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dc0a293a051ac489aac415322f03ab864198fc16 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/ring_theory/tensor_product.lean | 47187b81488234d759d5bee1f64838f8604a5974 | [
"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 | 26,768 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Johan Commelin
-/
import linear_algebra.tensor_product
import algebra.algebra.tower
/-!
# The tensor product of R-algebras
Let `R` be a (semi)ring and `A` an `R`-alg... |
8d3264e28f64d5533da762eab3f2ca3e50d43dc0 | bdb33f8b7ea65f7705fc342a178508e2722eb851 | /number_theory/pell.lean | 74c416633aafe8618125b4abe150897dddf221fc | [
"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 | 62,373 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.int.basic data.nat.prime data.nat.modeq
/-- The ring of integers adjoined with a square root of `d`.
These have the form `a + b √d` where `a b : ℤ`. Th... |
84f2021112565d7e81f022a2a9881906b27c4fa0 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/topology/sheaves/stalks.lean | fbfd05d3ef59aa1051a09cd14105a620667d715a | [
"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 | 3,744 | 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 topology.category.Top.open_nhds
import topology.sheaves.presheaf
import category_theory.limits.limits
universes v u v' u'
open category_theory
open Top
open ... |
9f4e596cb41205bd6cdf813ca9e8d776596de9d0 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/limits/lattice.lean | fce7bead9d70f536c39c27e85915f6724620a58d | [
"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 | 8,836 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Justus Springer
-/
import order.complete_lattice
import data.fintype.lattice
import category_theory.limits.shapes.pullbacks
import category_theory.category.preorder
imp... |
a9fd42accc46c62167499f627a62108de58f6a34 | 8d65764a9e5f0923a67fc435eb1a5a1d02fd80e3 | /src/topology/continuous_on.lean | 61304d6b532ddad6622a3faff8198f37ac9c57db | [
"Apache-2.0"
] | permissive | troyjlee/mathlib | e18d4b8026e32062ab9e89bc3b003a5d1cfec3f5 | 45e7eb8447555247246e3fe91c87066506c14875 | refs/heads/master | 1,689,248,035,046 | 1,629,470,528,000 | 1,629,470,528,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 47,036 | lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import topology.constructions
/-!
# Neighborhoods and continuity relative to a subset
This file defines relative versions
* `nhds_within` of `nhds`
* `co... |
90c9334d35fdda6c0da23a843016cb1a9d28f069 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/PPTopDownAnalyze.lean | 86ce9dd2fdfe5c04b362dc72ae7081f36a903235 | [
"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 | 13,644 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Selsam
-/
import Lean
open Lean Lean.Meta Lean.Elab Lean.Elab.Term Lean.Elab.Command
open Lean.PrettyPrinter
def checkDelab (e : Expr) (tgt? : Option Term) (name? : Opt... |
8d4329928f5a204f3c782686f01793e33319db78 | b074a51e20fdb737b2d4c635dd292fc54685e010 | /test/tactics.lean | b233c263c3ecd9329d77f9f971cd1966bd1eedcb | [
"Apache-2.0"
] | permissive | minchaowu/mathlib | 2daf6ffdb5a56eeca403e894af88bcaaf65aec5e | 879da1cf04c2baa9eaa7bd2472100bc0335e5c73 | refs/heads/master | 1,609,628,676,768 | 1,564,310,105,000 | 1,564,310,105,000 | 99,461,307 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,689 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Scott Morrison
-/
import tactic.interactive tactic.finish tactic.ext
example (m n p q : nat) (h : m + n = p) : true :=
begin
have : m + n = q,
{ generalize_hyp h' : m + ... |
4b5d14ade95ccd26a0f793c94d14baef361ef4c1 | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/data/finsupp/lattice.lean | 5b3434a493f570a0de62ac93e5f66f9aeac1ba31 | [
"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 | 3,000 | 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 data.finsupp.basic
/-!
# Lattice structure on finsupps
This file provides instances of ordered structures on finsupps.
-/
open_locale classical
noncomputab... |
528bed8178ed18e14dd0701b58e5c20344432e28 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/simp_all_duplicateHyps.lean | d70405cce6691f85f276d441a7d31c5eec429496 | [
"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 | 302 | lean | axiom q : Nat → Prop
axiom p : Nat → Prop
axiom q_eq_p : q = p
example (h₁ : ¬ q 0) (h₂ : ¬ q 0) : ¬ p 0 := by
trace_state
/-
h₁ : ¬ q 0
h₂ : ¬ q 0
⊢ ¬ p 0
-/
simp_all
/-
h₂ : ¬ q 0
⊢ ¬ p 0
-/
trace_state
rw [← q_eq_p]
assumption
|
07785853c4e07810026ed038128bd5cf9dac8c3c | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/pnat/xgcd_auto.lean | 287fda7fd53707048c067b686dd7039c25bf031a | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,849 | lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Neil Strickland
This file sets up a version of the Euclidean algorithm that works
only with natural numbers. Given a, b > 0, it computes the unique
system (w, x, y, z, d) such that ... |
ec26e69f0ca845bc89d2e1cd7f8aa46c02978d77 | 08bd4ba4ca87dba1f09d2c96a26f5d65da81f4b4 | /src/Lean/Meta/Match/MatchEqs.lean | 4196c4484de8f3f0bb8f0937339040381ce5ef0d | [
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"Apache-2.0",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | gebner/lean4 | d51c4922640a52a6f7426536ea669ef18a1d9af5 | 8cd9ce06843c9d42d6d6dc43d3e81e3b49dfc20f | refs/heads/master | 1,685,732,780,391 | 1,672,962,627,000 | 1,673,459,398,000 | 373,307,283 | 0 | 0 | Apache-2.0 | 1,691,316,730,000 | 1,622,669,271,000 | Lean | UTF-8 | Lean | false | false | 32,852 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.Match.Match
import Lean.Meta.Match.MatchEqsExt
import Lean.Meta.Tactic.Apply
import Lean.Meta.Tactic.Refl
import Lean.Meta.Tactic.Delta
imp... |
b3334392cc2fa4e2637e8eb76bc2dfd5dfd9eab2 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Meta/Tactic/ElimInfo.lean | 58fb1fa4ffe21ed67007a612d5182c86a4e2f511 | [
"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 | 6,816 | 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
import Lean.Meta.Check
import Lean.ScopedEnvExtension
namespace Lean.Meta
structure ElimAltInfo where
name : Name
declName... |
a858fc7c2412ec9e840849d3ed2d647456788745 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /tests/lean/run/new_obtains.lean | d7f7ac651d1406951031004cb126fe926072a3ab | [
"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 | 2,441 | lean | import data.nat
theorem tst2 (A B C D : Type) : (A × B) × (C × D) → C × B × A :=
assume p : (A × B) × (C × D),
obtain [a b] [c d], from p,
(c, b, a)
theorem tst (a b c d : Prop) : (a ∧ b) ∧ (c ∧ d) → c ∧ b ∧ a :=
assume H,
obtain [Ha Hb] Hc Hd, from H,
and.intro Hc (and.intro Hb Ha)
theorem tst22 (A B C D : Type) : ... |
f17c7544cdcc0035cd188ac10bfdb0f99913a11d | 19cc34575500ee2e3d4586c15544632aa07a8e66 | /src/analysis/normed_space/finite_dimension.lean | 1e311941e549ee125bdda110847c8d1b566670e8 | [
"Apache-2.0"
] | permissive | LibertasSpZ/mathlib | b9fcd46625eb940611adb5e719a4b554138dade6 | 33f7870a49d7cc06d2f3036e22543e6ec5046e68 | refs/heads/master | 1,672,066,539,347 | 1,602,429,158,000 | 1,602,429,158,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 18,936 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import analysis.normed_space.operator_norm
import topology.bases
import linear_algebra.finite_dimensional
import tactic.omega
/-!
