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values | content stringlengths 3 6.12M |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1a272a6df1086ca35e76762e6f80a973e1c9801b | bb31430994044506fa42fd667e2d556327e18dfe | /src/data/multiset/nodup.lean | 1d1b639604903a19da583fbe8ab48df616af3010 | [
"Apache-2.0"
] | permissive | sgouezel/mathlib | 0cb4e5335a2ba189fa7af96d83a377f83270e503 | 00638177efd1b2534fc5269363ebf42a7871df9a | refs/heads/master | 1,674,527,483,042 | 1,673,665,568,000 | 1,673,665,568,000 | 119,598,202 | 0 | 0 | null | 1,517,348,647,000 | 1,517,348,646,000 | null | UTF-8 | Lean | false | false | 9,302 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.list.nodup
import data.multiset.bind
import data.multiset.range
/-!
# The `nodup` predicate for multisets without duplicate elements.
-/
namespac... |
c0a0aebcc3a8c16412233178e1796746d939158c | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/trace1.lean | d1d140930d02dce76de78291d52b0dcff3a2576b | [
"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 | 296 | lean | open tactic
example : true :=
by do
when_tracing `app_builder $ do {
trace "hello",
trace "world" },
constructor
set_option trace.app_builder true
print "------------"
example : true :=
by do
when_tracing `app_builder $ do {
trace "hello",
trace "world" },
constructor
|
f68542955afd8822f5ad44992c1bbd9a7901a8c2 | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /tests/lean/interactive/plainGoal.lean | 9d94d59d9a2a61e361d6eece9e63d4530f112479 | [
"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 | 89 | lean | example : α → α := by
intro a
--^ $/lean/plainGoal
--^ $/lean/plainGoal
apply a
|
f433c139d85e0e8ab36a9049a776f22b4ea0147d | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/number_theory/zsqrtd/gaussian_int.lean | 408f76723e7cabebd9ff57c3ca66e638b84fc959 | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 12,543 | 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 number_theory.zsqrtd.basic
import data.complex.basic
import ring_theory.principal_ideal_domain
import number_theory.quadratic_reciprocity
/-!
# Gaussian integers
... |
e213cf9d14c490ef61c9786dee00114976e87260 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/analysis/complex/liouville.lean | 1a5aaddacc0163ea90fd4cc25fc3ad8ce22fa1e3 | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 5,711 | lean | /-
Copyright (c) 2022 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import analysis.complex.cauchy_integral
import analysis.calculus.fderiv_analytic
import analysis.normed_space.completion
/-!
# Liouville's theorem
In this f... |
bf844fcec6578816744bc09d7abc0b58aa02b6bd | ed27983dd289b3bcad416f0b1927105d6ef19db8 | /src/assignments/assignment_6/field_rename.lean | 2792ab6bbfa5bd1ee94c373d07e57c5322ff31d7 | [] | no_license | liuxin-James/complogic-s21 | 0d55b76dbe25024473d31d98b5b83655c365f811 | 13e03e0114626643b44015c654151fb651603486 | refs/heads/master | 1,681,109,264,463 | 1,618,848,261,000 | 1,618,848,261,000 | 337,599,491 | 0 | 0 | null | 1,613,141,619,000 | 1,612,925,555,000 | null | UTF-8 | Lean | false | false | 1,061 | lean | import inClassNotes.typeclasses.algebra
set_option old_structure_cmd true
/-
Inheriting two fields with same name
-/
open alg
-- need to enable "old_structure" option here
class another_two_muls (A : Type) extends mul_groupoid A renaming a_mul → mul1
mul_groupoid A renamin... |
12b1dfc9c49680d37a9a65c56873bbc09a74e323 | ce6917c5bacabee346655160b74a307b4a5ab620 | /src/ch2/ex0701.lean | f25e4623edc3bed263e25941f92100db04db0226 | [] | 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 | 400 | lean | namespace foo
def a : ℕ := 5
def f (x : ℕ) : ℕ := x + 7
def fa : ℕ := f a
def ffa : ℕ := f (f a)
#print "inside foo"
#check a
#check f
#check fa
#check ffa
#check foo.fa
end foo
#print "outside the namespace"
-- #check a
-- #check f
