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6608dda2783bbf13acff7e041ef5c0682ccffe1a | aa2345b30d710f7e75f13157a35845ee6d48c017 | /analysis/topology/topological_space.lean | 06eab0e6dc7e49706b8a9130de23b989f2a99d32 | [
"Apache-2.0"
] | permissive | CohenCyril/mathlib | 5241b20a3fd0ac0133e48e618a5fb7761ca7dcbe | a12d5a192f5923016752f638d19fc1a51610f163 | refs/heads/master | 1,586,031,957,957 | 1,541,432,824,000 | 1,541,432,824,000 | 156,246,337 | 0 | 0 | Apache-2.0 | 1,541,434,514,000 | 1,541,434,513,000 | null | UTF-8 | Lean | false | false | 86,976 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
Theory of topological spaces.
Parts of the formalization is based on the books:
N. Bourbaki: General Topology
I. M. James: Topologies and Uniformit... |
a42b48725d67a843a6b057e17ebc8c41b11f29de | 0179bcdbf094a112437450a02dc2bdc8b2f921d4 | /fabstract/Hales_T_et_al_Kepler_conj/fabstract.lean | d757ef120f1f593b5eda89a56066dcbbf2dfb88a | [
"CC-BY-4.0"
] | permissive | haselwarter/formalabstracts | cf0c129fc086526cef1bd65d95c6f95a9a7ec5c8 | eab6d94850308df9f09d23f3a9a2f7b5ac5c6c7a | refs/heads/master | 1,609,515,992,248 | 1,500,418,815,000 | 1,500,418,815,000 | 97,696,544 | 0 | 0 | null | 1,500,455,350,000 | 1,500,455,350,000 | null | UTF-8 | Lean | false | false | 2,890 | lean | import ...meta_data ...folklore.real_axiom
import data.list data.vector
namespace Hales_T_et_al_Kepler_conj
noncomputable theory
open classical nat set list vector real_axiom
-- cardinality of finite sets.
-- Surely this must exist somewhere. But where?
universe u
def set_of_list {α : Type u} : (list α) → set α
|... |
50d87cef1aec569e353b40badeac48e1b65e83c4 | fc086f79b20cf002d6f34b023749998408e94fbf | /src/tidy/tidy.lean | c07be6437a81c94db723cf77ae812bb75fbb7b14 | [] | no_license | semorrison/lean-tidy | f039460136b898fb282f75efedd92f2d5c5d90f8 | 6c1d46de6cff05e1c2c4c9692af812bca3e13b6c | refs/heads/master | 1,624,461,332,392 | 1,559,655,744,000 | 1,559,655,744,000 | 96,569,994 | 9 | 4 | null | 1,538,287,895,000 | 1,499,455,306,000 | Lean | UTF-8 | Lean | false | false | 1,524 | lean | -- Copyright (c) 2017 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Scott Morrison
import tactic.basic
import tactic.tidy
import tactic.rewrite_search
import .backwards_reasoning
import .forwards_reasoning
import .luxembourg_chain
import categor... |
6e1e49ace585cf4bc7ec4e107f99a286b525fa43 | 76df16d6c3760cb415f1294caee997cc4736e09b | /lean/src/tactic/cases_all.lean | 1d450184cc7340703e63cb01221792c95c2f67f7 | [
"MIT"
] | permissive | uw-unsat/leanette-popl22-artifact | 70409d9cbd8921d794d27b7992bf1d9a4087e9fe | 80fea2519e61b45a283fbf7903acdf6d5528dbe7 | refs/heads/master | 1,681,592,449,670 | 1,637,037,431,000 | 1,637,037,431,000 | 414,331,908 | 6 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 734 | lean | import tactic.basic
import tactic.induction
import .base
open tactic.interactive
setup_tactic_parser
/--
`cases_all h : e` is equivalent to `cases h : e; rewrite h at *`.
That is, it performs a case analysis on an expression and use the result
uniformly throughout the context and goal.
-/
@[interactive] meta def c... |
4978cfae364c8131790f3f3f5eba0d03e8bd684c | d1a52c3f208fa42c41df8278c3d280f075eb020c | /src/Leanpkg/Git.lean | 55ce109228d27eb3b2b91e9115dbf0829c4d9200 | [
"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 | 1,352 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner, Sebastian Ullrich
-/
import Leanpkg.LeanVersion
open System
namespace Leanpkg
def upstreamGitBranch :=
"master"
def gitdefaultRevision : Option String → Str... |
7413848f56aec45cb9b6ff765ba33d4dd634b915 | 7b9ff28673cd3dd7dd3dcfe2ab8449f9244fe05a | /src/jesse/finish_demo.lean | f63f02ecb271f55199d17ff843a3890689ca83ea | [] | no_license | jesse-michael-han/hanoi-lean-2019 | ea2f0e04f81093373c48447065765a964ee82262 | a5a9f368e394d563bfcc13e3773863924505b1ce | refs/heads/master | 1,591,320,223,247 | 1,561,022,886,000 | 1,561,022,886,000 | 192,264,820 | 1 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 3,940 | lean | import order.lattice data.nat.gcd tactic tactic.explode
class lattice' (α : Type*) extends lattice.has_inf α, lattice.has_sup α :=
(inf_comm : ∀ x y : α, x ⊓ y = y ⊓ x)
(inf_assoc : ∀ x y z : α, x ⊓ y ⊓ z = x ⊓ (y ⊓ z))
(sup_comm : ∀ x y : α, x ⊔ y = y ⊔ x)
(sup_assoc : ∀ x y z : α, x ⊔ y ⊔ z = x ⊔ (y ⊔ z))
(inf_absor... |
c17c6af5538047d0ab7cafd35697a4cdd57cfd94 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/category_theory/category/Bipointed.lean | 8b71cc51310e69e6ac2ac399013af73eeefcf41a | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 6,891 | 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 category_theory.category.Pointed
/-!
# The category of bipointed types
This defines `Bipointed`, the category of bipointed types.
## TODO
Monoidal structure
-/... |
68107d3e8d5f653efbea85139dfefe5f7d46986b | ba306bac106b8f27befb2a800f4357237f86c760 | /lean/love05_inductive_predicates_demo.lean | a9f566dc1ab7309ea2dc7782d961651348b892c8 | [] | no_license | qyqnl/logical_verification_2020 | 406aa4cc47797501275ea07de5d6f59f01e977d0 | 17dff35b56336acb671ddfb36871f98475bc0b96 | refs/heads/master | 1,672,501,336,112 | 1,603,724,260,000 | 1,603,724,260,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,868 | lean | import .love03_forward_proofs_demo
import .love04_functional_programming_demo
/- # LoVe Demo 5: Inductive Predicates
__Inductive predicates__, or inductively defined propositions, are a convenient
way to specify functions of type `⋯ → Prop`. They are reminiscent of formal
systems and of the Horn clauses of Prolog, t... |
8fc7aa614244eb216a04d4cc4c97da56d2b70e0f | 9b9a16fa2cb737daee6b2785474678b6fa91d6d4 | /src/category_theory/isomorphism.lean | 1d1001b91ff0995e30ed2697a9596246172c90a3 | [
"Apache-2.0"
] | permissive | johoelzl/mathlib | 253f46daa30b644d011e8e119025b01ad69735c4 | 592e3c7a2dfbd5826919b4605559d35d4d75938f | refs/heads/master | 1,625,657,216,488 | 1,551,374,946,000 | 1,551,374,946,000 | 98,915,829 | 0 | 0 | Apache-2.0 | 1,522,917,267,000 | 1,501,524,499,000 | Lean | UTF-8 | Lean | false | false | 6,533 | lean | -- Copyright (c) 2017 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Tim Baumann, Stephen Morgan, Scott Morrison
import category_theory.functor
universes v u -- declare the `v`'s first; see `category_theory.category` for an explanation
namespac... |
e61de8839068adaf08d020118406422800eb977f | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/category_theory/limits/preserves/shapes/equalizers.lean | a02122d528bfb56e3cf8d168add7864f0a44e07d | [
"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 | 7,363 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import category_theory.limits.shapes.split_coequalizer
import category_theory.limits.preserves.basic
/-!
