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d285567b863d12d2b26f4012a04f030a0d153326 | 8e31b9e0d8cec76b5aa1e60a240bbd557d01047c | /scratch/simplex_no_prebasis.lean | 6a480bc27131e63410d16cae1f1620b95a109096 | [] | no_license | ChrisHughes24/LP | 7bdd62cb648461c67246457f3ddcb9518226dd49 | e3ed64c2d1f642696104584e74ae7226d8e916de | refs/heads/master | 1,685,642,642,858 | 1,578,070,602,000 | 1,578,070,602,000 | 195,268,102 | 4 | 3 | null | 1,569,229,518,000 | 1,562,255,287,000 | Lean | UTF-8 | Lean | false | false | 12,544 | lean | import data.matrix data.rat.basic .misc tactic.fin_cases
import .matrix_pequiv order.order_iso .simplex_new_pivot
open matrix fintype finset function pequiv simplex simplex.prebasis
variables {m n k: ℕ}
local notation `rvec`:2000 n := matrix (fin 1) (fin n) ℚ
local notation `cvec`:2000 m := matrix (fin m) (fin 1) ℚ
... |
a48159ea13816dc24c9156efb1f7b1647953e313 | 432d948a4d3d242fdfb44b81c9e1b1baacd58617 | /src/algebra/lie/classical.lean | 4c367d69213d9ca8f50da84d091a3af4dbcf6c3f | [
"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 | 13,446 | lean | /-
Copyright (c) 2020 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import algebra.invertible
import algebra.lie.skew_adjoint
import algebra.lie.abelian
/-!
# Classical Lie algebras
This file is the place to find definitions and basic pro... |
cff42e258316d7b013ed294848b31aaadfe08e1c | 07c6143268cfb72beccd1cc35735d424ebcb187b | /src/data/nat/choose.lean | 26fe07a9839813c8504b036444daaad51869abd2 | [
"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 | 4,296 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Bhavik Mehta
-/
import data.nat.basic data.nat.prime
import algebra.big_operators algebra.commute
open nat
lemma nat.prime.dvd_choose {p k : ℕ} (hk : 0 < k) (hkp : k < p)... |
5bbfcf8aca75c9bf273a866be99df8e2e4cd13d2 | 0c1546a496eccfb56620165cad015f88d56190c5 | /library/tools/super/lpo.lean | 46584aa4836aba3ce68b56685e46a479dfcc6522 | [
"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 | 1,633 | lean | /-
Copyright (c) 2016 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner
-/
-- Polytime version of lexicographic path order as described in:
-- Things to know when implementing LPO, Bernd Löchner, ESFOR 2004
import .utils
open expr decidable m... |
a67c75c0ddd7a673e68a3f4f777f59d613db2230 | 4038e103ed66b0dd716900a90166626946bc33fd | /example/src/limits.lean | 1214da740143939749eb7c94c735b61b0c1812de | [
"Apache-2.0"
] | permissive | mpedramfar/format_lean | 4be57fda2840ed11aed56d3149597ce693b3a6bc | 6d9885532699fcf6bd8fa9048c68762d5b6bfd8d | refs/heads/master | 1,587,910,517,162 | 1,555,352,005,000 | 1,555,352,005,000 | 173,606,917 | 1 | 0 | Apache-2.0 | 1,553,459,953,000 | 1,551,634,180,000 | CSS | UTF-8 | Lean | false | false | 7,079 | lean | import data.real.basic
import algebra.pi_instances
import tactic.linarith
import xenalib.M1P1
noncomputable theory
local attribute [instance, priority 0] classical.prop_decidable
namespace M1P1
notation `|` x `|` := abs x
definition is_limit (a : ℕ → ℝ) (l : ℝ) : Prop :=
∀ ε > 0, ∃ N, ∀ n ≥ N, | a n - l | < ε
def... |
59d5d2fc2db9cfa251cac22eaf58e9a4a214370f | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/finset/lattice.lean | 7f4fd05ff626fd79583b04bc2c00e3973768122d | [
"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 | 30,805 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
-/
import data.finset.fold
import data.multiset.lattice
import order.order_dual
import order.complete_lattice
/-!
# Lattice operations on finsets
-/
variables {α β γ : ... |
59c06e091a8e97b73f578f133c0e7015e028cc97 | 3f7026ea8bef0825ca0339a275c03b911baef64d | /src/tactic/core.lean | 50a4dcd7e848407e3f5de5159a24b789b65a05e8 | [
"Apache-2.0"
] | permissive | rspencer01/mathlib | b1e3afa5c121362ef0881012cc116513ab09f18c | c7d36292c6b9234dc40143c16288932ae38fdc12 | refs/heads/master | 1,595,010,346,708 | 1,567,511,503,000 | 1,567,511,503,000 | 206,071,681 | 0 | 0 | Apache-2.0 | 1,567,513,643,000 | 1,567,513,643,000 | null | UTF-8 | Lean | false | false | 40,885 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Simon Hudon, Scott Morrison, Keeley Hoek
-/
import data.dlist.basic category.basic meta.expr meta.rb_map data.string.defs
namespace expr
open tactic
attribute [derive... |
827d08ac52977c424eaa1c239618363d3fdb30c9 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/ring_theory/perfection.lean | c4f8b0bb7bb69d571370d19e842512c2598f237a | [
"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 | 25,423 | 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.char_p.pi
import algebra.char_p.quotient
import algebra.char_p.subring
import algebra.ring.pi
import analysis.special_functions.pow
import field_theory.perfect_... |
9d29f368f3496df0a8fd85208e44a50c6bd000ac | 3f7026ea8bef0825ca0339a275c03b911baef64d | /src/category_theory/pempty.lean | 4866002e44c05a213f8aa5863bbc3365406227c4 | [
"Apache-2.0"
] | permissive | rspencer01/mathlib | b1e3afa5c121362ef0881012cc116513ab09f18c | c7d36292c6b9234dc40143c16288932ae38fdc12 | refs/heads/master | 1,595,010,346,708 | 1,567,511,503,000 | 1,567,511,503,000 | 206,071,681 | 0 | 0 | Apache-2.0 | 1,567,513,643,000 | 1,567,513,643,000 | null | UTF-8 | Lean | false | false | 1,044 | 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.discrete_category
import category_theory.equivalence
/-!
# The empty category
Defines a category structure on `pempty`, and the unique functo... |
6266b1e3a558057e957be339f8da33b4a346d8f6 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/data/nat/pow.lean | f7b3ff1ca9c3f8f7f16e6e9f9e0855470531ec47 | [
"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 | 11,344 | 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.order
/-! # `nat.pow`
Results on the power operation... |
4a0354a1e37cfd40a0464e2ec606256a6bc4e4bf | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /stage0/src/Lean/CoreM.lean | e2a3f6b2552f9f6efbf80ea432f5e8ff6539edfe | [
"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 | 4,375 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Util.RecDepth
import Lean.Util.Trace
import Lean.Environment
import Lean.Exception
import Lean.InternalExceptionId
import Lean.Eval
import Lean.... |
bcafbad784958cc8f22b73a59ef925a750781eea | 5749d8999a76f3a8fddceca1f6941981e33aaa96 | /src/geometry/manifold/manifold.lean | 844c6557bef8ef2b8b1b85d14837df187968c57f | [
"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 | 26,482 | 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 topology.local_homeomorph
/-!