#check foo.a
#check foo.f
#check foo.fa
#check foo.ffa
open... |
5bd337b3fb45d982ea15f59237a48ee1266de25a | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/data/equiv/fintype.lean | 46bf9c9ef9ce8d2e0c7f2d98279c97c70d351370 | [
"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 | 3,168 | lean | /-
Copyright (c) 2021 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
import data.equiv.basic
import data.fintype.basic
import group_theory.perm.sign
/-! # Equivalence between fintypes
This file contains some basic results on equiv... |
cdd1848923e4f15e21cc5374b105561b36066525 | ebb7367fa8ab324601b5abf705720fd4cc0e8598 | /homotopy/sample.hlean | 54a787cad3a8422d336041f63f43d292fde79398 | [
"Apache-2.0"
] | permissive | radams78/Spectral | 3e34916d9bbd0939ee6a629e36744827ff27bfc2 | c8145341046cfa2b4960ef3cc5a1117d12c43f63 | refs/heads/master | 1,610,421,583,830 | 1,481,232,014,000 | 1,481,232,014,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,372 | hlean | /-
Copyright (c) 2015 Ulrik Buchholtz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ulrik Buchholtz
-/
import types.trunc types.arrow_2 types.fiber homotopy.susp
open eq is_trunc is_equiv nat equiv trunc function fiber
namespace homotopy
definition is_conn [redu... |
0d4b41b203e47b2173ca4701aa086af5d8f504e7 | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /library/data/sigma.lean | c8c095b99a1be17b028dab7cd4181441eaa62b05 | [
"Apache-2.0"
] | permissive | tjiaqi/lean | 4634d729795c164664d10d093f3545287c76628f | d0ce4cf62f4246b0600c07e074d86e51f2195e30 | refs/heads/master | 1,622,323,796,480 | 1,422,643,069,000 | 1,422,643,069,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,431 | lean | -- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Author: Leonardo de Moura, Jeremy Avigad, Floris van Doorn
import logic.cast
open inhabited eq.ops sigma.ops
namespace sigma
universe variables u v
variables {A A' : Type.{u}}... |
d575e225902f7742b09f0c91d4db2fe8b5b21f96 | 26ac254ecb57ffcb886ff709cf018390161a9225 | /src/analysis/special_functions/trigonometric.lean | 660186f77d5d6ed16db0f172660ebaba68ef3198 | [
"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 | 65,365 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne
-/
import analysis.special_functions.exp_log
/-!
# Trigonometric functions
## Main definitions
This file contains the foll... |
d131d071dd0c5ded037b59f83c9901844de39263 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/topology/fiber_bundle.lean | d3be6e4d9ed65f75527567f321dd193102af28f1 | [
"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 | 57,961 | 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
import topology.algebra.ordered.basic
import data.bundle
/-!
# Fiber bundles
A topological fiber bundle with fiber `F` over a... |
9d7acd07f6ce6d25cebd1ee2cb30c22477ac6b08 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/analysis/inner_product_space/calculus.lean | 2af8f6f4df23179b12520ed588146356e7253d3e | [
"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 | 11,404 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import analysis.inner_product_space.basic
import analysis.special_functions.sqrt
/-!
# Derivative of the inner product
In this file we prove that the inner produc... |
53a4c135335fd9ceaf2c0b6e4015e2dc25c9fccd | 690889011852559ee5ac4dfea77092de8c832e7e | /src/analysis/calculus/deriv.lean | 96940cc0db793ad37f80fe9a87d82836d2cef972 | [
"Apache-2.0"
] | permissive | williamdemeo/mathlib | f6df180148f8acc91de9ba5e558976ab40a872c7 | 1fa03c29f9f273203bbffb79d10d31f696b3d317 | refs/heads/master | 1,584,785,260,929 | 1,572,195,914,000 | 1,572,195,913,000 | 138,435,193 | 0 | 0 | Apache-2.0 | 1,529,789,739,000 | 1,529,789,739,000 | null | UTF-8 | Lean | false | false | 52,597 | lean | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Sébastien Gouëzel
The Fréchet derivative.