# Preserving (co)equalizers
Constructions to relate the notions... |
34858d4b009981cdbca8100298d3f9a17c150c6b | 22e97a5d648fc451e25a06c668dc03ac7ed7bc25 | /src/analysis/specific_limits.lean | 21949bf1be4156c02d61987a48e5e5b874e80e8b | [
"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 | 23,680 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
A collection of specific limit computations.
-/
import analysis.normed_space.basic
import algebra.geom_sum
import topology.instances.ennreal
noncomputable theory
open_... |
630e0855fb435eb82dcfadce4631d4e8d41dc9ef | 4fa161becb8ce7378a709f5992a594764699e268 | /src/data/seq/wseq.lean | 37a19a3673528a8772af9a7df2eb5d65b4af763c | [
"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 | 54,997 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
-/
import data.seq.seq
import data.dlist
universes u v w
/-
coinductive wseq (α : Type u) : Type u
| nil : wseq α
| cons : α → wseq α → wseq α
| think : wseq α → ... |
10ac114d515036db199f377dabc47c576a4e6efc | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /08_Building_Theories_and_Proofs.org.34.lean | b0fc81842a5f0dba9475451d8b4fd83d7ec559d0 | [] | 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 | 81 | lean | import standard
import data.nat
open [declarations] nat (add add.assoc add.comm)
|
cf98150bc4cd2cf9acc891620e50c61d4acc616a | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/list/of_fn.lean | d5164175aef1f3ae99c3f56d19520566041ec5a3 | [
"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 | 9,861 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.fin.tuple.basic
import data.list.join
import data.list.pairwise
/-!
# Lists from functions
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to t... |
781ea295667c146e3f6cc41b06a8e3001ae721a7 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/data/mv_polynomial/funext.lean | b25387b185d159a303c47c3d9bef730cf0114325 | [
"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 | 3,161 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import data.polynomial.ring_division
import data.mv_polynomial.rename
import ring_theory.polynomial.basic
/-!
## Function extensionality for multivariate polynomials... |
375e6c16a9414ea9b940e0733e56ef1c479b3543 | fe84e287c662151bb313504482b218a503b972f3 | /src/combinatorics/enumeration.lean | 95cc39e0e54ae1c4b0b20cf970b8eb736c0013b0 | [] | no_license | NeilStrickland/lean_lib | 91e163f514b829c42fe75636407138b5c75cba83 | 6a9563de93748ace509d9db4302db6cd77d8f92c | refs/heads/master | 1,653,408,198,261 | 1,652,996,419,000 | 1,652,996,419,000 | 181,006,067 | 4 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 5,467 | lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Neil Strickland
This file defines a typeclass for types α with an ordered
enumeration of the elements (as opposed to a `fintype`
instance, which is an unordered enumeration). This... |
e80c3a4462af9c27d36da81c29a4201c0050a749 | 3f7026ea8bef0825ca0339a275c03b911baef64d | /src/data/rat/floor.lean | 347b70985871f85688bddc3b9585c0c43f9368b7 | [
"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 | 4,171 | 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.rat.cast
/-!
# Floor and Ceil Functions for Rational Numbers
## Summary
We define the `floor`, `ceil`, and `nat_ce... |
14e4d798f47dd88be7ea067c89ff7dc5de81cf23 | 57fdc8de88f5ea3bfde4325e6ecd13f93a274ab5 | /data/int/modeq.lean | 951b1af52a1199a00d77ba0f25e87dc6506816a9 | [
"Apache-2.0"
] | permissive | louisanu/mathlib | 11f56f2d40dc792bc05ee2f78ea37d73e98ecbfe | 2bd5e2159d20a8f20d04fc4d382e65eea775ed39 | refs/heads/master | 1,617,706,993,439 | 1,523,163,654,000 | 1,523,163,654,000 | 124,519,997 | 0 | 0 | Apache-2.0 | 1,520,588,283,000 | 1,520,588,283,000 | null | UTF-8 | Lean | false | false | 3,311 | 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.int.basic data.nat.modeq
namespace int
def modeq (n a b : ℤ) := a % n = b % n
notation a ` ≡ `:50 b ` [ZMOD `:50 n `]`:0 := modeq n a b
namespace modeq
v... |
251ec74bf1f88c722390b5c1c70edf6f3a89f08f | c777c32c8e484e195053731103c5e52af26a25d1 | /src/logic/nontrivial.lean | 99388b9a6b5a1f2a4c195882561600027b89c70e | [
"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 | 7,212 | 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.prod.basic
import data.subtype
import logic.function.basic
import logic.unique
/-!
# Nontrivial types
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
>... |
c1b1d56d7b6f6115baae6caed4fd0de8773e5684 | a7dd8b83f933e72c40845fd168dde330f050b1c9 | /src/tactic/rcases.lean | be1ec91bf6bd0fff514eec7cca585c1a0e516439 | [
"Apache-2.0"
] | permissive | NeilStrickland/mathlib | 10420e92ee5cb7aba1163c9a01dea2f04652ed67 | 3efbd6f6dff0fb9b0946849b43b39948560a1ffe | refs/heads/master | 1,589,043,046,346 | 1,558,938,706,000 | 1,558,938,706,000 | 181,285,984 | 0 | 0 | Apache-2.0 | 1,568,941,848,000 | 1,555,233,833,000 | Lean | UTF-8 | Lean | false | false | 17,139 | 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.dlist tactic.core
open lean lean.parser
namespace tactic
/-
These synonyms for `list` are used to clarify the meanings of the many
usages of lists in t... |
b7af278cdd5424917443ab1fc15805f756693185 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/field/opposite.lean | 2a6f100dcd73b93d611fcf9f52708d9283bdce88 | [
"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 | 558 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import algebra.field.basic
import algebra.ring.opposite
/-!
# Field structure on the multiplicative opposite
-/
variables (α : Type*)
namespace mul_opposite
instance [divis... |
27ea74ab73ae2e9eed0a30f2bbe7674f75026066 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/unify_tac1.lean | ab348a9841664ec016f2272bc2fd3f00771a1547 | [
"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 | 577 | lean | open tactic
example (A : Type) (a : A) (p : A → Prop) (H : p a) : ∃ x, p x :=
by do
constructor,
tgt ← target,
t ← get_local `H >>= infer_type,
unify tgt t, -- Succeeds unifying p a =?= p ?m_1
assumption
example (A : Type) (a : A) (p : A → Prop) (H : p a) : ∃ x, p x :=
by do
econstructor,
tgt ← target... |
5fb33ccf9b606d8982147a4dd9a8dedf9d3c9588 | ee8cdbabf07f77e7be63a449b8483ce308d37218 | /lean/src/test/imo-2019-q1.lean | 9fffcef4b7586c487475aab617e398a967fec1b5 | [
"MIT",
"Apache-2.0"
] | permissive | zeta1999/miniF2F | 6d66c75d1c18152e224d07d5eed57624f731d4b7 | c1ba9629559c5273c92ec226894baa0c1ce27861 | refs/heads/main | 1,681,897,460,642 | 1,620,646,361,000 | 1,620,646,361,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 331 | lean | /-
Copyright (c) 2021 OpenAI. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kunhao Zheng
-/
import data.int.basic
example (f : ℤ → ℤ) : ( ∀ a b, f ( 2 * a ) + ( 2 * f b ) = f ( f ( a + b ) ) ↔ ( ∀ z, f z = 0 \/ ∃ c, ∀ z, f z = 2 * z + c ) ) :=
begin
sorry
end
|
f7437ad44cffc10c30e95316938747182b65e3ca | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/quandle.lean | 6e98bb487b0e94f943ca1ebc3c8554fb514cbb5b | [
"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 | 26,284 | lean | /-
Copyright (c) 2020 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import algebra.hom.equiv.basic
import algebra.hom.aut
import data.zmod.defs
import tactic.group
/-!