# Manifolds
A manifold is a topological space M locally modelled on a model space H, i.e., the manifold is
covered by op... |
ed39cc688e7913a09243b3495254748f56d5cc86 | 33340b3a23ca62ef3c8a7f6a2d4e14c07c6d3354 | /lia/wf_sqe.lean | 1f0481ad0c9872ed574d32ae6e4de24754c9aef7 | [] | no_license | lclem/cooper | 79554e72ced343c64fed24b2d892d24bf9447dfe | 812afc6b158821f2e7dac9c91d3b6123c7a19faf | refs/heads/master | 1,607,554,257,488 | 1,578,694,133,000 | 1,578,694,133,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,380 | lean | import .sqe .wf
open list
lemma atom.unify_dvd (m d i k ks) :
k ≠ 0 → atom.unify m (atom.dvd d i (k::ks)) =
(let m' := has_div.div m k in
atom.dvd (m' * d) (m' * i) (1 :: list.map (λ x, m' * x) ks)) :=
begin intro hne, cases k, exfalso, apply hne, repeat {refl} end
lemma atom.unify_ndvd (m d i k ks) :
k ... |
bd57687399347b1f8e24ddbb405457b5299fc254 | 6d50885e7b3f72447a03f21d5268d6af87c0a404 | /instructor-notes/quiz1.lean | 6f178c08fdeb4fa458be82f4f121bce252e18078 | [] | no_license | kevinsullivan/uva-cs-dm-s20-old | 583c756cded281fcee7f1afc42cb3e08f89c2493 | 797672cb0ffae6a42a3518c9225d5807191fd113 | refs/heads/master | 1,607,500,914,982 | 1,578,752,991,000 | 1,578,752,991,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 355 | lean | def s1 := "Hello, "
def s2 := "Lean!"
def s3 := "Hello, Lean!"
theorem t1 : s1 ++ s2 = s3 := eq.refl "Hello, Lean!"
theorem t2 : 4 * 4 = 16 := eq.refl 16
def square : ℕ → ℕ
| n := n^2
theorem t3 : s1 ++ s2 = s3 ∧ square 5 = 25 :=
and.intro t1 (eq.refl 25)
theorem t4 : (s1 ++ s2 = s3 ∧ square 5 = 25) → (square 5 ... |
dd91d8639b958caf97e54f55fc753e2e20ffd2f1 | 22e97a5d648fc451e25a06c668dc03ac7ed7bc25 | /src/algebra/associated.lean | b7a3b895ba74efed8a6ebf532a877ea7e8d64d29 | [
"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 | 25,125 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker
-/
import data.multiset
/-!
# Associated, prime, and irreducible elements.
-/
variables {α : Type*} {β : Type*} {γ : Type*} {δ : Type*}
@[simp] theore... |
b6d7bc2bf4e2945ee7ca287f65737dd5f1448bc1 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Meta/Tactic/Simp/Types.lean | 5e43fd79f4f5a901bb5e3695d0d1bb38acd9b148 | [
"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 | 3,239 | 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.AppBuilder
import Lean.Meta.CongrTheorems
import Lean.Meta.Tactic.Simp.SimpTheorems
import Lean.Meta.Tactic.Simp.SimpCongrTheorems
namespa... |
d9f99297643bce7a49f118f819bc3f2698c8a3c3 | 38bf3fd2bb651ab70511408fcf70e2029e2ba310 | /src/ring_theory/integral_closure.lean | b62b126ac3f9f5cf6df98daf0cc967fdd53b8259 | [
"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 | 13,716 | lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
Integral closure of a subring.
-/
import ring_theory.adjoin linear_algebra.finsupp
universes u v
open polynomial submodule
variables (R : Type u) {A : Type v}
variables [comm... |
31f6be00945a29deec437b007dc2e67b4c561fc5 | e24425fbf75189e4b34ef6b29f5f274e70cd5011 | /src/cheatsheet.lean | 66819e2519c8460ec5f00a35b46c03d47b23c53f | [] | no_license | UVM-M52/week04-chuyisun | a654ea18050ca25b2d2865cfcf568c89cde593dd | ed1dafaa43d33e878e71dbdac00535118afd3afc | refs/heads/master | 1,609,225,390,456 | 1,581,527,077,000 | 1,581,527,077,000 | 238,504,390 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,905 | lean | -- Math 52: Cheatsheet
--------------------------------
-- BASIC GOAL TRANSFORMATIONS --
--------------------------------
-- Conjunctive Goal
-- Use `split`:
example (P Q : Prop) : P ∧ Q :=
begin
split,
-- you can use braces to separate the two resulting goals
{ sorry },
{ sorry },
end
-- Conditional Goal
-- Use `in... |
bd889dd5fe691bfd5f3a7c211f6daf08ba276eeb | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/data/polynomial/lifts.lean | 7287e62f4e9cffe5ade3ac61f22921e71cb07bfb | [
"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 | 10,845 | lean | /-
Copyright (c) 2020 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Riccardo Brasca
-/
import data.polynomial.algebra_map
import algebra.algebra.subalgebra
import algebra.polynomial.big_operators
import data.polynomial.erase_lead
import data.polynomia... |
4858fca8d9b4583a2ca12c719cb0b68e31c1dd87 | 5883d9218e6f144e20eee6ca1dab8529fa1a97c0 | /src/data/sigma/extra.lean | c3be336d7caf20262630a9adb505f5e58184b426 | [] | 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 | 770 | lean | /-
This file contains extra definitions and theorems for `sigma` and `psigma`.
-/
universes u v
namespace psigma ---------------------------------------------------------------
variables {A : Sort u} {B : A → Sort v} {a₁ a₂ : A} {b₁ : B a₁} {b₂ : B a₂}
@[simp]
theorem fst.unwrap (a : A) (b : B a) : (psigma.mk a b... |
7fdce22e41aefcf6d43b89e10dc51ce354ea6806 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/limits/small_complete.lean | ec2c0890459c543e17f80f78aa38717665243980 | [] | 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 | 1,404 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Bhavik Mehta
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.limits.shapes.products
import Mathlib.set_theory.cardinal
import Mathlib.PostPor... |
a06501afc585e4ea2dc08f44b0e13fc7f2388468 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/analysis/inner_product_space/projection.lean | da8e75c73031edb064da82fcb8de3c7501fc83a5 | [
"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 | 48,519 | lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Frédéric Dupuis, Heather Macbeth
-/
import analysis.inner_product_space.basic
import analysis.convex.basic
/-!
# The orthogonal projection
Given a nonempty complete sub... |
d1c9b2be233f04d8862a9d7f03ecb4a8e5e61cb1 | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/topology/uniform_space/separation.lean | aff8310e801ef3a5215b07c63f3fba0d43344c8c | [
"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 | 13,591 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot
Hausdorff properties of uniform spaces. Separation quotient.
-/
import topology.uniform_space.basic
open filter topological_space lattice set classica... |
0f5d3cf73322074c5a0889f61d387031768f5edb | 94e33a31faa76775069b071adea97e86e218a8ee | /src/algebraic_geometry/projective_spectrum/structure_sheaf.lean | 0e0ef27f638d37b82bd09b6e6512716deebcd0bf | [
"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 | 17,735 | lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
import algebraic_geometry.projective_spectrum.topology
import topology.sheaves.local_predicate
import ring_theory.graded_algebra.homogeneous_localization
import algebraic... |
589f97d2ce2e51a4f2783b674691e0680fd277b4 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /library/data/stream.lean | 0091bb758ee3d4069ada0f04af30ba10b8f0d2a2 | [
"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 | 22,500 | 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
-/
import data.nat data.list data.equiv
open nat function option
definition stream (A : Type) := nat → A
namespace stream
variables {A B C : Type}
definition... |
633178f0f5966c0b0d8993d6a6160238663b9dd5 | 5ec8f5218a7c8e87dd0d70dc6b715b36d61a8d61 | /cop.lean | 74e73a72826e5521c660b52ad39326c782c159ac | [] | no_license | mbrodersen/kremlin | f9f2f9dd77b9744fe0ffd5f70d9fa0f1f8bd8cec | d4665929ce9012e93a0b05fc7063b96256bab86f | refs/heads/master | 1,624,057,268,130 | 1,496,957,084,000 | 1,496,957,084,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 43,740 | lean |
/- Arithmetic and logical operators for the Compcert C and Clight languages -/
import .ctypes .memory
namespace cop
open ast integers floats values memory ctypes word
ctypes.intsize ctypes.floatsize ctypes.signedness
/- * Syntax of operators. -/
inductive unary_operation : Type
| Onotbool /- boolean ... |
76818fb20a39d8cb42215b4741e335e4836aa7f8 | 618003631150032a5676f229d13a079ac875ff77 | /src/data/real/irrational.lean | e8b361750c2f165fa1519f3fb11af14d6acbbdc4 | [
"Apache-2.0"
] | permissive | awainverse/mathlib | 939b68c8486df66cfda64d327ad3d9165248c777 | ea76bd8f3ca0a8bf0a166a06a475b10663dec44a | refs/heads/master | 1,659,592,962,036 | 1,590,987,592,000 | 1,590,987,592,000 | 268,436,019 | 1 | 0 | Apache-2.0 | 1,590,990,500,000 | 1,590,990,500,000 | null | UTF-8 | Lean | false | false | 8,234 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Yury Kudryashov.
-/
import data.real.basic
import algebra.gcd_domain
import ring_theory.multiplicity
/-!