Let `E` and `F` be normed spaces, `f : E → F`, and `f' : E →L[𝕜] F` a
continuous 𝕜-linear map, where `𝕜` is a non-discrete ... |
cdb925978a5877bbfb720a0d6e5eaf65f4e89681 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/algebraic_geometry/structure_sheaf.lean | 28074fcfb787d68de90d8193d30c2fe966cf4e3b | [
"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 | 44,252 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Scott Morrison
-/
import algebraic_geometry.prime_spectrum
import algebra.category.CommRing.colimits
import algebra.category.CommRing.limits
import topology.sheaves.loc... |
db1db7f856c7d507c74f66d0cfb466f549abb77b | 54c9ed381c63410c9b6af3b0a1722c41152f037f | /Lib4/PrePort.lean | 7c3de66c200c018821f7dd2c26353dde4a40ae36 | [
"Apache-2.0"
] | permissive | dselsam/binport | 0233f1aa961a77c4fc96f0dccc780d958c5efc6c | aef374df0e169e2c3f1dc911de240c076315805c | refs/heads/master | 1,687,453,448,108 | 1,627,483,296,000 | 1,627,483,296,000 | 333,825,622 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 183 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Selsam
-/
import PrePort.Numbers
|
2249ff5c1494c327c4ebd2e92a6e7ecbe2d6aab1 | 280e37a1b98242171ef310909eae7a9811cc5303 | /src/regex.lean | 555479eae4c6ebda92eaddaf81de0a53d317f828 | [] | no_license | foxthomson/regular | 6655d19258f80272e0740f4f19152e9dc2514d3b | 6c7c691eb226eb0e33a0995b027ba8641f1611bf | refs/heads/master | 1,672,642,114,346 | 1,603,122,446,000 | 1,603,122,446,000 | 300,912,418 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 2,889 | lean | import data.fintype.basic
import data.finset.basic
import NFA
universe u
inductive regex (α : Type u) : Type (u+1)
| RZero : regex
| RNull : regex
| RChar : α → regex
| RStar : regex → regex
| RPlus : regex → regex → regex
| RComp : regex → regex → regex
namespace regex
def match_null {α : Type u} : regex α → bool
... |
ca9ff6389cd09dadaa8caa6a713ce1b070157197 | 5719a16e23dfc08cdea7a5bf035b81690f307965 | /src/Init/Lean/Elab/Tactic/Basic.lean | 4f7b361dbd12a88ceb06b6e10eff22ababe3fd0f | [
"Apache-2.0"
] | permissive | postmasters/lean4 | 488b03969a371e1507e1e8a4df9ebf63c7cbe7ac | f3976fc53a883ac7606fc59357d43f4b51016ca7 | refs/heads/master | 1,655,582,707,480 | 1,588,682,595,000 | 1,588,682,595,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 17,742 | 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
-/
prelude
import Init.Lean.Util.CollectMVars
import Init.Lean.Meta.Tactic.Assumption
import Init.Lean.Meta.Tactic.Intro
import Init.Lean.Me... |
de40109c0367dae4ab2448ca7320f8bccd2674cc | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/ring/basic.lean | db475cd2577069c282512f7277c6155133ad17fd | [] | 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 | 46,571 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Amelia Livingston, Yury Kudryashov,
Neil Strickland
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.alg... |
81177b8276444c387219deb95f4a64738410cd5b | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/import_middle.lean | 123c4c9a29fbe4cd62bfc5e7ddac58cef7a955c8 | [
"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 | 54 | lean | import data.buffer
#print "hello"
import data.dlist
|
5019380d6b27f245ef77511a0567595bb5fb6730 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/topology/sheaves/sheaf_condition/unique_gluing.lean | b550cdebad637a0c84905be5d99f405af77caf3d | [
"Apache-2.0"
] | permissive | AntoineChambert-Loir/mathlib | 64aabb896129885f12296a799818061bc90da1ff | 07be904260ab6e36a5769680b6012f03a4727134 | refs/heads/master | 1,693,187,631,771 | 1,636,719,886,000 | 1,636,719,886,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,802 | lean | /-
Copyright (c) 2021 Justus Springer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Justus Springer
-/
import algebra.category.CommRing.limits
import topology.sheaves.forget
import topology.sheaves.sheaf
import category_theory.limits.shapes.types
import category_theo... |
c52288d0b271a31459569126c5051b4255d2b3fa | 9b9a16fa2cb737daee6b2785474678b6fa91d6d4 | /src/order/complete_lattice.lean | e0ce590b77b5d1b4dc896bd8cb63e90453bb4f1b | [
"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 | 33,344 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Theory of complete lattices.
-/
import order.bounded_lattice data.set.basic tactic.pi_instances
set_option old_structure_cmd true
open set
namespace lattice
universes... |
734aea32adbcd0a43dc4357d078ad2ea1458506c | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/homology/homological_complex.lean | 7c4851e060cc362dad54dc45b02479f6e3fc693e | [
"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 | 32,651 | lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Scott Morrison
-/
import algebra.homology.complex_shape
import category_theory.subobject.limits
import category_theory.graded_object
/-!
