
"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 | 2,655 | 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.basic
import set_theory.cardinal.ordinal
/-!
# Cardinality of W-types
This file proves some theorems about the cardinality of W-types. The main result is
... |
0197eb150234394214f9b83222605114e76bf40d | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/algebra/module/pi.lean | da7bf5be5c6715cd4a4df2cc50e0eaeaa3a029a9 | [
"Apache-2.0"
] | permissive | ilitzroth/mathlib | ea647e67f1fdfd19a0f7bdc5504e8acec6180011 | 5254ef14e3465f6504306132fe3ba9cec9ffff16 | refs/heads/master | 1,680,086,661,182 | 1,617,715,647,000 | 1,617,715,647,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,456 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot
-/
import algebra.module.basic
import algebra.ring.pi
/-!
# Pi instances for module and multiplicative actions
This file defines instances for module, mul_ac... |
c53b0a7bcec9b3f533d577cb157edae97f4896ae | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/list/range.lean | db50721f434e165d9a20a050478d3d8cb27a5d46 | [
"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 | 12,286 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kenny Lau, Scott Morrison
-/
import data.list.chain
import data.list.nodup
import data.list.of_fn
import data.list.zip
/-!
# Ranges of naturals as lists
This file sho... |
f00634488f69a791ca03a1e069fca40d2b1c4f29 | 7cdf3413c097e5d36492d12cdd07030eb991d394 | /world_experiments/world7/level15.lean | b79e46240d4fc04daf559a9d704a8605aff0aab1 | [] | 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 | 527 | lean | import mynat.definition -- hide
import mynat.add -- hide
import game.world2.level14 -- hide
namespace mynat -- hide
/-
# World 2 -- Addition World
## Level 15 -- `eq_zero_of_add_right_eq_self`
We have
* `succ_eq_add_one (n : mynat) : succ n = n + 1`
but sometimes the other way is also convenient.
-/
/- Theorem... |
441e7085f0c82bb3451ac175d3dcd0f47c0e1205 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/data/matrix/basic.lean | d44e796938c247586708f06a4a6a93b35403661e | [
"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 | 80,215 | lean | /-
Copyright (c) 2018 Ellen Arlt. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ellen Arlt, Blair Shi, Sean Leather, Mario Carneiro, Johan Commelin, Lu-Ming Zhang
-/
import algebra.algebra.basic
import algebra.big_operators.pi
import algebra.big_operators.ring
import ... |
28c65dea1e159447851419da6071568466efa4ea | 94e33a31faa76775069b071adea97e86e218a8ee | /src/linear_algebra/special_linear_group.lean | 8db2dd55e160b252dec4c304245be10b15aee51e | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 8,537 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import linear_algebra.matrix.adjugate
import linear_algebra.matrix.to_lin
/-!
# The Special Linear group $SL(n, R)$
This file defines the elements of the Special Linear g... |
87f299118e478225e1170a3eb0a00c6a9227e6b0 | 500f65bb93c499cd35c3254d894d762208cae042 | /src/topology/uniform_space/cauchy.lean | 7058b0c845db0d2d23e070f58bb86b9409b11c8a | [
"Apache-2.0"
] | permissive | PatrickMassot/mathlib | c39dc0ff18bbde42f1c93a1642f6e429adad538c | 45df75b3c9da159fe3192fa7f769dfbec0bd6bda | refs/heads/master | 1,623,168,646,390 | 1,566,940,765,000 | 1,566,940,765,000 | 115,220,590 | 0 | 1 | null | 1,514,061,524,000 | 1,514,061,524,000 | null | UTF-8 | Lean | false | false | 16,554 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
Theory of Cauchy filters in uniform spaces. Complete uniform spaces. Totally bounded subsets.
-/
import topology.uniform_space.basic
open filter topol... |
42a872b27d039dbdfccf84c2c357cd6e77d44a7d | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /library/data/finset/comb.lean | e03d3889d9841ecec267783af93b0e6ccfc3288b | [
"Apache-2.0"
] | permissive | davidmueller13/lean | 65a3ed141b4088cd0a268e4de80eb6778b21a0e9 | c626e2e3c6f3771e07c32e82ee5b9e030de5b050 | refs/heads/master | 1,611,278,313,401 | 1,444,021,177,000 | 1,444,021,177,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 18,886 | 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, Jeremy Avigad
Combinators for finite sets.
-/
import data.finset.basic logic.identities
open list quot subtype decidable perm function
namespace finset
/- i... |
a340b10a8f9557ab66371ae568edc465ff6a7e72 | 592f865bb4e2e537ae3552cb83c32fb99c8d4c68 | /src/to_qShannon_theory_maybe/state.lean | fa723cd550326f4dbb758824bae327eaf35f501e | [] | no_license | BassemSafieldeen/Entropy_and_reversible_catalysis | 250dbb9446690ab89d89a6a512c8f888e09e8596 | 5dd6ee062f61e26bbcf254477e3e24aa3fc489af | refs/heads/master | 1,678,747,213,156 | 1,615,540,586,000 | 1,615,540,586,000 | 322,216,014 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,427 | lean | import linear_algebra.eigenspace
import to_mathlib_maybe.Hilbert_space
open_locale tensor_product big_operators
variables {ℋ : Type} [complex_hilbert_space ℋ]
/--
A quantum state is a linear map from a Hilbert space to itself --
a.k.a., a linear operator, a.k.a, a module endomorphism -- with trace one and
only no... |
202aaff2dd12e533683ef7ecb839aa0db11e78b0 | e0f9ba56b7fedc16ef8697f6caeef5898b435143 | /src/measure_theory/l1_space.lean | a3826e109b7a74ce85cc0945c929fa7280b058cb | [
"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 | 28,704 | lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
-/
import measure_theory.ae_eq_fun
/-!
# Integrable functions and `L¹` space
In the first part of this file, the predicate `integrable` is defined and basic properties o... |
c4151eb9869502b0df4bbb35aad2edb8e25856ba | 947b78d97130d56365ae2ec264df196ce769371a | /tests/lean/run/borrowBug.lean | 6528df998996610c607be9656644d0e93c71a05f | [
"Apache-2.0"
] | permissive | shyamalschandra/lean4 | 27044812be8698f0c79147615b1d5090b9f4b037 | 6e7a883b21eaf62831e8111b251dc9b18f40e604 | refs/heads/master | 1,671,417,126,371 | 1,601,859,995,000 | 1,601,860,020,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 373 | lean | new_frontend
@[noinline] def g (x : Nat) : Nat × Nat := (x, x)
@[noinline] def p (x : Nat) : Bool := x > 10
set_option trace.compiler.ir.rc true
def f (x : Nat) (y : Nat) : Bool :=
let jp (x : Nat) : Bool := -- x must be owned
p x || p (x+1);
match x with
| 0 => let z := g y; jp z.1
| _ => let z := g x; jp z.1
de... |
cc5901ee7a52747b3298726dfa8392779f5186b7 | 367134ba5a65885e863bdc4507601606690974c1 | /src/algebra/lie/submodule.lean | 769bdc77c14b509bfadf6e0088fa758e827de6c5 | [
"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 | 28,729 | lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import algebra.lie.subalgebra
import ring_theory.noetherian
/-!