# Irrational re... |
35ee8d9b6f9e455de84da9e8d2e50850c64713f0 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/int/absolute_value.lean | 745c78c96b006721f6bae5a1ebba5106f6636312 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 1,409 | lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import algebra.module.basic
import algebra.order.absolute_value
import data.int.cast.lemmas
import data.int.units
import group_theory.group_action.units
/-!
# Absolute val... |
608d9899698c0f87411e837400a618909de006de | eb9357a70318e50e095b58730bebfe0cffee457f | /lean/love08_operational_semantics_demo.lean | 0da711cf2d2ee7fcb04009018a0fbfacb4c4b74f | [] | no_license | Vierkantor/logical_verification_2021 | 7485dd916953131d501760f023d5b30fbb74d36a | 9500b9c194e22a9ab4067321cfed7a1f445afcfc | refs/heads/main | 1,692,560,845,086 | 1,624,721,275,000 | 1,624,721,275,000 | 416,354,079 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 22,102 | lean | import .lovelib
/-! # LoVe Demo 8: Operational Semantics
In this and the next two lectures, we will see how to use Lean to specify the
syntax and semantics of programming languages and to reason about the
semantics. -/
set_option pp.beta true
set_option pp.generalized_field_notation false
namespace LoVe
/-! ## ... |
e7fa2a4925ea516d2ad09489609f1acadc27c12f | 968e2f50b755d3048175f176376eff7139e9df70 | /examples/prop_logic_theory/unnamed_601.lean | fb85cf8fad7cd4d72d173f54afcc6fa59f60ce2c | [] | no_license | gihanmarasingha/mth1001_sphinx | 190a003269ba5e54717b448302a27ca26e31d491 | 05126586cbf5786e521be1ea2ef5b4ba3c44e74a | refs/heads/master | 1,672,913,933,677 | 1,604,516,583,000 | 1,604,516,583,000 | 309,245,750 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 140 | lean | variables p q r : Prop
-- BEGIN
example (h₁ : p → q) (h₂ : q → r) (h₃ : p) : r :=
begin
show r, from h₂ (h₁ h₃)
end
-- END |
de10365672ca3c44ea1177549c6ebe68adaed394 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/eq5.lean | 77f9f9a7a8924423c173f9129e5ffe8f9a0e5a39 | [
"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 | 261 | lean | open nat
definition fib : nat → nat
| 0 := 1
| 1 := 1
| (x+2) := fib x + fib (x+1)
theorem fib0 : fib 0 = 1 :=
rfl
theorem fib1 : fib 1 = 1 :=
rfl
theorem fib_succ_succ (a : nat) : fib (a+2) = fib a + fib (a+1) :=
rfl
example : fib 8 = 34 :=
rfl
|
d30096efef9f2eb63435f02e428fba1a045c9568 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/polynomial/degree/trailing_degree.lean | b78c13868af37a7bc454ad5792977991cd91497a | [
"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 | 16,150 | lean | /-
Copyright (c) 2020 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import data.enat.basic
import data.polynomial.degree.definitions
/-!
# Trailing degree of univariate polynomials
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any chan... |
2c29ffbb64b1ab16ca0e3b1132740d36ebee5dfe | b392eb79fb36952401156496daa60628ccb07438 | /Lib4/Examples/Asymptotics.lean | 685573fef94c1be2cc344bb0948786ecada67597 | [
"Apache-2.0"
] | permissive | AurelienSaue/mathportsource | d9eabe74e3ab7774baa6a10a6dc8d4855ff92266 | 1a164e4fff7204c522c1f4ecc5024fd909be3b0b | refs/heads/master | 1,685,214,377,305 | 1,623,621,223,000 | 1,623,621,223,000 | 364,191,042 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,822 | lean | import Mathlib.analysis.normed_space.basic
import Mathlib.topology.local_homeomorph
namespace Mathlib
open filter
open set
namespace asymptotics
-- TODO: Type* syntax
variable {α : Type} {β : Type} {E : Type} {F : Type} {G : Type}
{E' : Type} {F' : Type} {G' : Type} {R : Type} {R' : Type}
variable [has_norm E] [... |
dc18626f2308c2820c4f4695d267ae699f1b2540 | 8b9f17008684d796c8022dab552e42f0cb6fb347 | /library/algebra/bundled.lean | ea41110d5eea5541e2601bdb75423a41ae1a1e30 | [
"Apache-2.0"
] | permissive | chubbymaggie/lean | 0d06ae25f9dd396306fb02190e89422ea94afd7b | d2c7b5c31928c98f545b16420d37842c43b4ae9a | refs/heads/master | 1,611,313,622,901 | 1,430,266,839,000 | 1,430,267,083,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,092 | lean | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.bundled
Authors: Jeremy Avigad
Bundled structures
-/
import algebra.group
namespace algebra
structure Semigroup :=
(carrier : Type) (struct : semigroup carrier)
attribute Sem... |
88bcd8de74dab09a4b456d539ac8c1ca888ce82d | 9a0b1b3a653ea926b03d1495fef64da1d14b3174 | /tidy/rewrite_search/discovery/collector/common.lean | 9af8e8640ddd53745a08ff117ce95e69d7b669dd | [
"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 | 614 | lean | import tidy.rewrite_all_wrappers
import ..screening
open tactic
namespace tidy.rewrite_search.discovery
meta def are_promising_rewrites (rws : list (expr × bool)) : list expr → tactic bool
| [] := return false
| (s :: rest) := do
-- TODO alternative (and probably better) condition:
-- tt if the rewrite list contain... |
e9995ed4550040e98410d68aa7f500648ba747f7 | b392eb79fb36952401156496daa60628ccb07438 | /Lib4/PostPort/Coe.lean | 421e9609549f3dfd774132b1b498260969f98384 | [
"Apache-2.0"
] | permissive | AurelienSaue/mathportsource | d9eabe74e3ab7774baa6a10a6dc8d4855ff92266 | 1a164e4fff7204c522c1f4ecc5024fd909be3b0b | refs/heads/master | 1,685,214,377,305 | 1,623,621,223,000 | 1,623,621,223,000 | 364,191,042 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 869 | lean | import Lean3Lib.init.coe
universes u v
variable {α : Sort u} {β : Sort v}
noncomputable instance hasCoe [inst : Mathlib.has_coe α β] : Coe α β := {
coe := @Mathlib.has_coe.coe _ _ inst
}
-- TODO: why does mathlib declare these instances directly?
-- topology/algebra/open_subgroup.lean:42:instance has_coe_set : has... |
b03a630aceb799e31902e8a4b1f4b8d434c5636f | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/group_theory/submonoid/default.lean | da25bc98ded11455a6ebed7a7bdcc44350f99588 | [
"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 | 41 | lean | import group_theory.submonoid.membership
|
102127d7b0bd5c152864660cabb582d503e39757 | c6da0300d417abe3464e750ab51a63502b93acfa | /src/struct_tact/traversals.lean | b0787afdfa51319d27a2bf939567227ffb550bff | [
"Apache-2.0"
] | permissive | uwplse/struct_tact | 55bc1d260fac498cff83a4d71461041f8ed74bd6 | 22188ea2e97705d1185f75dde24e6bab88054ab0 | refs/heads/master | 1,630,670,592,496 | 1,515,453,299,000 | 1,515,453,299,000 | 104,603,771 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,585 | lean | open tactic
def for_m {m : Type → Type} {α β : Type} [monad_m : monad m] (action : list α) (f : α → m β) : m (list β) :=
monad.mapm f action
private meta def until_first_hyp_aux (f : expr → tactic unit) : list expr → tactic unit
| [] := tactic.fail "until_first_hyp: provided tactic did not succed on any hypotheses"
|... |
f825c0c89f6064987314c8e1451bafdd18dd60b3 | fe25de614feb5587799621c41487aaee0d083b08 | /stage0/src/Lean/Parser/Term.lean | fc382501c8d1689bc136b57ed343e2800d159664 | [
"Apache-2.0"
] | permissive | pollend/lean4 | e8469c2f5fb8779b773618c3267883cf21fb9fac | c913886938c4b3b83238a3f99673c6c5a9cec270 | refs/heads/master | 1,687,973,251,481 | 1,628,039,739,000 | 1,628,039,739,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 18,069 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
import Lean.Parser.Attr
import Lean.Parser.Level
namespace Lean
namespace Parser
namespace Command
def commentBody : Parser :=
{ fn := ... |
1a3df664b7f79c86fb3c52565eb11484f79e8a2c | ebbdcbd7ddc89a9ef7c3b397b301d5f5272a918f | /qp/p1_categories/c2_limits/s2_products.lean | 4d37ffb3c0bb9940bb984c9270c6aeac0ff30a8d | [] | no_license | intoverflow/qvr | 34b9ef23604738381ca20b7d622fd0399d88f2dd | 0cfcd33fe4bf8d93851a00cec5bfd21e77105d74 | refs/heads/master | 1,616,591,570,371 | 1,492,575,772,000 | 1,492,575,772,000 | 80,061,627 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 46,643 | lean | /- -----------------------------------------------------------------------
Products and co-products.