# Homological complexes.
A `h... |
45fd3106531cc365f749f35ff880ddc926e0c6ed | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/algebra/group.lean | 41ad93fbb1b7e08039f628c70aa47e892256c035 | [
"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 | 39,217 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
Various multiplicative and additive structures.
-/
import tactic.interactive data.option.defs
section pending_1857
/- Transport multiplicative to add... |
1c98be3015120decdfe156a1eb8b0782d9fce6bd | e37bb385769d6f4ac9931236fd07b708397e086b | /src/exercises/src_35_algebraic_axioms.lean | 3c14302df16a1ca1b00e9ba34ea1687964b7eebc | [] | 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 | 8,462 | lean | import ..library.src_field
import tactic
namespace mth1001
namespace myreal
section grouplaws
variables {R : Type} [comm_group R]
/-
The following six lemmas are 'user-friendly' variants of the first four axioms of the real number
system. I have split each of the additive identity and additive inverse axioms into ... |
0b6cffb3816379b5e732e527a1a3c987107e8b48 | ea5678cc400c34ff95b661fa26d15024e27ea8cd | /test5.lean | 2e0b5dadebd5056ad5e6f695f43bef6107260841 | [] | no_license | ChrisHughes24/leanstuff | dca0b5349c3ed893e8792ffbd98cbcadaff20411 | 9efa85f72efaccd1d540385952a6acc18fce8687 | refs/heads/master | 1,654,883,241,759 | 1,652,873,885,000 | 1,652,873,885,000 | 134,599,537 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 546 | lean | import data.real.cardinality group_theory.quotient_group
instance rat_cast_is_add_group_hom : is_add_group_hom (coe : ℚ → ℝ) :=
{ to_is_add_hom := { map_add := by simp } }
noncomputable lemma real_equiv_real_mod_rat : ℝ ≃ quotient_add_group.quotient
(set.range (coe : ℚ → ℝ)) :=
calc ℝ ≃ quotient_add_group.quotient ... |
f0aad9a620918fd4a635899cbbf1db956d196e20 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/number_theory/bernoulli.lean | bf28b0906ff3e086d1963c18993584ca973545eb | [
"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 | 2,899 | 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.rat
import data.fintype.card
/-!
# Bernoulli numbers
The Bernoulli numbers are a sequence of numbers that frequently show up in number theory.
For exam... |
bff2d02a6633d9d8b3e7a68646982cac712c4eed | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Elab/InheritDoc.lean | b629a9e12429e3a9b90bb808fd158dbb9096f6ad | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 1,193 | lean | /-
Copyright (c) 2022 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Lean.Elab.InfoTree.Main
import Lean.DocString
namespace Lean
builtin_initialize
registerBuiltinAttribute {
name := `inherit_doc
descr := "in... |
d728534c5e58aa3b49b6c59d1522f26481116566 | 1437b3495ef9020d5413178aa33c0a625f15f15f | /category_theory/examples/monoids.lean | 84f53780e9188ca363fb4a780e85fc63b355a689 | [
"Apache-2.0"
] | permissive | jean002/mathlib | c66bbb2d9fdc9c03ae07f869acac7ddbfce67a30 | dc6c38a765799c99c4d9c8d5207d9e6c9e0e2cfd | refs/heads/master | 1,587,027,806,375 | 1,547,306,358,000 | 1,547,306,358,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,664 | lean | /- Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
Introduce Mon -- the category of monoids.
Currently only the basic setup.
-/
import category_theory.fully_faithful
import algebra.ring
universes u v
open category_t... |
1687731879c584ab5cfb48a7798d9517d31ee920 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/limits/constructions/filtered.lean | 42c8ea4d848019647342b67b385c54a5e4d12121 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 3,667 | lean | /-
Copyright (c) 2022 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import category_theory.limits.constructions.limits_of_products_and_equalizers
import category_theory.limits.opposites
/-!
# Constructing colimits from finite colimits ... |
43a0333404de5c7afb55459c5c45b0e9fee8fbb6 | 398b53a5e02ce35196531591f84bb2f6b034ce5a | /tpil/chapter5.lean | 4e6a85f52ec5145ffd2b19542acdcfc6f5cb6cea | [
"MIT"
] | permissive | crockeo/math-exercises | 64f07a9371a72895bbd97f49a854dcb6821b18ab | cf9150ef9e025f1b7929ba070a783e7a71f24f31 | refs/heads/master | 1,607,910,221,030 | 1,581,231,762,000 | 1,581,231,762,000 | 234,595,189 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 575 | lean | -- Exercise 1
--
-- Go back to the exercises in Chapter 3 and Chapter 4 and redo as many as you
-- can now with tactic proofs, using also rw and simp as appropriate.