# Racks and Quandles
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any ... |
e6ba3f9e4f79172fd019cddb2b2cbb6ee520df5b | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/omega/int/main.lean | cc7e4d77ce504b9931b3949f8182aebf06da8ea4 | [] | 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 | 727 | lean | /-
Copyright (c) 2019 Seul Baek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Seul Baek
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.tactic.omega.prove_unsats
import Mathlib.tactic.omega.int.dnf
import Mathlib.PostPort
namespace Mathl... |
f51a8073b670c35a8a21af377d1e73b0157f8f23 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/hash_map_auto.lean | 7cdd34121264f74a3a21be9174e8f7865a9de2b4 | [] | 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 | 19,942 | 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, Mario Carneiro
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.pnat.basic
import Mathlib.data.list.range
import Mathlib.dat... |
7dc5fdb8a9707d2aad5d22d8c730fc7b405b0058 | 37da0369b6c03e380e057bf680d81e6c9fdf9219 | /hott/init/funext.hlean | 4b5671d30a14fcd2bf3537d3f3f6ccc9d710144e | [
"Apache-2.0"
] | permissive | kodyvajjha/lean2 | 72b120d95c3a1d77f54433fa90c9810e14a931a4 | 227fcad22ab2bc27bb7471be7911075d101ba3f9 | refs/heads/master | 1,627,157,512,295 | 1,501,855,676,000 | 1,504,809,427,000 | 109,317,326 | 0 | 0 | null | 1,509,839,253,000 | 1,509,655,713,000 | C++ | UTF-8 | Lean | false | false | 12,783 | hlean | /-
Copyright (c) 2014 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer, Floris van Doorn
Ported from Coq HoTT
-/
prelude
import .trunc .equiv .ua
open eq is_trunc sigma function is_equiv equiv prod unit prod.ops lift
/-
We now pro... |
344cce0c70aa18d951dbb5d4e3fbf513d379f1c6 | 4bcaca5dc83d49803f72b7b5920b75b6e7d9de2d | /stage0/src/Lean/Widget/InteractiveDiagnostic.lean | 6bd29b89037927bb213cca0a7c20704ac7c61a3b | [
"Apache-2.0"
] | permissive | subfish-zhou/leanprover-zh_CN.github.io | 30b9fba9bd790720bd95764e61ae796697d2f603 | 8b2985d4a3d458ceda9361ac454c28168d920d3f | refs/heads/master | 1,689,709,967,820 | 1,632,503,056,000 | 1,632,503,056,000 | 409,962,097 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,038 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki
-/
import Lean.Data.Lsp
import Lean.Message
import Lean.Elab.InfoTree
import Lean.PrettyPrinter
import Lean.Server.Utils
import Lean.Server.Rpc.Basic
import... |
8e26b5056f6eca6a78f54090663dfe4a772bf814 | f57749ca63d6416f807b770f67559503fdb21001 | /hott/init/pathover.hlean | 8c3be3fb52e7c5f70a36c9294f4b56acbeae46e3 | [
"Apache-2.0"
] | permissive | aliassaf/lean | bd54e85bed07b1ff6f01396551867b2677cbc6ac | f9b069b6a50756588b309b3d716c447004203152 | refs/heads/master | 1,610,982,152,948 | 1,438,916,029,000 | 1,438,916,029,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,452 | hlean | /-
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
Basic theorems about pathovers
-/
prelude
import .path .equiv
open equiv is_equiv equiv.ops
variables {A A' : Type} {B B' : A → Type} {C : Πa, B a → Type}
... |
35859025dbdc0fce72db8b0f681f3f9cbd45800a | 6214e13b31733dc9aeb4833db6a6466005763162 | /src/qi.lean | cc23d318e92631b013c0583bc46e9eb7c33a1be0 | [] | no_license | joshua0pang/esverify-theory | 272a250445f3aeea49a7e72d1ab58c2da6618bbe | 8565b123c87b0113f83553d7732cd6696c9b5807 | refs/heads/master | 1,585,873,849,081 | 1,527,304,393,000 | 1,527,304,393,000 | 154,901,199 | 1 | 0 | null | 1,540,593,067,000 | 1,540,593,067,000 | null | UTF-8 | Lean | false | false | 95,400 | lean | -- quantifier instantiation
import .definitions3 .freevars .substitution .logic
lemma prop.has_call_p.term.inv {c: calltrigger} {t: term}: c ∉ calls_p t :=
assume t_has_call: prop.has_call_p c t,
show «false», by cases t_has_call
lemma prop.has_call_p.not.inv {c: calltrigger} {P: prop}: c ∈ calls_p P.not → c ∈ c... |
38133a3e4bee05c50c949fedefa13e6950ba0c07 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/logic/basic.lean | 02a810e41786baeb3601302fe93ecbe765a21845 | [
"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 | 49,098 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
-/
import tactic.doc_commands
/-!
# Basic logic properties
This file is one of the earliest imports in mathlib.
## Implementation notes
Theorems tha... |
84824a49d51576883977cec91d427b2ba9e3c448 | 94637389e03c919023691dcd05bd4411b1034aa5 | /src/inClassNotes/higherOrderFunctions/list_map.lean | a56a239dc3148c5432ff232f5b3dc0be138315a0 | [] | 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 | 131 | lean | def list_map {α β : Type} : (α → β) → (list α) → list β
| f list.nil := list.nil
| f (h::t) := (f h)::(list_map f t)
|
14ec90612dd5e83cb82a13ff8a220c2882b5409f | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/topology/order.lean | a6f9b80351e06a62090ed7b05d595965294f5c04 | [
"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 | 27,675 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import topology.basic
/-!
# Ordering on topologies and (co)induced topologies
Topologies on a fixed type `α` are ordered, by reverse inclusion.
That... |
69e5b2c7d629d94795b008c30dda5f8bca5132e1 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/category_theory/products/basic.lean | 6b52f8703c844f89e0092b149fa3341a31107baf | [
"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 | 10,628 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stephen Morgan, Scott Morrison
-/
import category_theory.eq_to_hom
import category_theory.functor.const
/-!
# Cartesian products of categories
We define the category instance on `C ×... |
e370bffed98cd038d0b162e974f7c7a887f81f9d | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /stage0/src/Init/Data/Nat.lean | 7afb1ce9e573267e281de32fdeeda93c179ab257 | [
"Apache-2.0"
] | permissive | WojciechKarpiel/lean4 | 7f89706b8e3c1f942b83a2c91a3a00b05da0e65b | f6e1314fa08293dea66a329e05b6c196a0189163 | refs/heads/master | 1,686,633,402,214 | 1,625,821,189,000 | 1,625,821,258,000 | 384,640,886 | 0 | 0 | Apache-2.0 | 1,625,903,617,000 | 1,625,903,026,000 | null | UTF-8 | Lean | false | false | 307 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import Init.Data.Nat.Basic
import Init.Data.Nat.Div
import Init.Data.Nat.Gcd
import Init.Data.Nat.Bitwise
import Init.Data.Nat.Control
|
0dc5a62b58017c41df258edeecc21daa17a0f667 | 02005f45e00c7ecf2c8ca5db60251bd1e9c860b5 | /src/analysis/calculus/deriv.lean | b0de23d04659d514ff284373289b20734d7c1c92 | [
"Apache-2.0"
] | permissive | anthony2698/mathlib | 03cd69fe5c280b0916f6df2d07c614c8e1efe890 | 407615e05814e98b24b2ff322b14e8e3eb5e5d67 | refs/heads/master | 1,678,792,774,873 | 1,614,371,563,000 | 1,614,371,563,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 78,060 | lean | /-
Copyright (c) 2019 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner, Sébastien Gouëzel
-/
import analysis.calculus.fderiv
import data.polynomial.derivative
/-!
# One-dimensional derivatives
This file defines the derivative of a function... |
2c5b2cd00361d1f189ddaeb71ed32e66d998ea8a | 77c5b91fae1b966ddd1db969ba37b6f0e4901e88 | /src/data/zmod/basic.lean | d97578ef65e46af98e1dd957c65bce84156bd726 | [
"Apache-2.0"
] | permissive | dexmagic/mathlib | ff48eefc56e2412429b31d4fddd41a976eb287ce | 7a5d15a955a92a90e1d398b2281916b9c41270b2 | refs/heads/master | 1,693,481,322,046 | 1,633,360,193,000 | 1,633,360,193,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 32,233 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import algebra.char_p.basic
import ring_theory.ideal.operations
import tactic.fin_cases
/-!