----------------------------------------------------------------------- -/
import .s1_limits
namespace qp
open stdaux
universe variables ℓ ℓobj ℓhom ℓobj₁ ℓhom₁ ℓobj₂ ℓhom₂
/- ------------------------------------... |
cca935c381146a0ec93c4a048d93ba493ef538ac | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/tactic1.lean | d50e4cfbc3cae046b562955c9223f159065b8e47 | [
"Apache-2.0"
] | permissive | soonhokong/lean | cb8aa01055ffe2af0fb99a16b4cda8463b882cd1 | 38607e3eb57f57f77c0ac114ad169e9e4262e24f | refs/heads/master | 1,611,187,284,081 | 1,450,766,737,000 | 1,476,122,547,000 | 11,513,992 | 2 | 0 | null | 1,401,763,102,000 | 1,374,182,235,000 | C++ | UTF-8 | Lean | false | false | 78 | lean | import logic
theorem tst {A B : Prop} (H1 : A) (H2 : B) : A
:= by assumption
|
b22233c22796b8d1795d0a389a15f9c130d67c62 | 928e43dd755d83a0986ba91420df8ad05b8d7c9f | /4_equality.lean | 4dff52ee970a87d935784636061ac54e369b1851 | [] | no_license | zmactep/llfgg | ea222b377095a42e0de5cf8d4846aff806ce0f31 | ed684ae69b94a4a042615c412fef68bdec8fc80c | refs/heads/master | 1,585,131,334,279 | 1,533,894,322,000 | 1,533,894,322,000 | 143,688,771 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,529 | lean | -- Отношения
universe u
variables α β : Type u -- Рассмотрим некоторый произвольный тип α
variable r : α → α → Prop -- Введем на нем бинарное отноешние r
variable trans_r : ∀ {x y z : α}, -- мы можем объявить его транзитивным, указав следующий ф... |
143ee6e56bc1991091c7806cd079af0ea25baa6a | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/linear_algebra/matrix/to_linear_equiv.lean | 6e63a780885efb1d1cd695932754bd9f03fb3c78 | [
"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 | 7,095 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-/
import linear_algebra.matrix.nonsingular_inverse
import linear_algebra.matrix.to_lin
import ring_theory.localization
/-!
# ... |
0c04a14152ec10e5e349d0a8f94b5ffe658d42fc | 6096e76aa1d83b3f250d2c69eeda5b692d6bd3e2 | /src/norms.lean | 945c250b1a93083587587359d9d384bf3b608385 | [] | no_license | ChrisHughes24/lean-differential-topology | 3782f1841e5205f76a122b7e8ceb9c65ace06088 | 0abdf5a61414459fb0833f39b4d04c3528404454 | refs/heads/master | 1,584,570,674,323 | 1,527,526,729,000 | 1,527,526,729,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 12,169 | lean | import analysis.real
import linear_algebra.prod_module
import algebra.pi_instances
import metric_space_fintype_pi
noncomputable theory
local notation f `→_{`:50 a `}`:0 b := filter.tendsto f (nhds a) (nhds b)
class normed_group (α : Type*) extends add_comm_group α, metric_space α :=
(norm : α → ℝ)
(dist_eq : ∀ x y, ... |
72f966bb5c5bb15214613e7ff29f1600106d44d4 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/topology/metric_space/closeds.lean | 1bfc5f88f691e101bef8434d1b77b791b6a726f5 | [
"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 | 22,426 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Sébastien Gouëzel
-/
import topology.metric_space.hausdorff_distance topology.opens
/-!
# Closed subsets
This file defines the metric and emetric space structure on the types of c... |
56110f789e3a86361125464b81b4d09ad0a1b6d7 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/order/monovary.lean | e9f9d840555e4cf552bb2415e447df4bfc8bf81b | [
"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 | 11,192 | lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import data.set.basic
/-!
# Monovariance of functions
Two functions *vary together* if a strict change in the first implies a change in the second.
This is in some sen... |
b9b92823f130804008a3993924da55cd23433383 | 367134ba5a65885e863bdc4507601606690974c1 | /src/category_theory/monad/basic.lean | 241833a1a3052cedbe6231d22b552b6540ff22c4 | [
"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 | 8,305 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Bhavik Mehta, Adam Topaz
-/
import category_theory.functor_category
import category_theory.fully_faithful
namespace category_theory
open category
universes v₁ u₁ -- d... |
3d54b3fd8deefc39f9e159013af5bcca8369af81 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/tactic/lift.lean | 525f972f60d7ae2930c9cfd9e880c159476d5088 | [
"Apache-2.0"
] | permissive | dupuisf/mathlib | 62de4ec6544bf3b79086afd27b6529acfaf2c1bb | 8582b06b0a5d06c33ee07d0bdf7c646cae22cf36 | refs/heads/master | 1,669,494,854,016 | 1,595,692,409,000 | 1,595,692,409,000 | 272,046,630 | 0 | 0 | Apache-2.0 | 1,592,066,143,000 | 1,592,066,142,000 | null | UTF-8 | Lean | false | false | 9,242 | lean | /-
Copyright (c) 2019 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import tactic.rcases
/-!
# lift tactic
This file defines the lift tactic, allowing the user to lift elements from one type to another
under a specified condition... |
20233da4173b2979a9948ba4eb57b4c9010d2b49 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/control/reader.lean | d5b8b3df112b8d4a7ddbd6032bf5f90b9b5bab5b | [] | 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 | 6,206 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
The reader monad transformer for passing immutable state.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.control.lift
import Mathlib.Lean3Lib.init.con... |
88c077d3b8cbedb3224982e18ed2f03a1cfdb8cb | 92b50235facfbc08dfe7f334827d47281471333b | /library/data/bool.lean | 65a43a79f06ad8fc971ce08ab7165b86e4be57d4 | [
"Apache-2.0"
] | permissive | htzh/lean | 24f6ed7510ab637379ec31af406d12584d31792c | d70c79f4e30aafecdfc4a60b5d3512199200ab6e | refs/heads/master | 1,607,677,731,270 | 1,437,089,952,000 | 1,437,089,952,000 | 37,078,816 | 0 | 0 | null | 1,433,780,956,000 | 1,433,780,955,000 | null | UTF-8 | Lean | false | false | 3,500 | 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
-/
import logic.eq
open eq eq.ops decidable
namespace bool
local attribute bor [reducible]
local attribute band [reducible]
theorem dichotomy (b : bool... |
14773e8c3b6b8600d615aa418355b5da91b5c43e | febba19712b2aefe4d6c7fb0230b8d7e272c98c4 | /src/proof.lean | 77bb3008e6cd36370b8b4c67f67f920dc84f56f4 | [] | no_license | hcheval/formalized-proof-mining | e6eb980feb644ae269f43d9af93ac584b7a47a17 | 216cc73fccd84900a1ba7eaae5f73732496d6afe | refs/heads/master | 1,689,621,410,792 | 1,629,912,272,000 | 1,629,912,272,000 | 399,855,572 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,645 | lean | import formula
import dialectica
import utils
section basics
variables {ι : Type} {gri : ground_interpretation ι}
local notation `𝔽` := formula ι gri
local notation `𝕋` := type ι gri
variables (greq : Π {i : ι}, ∥𝕏 i // gri ∥ → ∥𝕏 i // gri ∥ → 𝔽)
local infixr `≅` : 35 := formula.eqext @greq
stru... |
4e476b441308db7d2c359683660a246737b854cb | 3b1abba731363bfec018d9d2cfee7fd90e1dc93c | /lemmas_for_RT_n_m.lean | d62b154f2f958bea856b0e272cd7848bade655af | [] | no_license | minchaowu/Ramsey.lean | dcf4e0845cca6dc02ef898f3fd9123c079c5a1a9 | 8ebbead4869bdf3f4788137411c5f36f2e72943a | refs/heads/master | 1,610,462,544,433 | 1,488,596,497,000 | 1,488,596,497,000 | 72,063,527 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,229 | lean | import definitions
open classical set nat decidable prod subtype
section
-- the least number principle.