-- NOTE: I had alreadty been doing this, so I don't think I need to go back and
-- do them again... oops.
-- Exercise 2
--
-- Use tactic combinato... |
c58ae7015a7f2e41205ed06882bcff518fce224e | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /hott/default.hlean | d6dda5b5cf51b4378f9f6a1773690ced578eba58 | [
"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 | 244 | hlean | -- Copyright (c) 2014 Jeremy Avigad. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Author: Jeremy Avigad, Jakob von Raumer
-- hott.default
-- ============
-- A library for homotopy type theory
|
927205bc78f999a1357cb6cf4e3975c36a17dcb7 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/algebra/group_power/basic.lean | fae1bb920ec844df536cff391dab6e08fc1e441e | [
"Apache-2.0"
] | permissive | lacker/mathlib | f2439c743c4f8eb413ec589430c82d0f73b2d539 | ddf7563ac69d42cfa4a1bfe41db1fed521bd795f | refs/heads/master | 1,671,948,326,773 | 1,601,479,268,000 | 1,601,479,268,000 | 298,686,743 | 0 | 0 | Apache-2.0 | 1,601,070,794,000 | 1,601,070,794,000 | null | UTF-8 | Lean | false | false | 20,312 | lean | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis
-/
import algebra.order_functions
import deprecated.group
/-!
# Power operations on monoids and groups
The power operation on monoids and groups.
We sep... |
0e465fb7f6d718ff56821a9a8522260a97dab077 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/indicator_function.lean | c28ce86dcc9d06704aa80b4c7f2057c5ef3942e3 | [
"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 | 26,382 | lean | /-
Copyright (c) 2020 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
-/
import algebra.support
/-!
# Indicator function
- `indicator (s : set α) (f : α → β) (a : α)` is `f a` if `a ∈ s` and is `0` otherwise.
- `mul_indicator (s : set α) (... |
60178e0c4ca76dcd49ac0bf38d7376fbdd8ced99 | c8b4b578b2fe61d500fbca7480e506f6603ea698 | /src/number_theory/cyclotomic/galois_action_on_cyclo.lean | 82901c84ec87f72cc3b8eaf7944d57da66303fb1 | [] | no_license | leanprover-community/flt-regular | aa7e564f2679dfd2e86015a5a9674a6e1197f7cc | 67fb3e176584bbc03616c221a7be6fa28c5ccd32 | refs/heads/master | 1,692,188,905,751 | 1,691,766,312,000 | 1,691,766,312,000 | 421,021,216 | 19 | 4 | null | 1,694,532,115,000 | 1,635,166,136,000 | Lean | UTF-8 | Lean | false | false | 4,601 | lean | import number_theory.cyclotomic.cyclotomic_units
import number_theory.cyclotomic.gal
universes u
open finite_dimensional
open_locale number_field
theorem power_basis.rat_hom_ext {S S' : Type*} [comm_ring S] [hS : algebra ℚ S] [ring S']
[hS' : algebra ℚ S'] (pb : power_basis ℚ S) ⦃f g : S →+* S'⦄ (h : f pb.gen = ... |
c89eb7924a81c77c6569ec99460e681741d6d11f | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/analysis/convex/cone/basic.lean | 92aea1081b836da0c2c798605de3712f45f2794d | [
"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 | 34,844 | lean | /-
Copyright (c) 2020 Yury Kudryashov All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Frédéric Dupuis
-/
import analysis.inner_product_space.projection
/-!