# Lie submodules of a Lie algebra
In this file we define Lie submodules and Lie ideals, we construct the l... |
5b2db11455d2a80953081a6018c1e803432470df | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/logic/function/basic.lean | d76e65e62658a45d633ac9e71e6d9551a46b2ad2 | [
"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 | 27,152 | lean | /-
Copyright (c) 2016 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import logic.basic
import data.option.defs
/-!
# Miscellaneous function constructions and lemmas
-/
universes u v w
namespace function
section
var... |
3ddf7916a500c131de729a3200638f1c3cf1e427 | be30445afb85fcb2041b437059d21f9a84dff894 | /diagrams.hlean | d209884c422780196d1de4e57ab9f62bfa7b0d9a | [
"Apache-2.0"
] | permissive | EgbertRijke/GraphModel | 784efde97299c4f3cb1760369e8a260e02caafd5 | 2a473880764093dd151554a913292ed465e80e62 | refs/heads/master | 1,609,477,731,119 | 1,476,299,056,000 | 1,476,299,056,000 | 58,213,801 | 6 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,389 | hlean | import types graphmodel
open is_trunc eq sigma sigma.ops equiv is_equiv function sum graph
namespace diagram
structure ctx extends graph.ctx
structure fam (Γ : ctx) : Type :=
( pts : ctx.pts Γ → Type.{u} )
( edg : Π {i j : ctx.pts Γ}, (ctx.edg Γ i j) → pts i → pts j)
structure tm {Γ : ctx} (A : fam Γ... |
2b7453159e056948dbec9b0db985987aaca3496f | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/ring_theory/polynomial/dickson.lean | d28c781076a683202eedba1bdb58b9ddf7576a24 | [
"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 | 10,511 | lean | /-
Copyright (c) 2021 Julian Kuelshammer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Kuelshammer
-/
import ring_theory.polynomial.chebyshev
import ring_theory.localization
import data.zmod.basic
import algebra.char_p.invertible
/-!
# Dickson polynomials
... |
a84dd20255d0ea3e2f129622ae5cb56dd49f1e1c | 42610cc2e5db9c90269470365e6056df0122eaa0 | /hott/types/equiv.hlean | 725e2cfbed5f53259932bd2e7e9ea82fb4d287be | [
"Apache-2.0"
] | permissive | tomsib2001/lean | 2ab59bfaebd24a62109f800dcf4a7139ebd73858 | eb639a7d53fb40175bea5c8da86b51d14bb91f76 | refs/heads/master | 1,586,128,387,740 | 1,468,968,950,000 | 1,468,968,950,000 | 61,027,234 | 0 | 0 | null | 1,465,813,585,000 | 1,465,813,585,000 | null | UTF-8 | Lean | false | false | 11,891 | hlean | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Floris van Doorn
Ported from Coq HoTT
Theorems about the types equiv and is_equiv
-/
import .fiber .arrow arity ..prop_trunc cubical.square
open eq is_trunc sigma sigma.ops pi fibe... |
b74f3486daa452ca267bebd6191852fe337002be | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/topology/continuous_function/stone_weierstrass.lean | af6f6ce19e9e1c44212cb83c2f6b2deb0ef6adc8 | [
"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 | 19,785 | lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Heather Macbeth
-/
import topology.continuous_function.weierstrass
import analysis.complex.basic
/-!
# The Stone-Weierstrass theorem
If a subalgebra `A` of `C(X, ℝ)`,... |
c303bb7ecb87486dce42fa7db42666fd2b6b3bc4 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/order/bounds/order_iso.lean | b90ea907458e5448f521e4104b2096d8c11b8d53 | [
"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 | 2,090 | 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 Kudryashov
-/
import order.bounds.basic
import order.hom.set
/-!
# Order isomorhpisms and bounds.
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to thi... |
530ee920dce64fb9c4016b83865588d8d9019c11 | 4fa161becb8ce7378a709f5992a594764699e268 | /src/data/set/finite.lean | fa8d7c6f5bd2a81a7a809d6e6812589d9ed18de9 | [
"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 | 24,300 | 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.fintype.basic
import algebra.big_operators
/-!
# Finite sets
This file defines predicates `finite : set α → Prop` and `infinite : set α ... |
103a304faf6077f36dfdef0d67469bdae106293d | 947b78d97130d56365ae2ec264df196ce769371a | /src/Lean/Server.lean | 62f9ba41e6ce621ea9be28dbb70604fff9f8a409 | [
"Apache-2.0"
] | permissive | shyamalschandra/lean4 | 27044812be8698f0c79147615b1d5090b9f4b037 | 6e7a883b21eaf62831e8111b251dc9b18f40e604 | refs/heads/master | 1,671,417,126,371 | 1,601,859,995,000 | 1,601,860,020,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,283 | lean | /-
Copyright (c) 2020 Marc Huisinga. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Marc Huisinga, Wojciech Nawrocki
-/
import Init.System.IO
import Std.Data.RBMap
import Lean.Environment
import Lean.Server.Snapshots
import Lean.Data.Lsp
import Lean.Data.Json.FromToJ... |
3ffcf2019063a7e18c7413059fcc5c173b226591 | 0c1546a496eccfb56620165cad015f88d56190c5 | /library/init/data/prod.lean | b3deca10fe95475a6a00648279d57e3d0e50d02e | [
"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 | 850 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura, Jeremy Avigad
-/
prelude
import init.logic
universe variables u v
instance {α : Type u} {β : Type v} [inhabited α] [inhabited β] : inhabited (prod α β) :=
⟨(d... |
2cefbad90aa8330393ff8c681ebb928b0a30ec15 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/big_operators/nat_antidiagonal.lean | af55a195409c3763ca5f6568236b7744fb235a8f | [] | 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 | 2,453 | lean | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.finset.nat_antidiagonal
import Mathlib.algebra.big_operators.basic
import Mathlib.Post... |
920bf1d59183f6d57f09a9129db1dc8dd33f24f4 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/star/free.lean | fca485ba142037f0844f4b04f1ed8f81f673a012 | [
"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 | 2,365 | lean | /-
Copyright (c) 2020 Eric Weiser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Weiser
-/
import algebra.star.basic
import algebra.free_algebra
/-!