# Integers mod `n`
Definition of the integers mod n, and the field structur... |
e5bfaa89f215353e2e649acc8cf67e38fae1a75a | 037dba89703a79cd4a4aec5e959818147f97635d | /src/2021/sets/sheet5.lean | 38e5a64bbf529ceffbd8c6ad1f5a12eda51522f7 | [] | no_license | ImperialCollegeLondon/M40001_lean | 3a6a09298da395ab51bc220a535035d45bbe919b | 62a76fa92654c855af2b2fc2bef8e60acd16ccec | refs/heads/master | 1,666,750,403,259 | 1,665,771,117,000 | 1,665,771,117,000 | 209,141,835 | 115 | 12 | null | 1,640,270,596,000 | 1,568,749,174,000 | Lean | UTF-8 | Lean | false | false | 3,729 | lean | /-
Copyright (c) 2021 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author : Kevin Buzzard
-/
import tactic -- imports all the Lean tactics
/-!
# Sets in Lean, sheet 5 : subset (`⊆`), union (`∪`) and intersection (`∩`)
In this sheet we learn how to manipulat... |
772799bd606f483cfee98ca5ebad0ed9e71d1b62 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/number_theory/cyclotomic/gal.lean | 7b4245028d3764663f48a891f930e00a0bb51909 | [
"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 | 7,580 | lean | /-
Copyright (c) 2022 Eric Rodriguez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Rodriguez
-/
import number_theory.cyclotomic.primitive_roots
import field_theory.polynomial_galois_group
/-!
# Galois group of cyclotomic extensions
In this file, we show the r... |
56177e405a55a6ae05f27f853cdefc73c15deada | 7850aae797be6c31052ce4633d86f5991178d3df | /src/Lean/Server/FileWorker.lean | dfbff63e09886d282ed9cc4fa7f86fa1e0d99d35 | [
"Apache-2.0"
] | permissive | miriamgoetze/lean4 | 4dc24d4dbd360cc969713647c2958c6691947d16 | 062cc5d5672250be456a168e9c7b9299a9c69bdb | refs/heads/master | 1,685,865,971,011 | 1,624,107,703,000 | 1,624,107,703,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 17,484 | lean | /-
Copyright (c) 2020 Marc Huisinga. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Marc Huisinga, Wojciech Nawrocki
-/
import Init.System.IO
import Std.Data.RBMap
import Lean.Environment
import Lean.Data.Lsp
import Lean.Data.Json.FromToJson
import Lean.Server.Util... |
1977e83a6f472d2d1e7644bddf6ffd15c25c0cc6 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/algebra/infinite_sum/module.lean | ad9f0b35f7f745afbdaa1d4394e2db468369b936 | [
"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 | 4,121 | lean | /-
Copyright (c) 2020 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth, Yury Kudryashov, Frédéric Dupuis
-/
import topology.algebra.infinite_sum.basic
import topology.algebra.module.basic
/-! # Infinite sums in topological vector spaces ... |
84ac24234b70f365d15296a513dd0f82603bfe9a | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /src/Lean/Data/Format.lean | ebec3626d78ba9c7e56e86108e9c2db0d0ea1de1 | [
"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 | 1,696 | lean | /-
Copyright (c) 2018 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
import Lean.Data.Options
universes u v
namespace Std
namespace Format
open Lean
def getWidth (o : Options) : Nat := o.get `format.width defWidth
def ge... |
8f94dc8c44541e285993fa5779e915b4b246d0c7 | 0bd6c950c82dcba3e46dc8d8acb5ecc60b917520 | /Schroder_Bernstein.lean | 19093e38060d4312f3ca992960d2118eb9fae202 | [] | no_license | truonghoangle/formalabstracts | 976dbbdede5c71346a3c534a8f319456248d4610 | b889ec60143315053a51b1829a5dc4d82ba503b3 | refs/heads/master | 1,584,899,948,798 | 1,537,184,894,000 | 1,537,184,894,000 | 140,428,980 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 285 | lean |
import data.set.function
open set
variables α β : Type
variables A :set α
variables B :set β
variable f:α → β
variable g:β → α
theorem Schroder_Bernstein:
inj_on f A ∧ inj_on g B ∧ maps_to f A B ∧ maps_to g B A → ∃ h:α → β, bij_on h A B
:=
sorry
|
2614130c0273210d5079155a3c2569414c4934ea | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/category_theory/limits/shapes/wide_pullbacks.lean | 3ed9f987f14aa2c51cc33bd4d90b54bcbdf44ae2 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 16,849 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Jakob von Raumer
-/
import category_theory.limits.has_limits
import category_theory.thin
/-!
# Wide pullbacks
We define the category `wide_pullback_shape`, (resp. `wide_p... |
53d0b9e3ebfe04acb9175b0dd9bb220480c71556 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/data/option/basic.lean | a1a27ae0de13d65029a91fdb20aba7326a4bbf3f | [
"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 | 17,323 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import tactic.basic
import logic.is_empty
/-!
# Option of a type
This file develops the basic theory of option types.
If `α` is a type, then `option α` can be unde... |
1aeb83ea13bd8f81877517c4f9d3e84d9a86b1c5 | a7eef317ddec01b9fc6cfbb876fe7ac00f205ac7 | /src/measure_theory/lebesgue_measure.lean | 07055e50777e168bf95e5100eb10005ff8cbe53d | [
"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 | 12,268 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Lebesgue measure on the real line
-/
import measure_theory.measure_space
import measure_theory.borel_space
noncomputable theory
open classical set filter
open nnreal (o... |
3b916e6afd87a779bd8aaf41e3ec1415b1bc9f56 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /docs/tutorial/category_theory/intro.lean | f792d4364b26b77d9fb644b59a0f0dfb499f7dd7 | [
"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 | 9,298 | lean | import category_theory.functor_category -- this transitively imports
-- category_theory.category
-- category_theory.functor
-- category_theory.natural_transformation
/-!
# An introduction to category theory in Lean
This is an introduction to the basic usage of category theory (in the mathematical sense) in Lean.
We c... |
3c8ea5eb08fc5384f8fcead4ad749e9696c1015b | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/analysis/calculus/fderiv_analytic.lean | 42afc7b3f235324db56ab4cce0ae23f9d1ac7dcc | [
"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 | 7,194 | 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 analysis.calculus.deriv
import analysis.analytic.basic
import analysis.calculus.cont_diff
/-!
# Frechet derivatives of analytic functions.
A function expre... |
d4f0d3492a46a6a3a751c64d1f76b3c182bce551 | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/algebra/group/type_tags.lean | ece9c96213499128fb93c3f50bfb0e0cd04af24a | [
"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 | 11,620 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import algebra.group.hom
import data.equiv.basic
/-!
# Type tags that turn additive structures into multiplicative, and vice versa
We define two type tags:
* `addit... |
37386ef5918d07521cd25a5f7a1c51a71a93b901 | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/field_theory/algebraic_closure.lean | a102c520b092cc083ac2da734907e6c02cdef048 | [
"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 | 12,111 | 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.direct_limit
import field_theory.splitting_field
import analysis.complex.polynomial
/-!
# Algebraic Closure
In this file we define the typeclass for algebraic... |
cf1d761f5791ea4baf431c539617540fb2105406 | 3963b5943679836674f6eaad619c3add9b54cdf3 | /leanprover/leftpad.lean | 7e1f614a8ce4ede7836b1cbed0ca2682f9e69770 | [
"LicenseRef-scancode-unknown-license-reference",
"CC0-1.0"
] | permissive | hwayne/lets-prove-leftpad | f67dba7edf25c624b0b2df14e341a94815b5e01b | 6a1457fd190b2b44db049176663dcbef514fd16a | refs/heads/master | 1,693,274,833,535 | 1,692,309,655,000 | 1,692,309,655,000 | 132,528,683 | 568 | 64 | NOASSERTION | 1,694,694,020,000 | 1,525,736,917,000 | SystemVerilog | UTF-8 | Lean | false | false | 677 | lean | import data.nat.basic
import data.list
open list
universes u
variables {α : Type u}
def leftpad (n : ℕ) (a : α) (l : list α) : list α :=
repeat a (n - length l) ++ l
#eval list.as_string (leftpad 5 'b' (string.to_list "ac"))
theorem leftpad_length (n : ℕ) (a : α) (l : list α) :
length (leftpad n a l) = max n (leng... |
99837bb0881145d97f00a1ba0b593b9cf789d021 | 7c2dd01406c42053207061adb11703dc7ce0b5e5 | /src/solutions/tuto_lib.lean | 3cc334627bcfda3c61a7e04704d63feab611dc71 | [
"Apache-2.0"
] | permissive | leanprover-community/tutorials | 50ec79564cbf2ad1afd1ac43d8ee3c592c2883a8 | 79a6872a755c4ae0c2aca57e1adfdac38b1d8bb1 | refs/heads/master | 1,687,466,144,386 | 1,672,061,276,000 | 1,672,061,276,000 | 189,169,918 | 186 | 81 | Apache-2.0 | 1,686,350,300,000 | 1,559,113,678,000 | Lean | UTF-8 | Lean | false | false | 6,781 | lean | import analysis.specific_limits.basic
import data.int.parity
import topology.sequences
attribute [instance] classical.prop_decidable
/-
Lemmas from that file were hidden in my course, or restating things which
were proved without name in previous files.