# Finite dimensional normed s... |
5d76d894cbb57de0dae29de7af5ba49b24da5262 | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /library/data/quotient/util.lean | dbf8701e56355bd9007ade502af761674f3bef3d | [
"Apache-2.0"
] | permissive | tjiaqi/lean | 4634d729795c164664d10d093f3545287c76628f | d0ce4cf62f4246b0600c07e074d86e51f2195e30 | refs/heads/master | 1,622,323,796,480 | 1,422,643,069,000 | 1,422,643,069,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,564 | lean | -- 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
import logic ..prod algebra.relation
import tools.fake_simplifier
open prod eq.ops
open fake_simplifier
namespace quotient
-- auxliary facts about products
... |
a75daccd363201e73533dd46b3a59ae11baf832b | bb31430994044506fa42fd667e2d556327e18dfe | /src/algebra/parity.lean | e57fc2b87e6a5260ff5873a5002499c49924dc89 | [
"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 | 12,302 | lean | /-
Copyright (c) 2022 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import algebra.group_power.lemmas
/-! # Squares, even and odd elements
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding ... |
7494f058eb87d0ca1fd1d74fdf2fd4f2cc50d4e7 | f4bff2062c030df03d65e8b69c88f79b63a359d8 | /src/game/sets/sets_level03.lean | 57d44982198c6cc3e20089d5dbcbee05a0b1ed6b | [
"Apache-2.0"
] | permissive | adastra7470/real-number-game | 776606961f52db0eb824555ed2f8e16f92216ea3 | f9dcb7d9255a79b57e62038228a23346c2dc301b | refs/heads/master | 1,669,221,575,893 | 1,594,669,800,000 | 1,594,669,800,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,497 | lean | import game.sets.sets_level02 -- hide
namespace xena -- hide
open_locale classical -- hide
variable X : Type -- hide
/-
# Chapter 1 : Sets
## Level 3 : intersection (∩)
-/
/-
Now prove that for any two sets $A$ and $B$, $A ∩ B ⊆ A$.
You will need to rewrite the following term:
```
mem_inter_iff : x ∈ A ∩ B... |
2d78b330c57249cac137d418d10fd154e73bdeb5 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/structure_instance_bug.lean | bfc53b88695ceaacf75baf73ddf6d06761c9ecfa | [
"Apache-2.0"
] | permissive | GaloisInc/lean | aa1e64d604051e602fcf4610061314b9a37ab8cd | f1ec117a24459b59c6ff9e56a1d09d9e9e60a6c0 | refs/heads/master | 1,592,202,909,807 | 1,504,624,387,000 | 1,504,624,387,000 | 75,319,626 | 2 | 1 | Apache-2.0 | 1,539,290,164,000 | 1,480,616,104,000 | C++ | UTF-8 | Lean | false | false | 260 | lean | structure weird (A : Type) :=
{B : Type} (op : A → B → A)
definition foo1 : weird nat :=
{ op := nat.add }
definition foo2 : weird nat :=
⟨ nat.add ⟩
definition foo3 : weird nat :=
{ B := nat, op := nat.add } -- Error: implicit field being provided
|
ef60e383104431867b8e275cdb2f2231f765c10d | 2bafba05c98c1107866b39609d15e849a4ca2bb8 | /src/week_8/Part_A_G_modules.lean | 3224d9ec5364bea1cccdf7411c116c5e1bc76089 | [
"Apache-2.0"
] | permissive | ImperialCollegeLondon/formalising-mathematics | b54c83c94b5c315024ff09997fcd6b303892a749 | 7cf1d51c27e2038d2804561d63c74711924044a1 | refs/heads/master | 1,651,267,046,302 | 1,638,888,459,000 | 1,638,888,459,000 | 331,592,375 | 284 | 24 | Apache-2.0 | 1,669,593,705,000 | 1,611,224,849,000 | Lean | UTF-8 | Lean | false | false | 17,983 | lean | -- always import the tactics, we are mathematicians
import tactic
-- import the theory of G-module homomorphisms, for G a group
import algebra.group_action_hom
/-
# Introduction to G-modules in Lean
Let `G` be a group (with group law `*`) and let `M` be an abelian
group (with group law `+`). A `G`-action on `M` is j... |
a98664d6f30925051d45cd3d14ff603880195306 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/lake/Lake/Load/Package.lean | a206c1011f93a5055652c0f83f2bdd4aa9ef4f32 | [
"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 | 5,282 | lean | /-
Copyright (c) 2021 Mac Malone. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mac Malone
-/
import Lake.DSL.Attributes
import Lake.Config.Workspace
/-!
This module contains definitions to load configuration objects from
a package configuration file (e.g., `lakefile... |
af8d6bb66053c01bdf22c981519ec1d4778ddbf2 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebraic_geometry/presheafed_space/gluing.lean | 428a7c1d98c250b7587f9a78f05eac0e907ca647 | [
"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 | 26,233 | lean | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import topology.gluing
import algebraic_geometry.open_immersion
import algebraic_geometry.locally_ringed_space.has_colimits
/-!
# Gluing Structured spaces
Given a family ... |
a3358ac858ac197dd577c5f498c913227a1c6dcf | 94e33a31faa76775069b071adea97e86e218a8ee | /src/order/max.lean | 277283b83c401891823ae5ca269d8da6d759167d | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 10,006 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Yury Kudryashov, Yaël Dillies
-/
import order.synonym
/-!
# Minimal/maximal and bottom/top elements
This file defines predicates for elements to be minimal/maximal or b... |
c50d9bd77cc40b8ece9bbd4d0688f2fd7c916768 | e514e8b939af519a1d5e9b30a850769d058df4e9 | /src/tactic/rewrite_search/discovery/screening.lean | 0e7e9971b08dba7948a811334b814f4696974e85 | [] | no_license | semorrison/lean-rewrite-search | dca317c5a52e170fb6ffc87c5ab767afb5e3e51a | e804b8f2753366b8957be839908230ee73f9e89f | refs/heads/master | 1,624,051,754,485 | 1,614,160,817,000 | 1,614,160,817,000 | 162,660,605 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 1,983 | lean | import lib.tactic
import tactic.rewrite_search.core.common
open tactic tactic.interactive
namespace tactic.rewrite_search.discovery
meta def assert_acceptable_lemma (r : expr) : tactic unit := do
-- FIXME: unfold definitions to see if there is an eq or iff
ret ← pure tt, -- is_acceptable_lemma r,
if ret then ... |
4adfeac41204eed6ad0da5925ee71267f31e91e0 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/univ1.lean | 8946c0974b6aa8a5de83f3886ecd976a4ece81cc | [
"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 | 644 | lean | namespace S1
axiom I : Type*
definition F (X : Type*) : Type* := (X → Prop) → Prop
axiom {u} unfoldd : I.{u} → F I.{u}
axiom {l} foldd : F I.{l} → I.{l}
axiom iso1 : ∀x, foldd (unfoldd x) = x
end S1
namespace S2
universe u
axiom I : Type.{u}
definition F (X : Type*) : Type* := (X → Prop) → Prop
axiom unfoldd : I → F... |
4883c73b5233a6077740f3775ebc3b4728c0bace | f3a5af2927397cf346ec0e24312bfff077f00425 | /src/game/world5/level2.lean | 5aecf1ce1c3e98c9f6a3ce564170abdb8d7b5e2d | [
"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 | 3,349 | lean | import mynat.add -- + on mynat
import mynat.mul -- * on mynat
/- Tactic : intro
## Summary:
`intro p` will turn a goal `⊢ P → Q` into a hypothesis `p : P`
and goal `⊢ Q`. If `P` and `Q` are sets `intro p` means "let $p$ be an arbitrary element of $P$".
If `P` and `Q` are propositions then `intro p` says "assume $P... |
81c8bccc59a13ddc674cc6f9e3cb0ae7d68f3000 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/algebra/big_operators/finsupp.lean | 13e3f8ea821142d1914fca28b0e081254d74f000 | [
"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 | 1,615 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import algebra.big_operators.pi
import algebra.big_operators.ring
import data.finsupp
/-!