# A *-algebra structure on the free algebra.
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this fi... |
700c6876428ee58281a95eeae7b4a55d8edb3cf7 | f5f7e6fae601a5fe3cac7cc3ed353ed781d62419 | /src/tactic/interactive.lean | 8147ac85a13013c911fa6992f4791696cc829f3c | [
"Apache-2.0"
] | permissive | EdAyers/mathlib | 9ecfb2f14bd6caad748b64c9c131befbff0fb4e0 | ca5d4c1f16f9c451cf7170b10105d0051db79e1b | refs/heads/master | 1,626,189,395,845 | 1,555,284,396,000 | 1,555,284,396,000 | 144,004,030 | 0 | 0 | Apache-2.0 | 1,533,727,664,000 | 1,533,727,663,000 | null | UTF-8 | Lean | false | false | 28,446 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Simon Hudon, Sebastien Gouezel, Scott Morrison
-/
import data.dlist data.dlist.basic data.prod category.basic
tactic.basic tactic.rcases tactic.generalize_proofs
ta... |
d1b96c53aafe9fc42e5f409ce742777c91f3f1fe | 592ee40978ac7604005a4e0d35bbc4b467389241 | /Library/generated/mathscheme-lean/AdditiveUnital.lean | b0a730845e7c38fbb101b8a2e5e54b5ba8f67858 | [] | 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 | 7,394 | 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 AdditiveUnital
structure AdditiveUnital (A : Type) : Type :=
(zero : A)
(plus : (A → (A → A)))
(lunit_zero : (∀ {x : A} , (plus zero x) = x))
(run... |
2223044ec082c690d65aa14ad6a4f9c3e05bbcf8 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /test/monotonicity.lean | bbdb091a803c197d55589b2649f07a8126813b3b | [
"Apache-2.0"
] | permissive | abentkamp/mathlib | d9a75d291ec09f4637b0f30cc3880ffb07549ee5 | 5360e476391508e092b5a1e5210bd0ed22dc0755 | refs/heads/master | 1,682,382,954,948 | 1,622,106,077,000 | 1,622,106,077,000 | 149,285,665 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,581 | lean | /-
Copyright (c) 2019 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import tactic.monotonicity
import tactic.norm_num
import algebra.ordered_ring
import measure_theory.lebesgue_measure
import data.list.defs
open list tactic tactic.interact... |
f5ee64aa9d3657e86e697b31e126dc228e7e939b | 38bf3fd2bb651ab70511408fcf70e2029e2ba310 | /src/data/finset.lean | f0754f688432d4e16373f839aac7ce9a8ebaeea6 | [
"Apache-2.0"
] | permissive | JaredCorduan/mathlib | 130392594844f15dad65a9308c242551bae6cd2e | d5de80376088954d592a59326c14404f538050a1 | refs/heads/master | 1,595,862,206,333 | 1,570,816,457,000 | 1,570,816,457,000 | 209,134,499 | 0 | 0 | Apache-2.0 | 1,568,746,811,000 | 1,568,746,811,000 | null | UTF-8 | Lean | false | false | 89,279 | 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, Jeremy Avigad, Minchao Wu, Mario Carneiro
Finite sets.
-/
import logic.embedding algebra.order_functions
data.multiset data.sigma.basic data.set.lattice
op... |
3a4fa565f89de294de0fa32387d13999658fc6da | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /src/Lean/Elab/Level.lean | d487c480300d1bc6d474accc267e04d5fa9a30c8 | [
"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 | 3,296 | 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.Meta.LevelDefEq
import Lean.Elab.Exception
import Lean.Elab.Log
import Lean.Elab.AutoBound
namespace Lean.Elab.Level
structure Context where
... |
e200beffd6487a4cd54ef4c873a61cfda911e000 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /src/Lean/Meta/ForEachExpr.lean | 08f41d776ee2e4e9dc23e1654c484597ef3e634f | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | cipher1024/lean4 | 6e1f98bb58e7a92b28f5364eb38a14c8d0aae393 | 69114d3b50806264ef35b57394391c3e738a9822 | refs/heads/master | 1,642,227,983,603 | 1,642,011,696,000 | 1,642,011,696,000 | 228,607,691 | 0 | 0 | Apache-2.0 | 1,576,584,269,000 | 1,576,584,268,000 | null | UTF-8 | Lean | false | false | 2,096 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Expr
import Lean.Util.MonadCache
import Lean.Meta.Basic
namespace Lean.Meta
namespace ForEachExpr
abbrev M := MonadCacheT Expr Unit MetaM
mut... |
06934df2c7d201548f09d356aebd22626568a10c | 618003631150032a5676f229d13a079ac875ff77 | /src/tactic/lean_core_docs.lean | dbae033cfc5be7ccb50b410cb2d92b7a0062d43e | [
"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 | 22,856 | lean | /-
Copyright (c) 2020 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Bryan Gin-ge Chen, Robert Y. Lewis, Scott Morrison
-/
import tactic.doc_commands
/-!
# Core tactic documentation
This file adds the majority of the interactive tactics... |
9b7366a2a36354e2a825831060cff7ab48b7f81c | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/algebra/euclidean_domain.lean | 2c620dc21a53a1dfe154f00e2fa03f38505bf517 | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 17,980 | lean | /-
Copyright (c) 2018 Louis Carlin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Louis Carlin, Mario Carneiro
-/
import data.int.basic
import algebra.field.basic
/-!
# Euclidean domains
This file introduces Euclidean domains and provides the extended Euclidean alg... |
9a3922822b71098e9e927087e77e9fac2a32d39f | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/pkg/builtin_attr/UserAttr.lean | 28b59b34724068b78659ec1cd3359c1a1dd78b3c | [
"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 | 20 | lean | import UserAttr.Tst
|
c96ebaff73b68185192a487dcee912d4ffa5a342 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/analysis/calculus/dslope.lean | 48b5af6941003e2635fa76c263adbcda7b20d612 | [
"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 | 6,258 | lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import analysis.calculus.deriv
/-!
# Slope of a differentiable function
Given a function `f : 𝕜 → E` from a nontrivially normed field to a normed space over this... |
44050b48ba31e537651f808ea7e9d68c6a151e48 | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/order/boolean_algebra.lean | 0ae658512b673a516a0242fb204575e860a58ddb | [
"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 | 32,857 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Bryan Gin-ge Chen
-/
import order.bounded_lattice
/-!