-/
notation `|`x`|` := abs x
-- The mathlib version is unusab... |
4af8a3199e8c9a441c9db7d4832838ee218d984f | 6094e25ea0b7699e642463b48e51b2ead6ddc23f | /tests/lean/run/blast_grind1.lean | 08c382c1069c897c5866529b6048bdc9d352b2a3 | [
"Apache-2.0"
] | permissive | gbaz/lean | a7835c4e3006fbbb079e8f8ffe18aacc45adebfb | a501c308be3acaa50a2c0610ce2e0d71becf8032 | refs/heads/master | 1,611,198,791,433 | 1,451,339,111,000 | 1,451,339,111,000 | 48,713,797 | 0 | 0 | null | 1,451,338,939,000 | 1,451,338,939,000 | null | UTF-8 | Lean | false | false | 916 | lean | set_option blast.strategy "core_grind"
example (a b c : nat) : a = b ∨ a = c → b = c → b = a :=
by blast
example (f : nat → nat) (a b c : nat) : f a = f b ∨ f a = f c → f b = f c → f b = f a :=
by blast
definition ex1 (a : nat) : a = 0 → (λ x, x + a) = (λ x, x + 0) :=
by blast
print ex1
attribute Exists.intro [int... |
f65fef62aa5cb932017e86996752f0624d387423 | 958488bc7f3c2044206e0358e56d7690b6ae696c | /lean/tutorials/tutorial2.lean | 80ec0607feb35d4502a54fc5352e3a0415dc023a | [] | no_license | possientis/Prog | a08eec1c1b121c2fd6c70a8ae89e2fbef952adb4 | d4b3debc37610a88e0dac3ac5914903604fd1d1f | refs/heads/master | 1,692,263,717,723 | 1,691,757,179,000 | 1,691,757,179,000 | 40,361,602 | 3 | 0 | null | 1,679,896,438,000 | 1,438,953,859,000 | Coq | UTF-8 | Lean | false | false | 4,279 | lean | import data.real.basic
example : ∀ (a b c : ℝ), a ≤ b → c + a ≤ c + b :=
begin
intros a b c H₁, rw ← sub_nonneg,
have H₂ : c + b - (c + a) = b - a, by ring,
rw [H₂, sub_nonneg], assumption
end
example : ∀ (a b : ℝ), a ≤ b → ∀ (c : ℝ), a + c ≤ b + c :=
begin
intros a b H₁ c, rw ← sub_nonneg,
have H₂ : b + c ... |
479e610b0eef922091e4ae8d6eb76bfa048e72dc | 94e33a31faa76775069b071adea97e86e218a8ee | /src/category_theory/limits/shapes/finite_limits.lean | 56b4bc4ccb4c0d835e5a57f03cc009865bd771bf | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 8,521 | 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 category_theory.fin_category
import category_theory.limits.shapes.binary_products
import category_theory.limits.shapes.equalizers
import category_theory.limits... |
d86a2ec59a0eb18a1676eea3e81e129b6d076db7 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/interactive/complete_import.lean | 186a8e012311621c5714b7c56cbe0862c49c2c75 | [
"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 | 655 | lean | import -- should not trigger
--^ "command": "complete", "skip_completions": true
import
--^ "command": "complete", "skip_completions": true
import .
--^ "command": "complete", "skip_completions": true
import ..
--^ "command": "complete", "skip_completions": true
import foo
--^ "command": ... |
1aead9d313ff770d9af41d9733d1654217a83ab4 | f3849be5d845a1cb97680f0bbbe03b85518312f0 | /tests/lean/utf8.lean | 8455ee9cac7b1bee6ae4534bfb58126093e14c17 | [
"Apache-2.0"
] | permissive | bjoeris/lean | 0ed95125d762b17bfcb54dad1f9721f953f92eeb | 4e496b78d5e73545fa4f9a807155113d8e6b0561 | refs/heads/master | 1,611,251,218,281 | 1,495,337,658,000 | 1,495,337,658,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 248 | lean | open list
#eval length "α₁"
#eval length "α₁ → β₁"
#eval length "∀ α : nat → nat, α 0 ≥ 0"
#print "------------"
#eval utf8_length "α₁"
#eval utf8_length "α₁ → β₁"
#eval utf8_length "∀ α : nat → nat, α 0 ≥ 0"
|
4a6529084d11e57bcfe5b16a2891bec70a80b24a | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/tactic/omega/prove_unsats.lean | ed0252b8b541636af2b5c606078c6b0aed2b6551 | [
"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 | 2,079 | lean | /- Copyright (c) 2019 Seul Baek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Seul Baek
A tactic which constructs exprs to discharge
goals of the form `clauses.unsat cs`. -/
import tactic.omega.find_ees
import tactic.omega.find_scalars
import tactic.omega.lin_comb
... |
b75a11b3378fa83b9a754fed45448633840fe456 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/linear_algebra/bilinear_map.lean | 84cd7d4333f226e6bd890ea4db078cd91c4b39d6 | [
"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 | 15,333 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Mario Carneiro
-/
import linear_algebra.basic
import linear_algebra.basis
/-!
# Basics on bilinear maps
This file provides basics on bilinear maps. The most general form consi... |
3f8507372d67c893eb2ba9cec1c65200d999b4d7 | c45b34bfd44d8607a2e8762c926e3cfaa7436201 | /uexp/src/uexp/u_semiring.lean | fbf75eb2b882c22466b3d7ef6ee2357c34a8ce64 | [
"BSD-2-Clause"
] | permissive | Shamrock-Frost/Cosette | b477c442c07e45082348a145f19ebb35a7f29392 | 24cbc4adebf627f13f5eac878f04ffa20d1209af | refs/heads/master | 1,619,721,304,969 | 1,526,082,841,000 | 1,526,082,841,000 | 121,695,605 | 1 | 0 | null | 1,518,737,210,000 | 1,518,737,210,000 | null | UTF-8 | Lean | false | false | 6,743 | lean | -- definition of u-semiring
class denotation (A: Type) (B:Type) :=
(denote : A → B)
--def denote {A B: Type} [denotation A B] : A → B := @denotation.denote
constant datatype: Type
inductive tree (A:Type)
| node : tree → tree → tree
| leaf : A → tree
| empty {} : tree
definition Schema := tree datatype
constant d... |
bf015d47815c4df177abbddbbd0e1fa75ed68d4f | 86f6f4f8d827a196a32bfc646234b73328aeb306 | /examples/logic/unnamed_1056.lean | 076e47ca46040ef837265a2f8dbcb08d97ca5c85 | [] | no_license | jamescheuk91/mathematics_in_lean | 09f1f87d2b0dce53464ff0cbe592c568ff59cf5e | 4452499264e2975bca2f42565c0925506ba5dda3 | refs/heads/master | 1,679,716,410,967 | 1,613,957,947,000 | 1,613,957,947,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 181 | lean | import data.real.basic
variables a b : ℝ
-- BEGIN
example (h : a < b) : ¬ b < a :=
begin
intro h',
have : a < a,
from lt_trans h h',
apply lt_irrefl a this
end
-- END |
b769266629a914bbed9155f8a077b0706a3caa76 | c3f2fcd060adfa2ca29f924839d2d925e8f2c685 | /hott/init/hedberg.hlean | f22be3193e30c0040aed1b7d598f21af3a656b2e | [
"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 | 1,498 | hlean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
Hedberg's Theorem: every type with decidable equality is a hset
-/
prelude
import init.trunc
open eq eq.ops nat is_trunc sigma
-- TODO(Leo): move const coll... |
4b63d904a8f9647efdb2b655e350315aa223cbe9 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/linear_algebra/pi.lean | d7126156e85c67c90d5aa22f8c984b5d0c843095 | [
"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 | 19,030 | 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, Eric Wieser
-/
import linear_algebra.basic
import logic.equiv.fin
/-!