# Big operators for finsupps
This file contains theorems relevant to big operators ... |
6d5cfd3bc95527a4c1e7d7bac5f012cefc0db7e4 | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/analysis/normed_space/basic.lean | b75656993f21986a6d6896b50ac8ff1a4fb5ea39 | [
"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 | 24,385 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Normed spaces.
Authors: Patrick Massot, Johannes Hölzl
-/
import algebra.pi_instances
import topology.instances.nnreal topology.instances.complex
variables {α : Type*} {β : Type*} {γ : Type*}... |
6fc479ecaedc4b7aa29640f8768474935d77896c | 969dbdfed67fda40a6f5a2b4f8c4a3c7dc01e0fb | /src/linear_algebra/bilinear_form.lean | 173178b5473a4f6145ff7ec8e819be3746c4eec9 | [
"Apache-2.0"
] | permissive | SAAluthwela/mathlib | 62044349d72dd63983a8500214736aa7779634d3 | 83a4b8b990907291421de54a78988c024dc8a552 | refs/heads/master | 1,679,433,873,417 | 1,615,998,031,000 | 1,615,998,031,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 51,357 | lean | /-
Copyright (c) 2018 Andreas Swerdlow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Andreas Swerdlow, Kexing Ying
-/
import linear_algebra.matrix
import linear_algebra.tensor_product
import linear_algebra.nonsingular_inverse
/-!
# Bilinear form
This file defines a... |
f54757a55b02e9f9ada3ffbc53117e9fda1d1259 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/subobject/mono_over.lean | 619c45c78ae360bbf6f0c4291d78ea80b603d37a | [
"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 | 13,598 | 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.over
import category_theory.limits.shapes.images
import category_theory.adjunction.reflective
/-!
# Monomorphisms over a fi... |
b533609db5fee7a2c94a45bad425811b52335c50 | 766b82465c89f7c306a9c07004605f5d564fd7f7 | /src/game/basic/my-integers.lean | b2f5d3f6a3a31e36d0deec5c95c5c6abddef854b | [
"Apache-2.0"
] | permissive | stanescuUW/integer-number-game | ca4293a46c51db178f3bdb248118075caf87f582 | fced68b04a59ef0f4ea41b5beb2df87e0428c761 | refs/heads/master | 1,669,860,820,240 | 1,597,966,427,000 | 1,597,966,427,000 | 289,131,361 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,372 | lean | import tactic
import data.equiv.ring
namespace uwyo
-- Creating the integers starting from the natural numbers.
-- Peter J. Cameron: "Sets, Logic and Categories"
-- section 1.8, page 29
-- In this construction, think of an integer x as the solution to the equation:
-- x + natnat.snd = natnat.fs... |
9fc76cc946afa16271fa9c23cab26920ac2f885f | c3f2fcd060adfa2ca29f924839d2d925e8f2c685 | /tests/lean/run/group3.lean | ada7477fd51e597f93167c6e993aed794bff6c76 | [
"Apache-2.0"
] | permissive | respu/lean | 6582d19a2f2838a28ecd2b3c6f81c32d07b5341d | 8c76419c60b63d0d9f7bc04ebb0b99812d0ec654 | refs/heads/master | 1,610,882,451,231 | 1,427,747,084,000 | 1,427,747,429,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,234 | lean | -- Copyright (c) 2014 Jeremy Avigad. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Jeremy Avigad, Leonardo de Moura
-- algebra.group
-- =============
-- Various structures with 1, *, inv, including groups.
import logic.eq
import data.unit data.sigma data.prod... |
ee5be475720a9083b4b8d494bc5745ff5f7f3c15 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/logic/encodable/lattice.lean | fe4f3fe986991b1fff7d165d94b99c2d8314a362 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 1,700 | lean | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import logic.encodable.basic
import logic.pairwise
/-!
# Lattice operations on encodable types
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this ... |
c019a4360ab2e544c8c0bdf7b2d79d11b9555c7f | b522075d31b564daeb3347a10eb9bb777ee93943 | /pmap.lean | 01283cb0d4e3ee515c02784828555c9c0a223a1a | [] | no_license | truonghoangle/manifolds | e6c2534dd46579f56ba99a48e2eb7ce51640e7c0 | 9c0d731a480e88758180b31ce7c3b371771d426b | refs/heads/master | 1,638,501,090,139 | 1,557,991,948,000 | 1,557,991,948,000 | 185,779,631 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,527 | lean | import algebra.module data.pfun equiv
universes u v w
variables {α : Type u} {β : Type v} {γ : Type w}
local attribute [instance] classical.prop_decidable
namespace equiv
section instances
variables (e : α ≃ β)
protected def has_scalar [has_scalar γ β] : has_scalar γ α := ⟨λ (a:γ) x, e.symm ( a • e x)⟩
... |
347e38885f6ff23bb3ff910fbb0c09480e6ee8f4 | 969dbdfed67fda40a6f5a2b4f8c4a3c7dc01e0fb | /src/combinatorics/colex.lean | 42e03b840e516c056d565248d74fe8fdeaf9cdf5 | [
"Apache-2.0"
] | permissive | SAAluthwela/mathlib | 62044349d72dd63983a8500214736aa7779634d3 | 83a4b8b990907291421de54a78988c024dc8a552 | refs/heads/master | 1,679,433,873,417 | 1,615,998,031,000 | 1,615,998,031,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,857 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Alena Gusakov
-/
import data.finset
import data.fintype.basic
import algebra.geom_sum
import tactic
/-!
# Colex
We define the colex ordering for finite sets, and give a c... |
bf1a6250b23d4c8898af71d3772192e7d64c1f40 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/topology/category/Top/limits/cofiltered.lean | 980f9f23f4fe4c6a6d4ffc7f371ce707212e644a | [
"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 | 4,480 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Scott Morrison, Mario Carneiro, Andrew Yang
-/
import topology.category.Top.limits.basic
/-!
# Cofiltered limits in Top.
Given a *compatible* collection of topologica... |
e8d23fb180c7d23ab0f22ac9122c4f17e6061cb3 | d4df7c538bbc0b06771d7b7a6f46fbadebb8c5eb | /src/comonad_transformers/comonad.lean | 8dc25ccc2e59cfa7100637fc41d4ea5320f61ff7 | [] | no_license | breakerzirconia/LeanTransformers | 11bb924b59ac589d0c6b39586d27cccc8f9e939c | 3c52441b8990bab7d8cf1817df6e04f657a14e1c | refs/heads/main | 1,682,610,526,027 | 1,620,477,129,000 | 1,620,477,129,000 | 365,507,838 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 542 | lean | class has_extract (w : Type → Type) :=
(extract {α : Type} : w α → α)
prefix ` * `:100 := has_extract.extract
class has_extend (w : Type → Type) :=
(extend : Π α β : Type, (w α → β) → w α → w β)
infix ` <<= `:55 := has_extend.extend
infix ` =>> `:55 := flip has_extend.extend
class comonad (w : Type → Type) exte... |
0332683fd6cc8d8eaeed3ceef14c5632ce31b37d | 453dcd7c0d1ef170b0843a81d7d8caedc9741dce | /category_theory/category.lean | d2e646bbd97511645e0c34a60ad892d1e95d1e51 | [
"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 | 2,914 | 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
Defines a category, as a typeclass parametrised by the type of objects.
Introduces notations
`X ⟶ Y` for the morphism spaces,
`f ≫ g` for compositio... |
489164f2e0783ab8a91a0082e43f2a5552243701 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/334c.lean | 089be66d41e83d2b1e348d4e914429b5baa575f9 | [
"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 | 412 | lean | structure foo (H : Type) :=
(foo : H)
variables {H : Type} (G : foo H)
structure foo.bar (G : foo H) (P : H → Prop) : Prop :=
(bar : P G.foo)
example {P : H → Prop} (h : G.bar P) : true := trivial
structure foo.bar' (P : H → Prop) : Prop :=
(bar : P G.foo)
set_option pp.annotations true
set_option pp.all true
#pri... |
1cfdeb451b95865854cdc25040b4fdca4d8c4192 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/algebra/category/Module/epi_mono.lean | 5664600bd5530cff0f913866645506d4b365eb98 | [
"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 | 2,439 | lean | /-
Copyright (c) 2021 Scott Morrison All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import linear_algebra.quotient
import algebra.category.Group.epi_mono
import algebra.category.Module.basic
/-!