# (Generalized) Boolean algebras
A Boolean algebra is a bounded distributive lattice with a complement operator. ... |
fc40011faaf6b0e174ef4c50818927f995965af0 | 49bd2218ae088932d847f9030c8dbff1c5607bb7 | /src/linear_algebra/basic.lean | 7012f87fff682e0e221a73fd5ff2841d60753a15 | [
"Apache-2.0"
] | permissive | FredericLeRoux/mathlib | e8f696421dd3e4edc8c7edb3369421c8463d7bac | 3645bf8fb426757e0a20af110d1fdded281d286e | refs/heads/master | 1,607,062,870,732 | 1,578,513,186,000 | 1,578,513,186,000 | 231,653,181 | 0 | 0 | Apache-2.0 | 1,578,080,327,000 | 1,578,080,326,000 | null | UTF-8 | Lean | false | false | 72,869 | 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, Kevin Buzzard
-/
import algebra.pi_instances data.finsupp data.equiv.algebra order.order_iso
/-!
# Linear algebra
This file defines the basics of lin... |
90cfcfeaebc69d7101c84b2f0de0e1d6f905e04e | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/mv_polynomial/comm_ring.lean | ec1b5b6d175388034d69d13026723791a78fdc40 | [] | 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 | 4,797 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.mv_polynomial.variables
import Mathlib.PostPort
unive... |
ce0a0fe03a0fe607654a472b294d73bc5b2748af | bb31430994044506fa42fd667e2d556327e18dfe | /src/data/set/intervals/iso_Ioo.lean | a3cfa15ccf2366410f70b5cf88130bf8d8022946 | [
"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 | 1,582 | lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import order.monotone.odd
import tactic.field_simp
/-!
# Order isomorphism between a linear ordered field and `(-1, 1)`
In this file we provide an order isomorphi... |
7fac3a4c766567d711cbefe0d7f442ef6daa4015 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/def_brec2.lean | a2f67416e51ff4c18a2d42e48cf6ac1856d5dff4 | [
"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 | 232 | lean | set_option trace.eqn_compiler true
definition fib : nat → nat
| 0 := 1
| 1 := 1
| (n+2) := fib n + fib (n+1)
example : fib 0 = 1 := rfl
example : fib 1 = 1 := rfl
example (n : nat) : fib (n+2) = fib n + fib (n+1) := rfl
|
d52e92e9b45b4540a8c1e582852d277bda624d49 | 46125763b4dbf50619e8846a1371029346f4c3db | /src/data/equiv/denumerable.lean | 035ca1a1d3986f77c2f64c1b92d9b8a7bc4c7bf7 | [
"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 | 9,052 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
Denumerable (countably infinite) types, as a typeclass extending
encodable. This is used to provide explicit encode/decode functions
from nat, where the functions are kn... |
98b8bcf6180d8a566f17db637bc71dde76029ba2 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /library/logic/examples/negative.lean | 2e8d07afeed85d712bb0e7a44a7035524afa3d62 | [
"Apache-2.0"
] | permissive | davidmueller13/lean | 65a3ed141b4088cd0a268e4de80eb6778b21a0e9 | c626e2e3c6f3771e07c32e82ee5b9e030de5b050 | refs/heads/master | 1,611,278,313,401 | 1,444,021,177,000 | 1,444,021,177,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 783 | lean | /-
This example demonstrates why allowing types such as
inductive D : Type :=
| intro : (D → D) → D
would make the system inconsistent
-/
/- If we were allowed to form the inductive type
inductive D : Type :=
| intro : (D → D) → D
we would get the following
-/
universe l
-- The new type A
axiom D : Ty... |
ac6f6abf60cbb13a09e4db330ffafcadce975887 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/autoboundIssues.lean | 95d1233f96e069c6cbf5e7bf09018259817f9886 | [
"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 | 222 | lean | example : n.succ = 1 → n = 0 := by
intros h; injection h
example (h : n.succ = 1) : n = 0 := by
injection h
opaque T : Type
opaque T.Pred : T → T → Prop
example {ρ} (hρ : ρ.Pred σ) : T.Pred ρ ρ := sorry
|
5f125416c35fcf0ab33ad0f7ba50fd83f80449e0 | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/tst8.lean | 5d32c19ef1794c7203defe41ea588c2776d51687 | [
"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 | 232 | lean | import Int
check fun (A : Type) (a : A),
let b := a
in b
variable g : forall A : Type, A -> A
definition f (A: Type) (a : A) : A :=
let b := g A a,
c := g A b
in c
print f _ 10.
print f _ (- 10).
|
e583f755a283f501ec61459990e79afc0ce3ca76 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/algebra/group/ulift.lean | 6f74e32584af4174f70d859ac26c2424cfb24b8c | [
"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 | 6,623 | 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 data.int.cast.defs
import algebra.hom.equiv
/-!
# `ulift` instances for groups and monoids
This file defines instances for group, monoid, semigroup and relat... |
19873ef03dd924a33870176eb30c9370e93c9edb | 827a8a5c2041b1d7f55e128581f583dfbd65ecf6 | /crazy_hits.hlean | 5dab3c48406e9ef1bf662cbd73cded2fa2e78042 | [
"Apache-2.0"
] | permissive | fpvandoorn/leansnippets | 6af0499f6f3fd2c07e4b580734d77b67574e7c27 | 601bafbe07e9534af76f60994d6bdf741996ef93 | refs/heads/master | 1,590,063,910,882 | 1,545,093,878,000 | 1,545,093,878,000 | 36,044,957 | 2 | 2 | null | 1,442,619,708,000 | 1,432,256,875,000 | Lean | UTF-8 | Lean | false | false | 6,220 | hlean | import homotopy.circle
open circle eq int nat prod sum equiv function is_trunc
/---------------------------------------------------------------------------------------------------
We use the Licata trick to define
HIT X :=
| b : X
| s : (S¹ → X) → X
| p : b = b
--------
this is a W-suspension X with
A = bool
B ff = em... |
d186407c2345d4c59035997df932dfa2b25e71c3 | 5d166a16ae129621cb54ca9dde86c275d7d2b483 | /library/data/buffer/parser.lean | 06b9475d014bc9bc324ff0efecfbbd750eea6000 | [
"Apache-2.0"
] | permissive | jcarlson23/lean | b00098763291397e0ac76b37a2dd96bc013bd247 | 8de88701247f54d325edd46c0eed57aeacb64baf | refs/heads/master | 1,611,571,813,719 | 1,497,020,963,000 | 1,497,021,515,000 | 93,882,536 | 1 | 0 | null | 1,497,029,896,000 | 1,497,029,896,000 | null | UTF-8 | Lean | false | false | 6,828 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner
-/
import data.buffer data.dlist
universes u v
inductive parse_result (α : Type u)
| done (pos : ℕ) (result : α) : parse_result
| fail (pos : ℕ) (expected : dlist... |
d14960301de8935bbebfc52b129d8e75c446b8cb | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/nondepArrow.lean | 739c44cd7c86d52a30351cc8dec222f00daa44ce | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 70 | lean | #check _ → _ -- second metavariable should not depend on first one
|
a3caf8799663b004d64e3ae0420fc1c37c06abec | 07c76fbd96ea1786cc6392fa834be62643cea420 | /hott/homotopy/LES_of_homotopy_groups.hlean | 4bd1cb63e0de4ad6ebba9b814b04fe7a978fe26f | [
"Apache-2.0"
] | permissive | fpvandoorn/lean2 | 5a430a153b570bf70dc8526d06f18fc000a60ad9 | 0889cf65b7b3cebfb8831b8731d89c2453dd1e9f | refs/heads/master | 1,592,036,508,364 | 1,545,093,958,000 | 1,545,093,958,000 | 75,436,854 | 0 | 0 | null | 1,480,718,780,000 | 1,480,718,780,000 | null | UTF-8 | Lean | false | false | 32,895 | 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
We define the fiber sequence of a pointed map f : X →* Y. We mostly follow the proof in section 8.4
of the book.