# Pi types of modules
> THIS FILE IS SYNCHRONIZE... |
c905bee2a90051a978be65c3228572e8d326486b | aa5a655c05e5359a70646b7154e7cac59f0b4132 | /tests/lean/run/funext.lean | 9d97ef1344436089a4604d81ebff597e80838658 | [
"Apache-2.0"
] | permissive | lambdaxymox/lean4 | ae943c960a42247e06eff25c35338268d07454cb | 278d47c77270664ef29715faab467feac8a0f446 | refs/heads/master | 1,677,891,867,340 | 1,612,500,005,000 | 1,612,500,005,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 820 | lean | theorem ex1 : (fun y => y + 0) = (fun x => 0 + x) := by
funext x
rw [Nat.zeroAdd]
rfl
theorem ex2 : (fun y x => y + x + 0) = (fun x y => y + x) := by
funext x y
rw [Nat.addZero, Nat.addComm]
theorem ex3 : (fun (x : Nat × Nat) => x.1 + x.2) = (fun (x : Nat × Nat) => x.2 + x.1) := by
funext (a, b)
show a ... |
911748cf129d3ab15f4e134c3bbaaf2ce89f0249 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/struct_class.lean | 1cd37eb1ee8c6098143cdbad5aecd0bcdb6279f8 | [
"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 | 170 | lean | structure [class] point (A : Type*) (B : Type*) :=
mk :: (x : A) (y : B)
print classes
structure point2 (A : Type*) (B : Type*) :=
mk :: (x : A) (y : B)
print classes
|
806ea92aaca36e1b8859c2fa9e96c2be38db4699 | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /tests/lean/run/eq13.lean | 92f25ee9dfc1841a7d2a89337b31cfabef3ad58c | [
"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 | 320 | lean | open nat
definition f : nat → nat → nat,
f _ 0 := 0,
f 0 _ := 1,
f _ _ := arbitrary nat
theorem f_zero_right : ∀ a, f a 0 = 0,
f_zero_right 0 := rfl,
f_zero_right (succ _) := rfl
theorem f_zero_succ (a : nat) : f 0 (a+1) = 1 :=
rfl
theorem f_succ_succ (a b : nat) : f (a+1) (b+1) = arbitrary nat :=
rfl
|
ba8ed4708d5b6698d793f3b8d5bb1394754b5ece | ea97c777e51529c97caac532f9a6bbea417eca7a | /04_simplifier_lists.lean | 21c0701d487837f28e22eadebdf9f5d34975da39 | [] | no_license | gebner/avm2017_tutorial | 0fcd023fbcefd6e46384ca4919b90a0f6118368e | 3954983cdc8aef0e58e1a5809c0b3e217057ac4c | refs/heads/master | 1,624,860,271,990 | 1,505,717,496,000 | 1,505,717,496,000 | 103,569,052 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,799 | lean | universes u v w
-- We can typically set up the simplifier so that most theorems
-- can be proven by induction + simp
@[simp]
lemma reverse_nil {α : Type u} : [].reverse = ([] : list α) :=
rfl
lemma reverse_core {α : Type u} (xs ys : list α) :
list.reverse_core xs ys = xs.reverse ++ ys :=
by induction xs generali... |
d3d8f059da8300f3e3b4513285ed8e677084f95f | 91b8df3b248df89472cc0b753fbe2bac750aefea | /experiments/lean/src/ddl/host/evaluation.lean | 3d62120f3a0b3ccaed66a14e81da75b91f867778 | [
"Apache-2.0",
"LicenseRef-scancode-unknown-license-reference"
] | permissive | yeslogic/fathom | eabe5c4112d3b4d5ec9096a57bb502254ddbdf15 | 3960a9466150d392c2cb103c5cb5fcffa0200814 | refs/heads/main | 1,685,349,769,736 | 1,675,998,621,000 | 1,675,998,621,000 | 28,993,871 | 214 | 11 | Apache-2.0 | 1,694,044,276,000 | 1,420,764,938,000 | Rust | UTF-8 | Lean | false | false | 987 | lean | import ddl.host.basic
namespace ddl.host
variables {ℓ : Type}
/- 'Stuck' values -/
inductive value : expr ℓ → Prop
| bool (bv : bool) : value (expr.bool bv)
| nat (nv : ℕ) : value (expr.nat nv)
reserve infixl ` ⟹ `:50
reserve infixl ` ⟹* `:50
inductive step : expr ℓ → expr ℓ → Prop
infixl... |
b615c37cb4f48b5d3e4ffa6d95ee76ca445c79bb | 5e3548e65f2c037cb94cd5524c90c623fbd6d46a | /src_icannos_totilas/topologie-espaces-normés/cpge_ten_05b.lean | e213fd2128ef2cd5ebd74f3565c4b8d165c2695e | [] | no_license | ahayat16/lean_exos | d4f08c30adb601a06511a71b5ffb4d22d12ef77f | 682f2552d5b04a8c8eb9e4ab15f875a91b03845c | refs/heads/main | 1,693,101,073,585 | 1,636,479,336,000 | 1,636,479,336,000 | 415,000,441 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 700 | lean | import data.set.basic
import topology.basic
import algebra.module.basic
import algebra.module.submodule
import order.complete_lattice
import analysis.normed_space.basic
-- Soit E une espace vectoriel normé.
-- (b) Soient F et G deux fermés non vides et disjoints de E. Montrer qu'il existe deux ouverts U et V tels ... |
1a313cfc1515a9ed30486e04a665efb66564e745 | 853df553b1d6ca524e3f0a79aedd32dde5d27ec3 | /src/topology/metric_space/closeds.lean | 8488d332117acfe92a5ff598fb766e68e31ea7f4 | [
"Apache-2.0"
] | permissive | DanielFabian/mathlib | efc3a50b5dde303c59eeb6353ef4c35a345d7112 | f520d07eba0c852e96fe26da71d85bf6d40fcc2a | refs/heads/master | 1,668,739,922,971 | 1,595,201,756,000 | 1,595,201,756,000 | 279,469,476 | 0 | 0 | null | 1,594,696,604,000 | 1,594,696,604,000 | null | UTF-8 | Lean | false | false | 21,413 | 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
import analysis.specific_limits
/-!
# Closed subsets
This file defines the metric and emetric space structure o... |
43bd605c98043d1389ca7a575c209b3bab37431e | 2a70b774d16dbdf5a533432ee0ebab6838df0948 | /_target/deps/mathlib/src/analysis/specific_limits.lean | 1c199fa4d0bfc2838ebdf0a38f43f6fe454ab8d3 | [
"Apache-2.0"
] | permissive | hjvromen/lewis | 40b035973df7c77ebf927afab7878c76d05ff758 | 105b675f73630f028ad5d890897a51b3c1146fb0 | refs/heads/master | 1,677,944,636,343 | 1,676,555,301,000 | 1,676,555,301,000 | 327,553,599 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 29,432 | 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 algebra.geom_sum
import order.filter.archimedean
import order.iterate
import topology.instances.ennreal
import tactic.ring_exp
import analysis.asymptotics
/-!... |
af37191c29a3c4e20a01334cb9ecdb6462db8cee | 367134ba5a65885e863bdc4507601606690974c1 | /src/linear_algebra/matrix.lean | 9e675d7bbc1f902ef38aeedf577fb3c2ba3b13e4 | [
"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 | 58,693 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl, Patrick Massot, Casper Putz
-/
import linear_algebra.finite_dimensional
import linear_algebra.nonsingular_inverse
import linear_algebra.multilinear
import linear_algebra... |
688e6f68cf75633f9897a606d5b578f6e79b3e73 | 947b78d97130d56365ae2ec264df196ce769371a | /stage0/src/Lean/Elab/PreDefinition/WF.lean | 42d9fe9907d32328223f23d54112cdf96a09e415 | [
"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 | 395 | 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.Elab.PreDefinition.Basic
namespace Lean
namespace Elab
open Meta
def WFRecursion (preDefs : Array PreDefinition) : TermElabM Unit :=
throwErro... |
6fee70b3c86d5f97e70de606e0ff09ed3c552ae6 | 217bb195841a8be2d1b4edd2084d6b69ccd62f50 | /library/init/lean/parser/syntax.lean | d152243eaeeb66c5810787b5dc4580360a3d372c | [
"Apache-2.0"
] | permissive | frank-lesser/lean4 | 717f56c9bacd5bf3a67542d2f5cea721d4743a30 | 79e2abe33f73162f773ea731265e456dbfe822f9 | refs/heads/master | 1,589,741,267,933 | 1,556,424,200,000 | 1,556,424,281,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,482 | lean | /-
Copyright (c) 2018 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Sebastian Ullrich
-/
prelude
import init.lean.name init.lean.parser.parsec
namespace Lean
namespace Parser
--TODO(Sebastian): move
structure Substring :=
(start : String.OldIte... |
c31ae6273e6f613d9d3405d816cf8b4d684c4689 | e0f9ba56b7fedc16ef8697f6caeef5898b435143 | /src/tactic/converter/apply_congr.lean | fcf5084d8e6d2c9e29c5b0d6f1635c3830d33d39 | [
"Apache-2.0"
] | permissive | anrddh/mathlib | 6a374da53c7e3a35cb0298b0cd67824efef362b4 | a4266a01d2dcb10de19369307c986d038c7bb6a6 | refs/heads/master | 1,656,710,827,909 | 1,589,560,456,000 | 1,589,560,456,000 | 264,271,800 | 0 | 0 | Apache-2.0 | 1,589,568,062,000 | 1,589,568,061,000 | null | UTF-8 | Lean | false | false | 3,347 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lucas Allen, Scott Morrison
-/
import tactic.interactive
import tactic.converter.interactive
/-!