lemma alt_of_wf {A : set ℕ}: ∀ n, n ∈ A → ∃₀ a ∈ A, ∀₀ b ∈ A, a ≤ b :=
take n,
nat.strong_induction_on n
(take n, assume IH, assume ninA,
by_cases
(suppose ∃₀ m ∈ A, m < n,
obtain m (Hm : m ∈ A ∧ m < n), from ... |
14a7fd7f15b60c5fdd8af5ea93851a59143603c5 | 9dd3f3912f7321eb58ee9aa8f21778ad6221f87c | /tests/lean/run/overload2.lean | ce4c9fc8676e7d7a9f37a602c6dbbe61550dba33 | [
"Apache-2.0"
] | permissive | bre7k30/lean | de893411bcfa7b3c5572e61b9e1c52951b310aa4 | 5a924699d076dab1bd5af23a8f910b433e598d7a | refs/heads/master | 1,610,900,145,817 | 1,488,006,845,000 | 1,488,006,845,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 739 | lean | import standard
inductive F2 : Type
| O : F2
| I : F2
namespace F2
definition add : F2 → F2 → F2
| O O := O
| O I := I
| I O := I
| I I := O
infix + := F2.add
end F2
open F2 nat
eval (1 : nat) + 1
eval (1 : nat) + (1 : nat)
example : true :=
begin
assert H : (1 : nat) + (1 : nat) = 2,
reflexivity,
constructo... |
57e70bf079114e9326e6348ae04287d8ac402d1e | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/extra/lt_rec.lean | 36393c402d95591a2a4796141b33776af83eb62e | [
"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 | 589 | lean | open nat
set_option pp.implicit true
set_option pp.notation false
definition lt_trans : ∀ {a b c : nat}, a < b → b < c → a < c,
lt_trans h (lt.base _) := lt.step h,
lt_trans h₁ (lt.step h₂) := lt.step (lt_trans h₁ h₂)
definition lt_succ : ∀ {a b : nat}, a < b → succ a < succ b,
lt_succ (lt.base a) := lt.base (s... |
9f8791ce1db87baa3103a20c13589d168f7c7d1e | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/topology/algebra/continuous_functions.lean | e2e2ec485f7a3d54d0a74876b7e20b05e2fcc038 | [
"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 | 14,515 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Nicolò Cavalleri
-/
import topology.algebra.module
import topology.continuous_map
/-!
# Algebraic structures over continuous functions
In this file we define instance... |
038ffe2ab859d7516e5c826a2f8e71d44011bae9 | 75db7e3219bba2fbf41bf5b905f34fcb3c6ca3f2 | /tests/lean/extra/755.hlean | 193156c89e68b9acf2d70d33a033d4a06b81760a | [
"Apache-2.0"
] | permissive | jroesch/lean | 30ef0860fa905d35b9ad6f76de1a4f65c9af6871 | 3de4ec1a6ce9a960feb2a48eeea8b53246fa34f2 | refs/heads/master | 1,586,090,835,348 | 1,455,142,203,000 | 1,455,142,277,000 | 51,536,958 | 1 | 0 | null | 1,455,215,811,000 | 1,455,215,811,000 | null | UTF-8 | Lean | false | false | 1,735 | hlean | import types.eq types.pi hit.colimit
open eq is_trunc unit quotient seq_colim equiv
axiom mysorry : ∀ {A : Type}, A
namespace one_step_tr
section
parameters {A : Type}
variables (a a' : A)
protected definition R (a a' : A) : Type₀ := unit
parameter (A)
definition one_step_tr : Type := quotient R
parameter... |
f0ebe8952b2e943230e338a0dc414d13bfcbc77f | cc060cf567f81c404a13ee79bf21f2e720fa6db0 | /lean/20170212-problem-with-sigma-types.lean | bd35edcad840e1bfa79f903b452cdb591b5d5bec | [
"Apache-2.0"
] | permissive | semorrison/proof | cf0a8c6957153bdb206fd5d5a762a75958a82bca | 5ee398aa239a379a431190edbb6022b1a0aa2c70 | refs/heads/master | 1,610,414,502,842 | 1,518,696,851,000 | 1,518,696,851,000 | 78,375,937 | 2 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 785 | lean | universe variables u v
structure Category :=
(Obj : Type u)
(Hom : Obj → Obj → Type v)
(compose : Π { X Y Z : Obj }, Hom X Y → Hom Y Z → Hom X Z)
universe variables u1 v1 u2 v2
structure Functor (C : Category.{ u1 v1 }) (D : Category.{ u2 v2 }) :=
(onObjects : C^.Obj → D^.Obj)
(onMorphisms : Π { X Y : ... |
3c8516eadf628e93c0d35733bb09ef42cec276e7 | 969dbdfed67fda40a6f5a2b4f8c4a3c7dc01e0fb | /src/ring_theory/discrete_valuation_ring.lean | 43dc5b3b0e6a64bc8a4145ba51b4008e1a322fcd | [
"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 | 16,257 | lean | /-
Copyright (c) 2020 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard
-/
import ring_theory.principal_ideal_domain
import order.conditionally_complete_lattice
import ring_theory.multiplicity
import ring_theory.valuation.basic
/-!
# Discret... |
913996c6bd48bf1e300adb22a765664408ff79e4 | 8cb37a089cdb4af3af9d8bf1002b417e407a8e9e | /library/init/cc_lemmas.lean | 25b276c849a53afa6231e65415f4f4cdfc2826a7 | [
"Apache-2.0"
] | permissive | kbuzzard/lean | ae3c3db4bb462d750dbf7419b28bafb3ec983ef7 | ed1788fd674bb8991acffc8fca585ec746711928 | refs/heads/master | 1,620,983,366,617 | 1,618,937,600,000 | 1,618,937,600,000 | 359,886,396 | 1 | 0 | Apache-2.0 | 1,618,936,987,000 | 1,618,936,987,000 | null | UTF-8 | Lean | false | false | 4,653 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.propext init.classical
/- Lemmas use by the congruence closure module -/
lemma iff_eq_of_eq_true_left {a b : Prop} (h : a = true) : (a... |
d2153bc80c106e90d25671b52b4f2b4f999e7902 | ac89c256db07448984849346288e0eeffe8b20d0 | /src/Lean/Elab/DeclModifiers.lean | e241a6de6b5a7ea518bb2f465fd14a24d3e7b54e | [
"Apache-2.0"
] | permissive | chepinzhang/lean4 | 002cc667f35417a418f0ebc9cb4a44559bb0ccac | 24fe2875c68549b5481f07c57eab4ad4a0ae5305 | refs/heads/master | 1,688,942,838,326 | 1,628,801,942,000 | 1,628,801,995,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,050 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
import Lean.Modifiers
import Lean.DocString
import Lean.Elab.Attributes
import Lean.Elab.Exception
import Lean.Elab.DeclUtil
namespace L... |
ea188f9b6a820788f35555145827ead55bb800d8 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Meta/Match.lean | 676da5b6b7e8a39923fe17bf498a73b4662f4fe8 | [
"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 | 414 | 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
import Lean.Met... |
46d0dff5e78fce0192b953decc3f84c117736218 | 22e97a5d648fc451e25a06c668dc03ac7ed7bc25 | /src/ring_theory/polynomial.lean | acb707d31a442519e6b2baa82bd16c58378b9e6e | [
"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 | 17,126 | lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
Ring-theoretic supplement of data.polynomial.
Main result: Hilbert basis theorem, that if a ring is noetherian then so is its polynomial ring.
-/
import data.mv_polynomial
impor... |
4384bc7eabea5f0cd3dc07a01d1110a600baba9c | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/matrix/pequiv.lean | 4ff339d17176f44c01c92f68946c88241dae1d07 | [
"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 | 5,699 | lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import data.matrix.basic
import data.pequiv
/-!
# partial equivalences for matrices
Using partial equivalences to represent matrices.