PART 1:
We define a sequence fiber_sequence as in ... |
bd2308b28e7e71a8a67ec2bff58adbc83ac4aa04 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/order/liminf_limsup.lean | f135e1fe1c8ed427f4dd4d689688fc1932b1ced8 | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 29,083 | lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Johannes Hölzl, Rémy Degenne
-/
import order.filter.cofinite
/-!
# liminfs and limsups of functions and filters
Defines the Liminf/Limsup of a function taking v... |
f05da301105a1076ca0983627ed28c2ce9251d0b | 4727251e0cd73359b15b664c3170e5d754078599 | /src/category_theory/graded_object.lean | 394d339fe27a8831284320a122e333a748db9914 | [
"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 | 6,806 | 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 data.int.basic
import algebra.group_power.lemmas
import category_theory.pi.basic
import category_theory.shift
import category_theory.concrete_category.basic
/... |
6d60024d11e64c43d416d0d15611a3ad69bd0117 | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /doc/demo/subst.lean | a13a42f69bde86b61e0b4e8ef42c0bc23b4ad762 | [
"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 | 229 | lean | variable q : Nat → Bool
variable f : Nat → Nat → Nat
theorem T1 (a b : Nat) (H1 : a = b) (H2 : q (f (f a a) (f a a))) : q (f (f a b) (f a a))
:= subst H2 H1
check @subst
set_option pp::implicit true
print environment 1
|
6733505344d11dbc08f94e7dc34256b285a3ed0d | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/eval_expr_partial.lean | f02925ed454865e851cd1eda4192743c11eacd88 | [
"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 | 75 | lean | open tactic
run_cmd to_expr ``(bit0 1) >>= eval_expr nat >>= tactic.trace
|
d61d0d921faf26cf2836f1dfac8639dbfc57af58 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /13_More_Tactics.org.3.lean | 01a5c70347ed7a02a96789bd06dc8447340a0695 | [] | 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 | 579 | lean | import standard
import data.finset data.nat
open finset nat
variables (A : Type) [deceqA : decidable_eq A]
include deceqA
-- BEGIN
theorem card_add_card (s₁ s₂ : finset A) : card s₁ + card s₂ = card (s₁ ∪ s₂) + card (s₁ ∩ s₂) :=
begin
induction s₂ using finset.induction with a s₂ hs₂ ih,
show card s₁ + card (∅:finset... |
c6dd042820ac9bf02d8c794560aa90654f87ce81 | 453dcd7c0d1ef170b0843a81d7d8caedc9741dce | /tests/tactics.lean | 9543b67e3bae653cc242606923ced478328ea86a | [
"Apache-2.0"
] | permissive | amswerdlow/mathlib | 9af77a1f08486d8fa059448ae2d97795bd12ec0c | 27f96e30b9c9bf518341705c99d641c38638dfd0 | refs/heads/master | 1,585,200,953,598 | 1,534,275,532,000 | 1,534,275,532,000 | 144,564,700 | 0 | 0 | null | 1,534,156,197,000 | 1,534,156,197,000 | null | UTF-8 | Lean | false | false | 15,021 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import tactic data.set.lattice data.prod
tactic.rewrite
section solve_by_elim
example {a b : Prop} (h₀ : a → b) (h₁ : a) : b :=
begin
apply_assumption,
apply_as... |
040544597a75edf488ab96914d3fd266311892ff | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/multiset/range_auto.lean | 39e879c5273378275ae8e53e81c666e06347d208 | [] | 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 | 1,130 | lean | /-
Copyright (c) 2015 Microsoft Corporation. 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.multiset.basic
import Mathlib.data.list.range
import Mathlib.PostPort
namespace... |
cd6dc9596c4ea5f123b6a28d632549b3d879ecff | 618003631150032a5676f229d13a079ac875ff77 | /src/category_theory/limits/cones.lean | bc04d5549954f1b7da45c85f58fc3f88c388b336 | [
"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 | 13,269 | 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, Floris van Doorn
-/
import category_theory.const
import category_theory.yoneda
universes v u u' -- declare the `v`'s first; see `category_theory.catego... |
62a97480add94b25ca07221c9c3c7e84becc11da | 5883d9218e6f144e20eee6ca1dab8529fa1a97c0 | /src/vset.lean | a387154492cc9b3176e088f8448ab2f1aaad8c76 | [] | no_license | spl/alpha-conversion-is-easy | 0d035bc570e52a6345d4890e4d0c9e3f9b8126c1 | ed937fe85d8495daffd9412a5524c77b9fcda094 | refs/heads/master | 1,607,649,280,020 | 1,517,380,240,000 | 1,517,380,240,000 | 52,174,747 | 4 | 0 | null | 1,456,052,226,000 | 1,456,001,163,000 | Lean | UTF-8 | Lean | false | false | 2,620 | lean | /-
This files contains the `vset` type class definition and instances.