## Introduce the `apply_congr` conv mode tactic.
`apply_congr` will apply congruence ... |
b4b2814386fec4cdf1a0f6a4471dd89236e6d362 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/topology/uniform_space/cauchy.lean | ac31a3cdfac01e766d4bbd71af4bd35ade22f7b1 | [
"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 | 33,876 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import topology.bases
import topology.uniform_space.basic
/-!
# Theory of Cauchy filters in uniform spaces. Complete uniform spaces. Totally bounded s... |
6816264cb3892619b610b34e57099313e264f600 | f083c4ed5d443659f3ed9b43b1ca5bb037ddeb58 | /tactic/rcases.lean | fd3580dfe47c1fa446fb272c589b2ce9ce873564 | [
"Apache-2.0"
] | permissive | semorrison/mathlib | 1be6f11086e0d24180fec4b9696d3ec58b439d10 | 20b4143976dad48e664c4847b75a85237dca0a89 | refs/heads/master | 1,583,799,212,170 | 1,535,634,130,000 | 1,535,730,505,000 | 129,076,205 | 0 | 0 | Apache-2.0 | 1,551,697,998,000 | 1,523,442,265,000 | Lean | UTF-8 | Lean | false | false | 12,305 | 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.dlist tactic.cache
open lean lean.parser
namespace tactic
/-
These synonyms for `list` are used to clarify the meanings of the many
usages of lists in ... |
8ecbf14d6bccbc82be9033500695121ca7debff1 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/W/basic.lean | c359b858fd78825ae8fa2726e22090063e4b7d77 | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 6,714 | lean | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
import logic.equiv.list
/-!
# W types
Given `α : Type` and `β : α → Type`, the W type determined by this data, `W_type β`, is the
inductively defined type of trees wh... |
721a283a84aeb3f6c92d3acf356119cb248b94dd | 58d00ddf42e87fdba91a6057c0b803d889c85901 | /src/solutions/thursday/linear_algebra.lean | 6320ea784dab427e825cd9cc91501f4c09d9e98a | [] | no_license | zeta1999/lftcm2020 | 213d0324ec8d4425bd3320a631e906da1c28e230 | a2eea082d479d82e300ca85d77b87b597e6330d6 | refs/heads/master | 1,671,857,495,610 | 1,602,037,058,000 | 1,602,037,058,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,288 | lean | import analysis.normed_space.inner_product
import data.matrix.notation
import linear_algebra.bilinear_form
import linear_algebra.matrix
import tactic
universes u v
section exercise1
namespace semimodule
variables (R M : Type*) [comm_semiring R] [add_comm_monoid M] [semimodule R M]
/- - - - - - - - - - - - - - - - ... |
b714c5e005a9e082ea21973841c6b217cdf9f192 | 618003631150032a5676f229d13a079ac875ff77 | /src/data/set/countable.lean | 9b785262fe7885685ca209a4e80782c703b4f243 | [
"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 | 8,334 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
-/
import data.equiv.list
import data.set.finite
/-!
# Countable sets
-/
noncomputable theory
open function set encodable
open classical (hiding some)
open_locale clas... |
b211d1ccf5af88240354c3d50e4010240b7a30da | cc62cd292c1acc80a10b1c645915b70d2cdee661 | /src/category_theory/presheaves/sheaves.lean | e586a477828ec9f0a43fd1b4dcfcb17cf9d73a5d | [] | no_license | RitaAhmadi/lean-category-theory | 4afb881c4b387ee2c8ce706c454fbf9db8897a29 | a27b4ae5eac978e9188d2e867c3d11d9a5b87a9e | refs/heads/master | 1,651,786,183,402 | 1,565,604,314,000 | 1,565,604,314,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,021 | lean | -- import category_theory.opposites
-- import category_theory.full_subcategory
-- import category_theory.limits.types
-- import topology.Top.basic
-- import category_theory.limits.obviously
-- open category_theory
-- open category_theory.limits
-- open topological_space
-- universes u v u₁ v₁ u₂ v₂
-- variable (X :... |
ef92368b6a7dcb5f30d7b001551bf62288cc8381 | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/category_theory/core.lean | 8b3274969ae29b56e3fdb9cb2c25cffad47763b7 | [
"Apache-2.0"
] | permissive | ChrisHughes24/mathlib | 98322577c460bc6b1fe5c21f42ce33ad1c3e5558 | a2a867e827c2a6702beb9efc2b9282bd801d5f9a | refs/heads/master | 1,583,848,251,477 | 1,565,164,247,000 | 1,565,164,247,000 | 129,409,993 | 0 | 1 | Apache-2.0 | 1,565,164,817,000 | 1,523,628,059,000 | Lean | UTF-8 | Lean | false | false | 1,546 | lean | /-
Copyright (c) 2019 Scott Morrison All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
The core of a category C is the groupoid whose morphisms are all the
isomorphisms of C.
-/
import category_theory.groupoid
import category_theory.whiskering
namespace ... |
b91bca5b7309c680a894826a667319ed0ef53832 | df7bb3acd9623e489e95e85d0bc55590ab0bc393 | /lean/love06_monads_exercise_solution.lean | 03cb9908561d3c4f63fc457aa20b25c782fa77a7 | [] | no_license | MaschavanderMarel/logical_verification_2020 | a41c210b9237c56cb35f6cd399e3ac2fe42e775d | 7d562ef174cc6578ca6013f74db336480470b708 | refs/heads/master | 1,692,144,223,196 | 1,634,661,675,000 | 1,634,661,675,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,015 | lean | import .love06_monads_demo
/- # LoVe Exercise 6: Monads -/
set_option pp.beta true
set_option pp.generalized_field_notation false
namespace LoVe
/- ## Question 1: A State Monad with Failure
We introduce a richer notion of lawful monad that provides an `orelse`
operator `<|>` satisfying some laws, given below. `... |
d6cc43106ec00f5acffe7475a2db90b986b50501 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/idempotents/homological_complex.lean | bbfffb7bf85cad9c907f91756cab0503c46d8b4e | [
"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 | 7,269 | lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import algebra.homology.additive
import category_theory.idempotents.karoubi
/-!
# Idempotent completeness and homological complexes
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4... |
65940acdaf13f3fef389c51f4d2e083c9fa92f77 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/geometry/euclidean/monge_point.lean | f6e741a38b2878a5d8b85034de6f46a7415df092 | [
"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 | 38,046 | lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import geometry.euclidean.circumcenter
/-!