# Convex cones
In a `𝕜`-module `E`, we define a convex cone as a set `s` such that `a • x + b ... |
a379476f2d71c350a5880b1d83cedf2f35794adc | a4673261e60b025e2c8c825dfa4ab9108246c32e | /src/Lean/Data/Lsp.lean | b33f8bfce339d85041698413969361eab3a039da | [
"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 | 450 | 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 Lean.Data.Lsp.Basic
import Lean.Data.Lsp.Capabilities
import Lean.Data.Lsp.Communication
import Lean.Data.Lsp.Diagnostics
import Lean.Data.Ls... |
70e393bb669b895bf46b988588ae13eba0412554 | e151e9053bfd6d71740066474fc500a087837323 | /src/hott/types/nat/div.lean | b74ca09c9bd23540f2d8a52f6974e48cca82b1da | [
"Apache-2.0"
] | permissive | daniel-carranza/hott3 | 15bac2d90589dbb952ef15e74b2837722491963d | 913811e8a1371d3a5751d7d32ff9dec8aa6815d9 | refs/heads/master | 1,610,091,349,670 | 1,596,222,336,000 | 1,596,222,336,000 | 241,957,822 | 0 | 0 | Apache-2.0 | 1,582,222,839,000 | 1,582,222,838,000 | null | UTF-8 | Lean | false | false | 26,655 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
Definitions prod properties of div prod mod. Much of the development follows Isabelle's library.
-/
#exit
import .sub
universes u v w
hott_theory
names... |
504f374794ce2b941f0ac1cf0eda6d3ddbe47213 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/order/rel_classes.lean | edd890a81faed8f3de10daebe3b24d95439cb4b9 | [
"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 | 24,225 | lean | /-
Copyright (c) 2020 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Mario Carneiro, Yury G. Kudryashov
-/
import order.basic
import logic.is_empty
/-!
# Unbundled relation classes
In this file we prove some properties of `is_*` classes ... |
5d8d6c96640f5dede71764593cc39d63a5295953 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/epi_mono.lean | b23311392e635c090e358cc657dca495c5c9475d | [
"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 | 9,331 | lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Scott Morrison
-/
import category_theory.opposites
import category_theory.groupoid
/-!
# Facts about epimorphisms and monomorphisms.
> THIS FILE IS SYNCHRONIZED WITH MATHLI... |
c18ad0b6e872a6c59652f1b3c13bac079fd770b0 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/topology/continuous_on.lean | 206afc241cc2c8a43087bf39a153733ae1c10ed3 | [
"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 | 44,633 | lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import topology.constructions
/-!
# Neighborhoods and continuity relative to a subset
This file defines relative versions
* `nhds_within` of `nhds`
* `co... |
dcca8385d53047b7f9a2c2bb8a3d12d9bbe4ddce | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/algebra/char_p/quotient.lean | 286bada40ccd08c3f4bd592fa7f8abe20e9ee876 | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 1,455 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Eric Wieser
-/
import algebra.char_p.basic
import ring_theory.ideal.quotient
/-!
# Characteristic of quotients rings
-/
universes u v
namespace char_p
theorem quotient (R : ... |
8d55a017a87d614557ecc95139a8fd31d5e46fcb | b3fced0f3ff82d577384fe81653e47df68bb2fa1 | /src/ring_theory/power_series.lean | 8d03fea7c30d7db8beaccc95ee8390b327f91cac | [
"Apache-2.0"
] | permissive | ratmice/mathlib | 93b251ef5df08b6fd55074650ff47fdcc41a4c75 | 3a948a6a4cd5968d60e15ed914b1ad2f4423af8d | refs/heads/master | 1,599,240,104,318 | 1,572,981,183,000 | 1,572,981,183,000 | 219,830,178 | 0 | 0 | Apache-2.0 | 1,572,980,897,000 | 1,572,980,896,000 | null | UTF-8 | Lean | false | false | 56,770 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Kenny Lau
-/
import data.finsupp order.complete_lattice algebra.ordered_group data.mv_polynomial
import algebra.order_functions
import ring_theory.ideal_operations
/-... |
618a0c0e59207602049c134dd81b60221f89c230 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/measure_theory/function/locally_integrable.lean | 68bd275ea26476fce224bacc3f93d1e7ed143846 | [
"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 | 8,051 | lean | /-
Copyright (c) 2022 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import measure_theory.integral.integrable_on
/-!