# Monomorphisms in `Module R`
This file shows that an ... |
c2ca07d04660d058915e09aca2484356db77ccd6 | 432d948a4d3d242fdfb44b81c9e1b1baacd58617 | /src/ring_theory/power_series/basic.lean | 498a9c0b67854cecf710cd12871ac6d762787cd6 | [
"Apache-2.0"
] | permissive | JLimperg/aesop3 | 306cc6570c556568897ed2e508c8869667252e8a | a4a116f650cc7403428e72bd2e2c4cda300fe03f | refs/heads/master | 1,682,884,916,368 | 1,620,320,033,000 | 1,620,320,033,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 64,436 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Kenny Lau
-/
import data.mv_polynomial
import linear_algebra.std_basis
import ring_theory.ideal.operations
import ring_theory.multiplicity
import ring_theory.algebra_to... |
6abb485aaf150f7f3931b413f81ec4833f45612e | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/topology/algebra/uniform_group.lean | ce8d8f96b504d1c4c2ea5b604c221415c5b2efbb | [
"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 | 19,517 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
-/
import topology.uniform_space.uniform_embedding
import topology.uniform_space.complete_separated
import topology.algebra.group
import tactic.abel
/-!... |
640510c28ce03242790138d67ac406fa0c9f7076 | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/data/polynomial/degree/basic.lean | 1dbb400615cdf56acb5d4e7232257a1efba30f47 | [
"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 | 34,819 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
-/
import data.polynomial.coeff
import data.nat.with_bot
/-!
# Theory of univariate polynomials
The definitions include
`de... |
bcfe469a9bf2b763e7868ce032f373bc5f30a190 | 8c02fed42525b65813b55c064afe2484758d6d09 | /src/smtcompile.lean | 1ddfed8f21f1e074866350642b830edd60f41c75 | [
"LicenseRef-scancode-generic-cla",
"MIT"
] | permissive | microsoft/AliveInLean | 3eac351a34154efedd3ffc4fe2fa4ec01b219e0d | 4b739dd6e4266b26a045613849df221374119871 | refs/heads/master | 1,691,419,737,939 | 1,689,365,567,000 | 1,689,365,568,000 | 131,156,103 | 23 | 18 | NOASSERTION | 1,660,342,040,000 | 1,524,747,538,000 | Lean | UTF-8 | Lean | false | false | 3,898 | lean | -- Copyright (c) Microsoft Corporation. All rights reserved.
-- Licensed under the MIT license.
import .smtexpr
import smt2.syntax
import smt2.builder
namespace smt
-- A sample optimizing function.
@[reducible] def optimize_add_zero {sz:size} : sbitvec sz → sbitvec sz
| (sbitvec.add (sbitvec.const _ 0) y) := y
| s :... |
698dc266e9306af685e444efa94ef5c437105ada | 4a092885406df4e441e9bb9065d9405dacb94cd8 | /src/for_mathlib/localization.lean | 644c2cdb6b854b5316b1b15e570478ee3553d3c4 | [
"Apache-2.0"
] | permissive | semorrison/lean-perfectoid-spaces | 78c1572cedbfae9c3e460d8aaf91de38616904d8 | bb4311dff45791170bcb1b6a983e2591bee88a19 | refs/heads/master | 1,588,841,765,494 | 1,554,805,620,000 | 1,554,805,620,000 | 180,353,546 | 0 | 1 | null | 1,554,809,880,000 | 1,554,809,880,000 | null | UTF-8 | Lean | false | false | 445 | lean | import ring_theory.localization
namespace localization
-- line 170
/-
@[simp] lemma mk_zero {x : α} {hx : x ∈ S} :
(mk 0 ⟨x, hx⟩ : localization α S) = 0 :=
quotient.sound ⟨1, is_submonoid.one_mem S, by simp⟩
-/
theorem localization.mk_zero {α : Type*} [comm_ring α] {S : set α}
[is_submonoid S] {x : α} {hx : x ... |
3197849c1fc54f82ae094e1719fa7d17dd007df4 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/category_theory/functor/fully_faithful.lean | 085ad8da71383e44ce83cdd6792d1f4404e4a6be | [
"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 | 10,861 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.natural_isomorphism
import logic.equiv.basic
/-!
# Full and faithful functors
We define typeclasses `full` and `faithful`, decorating functor... |
b763d77d1f80d8d5647a15aee0c7a11db445c0bb | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /archive/imo/imo2008_q4.lean | c1cae17f559fa07ee9bb132821fc3b8f37db591e | [
"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 | 4,759 | lean | /-
Copyright (c) 2021 Manuel Candales. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Manuel Candales
-/
import data.real.basic
import data.real.sqrt
import data.real.nnreal
import tactic.linear_combination
/-!
# IMO 2008 Q4
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.... |
6ae90408a87baa52a3146793e85918c36e471a3b | 74924b1fe80b8f61262cefcfc0cd4d96135c8731 | /src/analysis/normed_space/real_inner_product.lean | 1296b2e289c4668887ecd5a4c27b8945d0380cbf | [
"Apache-2.0"
] | permissive | 101damnations/mathlib | 0938b3806a09032d8716d3642cbab65db7688c23 | 900c53ae6d5e3f8cc47953363479593e8debc4d8 | refs/heads/master | 1,593,832,305,164 | 1,565,631,735,000 | 1,565,631,735,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 20,725 | 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 analysis.convex
import algebra.quadratic_discriminant
import tactic.monotonicity
import analysis.specific_limits
/-!
# Inner Product Space
Define inne... |
5c6cac0bf9b4fd26a4b49e82e697c7aee0a2da86 | 36938939954e91f23dec66a02728db08a7acfcf9 | /lean/deps/typed_smt2/src/galois/smt2/atom.lean | d1292b4b48baa4432f364f3b8cbe227a7e675406 | [
"Apache-2.0"
] | permissive | pnwamk/reopt-vcg | f8b56dd0279392a5e1c6aee721be8138e6b558d3 | c9f9f185fbefc25c36c4b506bbc85fd1a03c3b6d | refs/heads/master | 1,631,145,017,772 | 1,593,549,019,000 | 1,593,549,143,000 | 254,191,418 | 0 | 0 | null | 1,586,377,077,000 | 1,586,377,077,000 | null | UTF-8 | Lean | false | false | 2,567 | lean | import galois.sexpr
import .symbol
namespace smt2
------------------------------------------------------------------------
-- atom
/- A atomic expression within an SMTLIB s-expression. -/
inductive atom
| reserved_word (r:reserved_word) : atom
| symbol : symbol → atom
| numeral : ℕ → atom
namespace symbol
/-- Con... |
6065b53bfb7c73fb7c5764bd24fa7e04deb62f30 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/buffer/basic.lean | cdff3d2644bd8bd247261e32075b49f6384dff8e | [
"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 | 7,360 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
General utility functions for buffers.
-/
import data.array.lemmas
import control.traversable.instances
import control.traversable.equiv
namespace buffer
open function
var... |
3adb2d1303c1b991925bddfec4725fe0ccb8268d | 22e97a5d648fc451e25a06c668dc03ac7ed7bc25 | /src/linear_algebra/basic.lean | 5db6aed58a7becbb3e8e04c82111f80d316f12e7 | [
"Apache-2.0"
] | permissive | keeferrowan/mathlib | f2818da875dbc7780830d09bd4c526b0764a4e50 | aad2dfc40e8e6a7e258287a7c1580318e865817e | refs/heads/master | 1,661,736,426,952 | 1,590,438,032,000 | 1,590,438,032,000 | 266,892,663 | 0 | 0 | Apache-2.0 | 1,590,445,835,000 | 1,590,445,835,000 | null | UTF-8 | Lean | false | false | 84,894 | 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, Yury Kudryashov
-/
import algebra.pi_instances
import data.finsupp
/-!