This file introduces the function ... |
8bed00217d8e19d94f513a9eb43ba23636a2edf9 | a4673261e60b025e2c8c825dfa4ab9108246c32e | /src/Lean/MetavarContext.lean | 8747a98ee14142bcc0843d8b54e79fa0a18dfbc7 | [
"Apache-2.0"
] | permissive | jcommelin/lean4 | c02dec0cc32c4bccab009285475f265f17d73228 | 2909313475588cc20ac0436e55548a4502050d0a | refs/heads/master | 1,674,129,550,893 | 1,606,415,348,000 | 1,606,415,348,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 52,080 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Util.MonadCache
import Lean.LocalContext
namespace Lean
/-
The metavariable context stores metavariable declarations and their
assignments. It... |
08af41d11581e82392b8a4175555adf447f9636e | 2a70b774d16dbdf5a533432ee0ebab6838df0948 | /_target/deps/mathlib/src/set_theory/cofinality.lean | 6e3cc4761f1d606f0b0c092efd2e266bebb6255f | [
"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 | 22,078 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
-/
import set_theory.cardinal_ordinal
/-!
# Cofinality on ordinals, regular cardinals
-/
noncomputable theory
open function cardinal set
open_locale classical
universes... |
48fb38b042ebe5804fcb8c62622712cc97a9b266 | 0c1546a496eccfb56620165cad015f88d56190c5 | /tests/lean/interactive/my_tac_class.lean | 99814a66e7f8d98ca02cddf11d62589d076a973a | [
"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 | 1,654 | lean | meta def mytac :=
state_t nat tactic
meta instance : monad mytac :=
state_t.monad _ _
meta instance : monad.has_monad_lift tactic mytac :=
monad.monad_transformer_lift (state_t nat) tactic
meta instance (α : Type) : has_coe (tactic α) (mytac α) :=
⟨monad.monad_lift⟩
namespace mytac
meta def step {α : Type} (t : my... |
7cfc8cbec4bd5ce7cf9948fe8df781d0fa2ee232 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/491.lean | a4fa2f8a12753387036ba2e9c0b0d0c670cee9ee | [
"Apache-2.0"
] | permissive | soonhokong/lean | cb8aa01055ffe2af0fb99a16b4cda8463b882cd1 | 38607e3eb57f57f77c0ac114ad169e9e4262e24f | refs/heads/master | 1,611,187,284,081 | 1,450,766,737,000 | 1,476,122,547,000 | 11,513,992 | 2 | 0 | null | 1,401,763,102,000 | 1,374,182,235,000 | C++ | UTF-8 | Lean | false | false | 134 | lean | import data.int
open eq.ops int
variable A : Type
variables a b : A
variable H : a = b
check H⁻¹
check -(1:int)
check (1:int) + -2
|
718ee3fcb5e9eb83906d1398355f2e39a0014c28 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/algebra/order/upper_lower.lean | 3f36d91f00fa137120bd1d9a16f2c34f2352b743 | [
"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 | 7,787 | 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 algebra.order.group.defs
import data.set.pointwise.smul
import order.upper_lower.basic
/-!
# Algebraic operations on upper/lower sets
> THIS FILE IS SYNCHRONIZED... |
1cbcaa9ed049f1eeb2f9db1cd32e47c99837cb7b | 79cc757e5e5b09c7a522f717a6c490d321d36469 | /src/mywork/sep_13_2021.lean | 1ddf1be24c5b36523afaa575108ec5ea82f3c3de | [] | no_license | LukeMathe/cs2120f21 | 534c3b8868dcfdea98a9d22513180c8a062794c6 | d51940b174569a8782e62ae027b108b5f099a9aa | refs/heads/main | 1,693,418,664,935 | 1,634,585,653,000 | 1,634,585,653,000 | 403,762,076 | 0 | 0 | null | 1,630,963,485,000 | 1,630,963,485,000 | null | UTF-8 | Lean | false | false | 284 | lean | axioms (P Q : Prop)
def if_P_is_true_then_so_is_Q : Prop := P → Q
axiom p : P
-- assume P is true
-- assume we have a proof of P (p)
axiom pq : P → Q
-- assume that we have a proof pq of P implies Q
--intro for assume premise show conclusion
-- elimination rule for implies: |
4612916313a150354338f0f79676249812a39119 | a7eef317ddec01b9fc6cfbb876fe7ac00f205ac7 | /src/group_theory/perm/sign.lean | f52e0406e33f64c75cd07ff26cb31ce3141db0c0 | [
"Apache-2.0"
] | permissive | kmill/mathlib | ea5a007b67ae4e9e18dd50d31d8aa60f650425ee | 1a419a9fea7b959317eddd556e1bb9639f4dcc05 | refs/heads/master | 1,668,578,197,719 | 1,593,629,163,000 | 1,593,629,163,000 | 276,482,939 | 0 | 0 | null | 1,593,637,960,000 | 1,593,637,959,000 | null | UTF-8 | Lean | false | false | 32,214 | 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 data.fintype.basic
import algebra.big_operators
universes u v
open equiv function fintype finset
open_locale big_operators
variables {α : Type u} {β : Type v}
na... |
830ec6d8fa8eb24875646c19785baea882effa1e | 3618c6e11aa822fd542440674dfb9a7b9921dba0 | /src/tactic/group1r.lean | 98a1362f3a41928bcd31f1b450b2385957390a6d | [] | no_license | ChrisHughes24/single_relation | 99ceedcc02d236ce46d6c65d72caa669857533c5 | 057e157a59de6d0e43b50fcb537d66792ec20450 | refs/heads/master | 1,683,652,062,698 | 1,683,360,089,000 | 1,683,360,089,000 | 279,346,432 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,814 | lean | import solve tactic.group
open expr tactic free_group
local notation `C∞` := multiplicative ℤ
meta structure cache :=
(G : expr)
(univ : level)
(red : transparency)
(ic : ref instance_cache) -- instance_cache for G
(atoms : ref (buffer expr))
@[derive [monad, alternative]]
meta def group1r_m (α : Type) : Type :=
re... |
59adc6fef4d3714f5a193a2d16ab4c15a570a841 | 75bd9c50a345718d735a7533c007cf45f9da9a83 | /src/ring_theory/algebra_tower.lean | 9ba0e28ffc9adcc088e58a6d33403aec3ee49c6b | [
"Apache-2.0"
] | permissive | jtbarker/mathlib | a1a3b1ddc16179826260578410746756ef18032c | 392d3e376b44265ef2dedbd92231d3177acc1fd0 | refs/heads/master | 1,671,246,411,096 | 1,600,801,712,000 | 1,600,801,712,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,601 | 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 ring_theory.adjoin
/-!
# Towers of algebras
We set up the basic theory of algebra towers.
An algebra tower A/S/R is expressed by having instances of `algebra A S`,
`a... |
0c989dc7e6b5a11c36ed863f0032db13ba13b917 | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /src/Lean/PrettyPrinter/Delaborator/Builtins.lean | ca2b3ced565c0e8f32e61333a49a7347735c8224 | [
"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 | 23,815 | lean | /-
Copyright (c) 2020 Sebastian Ullrich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
-/
import Lean.PrettyPrinter.Delaborator.Basic
import Lean.Parser
namespace Lean.PrettyPrinter.Delaborator
open Lean.Meta
open Lean.Parser.Term
@[builtinDelab f... |
a866e2df8d332b2534abb7e68a91b5454abdc393 | 618003631150032a5676f229d13a079ac875ff77 | /src/analysis/normed_space/basic.lean | 840262fe5124da1332844174d081cdd6b7635934 | [
"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 | 46,118 | 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.instances.nnreal
import topology.instances.complex
import topology.algebra.module
import topology.metric_space.antilipschitz
/-!
# No... |
01df073e5c099df2322666deab1acb4d6f6eead9 | 4fa161becb8ce7378a709f5992a594764699e268 | /src/category_theory/limits/shapes/regular_mono.lean | f200db75a0465f041a3ae1950a1f6b358b5f5a75 | [
"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 | 6,557 | 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.limits.shapes.kernels
import category_theory.limits.shapes.strong_epi
/-!