# Locally integrable functions
A function is called *locally integrable* (`measure_theory.locally_integrable`) ... |
6e3ebd0151837f8069979dead6beeaa3d415043d | 618003631150032a5676f229d13a079ac875ff77 | /test/wlog.lean | b225dd563431ab9b813d941abfe5246344d6ca63 | [
"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 | 3,111 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import tactic.wlog
section wlog
example {x y : ℕ} (a : x = 1) : true :=
begin
suffices : false, trivial,
wlog h : x = y,
{ guard_target x = y ∨ y = x,
admit },
... |
74c01473f4f62011d70f73a31459f0df2fe1829c | 4bcaca5dc83d49803f72b7b5920b75b6e7d9de2d | /src/Lean/Parser/Command.lean | 82a797c355645cb53cb276fb09ff2de8873197bd | [
"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 | 10,972 | 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.Term
import Lean.Parser.Do
namespace Lean
namespace Parser
/--
Syntax quotation for terms and (lists of) commands.... |
c4274ad56005b09c4bca5181b460de999f70184b | ee8cdbabf07f77e7be63a449b8483ce308d37218 | /lean/src/valid/mathd-algebra-28.lean | fc3aea02e6e3cdf7c6f766c7921f16f38a9858e0 | [
"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 | 308 | 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.real.basic
example (c : ℝ) (f : ℝ → ℝ) (h₀ : ∀ x, f x = 2 * x ^ 2 + 5 * x + c) (h₁ : ∃ x, f x ≤ 0) : c ≤ 25/8 :=
begin
sorry
end
|
9d2c3f573171f741fb75acfe9b14b3ca5de2b5a9 | df561f413cfe0a88b1056655515399c546ff32a5 | /6-advanced-addition-world/l9.lean | 419a5350ee7bde6335086b2243f61ea3ee1a972c | [] | no_license | nicholaspun/natural-number-game-solutions | 31d5158415c6f582694680044c5c6469032c2a06 | 1e2aed86d2e76a3f4a275c6d99e795ad30cf6df0 | refs/heads/main | 1,675,123,625,012 | 1,607,633,548,000 | 1,607,633,548,000 | 318,933,860 | 3 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 93 | lean | theorem succ_ne_zero (a : mynat) : succ a ≠ 0 :=
begin
symmetry,
exact zero_ne_succ a,
end |
4f183af41a366b45404594c54acea95246846fab | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/continued_fractions/basic.lean | c44bfc93f32a1f040b4cfbbdadbe02e70d4d2115 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,692 | lean | /-
Copyright (c) 2019 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.seq.seq
import Mathlib.algebra.field
import Mathlib.PostPort
universes u_1 l u_2 ... |
aca07ae8f489d6c2dbb7380d1ded1d7fdfd61dbd | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /archive/imo/imo1962_q1.lean | bd586605533fb542a76d73810b01e0795700349d | [
"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 | 5,591 | lean | /-
Copyright (c) 2020 Kevin Lacker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker
-/
import data.nat.digits
/-!
# IMO 1962 Q1
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
Find the smalle... |
bbacd4a8188e941516cad471b36acf4de4f28f8f | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/tactic/algebra.lean | 099afdee506badcbcd3db91acc2da43bb8370b4b | [
"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 | 1,854 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import tactic.core
open lean.parser
namespace tactic
@[user_attribute]
meta def ancestor_attr : user_attribute unit (list name) :=
{ name := `ancestor,
descr := "ance... |
2c8534fd7feca9131431086805076514346b35e1 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/algebra/category/Module/adjunctions.lean | 721fc2c6e4e0f3887b3f4d5b47ccd22f929b074e | [
"Apache-2.0"
] | permissive | stjordanis/mathlib | 51e286d19140e3788ef2c470bc7b953e4991f0c9 | 2568d41bca08f5d6bf39d915434c8447e21f42ee | refs/heads/master | 1,631,748,053,501 | 1,627,938,886,000 | 1,627,938,886,000 | 228,728,358 | 0 | 0 | Apache-2.0 | 1,576,630,588,000 | 1,576,630,587,000 | null | UTF-8 | Lean | false | false | 10,193 | lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Johan Commelin
-/
import algebra.category.Module.monoidal
import category_theory.monoidal.functorial
import category_theory.monoidal.types
import linear_algebra.direct_... |
970e5d83d86c8c779645f517fdb7fb6f3d3b9e5c | c777c32c8e484e195053731103c5e52af26a25d1 | /src/topology/sheaves/punit.lean | c036317c91fdfa6482263d18cc8f878f5efe5882 | [
"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 | 2,030 | 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 topology.sheaves.sheaf_condition.sites
/-!
# Presheaves on punit
Presheaves on punit satisfy sheaf condition iff its value at empty set is a terminal object.
-/
... |
1441cd307db45bd752ff96040dd0cb443785eaf2 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/analysis/normed_space/M_structure.lean | 6f38dbc4af33565e32e0125402c449aa13a733f9 | [
"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 | 13,587 | lean | /-
Copyright (c) 2022 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin
-/
import algebra.ring.idempotents
import tactic.noncomm_ring
import analysis.normed.group.basic
/-!