# Linear algebra
This file defines the basics of linear algebra.... |
95c6dbb00cb05eca76a28ead27cd23cb8dbbf76a | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/algebra/field.lean | 28fc333226da4ee08878f91bb8ecbe99e79a6b81 | [
"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 | 14,012 | lean | /-
Copyright (c) 2014 Robert Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Lewis, Leonardo de Moura, Johannes Hölzl, Mario Carneiro
-/
import algebra.ring.basic
import algebra.group_with_zero
/-!
# Fields and division rings
This file introduces fields ... |
e998d29050a13b2f901d89c23f3ad5bdabcd1dfc | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /src/Init/Control/Basic.lean | 6e48be7cbcb454eaac634e4c1742fcfb8c66008f | [
"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 | 3,805 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura, Sebastian Ullrich
-/
prelude
import Init.Core
universes u v w
@[reducible] def Functor.mapRev {f : Type u → Type v} [Functor f] {α β : Type u} : f α → (α → β... |
21e2a6329cceab3f2bae1cfb6da764f4bbd843d1 | 05b503addd423dd68145d68b8cde5cd595d74365 | /src/measure_theory/simple_func_dense.lean | 195220b25b99a1844be4eb2da053c7e1a6e4be75 | [
"Apache-2.0"
] | permissive | aestriplex/mathlib | 77513ff2b176d74a3bec114f33b519069788811d | e2fa8b2b1b732d7c25119229e3cdfba8370cb00f | refs/heads/master | 1,621,969,960,692 | 1,586,279,279,000 | 1,586,279,279,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,942 | 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.l1_space
/-!
# Density of simple functions
Show that each Borel measurable function can be approximated,
both pointwise and in `L¹` norm, by a ... |
b22e62c5148c449590a2f630cdb4c03ce23cd7e2 | 82b86ba2ae0d5aed0f01f49c46db5afec0eb2bd7 | /src/Std/Data/PersistentArray.lean | 17a6b3c770e5b9de2fc0a7b94f3ea4f21e96a45f | [
"Apache-2.0"
] | permissive | banksonian/lean4 | 3a2e6b0f1eb63aa56ff95b8d07b2f851072d54dc | 78da6b3aa2840693eea354a41e89fc5b212a5011 | refs/heads/master | 1,673,703,624,165 | 1,605,123,551,000 | 1,605,123,551,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,778 | 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
-/
universes u v w
namespace Std
inductive PersistentArrayNode (α : Type u)
| node (cs : Array (PersistentArrayNode α)) : PersistentArrayNode α
| leaf (v... |
b30d76be94a6e852a3845d2aba050eec1a7c49aa | 947b78d97130d56365ae2ec264df196ce769371a | /src/Lean/Meta/Match.lean | c4e9c0c8239bb59ef55acdf55558158ff23be0fa | [
"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 | 412 | 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.Match.MatchPatternAttr
import Lean.Meta.Match.Match
import Lean.Meta.Match.CaseValues
import Lean.Meta.Match.CaseArraySizes
namespace Lean... |
530ce870d70718c943789d2cbbe37d9216794836 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/category_theory/category/Cat/limit.lean | 77ae621b6aaf73274a8752e491dd857628705d8a | [
"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 | 5,187 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.category.Cat
import category_theory.limits.types
import category_theory.limits.preserves.basic
/-!
# The category of small categories has all ... |
96df0edc7b312c941d383ca87f679f505c94a687 | 5749d8999a76f3a8fddceca1f6941981e33aaa96 | /src/measure_theory/integration.lean | a233fe415dca37e2556dc1982fde4feda71e1f03 | [
"Apache-2.0"
] | permissive | jdsalchow/mathlib | 13ab43ef0d0515a17e550b16d09bd14b76125276 | 497e692b946d93906900bb33a51fd243e7649406 | refs/heads/master | 1,585,819,143,348 | 1,580,072,892,000 | 1,580,072,892,000 | 154,287,128 | 0 | 0 | Apache-2.0 | 1,540,281,610,000 | 1,540,281,609,000 | null | UTF-8 | Lean | false | false | 56,409 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl
Lebesgue integral on `ennreal`.
We define simple functions and show that each Borel measurable function on `ennreal` can be
approximated by a sequence ... |
1e2b197cd551350121d834a4addde9a6b7c4fdbb | bb31430994044506fa42fd667e2d556327e18dfe | /src/measure_theory/group/action.lean | 250c467310882166ce7dd1e9f7a4bc46947e525a | [
"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 | 10,575 | lean | /-
Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import measure_theory.group.measurable_equiv
import measure_theory.measure.regular
import dynamics.ergodic.measure_preserving
import dynamics.minimal
/-!
# M... |
49904f91d813646a827a79c1529d68303faf1065 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/polynomial/taylor.lean | 1fd7131492a7b989b5d3e4d116f35d4b767f2599 | [
"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 | 4,738 | lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import data.polynomial.algebra_map
import data.polynomial.hasse_deriv
/-!
# Taylor expansions of polynomials
## Main declarations
* `polynomial.taylor`: the Taylo... |
b17e51a3fabaf689165b0494788e5226547f0cc5 | ce6917c5bacabee346655160b74a307b4a5ab620 | /src/ch4/ex0408.lean | 8056f59f6075af6086f818fd6a95e38655cfbe01 | [] | no_license | Ailrun/Theorem_Proving_in_Lean | ae6a23f3c54d62d401314d6a771e8ff8b4132db2 | 2eb1b5caf93c6a5a555c79e9097cf2ba5a66cf68 | refs/heads/master | 1,609,838,270,467 | 1,586,846,743,000 | 1,586,846,743,000 | 240,967,761 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 145 | lean | variables (α : Type) (p q : α → Prop)
example : (∃ x, p x ∧ q x) -> ∃ x, q x ∧ p x :=
assume ⟨w, hpw, hqw⟩, ⟨w, hqw, hpw⟩
|
30d3bb5137e652fa0f6b277a9dfc8d85e82f8a72 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/1380.lean | d5816d8a6c3e3c5c50d02fecb631e4efa3042932 | [
"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 | 473 | lean | theorem Nat.ne_of_gt {a b : Nat} (h : a < b) : b ≠ a := sorry
theorem Nat.lt_succ_iff {m n : Nat} : m < succ n ↔ m ≤ n := sorry
variable (n v₁ v₂) (hv₁: v₁ < n + 1) (hv₂: v₂ < n + 1)
theorem foo (_: ¬ Fin.mk v₂ hv₂ = Fin.mk v₁ hv₁ ): True := trivial
set_option trace.Meta.Tactic.simp true in
example (hv: v₁ < v₂) : Tru... |
aef74628dc79bf012e830d485a4c3c6884a0f017 | 205f0fc16279a69ea36e9fd158e3a97b06834ce2 | /src/13_Relations/practice.lean | 0977431ceb64e5f4f5cebcad1cd231f73606ff19 | [] | 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 | 905 | lean | /-
Complete the following sentences using
precise but informal English:
A relation, R, is said to be reflexive
if for all x, ...
A relation, R, is said to be transitive
if for all x, y, z, if x R y ...
A relation, R, is said to be transitive
if for all x, y, z, if x R y ...