# Definitions and basic properties of regular and normal monomorphis... |
1ba53c5f64bd208eaaa92ce2c886e0f4fec21d6c | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/tactic/rewrite_all/basic.lean | f054942d78f672c5af320de392c625088255c9d1 | [
"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 | 1,931 | lean | /-
Copyright (c) 2018 Keeley Hoek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Keeley Hoek, Scott Morrison
-/
import data.option.defs data.mllist
open tactic
@[derive decidable_eq]
inductive side
| L
| R
def side.other : side → side
| side.L := side.R
| side.R :=... |
0abf989770f204aee769871622961e49964fe232 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /tests/lean/run/notation_priority.lean | 9ffaa104dc953deb192500eccb73d481e35c6181 | [
"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 | 597 | lean | constant f : nat → nat → nat
constant g : nat → nat → nat
infix [priority 10] + := f
infix [priority 20] + := g
variables a b : nat
example : a + b = g a b := rfl
infix [priority 5] + := g
example : a + b = f a b := rfl
infix [priority 15] + := g
example : a + b = g a b := rfl
infix [priority std.priority.default+... |
7336114f408d4b536ae83f9d6ce3f054208953e3 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/polynomial/identities.lean | 642cf06533b7d4b7817297b50177cd73aa57af42 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 3,647 | 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.derivative
import tactic.linear_combination
import tactic.ring_exp
/-!
# Theory of univariate poly... |
b7018a37f6d32b6bc5b34aaab50c12ae4a4debef | 618003631150032a5676f229d13a079ac875ff77 | /src/linear_algebra/dual.lean | 5c54bd969f89f84ce40a2af70db15a0d403d0382 | [
"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 | 10,102 | 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... |
a4416d8a472f6d7f2e33fd615cb262c18f8d03ac | 1963cb8789bf8cf695607cc2d4106d7fdd8fb9f2 | /homework1/homework1.lean | 481a34c5acc82311ef2af6283788a101087f5095 | [] | no_license | mtegene/homework-mtegene-master | ed43dd0b8cbcea936b6eec82c614842eca02a406 | 5f9b3623a46d2d3b98c54d8cbc82962d3fef49f5 | refs/heads/master | 1,610,605,612,607 | 1,488,481,866,000 | 1,488,481,866,000 | 81,875,687 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,407 | lean | /-
Dependent types
In class, I presented "vector α n" and "matrix α m n" as examples of
dependent types. Make up some operations on these types -- like
"vector_add" or "vector_reverse" -- and declare constants of the
right type to describe them. Use implicit arguments for parameters
that can be inferred. T... |
3ac43255a5ca95ef5b99f024ecd4e236f8ad3490 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/do_match_else.lean | e8181c79be4867501f3aa5f13aa8e84301060ae0 | [
"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 | 564 | lean | open tactic
set_option pp.all true
definition app2 (f a b : expr) :=
expr.app (expr.app f a) b
example (a b c x y : nat) (H : nat.add (nat.add x y) y = 0) : true :=
by do
a ← get_local `a, b ← get_local `b, c ← get_local `c,
H ← get_local `H >>= infer_type,
(lhs, rhs) ← match_eq H,
nat_add : expr ← mk_const ... |
7e9eaf892d9d619fffd7d023a427224a7be48d04 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/dottedCtorNamedArgPattern.lean | 7f75b9aec9eb99e896331f58c779daa305d4578f | [
"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 | 316 | lean | import Lean
def f (x : Nat × Nat) :=
match x with
| .mk (snd := snd) .. => snd
example : f (10, 20) = 20 := rfl
open Lean
def g (e : Expr) : Expr :=
match e with
| .forallE (binderType := type) .. => type
| e => e
def h (x : Nat × Nat) :=
match x with
| .mk (α := .(Nat)) (snd := snd) .. => snd
|
070d077c6305938b1b9a34506fecf9215e3850ab | 46ee5dc7248ccc9ee615639c0c003c05f58975cd | /src/interpolation.lean | ac88d4c8beb4a40f23dd948723d8056b5e3d18a7 | [
"Apache-2.0"
] | permissive | m4lvin/tablean | e61d593b4dde6512245192c577edeb36c48f63c0 | 836202612fc2bfacb5545696412e7d27f7704141 | refs/heads/main | 1,685,613,112,076 | 1,676,755,678,000 | 1,676,755,678,000 | 454,064,275 | 8 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 1,061 | lean | -- INTERPOLATION
import syntax
import completeness
import partitions
open hasVocabulary
def interpolant (φ : formula) (ψ : formula) (θ : formula) :=
tautology (φ ↣ θ) ∧ tautology (θ ↣ ψ) ∧ voc θ ⊆ (voc φ ∩ voc ψ)
lemma interpolation {ϕ ψ} : tautology (ϕ ↣ ψ) → ∃ θ, interpolant ϕ ψ θ :=
begin
intros hyp,
l... |
453cfe184ad2a32f39905a8043e99ab9ac99af29 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/run/tactic_io.lean | 63b9f9e95dbf2fa5f52903370a74ae89a391f998 | [
"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 | 246 | lean | import system.io
section
variable [io.interface]
def tst_io : io string :=
do b ← io.fs.read_file "tactic_io.lean",
return b^.to_string
end
open tactic
meta def tac : tactic unit :=
do s ← tactic.run_io @tst_io,
trace s
run_cmd tac
|
9e346671ba03d9af21c2839bb9c000a64d4f9953 | e37bb385769d6f4ac9931236fd07b708397e086b | /src/library/src_ordered_field_lemmas.lean | e1a397a4efe7a5071bbc611eb0e700c87fead954 | [] | no_license | gihanmarasingha/ems_reals | 5f5d5b9d9dfb5a10da465046336d74995132dff6 | 9df527742db69d0a389add44b506538fdb4d0800 | refs/heads/master | 1,675,327,747,064 | 1,608,036,820,000 | 1,608,036,820,000 | 315,825,726 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,992 | lean | import .src_ordered_field tactic
namespace mth1001
namespace myreal
section ordered
variables {R : Type} [myordered_field R]
open_locale classical
open myordered_field
lemma pos_one : pos (1 : R) :=
begin
rcases trichotomy (1 : R) with ⟨hpo, _, _ ⟩ | ⟨_, hoe, _ ⟩ | ⟨hnpo, hnoe, hpno⟩ ,
{ exact hpo, },
{ e... |
d2bf3f99d7885822a64887a33b18588f1b150580 | 0845ae2ca02071debcfd4ac24be871236c01784f | /library/init/control/functor.lean | a8d49fee4968718acdaaebac04e6f4986f3738c4 | [
"Apache-2.0"
] | permissive | GaloisInc/lean4 | 74c267eb0e900bfaa23df8de86039483ecbd60b7 | 228ddd5fdcd98dd4e9c009f425284e86917938aa | refs/heads/master | 1,643,131,356,301 | 1,562,715,572,000 | 1,562,715,572,000 | 192,390,898 | 0 | 0 | null | 1,560,792,750,000 | 1,560,792,749,000 | null | UTF-8 | Lean | false | false | 873 | lean | /-
Copyright (c) Luke Nelson and Jared Roesch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Luke Nelson, Jared Roesch, Sebastian Ullrich, Leonardo de Moura
-/
prelude
import init.core
open Function
universes u v
class Functor (f : Type u → Type v) : Type (max (u+1) ... |
10058fd5e8122f4db8cd9fbe909025520ab0ec6d | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /tests/lean/autoIssue.lean | fd4b9dec2456d71c1d66284fa6dbd8bbf86b5ae3 | [
"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 | EdAyers/lean4 | 57ac632d6b0789cb91fab2170e8c9e40441221bd | 37ba0df5841bde51dbc2329da81ac23d4f6a4de4 | refs/heads/master | 1,676,463,245,298 | 1,660,619,433,000 | 1,660,619,433,000 | 183,433,437 | 1 | 0 | Apache-2.0 | 1,657,612,672,000 | 1,556,196,574,000 | Lean | UTF-8 | Lean | false | false | 1,105 | lean | import Lean
structure A :=
x : Nat
a' : x = 1 := by trivial
#check @A.a'
example (z : A) : z.x = 1 := by
have := z.a'
trace_state
exact this
example (z : A) : z.x = 1 := by
have := z.2
trace_state
exact this
#check @A.rec
example (z : A) : z.x = 1 := by
have ⟨x, a'⟩ := z
trace_state
subst a'
... |
e4349d93261a9a05c7d561a0f676e63b0ab632ad | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/exfalso1.lean | e7637709c2075fc95a8181a35b91645bdb25fa51 | [
"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 | 236 | lean | open tactic nat
example (a b : nat) : a = 0 → b = 1 → a = b → a + b * b ≤ 10000 :=
by do
intro_lst [`a0, `a1, `ab],
exfalso,
trace_state,
get_local `a >>= subst,
get_local `b >>= subst,
trace_state,
contradiction
|
ea27381c92bcf484f33264740f7f3f6bd816fe9a | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/algebra/module/ordered.lean | 1e7d79d129c016315be71d365fc43245fd167a16 | [
"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 | 7,866 | 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 algebra.module.pi
import algebra.ordered_pi
import algebra.module.prod
import algebra.ordered_field
/-!