# Monge point and orthocenter
This file defines the orthocenter of a triangle, via its n-dimensional
generalization, the Mong... |
ad6745e92ff047b0bd935223e1070c4e64f62353 | 618003631150032a5676f229d13a079ac875ff77 | /src/category_theory/action.lean | 4c330c84d59dc8a2f7d45e6380d0342a3ecf0c9e | [
"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 | 3,165 | lean | /-
Copyright (c) 2020 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
import category_theory.elements
import category_theory.single_obj
/-!
# Actions as functors and as categories
From a multiplicative action M ↻ X, we can construct a functor... |
35fe33d8444dba74cc4c26a326fb490a00e80bea | 65b579fba1b0b66add04cccd4529add645eff597 | /test1.lean | 337dfe72c99bacf5627612b295879bb9bdf5fbdb | [] | no_license | teodorov/sf_lean | ba637ca8ecc538aece4d02c8442d03ef713485db | cd4832d6bee9c606014c977951f6aebc4c8d611b | refs/heads/master | 1,632,890,232,054 | 1,543,005,745,000 | 1,543,005,745,000 | 108,566,115 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,529 | lean |
--debrujin indices, a fancy natural number
inductive IN {A : Type} (x : A) : list A → Type
| zero : ∀ {xs}, IN (x::xs)
| succ : ∀ {y xs}, IN (x::xs) → IN (y::xs)
#check (IN.zero [1, 2, 3])
#check (IN.succ (IN.zero [1, 2, 3]))
#reduce (IN 2 [2 , 3])
#eval (IN (20) [2 , 3])
-- the environment which has elements of di... |
01ebcefaed5a859e8e33fd3e5112f88c87c21db3 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/find.lean | 82a6d8424618fa5fca1b0d9311d83527787927fc | [] | 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 | 620 | lean | /-
Copyright (c) 2017 Sebastian Ullrich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.tactic.core
import Mathlib.PostPort
namespace Mathlib
/--
The `find` command from `... |
60630237064dddbc729ce965462a74b716ec5173 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/mvar_fvar.lean | 804b5a179490d759498555dd5663225bceff9be9 | [
"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 | 393 | lean | import Lean
open Lean
instance : Coe Name FVarId where
coe n := { name := n }
instance : Coe Name MVarId where
coe n := { name := n }
#eval (mkFVar `a).hasFVar
#eval (mkApp (mkConst `foo) (mkFVar `a)).hasFVar
#eval (mkApp (mkConst `foo) (mkConst `a)).hasFVar
#eval (mkMVar `a).hasMVar
#eval (mkApp (mkConst `foo... |
d0cd1b53c79f9c679c721067f487cf39af4f873f | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/order/conditionally_complete_lattice.lean | 29a9e2fc4f52d9419a1c8c656394aff5d367b47a | [
"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 | 39,052 | lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import data.nat.enat
import data.set.intervals.ord_connected
/-!
# Theory of conditionally complete lattices.
A conditionally complete lattice is a lattice in... |
841ec23c99414a4b9cc03dd824deeccde28539f6 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/analysis/normed_space/lp_space.lean | 63ebebb327537fbf26bb57b2d33106b37f508581 | [
"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 | 42,897 | lean | /-
Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import analysis.mean_inequalities
import analysis.mean_inequalities_pow
import analysis.normed.group.pointwise
import topology.algebra.order.liminf_limsup
/-!
# ℓp... |
02cf3700ac0b3b3a5c235cac5847123d1ad44657 | c678b448c073e84fd00f1777ac278c36a7bb9a83 | /data/containers/rbtree/delete.lean | 2fd30f152c0c4aeacca0a1e6800e415710498cfe | [] | no_license | GaloisInc/lean-containers | 9d714d9a355381d66f4bf9b686589a85ce7afcc4 | c3359c6e439a611926168e2c86496d0d90a67f9b | refs/heads/master | 1,587,884,399,036 | 1,548,187,422,000 | 1,548,187,422,000 | 173,382,186 | 0 | 0 | null | 1,551,483,637,000 | 1,551,483,637,000 | null | UTF-8 | Lean | false | false | 26,876 | lean | import .basic
namespace data.containers
namespace rbtree
namespace delete
lemma cancel_plus (k x y:ℕ) :
x + k = y + k →
x = y :=
begin
induction k; simp
end.
open color
open rbtree
universe u
inductive delete_result (E:Type u)
-- The deleted node and a tree result with black-height equal to the original tre... |
4e23c9fe0110ad2d180eba38fe3bf3332ecf1f38 | ce6917c5bacabee346655160b74a307b4a5ab620 | /src/ch3/ex0301.lean | 773c849f519ad70d62dcfd013cdcd5aa9e2e4417 | [] | 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 | 103 | lean | variables p q : Prop
#check p → q → p ∧ q
#check ¬p → p ↔ false
#check p ∨ q → q ∨ p
|
d9d35c897222f30e60f336bf81abba3069810b8e | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/algebraic_geometry/prime_spectrum/is_open_comap_C.lean | 6df1e5afccdf6cf6a010787057078af229f329b7 | [
"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 | 3,042 | lean | /-
Copyright (c) 2021 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import algebraic_geometry.prime_spectrum.basic
import ring_theory.polynomial.basic
/-!
The morphism `Spec R[x] --> Spec R` induced by the natural inclusion `R --> R[x]`... |
881c76c4758d9ea9304a3b80eb10979db4db4fc2 | 54f4ad05b219d444b709f56c2f619dd87d14ec29 | /my_project/src/love05_inductive_predicates_demo.lean | 55f73034485b8251806502cd8942dbf81b315d49 | [] | no_license | yizhou7/learning-lean | 8efcf838c7276e235a81bd291f467fa43ce56e0a | 91fb366c624df6e56e19555b2e482ce767cd8224 | refs/heads/master | 1,675,649,087,737 | 1,609,022,281,000 | 1,609,022,281,000 | 272,072,779 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,899 | lean | import .love03_forward_proofs_demo
import .love04_functional_programming_demo
/-! # LoVe Demo 5: Inductive Predicates
__Inductive predicates__, or inductively defined propositions, are a convenient
way to specify functions of type `⋯ → Prop`. They are reminiscent of formal
systems and of the Horn clauses of Prolog, ... |
11386e23f35c69561cbdab459661215fb5c48e97 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/ring_theory/fintype_auto.lean | e233355d73e14fe94d775999ff99b950c49fda70 | [] | 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 | 590 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.associated
import Mathlib.data.fintype.basic
import Mathlib.PostPort
universes u_1... |
44e52d156f7ad3bb2e7c943f8c89127a2dea482f | 46125763b4dbf50619e8846a1371029346f4c3db | /src/tactic/tidy.lean | e1ee2c0c475a774f440e92f70ce30101166c6022 | [
"Apache-2.0"
] | permissive | thjread/mathlib | a9d97612cedc2c3101060737233df15abcdb9eb1 | 7cffe2520a5518bba19227a107078d83fa725ddc | refs/heads/master | 1,615,637,696,376 | 1,583,953,063,000 | 1,583,953,063,000 | 246,680,271 | 0 | 0 | Apache-2.0 | 1,583,960,875,000 | 1,583,960,875,000 | null | UTF-8 | Lean | false | false | 3,378 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import tactic.ext
import tactic.auto_cases
import tactic.chain
import tactic.solve_by_elim
import tactic.norm_cast
import tactic.hint
import tactic.interactive
names... |
cc054666513d355bd143ec0cc007db24d30e5f2f | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/tactic/core.lean | 3cfe7562dfd38ef582d383e43ecf5db2fe396358 | [
"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 | 92,513 | 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
import logic.function.basic
import control.basic
import meta.expr
import meta.rb_map
import data.boo... |
edc91649f7f624b98852939a8196ac61ee25ae96 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/algebra/char_zero.lean | 72396151061de31b44d20fe4b4a30c6467f4630a | [
"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 | 6,046 | lean | /-
Copyright (c) 2014 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.nat.cast
import data.fintype.basic
import tactic.wlog
/-!
# Characteristic zero
A ring `R` is called of characteristic zero if every natural number `n`... |
709f2a9bbe2da412bb3a55f3467b51a4ffc5e923 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/polynomial/integral_normalization_auto.lean | 6d809a779520f3fac7a2520a251a7e31551577a5 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,095 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.polynomial.algebra_map
import Mathlib.data... |
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