A relation, R, is said to be an equivalen... |
30ca3c0fc623900fda32b208b2ed52d6ee1b7746 | f4bff2062c030df03d65e8b69c88f79b63a359d8 | /src/game/sets/sets_level06.lean | 056a71a929af3ef86905b2d3e90199a3c39b4c14 | [
"Apache-2.0"
] | permissive | adastra7470/real-number-game | 776606961f52db0eb824555ed2f8e16f92216ea3 | f9dcb7d9255a79b57e62038228a23346c2dc301b | refs/heads/master | 1,669,221,575,893 | 1,594,669,800,000 | 1,594,669,800,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,110 | lean | import game.sets.sets_level05 -- hide
import tactic -- hide
namespace xena -- hide
variable X : Type
open_locale classical -- hide
/-
# Chapter 1 : Sets
## Level 6 : `sdiff` and `neg`
-/
/-
The set-theoretic difference `A \ B` satisfies the following property:
```
lemma mem_sdiff_iff : x ∈ A \ B ↔ x ∈ A ∧ x ∉ ... |
3268f86c9c98f68245bfd9287da992baf4c27320 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/data/finite/defs.lean | ef16b491da1965e78a52d28ce763e06fcf0dfd10 | [
"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 | 3,976 | lean | /-
Copyright (c) 2022 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import logic.equiv.basic
/-!
# Definition of the `finite` typeclass
This file defines a typeclass `finite` saying that `α : Sort*` is finite. A type is `finite` if it
is ... |
5167ebb1e444f8f737130ea2dc1030670457c04f | b2fe74b11b57d362c13326bc5651244f111fa6f4 | /src/data/nat/basic.lean | 7e6fa3f0f562f042bee74b374377bafd16b5249e | [
"Apache-2.0"
] | permissive | midfield/mathlib | c4db5fa898b5ac8f2f80ae0d00c95eb6f745f4c7 | 775edc615ecec631d65b6180dbcc7bc26c3abc26 | refs/heads/master | 1,675,330,551,921 | 1,608,304,514,000 | 1,608,304,514,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 62,721 | lean | /-
Copyright (c) 2014 Floris van Doorn (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
import algebra.group_power.basic
import algebra.order_functions
/-!
# Basic oper... |
01094b80fec28a32c0d0288c7cfd2ec42b1d95e4 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/continued_fractions/computation/correctness_terminating.lean | d8d086b85e8c3a69b7aac0b5f828c612d6432e02 | [
"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 | 12,529 | lean | /-
Copyright (c) 2020 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import algebra.continued_fractions.computation.translations
import algebra.continued_fractions.terminated_stable
import algebra.continued_fractions.continuants_re... |
532eff19104ab0c1a6ebb75b29778c4bdb917461 | 6e36ebd5594a0d512dea8bc6ffe78c71b5b5032d | /src/mywork/Practice/9.20.21_notes.lean | 7b12118f79ea2866e35400c878a515e7945e1796 | [] | no_license | wrw2ztk/cs2120f21 | cdc4b1b4043c8ae8f3c8c3c0e91cdacb2cfddb16 | f55df4c723d3ce989908679f5653e4be669334ae | refs/heads/main | 1,691,764,473,342 | 1,633,707,809,000 | 1,633,707,809,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 551 | lean | -- Using ¬
example : false :=
begin
end
example : ¬ false :=
begin
assume f,
exact f,
end
example : ¬ 0 = 1 :=
begin
assume h,
end
example : ∀ (P Q R : Prop), P ∨ Q → R :=
begin
assume P Q R,
assume pq,
cases pq,
end
example : true → true :=
begin
assume t,
cases t,
exact true.intro,
end
exam... |
10de04a5ec553cd3708af705365a6e741de941ff | 367134ba5a65885e863bdc4507601606690974c1 | /src/category_theory/eq_to_hom.lean | 11c830fc7e065d93cffa122e23435633311caf8b | [
"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 | 4,928 | 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
-/
import category_theory.opposites
universes v₁ v₂ u₁ u₂ -- declare the `v`'s first; see `category_theory.category` for an explanation
namespace category_th... |
9dccd7ddbefbd232bc98cf0ca5444bd8d777afab | cbcb0199842f03e7606d4e43666573fc15dd07a5 | /src/topology/instances/ennreal.lean | f4f529e650d4ac4ba379d0b3231dc56a8520bf7e | [
"Apache-2.0"
] | permissive | truonghoangle/mathlib | a6a7c14b3767ec71156239d8ea97f6921fe79627 | 673bae584febcd830c2c9256eb7e7a81e27ed303 | refs/heads/master | 1,590,347,998,944 | 1,559,728,860,000 | 1,559,728,860,000 | 187,431,971 | 0 | 0 | null | 1,558,238,525,000 | 1,558,238,525,000 | null | UTF-8 | Lean | false | false | 28,767 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
Extended non-negative reals
-/
import topology.instances.nnreal data.real.ennreal
noncomputable theory
open classical set lattice filter metric
local attribute [instance... |
931a296be9d79fb94fb32c595591bd8b085a6bb1 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/2188.lean | f7fa1f55c1495fd00cf366d4427e4c182f5b755f | [
"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 | 49 | lean | structure O (c : False = False) where
m : Prop
|
fd2c74cd4236df5fefbd487c3949350092d66afd | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/analysis/calculus/tangent_cone.lean | e4c4a2958f718f3c5b99b2793abeec3cfd7e79f2 | [
"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 | 18,585 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import analysis.convex.basic
import analysis.normed_space.bounded_linear_maps
import analysis.specific_limits
/-!
# Tangent cone
In this file, we define two p... |
5be63c52fcc0e98e3150fad16e4677eb71f58427 | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /tests/lean/run/frontend1.lean | f3854be0bdca5612bcf2193f0eb308376c3008f7 | [
"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 | 7,146 | lean | #lang lean4
import Lean.Elab
open Lean
open Lean.Elab
def runM (input : String) (failIff : Bool := true) : CoreM Unit := do
let env ← getEnv;
let opts ← getOptions;
let (env, messages) ← process input env opts;
messages.forM fun msg => do IO.println (← msg.toString)
when (failIff && messages.hasErrors) $ throwError "... |
e38364b5ea5b48f430b979196a0ac176805a8625 | 8e2026ac8a0660b5a490dfb895599fb445bb77a0 | /library/tools/smt2/syntax.lean | 02cebae4656d748eba47c76d09a8aee2efbc7852 | [
"Apache-2.0"
] | permissive | pcmoritz/lean | 6a8575115a724af933678d829b4f791a0cb55beb | 35eba0107e4cc8a52778259bb5392300267bfc29 | refs/heads/master | 1,607,896,326,092 | 1,490,752,175,000 | 1,490,752,175,000 | 86,612,290 | 0 | 0 | null | 1,490,809,641,000 | 1,490,809,641,000 | null | UTF-8 | Lean | false | false | 2,319 | lean | namespace smt2
@[reducible] def symbol : Type := string
@[reducible] def identifier : Type := string
inductive special_constant : Type
| number : int → special_constant
| string : string → special_constant
inductive sort : Type
| id : identifier → sort
| apply : identifier → list sort → sort
instance : has_coe stri... |
de103e38409c587fbf1a9e82241eed7eef120a92 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/measure_theory/group/arithmetic.lean | e172bc699b6fd335924c3d25332df826cbb76c4c | [
"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 | 27,897 | 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.measure_space
/-!
# Typeclasses for measurability of operations
In this file we define classes `has_measurable_mul` etc and prove do... |
21bcd253f7303285b3c04c6213a49bcd48065b08 | e514e8b939af519a1d5e9b30a850769d058df4e9 | /src/lib/num.lean | cd8c6051a51f9f507e2f3eff2420f3fd7c43430d | [] | no_license | semorrison/lean-rewrite-search | dca317c5a52e170fb6ffc87c5ab767afb5e3e51a | e804b8f2753366b8957be839908230ee73f9e89f | refs/heads/master | 1,624,051,754,485 | 1,614,160,817,000 | 1,614,160,817,000 | 162,660,605 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 675 | lean | import data.nat.basic
def fin.with_max (n m : ℕ) (h : m > 0) : fin m :=
⟨ min n (m-1), begin
have p := min_le_right n (nat.pred m),
have q := nat.lt_succ_of_le p,
rw nat.succ_pred_eq_of_pos at q,
exact q,
assumption
end... |
25e09abeb2e4e6afe33ff0178833152edc35efd5 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/linear_algebra/dual.lean | da7290cd6711342964ea123d905ffd8105c5cd93 | [
"Apache-2.0"
] | permissive | Lix0120/mathlib | 0020745240315ed0e517cbf32e738d8f9811dd80 | e14c37827456fc6707f31b4d1d16f1f3a3205e91 | refs/heads/master | 1,673,102,855,024 | 1,604,151,044,000 | 1,604,151,044,000 | 308,930,245 | 0 | 0 | Apache-2.0 | 1,604,164,710,000 | 1,604,163,547,000 | null | UTF-8 | Lean | false | false | 12,724 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Fabian Glöckle
-/
import linear_algebra.finite_dimensional
import tactic.apply_fun
noncomputable theory
/-!