# Ordered modules
In this file we define
* `order... |
cb8b74a767c10dbdfbe4c3758731aca956d68ed0 | ebbdcbd7ddc89a9ef7c3b397b301d5f5272a918f | /qp/p0_stdlib.lean | 570b1400006e56bbd96820ddbb52b26cf7e02808 | [] | no_license | intoverflow/qvr | 34b9ef23604738381ca20b7d622fd0399d88f2dd | 0cfcd33fe4bf8d93851a00cec5bfd21e77105d74 | refs/heads/master | 1,616,591,570,371 | 1,492,575,772,000 | 1,492,575,772,000 | 80,061,627 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 167 | lean | import .p0_stdlib.c0_misc
import .p0_stdlib.c1_fin
import .p0_stdlib.c2_finite_type
import .p0_stdlib.c3_order
import .p0_stdlib.c4_algebra
import .p0_stdlib.c5_dlist
|
9fb7c238b1248c7f2db6667824aab5e812f911c5 | 5de7964e7bf47062fd89c1c93ee8e66af8e43c56 | /config_backup/.config.lean | 01e9555bf19fb9ff9cfa5557eff9dd6bc42cb3eb | [
"MIT"
] | permissive | doppelkalt/MT1300 | 6cec000163a56100c8e36069e41e553429cf8aae | bc252f1601748549ec0c936871ac05f243d1055d | refs/heads/main | 1,678,470,446,990 | 1,613,995,552,000 | 1,613,995,552,000 | 341,185,676 | 10 | 0 | MIT | 1,613,995,253,000 | 1,613,995,253,000 | null | UTF-8 | Lean | false | false | 248,661 | lean | #
# Automatically generated file; DO NOT EDIT.
# OpenWrt Configuration
#
CONFIG_MODULES=y
CONFIG_HAVE_DOT_CONFIG=y
# CONFIG_TARGET_sunxi is not set
# CONFIG_TARGET_apm821xx is not set
# CONFIG_TARGET_ath25 is not set
# CONFIG_TARGET_ar71xx is not set
# CONFIG_TARGET_ath79 is not set
# CONFIG_TARGET_bcm27xx is not set
... |
392cb1d16740c9afe17f9fcc4ffca184e4ec0608 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/data/rat/cast.lean | 92abef91da186c080ba112dae7a1e34c15021aad | [
"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 | 14,957 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import data.rat.order
import data.int.char_zero
import algebra.field.opposite
/-!
# Casts for Rational Numbers
## Summary
We define the canonical i... |
16f436a48f9e8a36ee29d3839b68f367ab2bb103 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/algebra/module/dedekind_domain.lean | eee85d418a999a543e1311cbf7b53e687bf44ae0 | [
"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 | 3,774 | lean | /-
Copyright (c) 2022 Pierre-Alexandre Bazin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pierre-Alexandre Bazin
-/
import algebra.module.torsion
import ring_theory.dedekind_domain.ideal
/-!
# Modules over a Dedekind domain
Over a Dedekind domain, a `I`-torsion mo... |
f380e6f38cf0eba9b022ccd30c4128bc653c40cb | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/order/lattice.lean | a71bc2d152c4a41e1e6239b3cb40237f664ae7ab | [
"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 | 18,063 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Defines the inf/sup (semi)-lattice with optionally top/bot type class hierarchy.
-/
import order.basic
set_option old_structure_cmd true
universes u v w
variables {α... |
93196a26ea846e24061600722cc2a32aa73fb9cb | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/class_bug1.lean | 912bbdb509b31e5430e4c81aea37c6f73b601f7b | [
"Apache-2.0"
] | permissive | soonhokong/lean | cb8aa01055ffe2af0fb99a16b4cda8463b882cd1 | 38607e3eb57f57f77c0ac114ad169e9e4262e24f | refs/heads/master | 1,611,187,284,081 | 1,450,766,737,000 | 1,476,122,547,000 | 11,513,992 | 2 | 0 | null | 1,401,763,102,000 | 1,374,182,235,000 | C++ | UTF-8 | Lean | false | false | 986 | lean | import logic
inductive category (ob : Type) (mor : ob → ob → Type) : Type :=
mk : Π (comp : Π⦃A B C : ob⦄, mor B C → mor A B → mor A C)
(id : Π {A : ob}, mor A A),
(Π {A B C D : ob} {f : mor A B} {g : mor B C} {h : mor C D},
comp h (comp g f) = comp (comp h g) f) →
(Π {A B... |
2c8b60eee0b735386cdbb8cc0ba5e6bdb688daeb | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/user_attribute.lean | 7d3539bab7ccc26048c490305e1fb4ee5d55e679 | [
"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 | 782 | lean | @[user_attribute]
meta def foo_attr : user_attribute := { name := `foo, descr := "bar" }
attribute [foo] eq.refl
#print [foo]
#print eq.refl
run_cmd attribute.get_instances `foo >>= tactic.pp >>= tactic.trace
#print "---"
-- compound names
@[user_attribute]
meta def foo_baz_attr : user_attribute := { name := `foo.ba... |
31e9e957159771dff8f4df09134c06fc33abe947 | 5aaf2c36656c8e760e9c8e4d3b19422402d70634 | /src/tut3.lean | 534a48466b78161cbb1d65e61a46f2c2ec148f24 | [] | no_license | BassemSafieldeen/Lean-tutorials | 535746ccf8d4419419f4fcb544c1687dc564b537 | 031a14fa9700898e9895c9d41be8495275618c46 | refs/heads/main | 1,673,748,866,999 | 1,605,459,118,000 | 1,605,459,118,000 | 307,048,364 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 768 | lean | import linear_algebra.tensor_product
import tut2
open_locale tensor_product
variables {ℋ : Type} [complex_hilbert_space ℋ]
{ρ σ τ : ℋ →ₗ[ℂ] ℋ} [quantum_state ρ] [quantum_state σ] [quantum_state τ]
#check tensor_product
#check ρ ⊗ₜ[ℂ] σ
notation A ` ⊗ ` B := A ⊗ₜ[ℂ] B
example {a : ℂ} : a • (ρ ⊗ σ) = (a • ρ) ⊗ σ :=... |
37b29d4a476c961aff062d9e3face6c384cd6ad0 | 26ac254ecb57ffcb886ff709cf018390161a9225 | /src/order/order_iso.lean | 5f74573214da472b99d648c7580bc0acd69b0eab | [
"Apache-2.0"
] | permissive | eric-wieser/mathlib | 42842584f584359bbe1fc8b88b3ff937c8acd72d | d0df6b81cd0920ad569158c06a3fd5abb9e63301 | refs/heads/master | 1,669,546,404,255 | 1,595,254,668,000 | 1,595,254,668,000 | 281,173,504 | 0 | 0 | Apache-2.0 | 1,595,263,582,000 | 1,595,263,581,000 | null | UTF-8 | Lean | false | false | 16,516 | 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 logic.function.iterate
import order.rel_classes
open function
universes u v w
variables {α : Type*} {β : Type*} {γ : Type*}
{r : α →... |
b7d9dd65657a2c2a9b48067fdd77b9ad00be15e6 | 1a61aba1b67cddccce19532a9596efe44be4285f | /library/algebra/order.lean | cabf2121948289308dbc5cb75caa4afdaec39583 | [
"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 | 16,652 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
Weak orders "≤", strict orders "<", and structures that include both.
-/
import logic.eq logic.connectives algebra.binary algebra.priority
open eq eq.ops
namespace algebr... |
96ed1dc9ffcc9ac36e93bed9fc26b4eed7aed2ba | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /10_Structures_and_Records.org.9.lean | d3576e50b760d5496706428a5b43807175509f6a | [] | 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 | 136 | lean | import standard
open nat
structure point (A : Type) :=
mk :: (x : A) (y : A)
-- BEGIN
check ⦃ point nat, x := 10, y := 20 ⦄
-- END
|
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