-/
import data.fresh
universes u v
namespace acie -----------------------------------------------------------------
/-
The type class `vset V S` defines the requirements for a finite set `S` of
variable names allocated from the infinite set of... |
0cca2374bcfcbfbc9e4303fe097e6eae09679f89 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/algebra/module/finite_dimension.lean | fe65f4c3628e89db1e3929bef697d70580f96a10 | [
"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 | 22,268 | lean | /-
Copyright (c) 2022 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Anatole Dedecker
-/
import analysis.locally_convex.balanced_core_hull
import linear_algebra.free_module.finite.matrix
import topology.algebra.module.simple
import ... |
d989fc097d20d46b6b84c25349cc9ad129ebff4d | 3dc4623269159d02a444fe898d33e8c7e7e9461b | /.github/workflows/project_1_a_decrire/lean-scheme-submission/src/sheaves/presheaf_on_basis.lean | 9444ec6f493417336cad742fb2defd4385c83054 | [] | no_license | Or7ando/lean | cc003e6c41048eae7c34aa6bada51c9e9add9e66 | d41169cf4e416a0d42092fb6bdc14131cee9dd15 | refs/heads/master | 1,650,600,589,722 | 1,587,262,906,000 | 1,587,262,906,000 | 255,387,160 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,505 | lean | /-
Presheaf (of types) on basis.
https://stacks.math.columbia.edu/tag/009I
-/
import topology.basic
import topology.opens
universes u v
open topological_space
-- Presheaf of types where we only define sections on basis elements.
structure presheaf_on_basis (α : Type u) [T : topological_space α]
{B : set (ope... |
b34c6af215128bb6f7a5723385b44c6c3a8f0c41 | bb31430994044506fa42fd667e2d556327e18dfe | /src/analysis/convex/function.lean | 27795ab9b7fedd1aed8a4ae124b21612d39f802b | [
"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 | 44,322 | lean | /-
Copyright (c) 2019 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, François Dupuis
-/
import analysis.convex.basic
/-!
# Convex and concave functions
This file defines convex and concave functions in vector spaces and proves ... |
2faa9ee9614203c1f92617ed90349360e5821df4 | 54deab7025df5d2df4573383df7e1e5497b7a2c2 | /topology/uniform_space.lean | 964a4a791781fb67d4a82aee1829d437c51f219c | [
"Apache-2.0"
] | permissive | HGldJ1966/mathlib | f8daac93a5b4ae805cfb0ecebac21a9ce9469009 | c5c5b504b918a6c5e91e372ee29ed754b0513e85 | refs/heads/master | 1,611,340,395,683 | 1,503,040,489,000 | 1,503,040,489,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 70,628 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Theory of uniform spaces.
Uniform spaces are a generalization of metric spaces and topological groups. Many concepts directly
generalize to uniform spaces, e.g.
* com... |
a3bae495cb4948125d871dc58738d5a12ff83210 | 1a61aba1b67cddccce19532a9596efe44be4285f | /hott/init/reserved_notation.hlean | dbf2d60f07828e7efcbe5d3371382d5fc5771c96 | [
"Apache-2.0"
] | permissive | eigengrau/lean | 07986a0f2548688c13ba36231f6cdbee82abf4c6 | f8a773be1112015e2d232661ce616d23f12874d0 | refs/heads/master | 1,610,939,198,566 | 1,441,352,386,000 | 1,441,352,494,000 | 41,903,576 | 0 | 0 | null | 1,441,352,210,000 | 1,441,352,210,000 | null | UTF-8 | Lean | false | false | 2,183 | 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
-/
prelude
import init.datatypes
notation `assume` binders `,` r:(scoped f, f) := r
notation `take` binders `,` r:(scoped f, f) := r
/-
Global declaratio... |
b8778326357f963c89b241885f99bc61ba1d8837 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/field_theory/galois.lean | f1bc6f0db964379fa9be37e1d8461d619a0ad830 | [
"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 | 18,857 | lean | /-
Copyright (c) 2020 Thomas Browning, Patrick Lutz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning, Patrick Lutz
-/
import field_theory.primitive_element
import field_theory.fixed
import group_theory.group_action.fixing_subgroup
/-!
# Galois Extensio... |
63edaf4516f10647e5b4e44ec4909a8b7225cb2c | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/convex/join.lean | 1a0ec117a51c703eb0a3d889a04fd4d08eb97f89 | [
"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 | 10,316 | lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import analysis.convex.combination
/-!
# Convex join
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
This... |
f086d0d4adf8f01e5d860cca3ae63cbcbdb52df4 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/category_theory/adjunction/basic.lean | 5bdfc3a91b088ad32d4365fbed9e669abe012f8b | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 19,646 | 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, Bhavik Mehta
-/
import category_theory.equivalence
/-!
# Adjunctions between functors
`F ⊣ G` represents the data of an adjunction between two functors
`F :... |
37c4bb18652c493578bcb0ca2d26489eea1e06a6 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /03_Propositions_and_Proofs.org.37.lean | 3045eb2f68cb2f5f41c82459e4ced7c6920f4989 | [] | 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 | 5,709 | lean | /- page 44 -/
import standard
open classical
variables p q r s : Prop
-- commutativity of ∧ and ∨
example : p ∧ q ↔ q ∧ p :=
let swap := λ (p q : Prop),
and.rec (λ (Hp : p) (Hq : q), and.intro Hq Hp)
in iff.intro (swap p q) (swap q p)
example : p ∨ q ↔ q ∨ p :=
let swap := λ (p q : Prop),
... |
cfe4af02112bf59b620e00a4af53a7425f25944f | ad3e8f15221a986da27c99f371922c0b3f5792b6 | /src/week-02/solutions/e04-trees.lean | 491bbea8093c31328a055329b489217027807447 | [] | no_license | VArtem/lean-itmo | a0e1424c8cc4c2de2ac85ab6fd4a12d80e9b85f1 | dc44cd06f9f5b984d051831b3aaa7364e64c2dc4 | refs/heads/main | 1,683,761,214,467 | 1,622,821,295,000 | 1,622,821,295,000 | 357,236,048 | 12 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,298 | lean | import data.nat.basic
import tactic
namespace tree
-- Определим двоичное дерево, где у каждой внутренней вершины ровно два ребенка
-- Такое дерево либо состоит из одной вершины - листа, либо состоит из корня, у которого есть левое и правое поддерево
inductive Tree
| Leaf : Tree
| Branch (left : Tree) (right : Tree) :... |
936843c5aeef894ae61b9cd19420bf44ed4d2616 | 2a2864136cf8f2871e86f5fd14e624e3daa8fd24 | /Monads/List.lean | 43928dc99d93e8a85d8a24f632d866f250614ca6 | [
"MIT"
] | permissive | hargoniX/lean-monads | d054ac71a351b7c86f318a477977cc166117b8ec | 2e87ca7ddf394641ea1b16bcbd8c384026d68e2f | refs/heads/main | 1,693,530,528,286 | 1,633,100,386,000 | 1,633,100,386,000 | 412,509,769 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,843 | lean | import Monads.Functor
import Monads.Applicative
import Monads.Monad
namespace Monads
inductive List (α : Type u) where
| nil : List α
| cons : α → List α → List α
deriving Repr
namespace List
section Functor
def map {α β : Type u} : (α → β) → (List α) → (List β)
| f, nil => nil
| f, ... |
5855dc61a24f4fd4d875ca8f200d40294a11caec | b147e1312077cdcfea8e6756207b3fa538982e12 | /group_theory/subgroup.lean | 43d88f2e31c30f7ae22d80730a95602ae805b6ff | [
"Apache-2.0"
] | permissive | SzJS/mathlib | 07836ee708ca27cd18347e1e11ce7dd5afb3e926 | 23a5591fca0d43ee5d49d89f6f0ee07a24a6ca29 | refs/heads/master | 1,584,980,332,064 | 1,532,063,841,000 | 1,532,063,841,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,670 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mitchell Rowett, Scott Morrison
-/
import group_theory.submonoid
open set function
variables {α : Type*} {β : Type*} {s : set α} {a a₁ a₂ b c: α}
section group
variab... |
9d71b8987411deed4720fe38eaa23f105df94320 | 9a0b1b3a653ea926b03d1495fef64da1d14b3174 | /tidy/rewrite_search/discovery/collector/bundle.lean | 7b11385ed64e1795110feae60ca4a989b0e318d8 | [
"Apache-2.0"
] | permissive | khoek/mathlib-tidy | 8623b27b4e04e7d598164e7eaf248610d58f768b | 866afa6ab597c47f1b72e8fe2b82b97fff5b980f | refs/heads/master | 1,585,598,975,772 | 1,538,659,544,000 | 1,538,659,544,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,054 | lean | import data.rat
import data.list
import tidy.lib.list
import tidy.rewrite_search.core.shared
import ..types
import .common
open tactic
open tidy.rewrite_search
namespace tidy.rewrite_search.discovery
def BUNDLE_CHUNK_SIZE := 1
-- TODO Be smarter about calculating this.