# Dual vector spaces
The dual space of an R-module M is th... |
9521d84c8977f46ab67055e1e5cc263ead2c974f | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/algebra/semiconj.lean | 66c2906e7879cc448ec1188449568de371e2ab39 | [
"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 | 9,175 | lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
Some proofs and docs came from `algebra/commute` (c) Neil Strickland
-/
import algebra.ring algebra.group_power data.equiv.mul_add
/-!
# Semiconjugate elements of a ... |
1fc993dc5caac7fcad0e774728e94188afd54b4d | b24beef0a8b1a8e92be756a25aa78e24908b2b14 | /src/exercises_sources/thursday/morning/order.lean | 639b2432461495dd55734fac53d592cdbdf83b2b | [] | permissive | ChristopheMargerin/lftcm2020 | 14967e74cbe92a7b61d32d8130f32cfa09b5172b | 589180047fa4fdfb3179636db58b0b0320549871 | refs/heads/master | 1,668,536,269,632 | 1,594,891,664,000 | 1,594,891,664,000 | 280,112,730 | 0 | 0 | MIT | 1,594,891,963,000 | 1,594,891,962,000 | null | UTF-8 | Lean | false | false | 17,576 | lean | /-
# Orders
Groups, rings, fields, modules etc are in the "algebra hierarchy".
Metric and topological spaces are in the "topology hierarchy".
The other important hierarchy is the "order hierarchy".
It starts with partially ordered sets, and then goes on to lattices.
Because I like algebra, let's demonstrate the or... |
1afabc802920c97e043f86eb1a512b13da04f1ed | 1fbca480c1574e809ae95a3eda58188ff42a5e41 | /src/util/data/nat.lean | 4e632b002c79b3f6f7a32997e82153e35eb41554 | [] | no_license | unitb/lean-lib | 560eea0acf02b1fd4bcaac9986d3d7f1a4290e7e | 439b80e606b4ebe4909a08b1d77f4f5c0ee3dee9 | refs/heads/master | 1,610,706,025,400 | 1,570,144,245,000 | 1,570,144,245,000 | 99,579,229 | 5 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,708 | lean |
import data.num.lemmas
namespace nat
lemma eq_zero_of_le {n : ℕ}
(h : n ≤ 0)
: n = 0 :=
by { apply le_antisymm h, apply zero_le }
theorem lt_of_not_le {m n : ℕ} (h : ¬ m ≤ n) : n < m :=
begin
cases lt_or_ge n m with h' h',
{ apply h' },
{ cases h h' }
end
theorem mod_of_lt {m n : ℕ} (h : n > m) : m % n = m... |
5a0f91841322f464067cf71f8bda4f5b968681fe | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/Reformat/Input.lean | 624ba69d4d157c8a517bc057e9db790481abc70a | [
"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 | 9,621 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
universe u v w
@[inline] def id {α : Sort u} (a : α) : α := a
/-
The kernel definitional equality test (t =?= s) has special support for idDelta ... |
6b83e2d4c75a06c695ffc97afca5fff81529e9b4 | 7b02c598aa57070b4cf4fbfe2416d0479220187f | /homotopy/susp.hlean | e192d0a3c543d7be54a87e7afbb8075b128fdddc | [
"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 | 3,409 | hlean | import homotopy.susp types.pointed2
open susp eq pointed function is_equiv
namespace susp
variables {X X' Y Y' Z : Type*}
definition susp_functor_pconst_homotopy [unfold 3] {X Y : Type*} (x : psusp X) :
psusp_functor (pconst X Y) x = pt :=
begin
induction x,
{ reflexivity },
{ exact (merid pt)⁻¹... |
51f32fef7b4277b1d6b36320e365a0b5c954950a | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/module/pi.lean | 3b7254fd9e84479ed4822a57233797d2d3157e90 | [
"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 | 3,418 | 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.regular.smul
import algebra.ring.pi
import group_theory.group_action.pi
/-!
# Pi instances for modules
This fil... |
d55d666c6d4eb8c7cd6dab333c2dc5a572d7008d | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/combinatorics/colex.lean | 20b280456c4a196962c34676914cd02fc14b352d | [
"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 | 11,854 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Alena Gusakov
-/
import data.finset
import data.fintype.basic
import algebra.geom_sum
import tactic
/-!
# Colex
We define the colex ordering for finite sets, and give a c... |
43c60f0399fe6626c087f090ef91ab814e8e9200 | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /doc/demo/congr.lean | a0d5d980f3ec3dcacfa60f923cd5d3f09bee3e8a | [
"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 | 493 | lean | rewrite_set simple
add_rewrite and_truer and_truel and_falser and_falsel or_falsel : simple
(*
add_congr_theorem("simple", "and_congr")
add_congr_theorem("simple", "or_congr")
*)
variables a b c : Nat
(*
local t = parse_lean([[a = 1 ∧ (¬ b = 0 ∨ c ≠ 0 ∨ b + c > a)]])
local s, pr = simplify(t, "simple")
print(s)
p... |
c53c950d88fa154d4b132b60d4ff18fc880aca7e | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/topology/instances/ennreal.lean | 3e03bf91941aeb5ebd4f0b35554354f0c504ca79 | [
"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 | 60,745 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import topology.instances.nnreal
import order.liminf_limsup
import topology.metric_space.lipschitz
/-!
# Extended non-negative reals
-/
noncomputable theory
open cl... |
1473f48e4fe1f72ca6653e5d55f6509492790cfc | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/ring_theory/jacobson_ideal.lean | 1ccdf78ffefe3371fe7c84f9cec5fe5e02376418 | [
"Apache-2.0"
] | permissive | Lix0120/mathlib | 0020745240315ed0e517cbf32e738d8f9811dd80 | e14c37827456fc6707f31b4d1d16f1f3a3205e91 | refs/heads/master | 1,673,102,855,024 | 1,604,151,044,000 | 1,604,151,044,000 | 308,930,245 | 0 | 0 | Apache-2.0 | 1,604,164,710,000 | 1,604,163,547,000 | null | UTF-8 | Lean | false | false | 11,710 | lean | /-
Copyright (c) 2020 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Devon Tuma
-/
import ring_theory.ideal.operations
/-!
# Jacobson radical
The Jacobson radical of a ring `R` is defined to be the intersection of all maximal ideals of `R`.
Thi... |
ea000cb586bcced331d055f4632cebb0081d1b00 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /src/Init/Data/ToString/Basic.lean | 28e2338aab1e9709e2eb1c8417ced28a224d5907 | [
"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 | 4,414 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import Init.Data.String.Basic
import Init.Data.UInt
import Init.Data.Nat.Div
import Init.Data.Repr
import Init.Data.Int.Basic
import Init.Data.Format... |
d1f07d687977af126483a709dd5bd2e314baba5c | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/analysis/normed_space/units.lean | 1dd2104580a840434bad521346b702759acc24ec | [
"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 | 13,679 | 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.specific_limits.normed
/-!
# The group of units of a complete normed ring
This file contains the basic theory for the group of units (invertible e... |
63e696111fafde1a593fffa681bd252516e7f028 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/order/complete_boolean_algebra.lean | 40ca9fd758684e19821e6fc1dcdacef2056a7a35 | [
"Apache-2.0"
] | permissive | Lix0120/mathlib | 0020745240315ed0e517cbf32e738d8f9811dd80 | e14c37827456fc6707f31b4d1d16f1f3a3205e91 | refs/heads/master | 1,673,102,855,024 | 1,604,151,044,000 | 1,604,151,044,000 | 308,930,245 | 0 | 0 | Apache-2.0 | 1,604,164,710,000 | 1,604,163,547,000 | null | UTF-8 | Lean | false | false | 4,499 | 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 complete Boolean algebras.
-/
import order.complete_lattice
set_option old_structure_cmd true
universes u v w
variables {α : Type u} {β : Type v} {ι : Sort ... |
d7ced6fd0a49486692290cb4f9e93b45c84fc024 | 022547453607c6244552158ff25ab3bf17361760 | /src/algebra/algebra/basic.lean | 1a9c7b946971a4b8299134f5b95751f45d7bc097 | [
"Apache-2.0"
] | permissive | 1293045656/mathlib | 5f81741a7c1ff1873440ec680b3680bfb6b7b048 | 4709e61525a60189733e72a50e564c58d534bed8 | refs/heads/master | 1,687,010,200,553 | 1,626,245,646,000 | 1,626,245,646,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 61,401 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov
-/
import tactic.nth_rewrite
import data.matrix.basic
import data.equiv.ring_aut
import linear_algebra.tensor_product
import ring_theory.subring
import deprecated... |
ed5e0e096f20e89af3ef6154c0a25d62d9480830 | e151e9053bfd6d71740066474fc500a087837323 | /src/hott/types/lift.lean | 7a27b8929e5bec0a0c8e213f804140a2ac3fa003 | [
"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 | 5,986 | lean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Floris van Doorn
Theorems about lift
-/
import ..function
universes u v w
hott_theory
namespace hott
open hott.equiv hott.is_equiv is_trunc pointed ulift
namespace ulift
variabl... |
8a290d680aa293f5317eaac8a4fe71540411f5fe | 995658a556256a6694fe5c98b91f7f6f6c11bb77 | /src/riemann_hypothesis.lean | 2d2207a375e0770399a2f58eba73c216c1911493 | [
"MIT"
] | permissive | bhgomes/lean-riemann-hypothesis | d803047f27ea21f03414bbfb59395608ed0bc05f | c36b744a2dc4a7a50c7de770096bd9a051f42ab9 | refs/heads/master | 1,678,533,614,591 | 1,614,755,910,000 | 1,614,755,910,000 | 275,204,877 | 16 | 3 | null | null | null | null | UTF-8 | Lean | false | false | 1,385 | lean | /- ------------------------------------------------------------------------- -|
| @project: riemann_hypothesis |
| @file: riemann_hypothesis.lean |
| @authors: Brandon H. Gomes, Alex Kontorovich |
... |
934870f6b0f52d02b573be5859b4192b1d0f9b08 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/algebra/category/Mon/colimits.lean | 8b9f06632bb14a289252e7645c27c14f6c08ebb5 | [
"Apache-2.0"
] | permissive | Lix0120/mathlib | 0020745240315ed0e517cbf32e738d8f9811dd80 | e14c37827456fc6707f31b4d1d16f1f3a3205e91 | refs/heads/master | 1,673,102,855,024 | 1,604,151,044,000 | 1,604,151,044,000 | 308,930,245 | 0 | 0 | Apache-2.0 | 1,604,164,710,000 | 1,604,163,547,000 | null | UTF-8 | Lean | false | false | 7,532 | 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.Mon.basic
import category_theory.limits.limits
import category_theory.limits.concrete_category
/-!
# The category of monoids has all colimits... |
6bf666773f6762eba95d96190de384c6282581be | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/matrix/char_p.lean | f03da05daa31613bddfe5ffb89c3f8eaf9956779 | [
"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 | 586 | 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 data.matrix.basic
import algebra.char_p.basic
/-!
# Matrices in prime characteristic
-/
open matrix
variables {n : Type*} [fintype n] {R : Type*} [ring R]
in... |
c4973766e87e5d458523f8ddf0bdef8c8d1d90b8 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/asymptotics/theta.lean | 98375933808fcfac731d38174c61c77366be1cd1 | [
"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 | 9,086 | 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.asymptotics.asymptotics
/-!
# Asymptotic equivalence up to a constant
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file ... |
450f411dbee924b71dd18b5e9dbd0abf14bce7bf | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/combinatorics/composition.lean | a9236a5cd848cee1709c8e4952ae3716acdc9434 | [
"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 | 34,324 | lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import data.fintype.card
import data.finset.sort
import tactic.omega
/-!
# Compositions
A composition of an integer `n` is a decomposition `n = i₀ + ... + i_{... |
a6f280fd18d30148c29d29be9362800de53b93fb | 01ae0d022f2e2fefdaaa898938c1ac1fbce3b3ab | /categories/opposites.lean | bb869f76a9dd629fb1d585532adb0f01ad987821 | [] | 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 | 1,729 | 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 .functor
import .products
import .types
open categories
open categories.functor
open categories.products
open categories.types
namespace ... |
b055472e7ee404a69c9aea4f5e20ca748235c984 | a7602958ab456501ff85db8cf5553f7bcab201d7 | /Notes/Logic_and_Proof/Chapter4/4.11.lean | 742f0000304c6a3a67d31154b38f4399908331a2 | [] | no_license | enlauren/math-logic | 081e2e737c8afb28dbb337968df95ead47321ba0 | 086b6935543d1841f1db92d0e49add1124054c37 | refs/heads/master | 1,594,506,621,950 | 1,558,634,976,000 | 1,558,634,976,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 449 | lean | -- Simple proof of A /\ A, with a variable, and hypothesis assumption.
variable A: Prop
-- See how instead of explicitly writing the assumption |h1| as a variable, we
-- can still create this hypothesis on the fly when we need it via 'assume'.
-- We put a comma after the localized hypothesis, and we can refer to it l... |
8f0402a7f70b3e7931f4ca6e62b0c83fff975357 | 94637389e03c919023691dcd05bd4411b1034aa5 | /src/inClassNotes/langs/bool_expr.lean | fa2d87b1ace5863439f7f1fdee570d696598eb49 | [] | 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 | 2,448 | lean | inductive bool_var : Type
| mk (n : nat)
open bool_var
/-
Abstract syntax
-/
inductive bool_expr : Type
| lit_expr : bool → bool_expr
| var_expr : bool_var → bool_expr
| and_expr : bool_expr → bool_expr → bool_expr
| or_expr : bool_expr → bool_expr → bool_expr
| impl_expr : bool_expr → bool_expr → bool_expr -- N... |
4eed6008e97508c7930af83803c4dda2a854b56a | 5ee26964f602030578ef0159d46145dd2e357ba5 | /src/for_mathlib/equiv.lean | 513d4b474aa76f7e94316828c3cb2a993ae91f39 | [
"Apache-2.0"
] | permissive | fpvandoorn/lean-perfectoid-spaces | 569b4006fdfe491ca8b58dd817bb56138ada761f | 06cec51438b168837fc6e9268945735037fd1db6 | refs/heads/master | 1,590,154,571,918 | 1,557,685,392,000 | 1,557,685,392,000 | 186,363,547 | 0 | 0 | Apache-2.0 | 1,557,730,933,000 | 1,557,730,933,000 | null | UTF-8 | Lean | false | false | 5,384 | lean | import data.equiv.basic algebra.group
import order.basic logic.basic -- needed for order stuff
import for_mathlib.with_zero
import data.equiv.algebra
def equiv.with_zero_equiv {α β : Type*} (h : α ≃ β) : (with_zero α) ≃ (with_zero β) :=
{ to_fun := with_zero.map h,
inv_fun := with_zero.map h.symm,
left_inv := λ x,... |
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