meta def score_bundle (b : bundle_ref) (samp... |
795a511c19f9a73c18236999bf0d95faddd06d44 | ca1ad81c8733787aba30f7a8d63f418508e12812 | /clfrags/src/hilbert/wr/pt_neg.lean | aed1951b410c233d2a63db667332a706a2761556 | [] | no_license | greati/hilbert-classical-fragments | 5cdbe07851e979c8a03c621a5efd4d24bbfa333a | 18a21ac6b2e890060eb4ae65752fc0245394d226 | refs/heads/master | 1,591,973,117,184 | 1,573,822,710,000 | 1,573,822,710,000 | 194,334,439 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 635 | lean | import core.connectives
import hilbert.wr.pt
import hilbert.wr.proofs.pt
namespace clfrags
namespace hilbert
namespace wr
namespace pt_neg
axiom n₁ : Π {a b : Prop}, a → neg a → b
axiom ptn₁ : Π {a b c : Prop}, neg (pt a b c) → pt (neg a) b c
axi... |
d6a6cb8425bab9ce462c6a6eba8e386773e1acb4 | a45212b1526d532e6e83c44ddca6a05795113ddc | /test/library_search/basic.lean | 8bd6ba46087662c85170345d646b8cc077060351 | [
"Apache-2.0"
] | permissive | fpvandoorn/mathlib | b21ab4068db079cbb8590b58fda9cc4bc1f35df4 | b3433a51ea8bc07c4159c1073838fc0ee9b8f227 | refs/heads/master | 1,624,791,089,608 | 1,556,715,231,000 | 1,556,715,231,000 | 165,722,980 | 5 | 0 | Apache-2.0 | 1,552,657,455,000 | 1,547,494,646,000 | Lean | UTF-8 | Lean | false | false | 1,746 | lean | import data.nat.basic
import tactic.library_search
-- Turn off trace messages so they don't pollute the test build:
set_option trace.silence_library_search true
-- For debugging purposes, we can display the list of lemmas:
-- set_option trace.library_search true
-- Check that `library_search` fails if there are no go... |
c3ae2bddd9f8ff5a0096c7d5b79ebf7c12448281 | 367134ba5a65885e863bdc4507601606690974c1 | /src/tactic/omega/main.lean | e2b6b50acfb71b58cea65539236097a28ed73cb3 | [
"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 | 5,673 | lean | /-
Copyright (c) 2019 Seul Baek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Seul Baek
-/
/-
A tactic for discharging linear integer & natural
number arithmetic goals using the Omega test.
-/
import tactic.omega.int.main
import tactic.omega.nat.main
namespace omeg... |
e2538f2b9055a963f0702719ba346f0114957baf | 07c6143268cfb72beccd1cc35735d424ebcb187b | /src/topology/instances/real.lean | 2bb2fc59628e5f2151462514a77e57b273bf8930 | [
"Apache-2.0"
] | permissive | khoek/mathlib | bc49a842910af13a3c372748310e86467d1dc766 | aa55f8b50354b3e11ba64792dcb06cccb2d8ee28 | refs/heads/master | 1,588,232,063,837 | 1,587,304,803,000 | 1,587,304,803,000 | 176,688,517 | 0 | 0 | Apache-2.0 | 1,553,070,585,000 | 1,553,070,585,000 | null | UTF-8 | Lean | false | false | 14,892 | 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... |
c72e5c6cdc62f71d4f39f24f1e8dab054ad0ab88 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/measure_theory/outer_measure.lean | 2f7a672caf5379c8abdc4fafc1cab5eaf2cd3eb4 | [
"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 | 35,360 | 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 analysis.specific_limits
import measure_theory.measurable_space
import topology.algebra.infinite_sum
/-!
# Outer Measures
An outer measure is... |
20838783f091eec8665507f5edccdeb4a81b7dac | 4bcaca5dc83d49803f72b7b5920b75b6e7d9de2d | /stage0/src/Lean/Elab/Quotation.lean | 34716cc4dd62009740b57edb79a2f8b8e4c83589 | [
"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 | 24,851 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
Elaboration of syntax quotations as terms and patterns (in `match_syntax`). See also `./Hygiene.lean` for the basic
hygiene workings and data types.
-/
import... |
56cb56ae5c7d6a2799a813ca42f316031b8d8cdb | 4727251e0cd73359b15b664c3170e5d754078599 | /src/analysis/special_functions/exp.lean | 7ab72f07801bc417fd3141f388add2b386761d64 | [
"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 | 11,534 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne
-/
import analysis.complex.basic
import data.complex.exponential
/-!
# Complex and real exponential
In this file we prove c... |
cdd2dceec7b8b1be8516bca7f6c97e12c1b032ff | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/combinatorics/simple_graph/metric.lean | 53bef525762481b384c28a09cbe536dba3249a56 | [
"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 | 3,653 | lean | /-
Copyright (c) 2022 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller, Vincent Beffara
-/
import combinatorics.simple_graph.connectivity
import data.nat.lattice
/-!
# Graph metric
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to thi... |
14cd1cf8c0a7b67acb9eb0f047fe9a283573340d | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/field_theory/intermediate_field.lean | a7bb7bfd6fbd16f6ff791468ceb8cff7eed42e0b | [
"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 | 21,916 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import field_theory.minpoly
import field_theory.subfield
import field_theory.tower
/-!
# Intermediate fields
Let `L / K` be a field extension, given as an instance `alge... |
3a58d471592b684dad0767ce6577ff5caf97362f | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/ring_theory/localization.lean | b922cbcf17c99521dff2779f971c848af82585a2 | [] | 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 | 74,815 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.equiv.ring
import Mathlib.group_theory.monoid... |
f993c7f320a9c913500e570ebd0368ba4f2d7352 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/analysis/calculus/fderiv_symmetric.lean | a05a77aae3bf498ec008813bec2ea0005f7fd9b5 | [
"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 | 19,496 | lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import analysis.calculus.deriv
import analysis.calculus.mean_value
import analysis.convex.topology
/-!
# Symmetry of the second derivative
We show that, over ... |
d56cbf56625298685b10eb906aabdeeffe00606e | c777c32c8e484e195053731103c5e52af26a25d1 | /src/category_theory/monoidal/internal/Module.lean | ba73dec00fd2aac68071f670f30668a0f6f6af39 | [
"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 | 5,945 | 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.Module.monoidal
import algebra.category.Algebra.basic
import category_theory.monoidal.Mon_
/-!
# `Mon_ (Module R) ≌ Algebra R`
The category... |
e5cdad63ad234aad38bc9bf29461a92a7d0e5949 | 159fed64bfae88f3b6a6166836d6278f953bcbf9 | /Structure/AbstractBuildingBlocks.lean | 753381efc018da6507919214c3c8e0044abed6b2 | [
"MIT"
] | permissive | SReichelt/lean4-experiments | 3e56830c8b2fbe3814eda071c48e3c8810d254a8 | ff55357a01a34a91bf670d712637480089085ee4 | refs/heads/main | 1,683,977,454,907 | 1,622,991,121,000 | 1,622,991,121,000 | 340,765,677 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,535 | lean | -- An abstract formalization of "isomorphism is equality up to relabeling"
-- -------------------------------------------------------------------------
--
-- See `README.md` for more info.
--
-- In this file, we define some basic building blocks which are closely related to the cases mentioned in
-- `README.md`.
im... |
c7b69fecb0bfff6b178f50bea4641f719c9c013d | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/preadditive/biproducts_auto.lean | 1e15c4041374c4455805d01624008d0ed8ba66ad | [] | 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 | 14,016 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.tactic.abel
import Mathlib.category_theory.limits.shapes.biproducts
import Mathlib.category... |
77e63ad05af38be264e9d555471409504f853057 | 8be24982c807641260370bd09243eac768750811 | /src/e_trans_helpers2.lean | 534e9fae9d32df4cbcef04f919c549033ba78da9 | [] | no_license | jjaassoonn/transcendental | 8008813253af3aa80b5a5c56551317e7ab4246ab | 99bc6ea6089f04ed90a0f55f0533ebb7f47b22ff | refs/heads/master | 1,607,869,957,944 | 1,599,659,687,000 | 1,599,659,687,000 | 234,444,826 | 9 | 1 | null | 1,598,218,307,000 | 1,579,224,232,000 | HTML | UTF-8 | Lean | false | false | 40,845 | lean | import measure_theory.interval_integral
import measure_theory.lebesgue_measure
import analysis.special_functions.exp_log
import small_things
noncomputable theory
open_locale classical
open_locale big_operators
notation α`[X]` := polynomial α
/-- # Definition and some theorems about differentiating multiple times
-/... |
ebfa5fe4f5f9373e8c8ea8fc7d310ff14097aaef | 2a70b774d16dbdf5a533432ee0ebab6838df0948 | /_target/deps/mathlib/src/order/rel_iso.lean | 3e409717f4b5fc0807d8a711ccbe77054a9c9114 | [
"Apache-2.0"
] | permissive | hjvromen/lewis | 40b035973df7c77ebf927afab7878c76d05ff758 | 105b675f73630f028ad5d890897a51b3c1146fb0 | refs/heads/master | 1,677,944,636,343 | 1,676,555,301,000 | 1,676,555,301,000 | 327,553,599 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 29,284 | 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 logic.embedding
import order.rel_classes
import data.set.intervals.basic
open function
universes u v w
variables {α : Type*} {β : Type*} {γ : Type*}
{r : α... |
ac5c7de6275eeabf84a521593daf20c78a06ea9e | 9c1ad797ec8a5eddb37d34806c543602d9a6bf70 | /enriched/two_category.lean | 8e41958fd0d9df8565a28b940a4c5cdbb8ef9348 | [] | no_license | timjb/lean-category-theory | 816eefc3a0582c22c05f4ee1c57ed04e57c0982f | 12916cce261d08bb8740bc85e0175b75fb2a60f4 | refs/heads/master | 1,611,078,926,765 | 1,492,080,000,000 | 1,492,080,000,000 | 88,348,246 | 0 | 0 | null | 1,492,262,499,000 | 1,492,262,498,000 | null | UTF-8 | Lean | false | false | 3,387 | 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 .enriched_category
import ..examples.categories.cartesian_product
open tqft.categories
open tqft.categories.functor
open tqft.categories.natural_transform... |
f7c8c51cfd255f3e6794f70fb21404148279e335 | abd85493667895c57a7507870867b28124b3998f | /src/data/pnat/basic.lean | 2240d061d62d3a9f987b21b56162539a35bd353c | [
"Apache-2.0"
] | permissive | pechersky/mathlib | d56eef16bddb0bfc8bc552b05b7270aff5944393 | f1df14c2214ee114c9738e733efd5de174deb95d | refs/heads/master | 1,666,714,392,571 | 1,591,747,567,000 | 1,591,747,567,000 | 270,557,274 | 0 | 0 | Apache-2.0 | 1,591,597,975,000 | 1,591,597,974,000 | null | UTF-8 | Lean | false | false | 13,473 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro, Neil Strickland
-/
import data.nat.prime
/-- `ℕ+` is the type of positive natural numbers. It is defined as a subtype,
and the VM representation of `ℕ+` is the... |
deaac220bae4542c3b08fb4b13f8e161883f549d | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/geometry/manifold/times_cont_mdiff_map.lean | a66010898bfa938d242ccb051306036bef3a8088 | [
"Apache-2.0"
] | permissive | abentkamp/mathlib | d9a75d291ec09f4637b0f30cc3880ffb07549ee5 | 5360e476391508e092b5a1e5210bd0ed22dc0755 | refs/heads/master | 1,682,382,954,948 | 1,622,106,077,000 | 1,622,106,077,000 | 149,285,665 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,693 | lean | /-
Copyright © 2020 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri
-/
import geometry.manifold.times_cont_mdiff
import topology.continuous_function.basic
/-!
# Smooth bundled map
In this file we define the type `times_cont_mdiff_ma... |
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