# M-structure
A projection P on a normed space X is said t... |
a10d80d6b84538cde51486888cf4356e7e3b23d5 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/analysis/normed_space/ball_action.lean | c30e8f1deec4e65616eeebcac919eb85fc3306bd | [
"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 | 4,175 | lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Heather Macbeth
-/
import analysis.normed.field.unit_ball
import analysis.normed_space.basic
/-!
# Multiplicative actions of/on balls and spheres
Let `E` be a norme... |
4c9172b0b9f69aa1d475b284a81fa20eacca2583 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/logic/equiv/basic.lean | af1fdde196ec5cbe660cbde99f62d364adc7f171 | [
"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 | 95,788 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Mario Carneiro
-/
import data.fun_like.equiv
import data.option.basic
import data.prod.basic
import data.quot
import data.sigma.basic
import data.subtype
impo... |
832b3140afadc167f9351f406434732c645688d7 | 2272e503179a58556187901b8698b789fad7e0c4 | /src/examples.lean | 8293339cc04858c58020dc287df43e8f9fdb90b1 | [] | no_license | kckennylau/category-theory | f15e582be862379453a5341d83b8cd5ebc686729 | b24962838c7370b5257e38b7648040aec95922bb | refs/heads/master | 1,583,605,043,449 | 1,525,154,882,000 | 1,525,154,882,000 | 127,633,452 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,096 | lean | import .basic .group_action .free_group
universes u v
namespace category
namespace examples
@[reducible] def Set : category (Type u) :=
{ Mor := λ S T, S → T,
Comp := λ S T U, (∘),
Id := @id,
Hid_left := λ S T f, rfl,
Hid_right := λ S T f, rfl,
Hassoc := λ S T U V f g h, rfl }
@[reducible... |
b3c80e8f0440e156a38b169efbbfb0e528f32b89 | f5f7e6fae601a5fe3cac7cc3ed353ed781d62419 | /src/category_theory/types.lean | 9eca6f87183b6333b0e9fe6c00962f78f4622425 | [
"Apache-2.0"
] | permissive | EdAyers/mathlib | 9ecfb2f14bd6caad748b64c9c131befbff0fb4e0 | ca5d4c1f16f9c451cf7170b10105d0051db79e1b | refs/heads/master | 1,626,189,395,845 | 1,555,284,396,000 | 1,555,284,396,000 | 144,004,030 | 0 | 0 | Apache-2.0 | 1,533,727,664,000 | 1,533,727,663,000 | null | UTF-8 | Lean | false | false | 3,109 | 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, Johannes Hölzl
import category_theory.functor_category
import category_theory.fully_faithful
namespace category_theory
universes v v' w u u' --... |
bb77d97e1d89471570e19c6d550237df8f46a3e0 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/data/equiv/fintype.lean | ad9243600b0be64bfcc58ea9375cda0715b9c331 | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 5,401 | lean | /-
Copyright (c) 2021 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
import data.equiv.basic
import data.set.finite
import group_theory.perm.sign
/-! # Equivalence between fintypes
This file contains some basic results on equivale... |
86c8f547e81432bd017ec0e472690e2ea3137cc2 | dfbb669f3f58ceb57cb207dcfab5726a07425b03 | /vscode-lean4/test/test-fixtures/lean3/Main.lean | 7cd8891b15bb64a888ae7059c74f9c4a1e365966 | [
"Apache-2.0"
] | permissive | leanprover/vscode-lean4 | 8bcf7f06867b3c1d42007fe6da863a7a17444dbb | 6ef0bfa668bdeaad0979e6df10551d42fcc01094 | refs/heads/master | 1,692,247,771,767 | 1,691,608,804,000 | 1,691,608,804,000 | 325,845,305 | 64 | 24 | Apache-2.0 | 1,694,176,429,000 | 1,609,435,614,000 | TypeScript | UTF-8 | Lean | false | false | 341 | lean | -- Live WebAssembly version of Lean
#eval let v := lean.version in let s := lean.special_version_desc in string.join
["Lean (version ", v.1.repr, ".", v.2.1.repr, ".", v.2.2.repr, ", ",
if s ≠ "" then s ++ ", " else s, "commit ", (lean.githash.to_list.take 12).as_string, ")"]
example (m n : ℕ) : m + n = n + m :=
by si... |
1b90624a4a733eee450357363e774a604047a475 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/chain_auto.lean | 6945a779488b48866587019b21bbd473e124dfb7 | [] | 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 | 903 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Mario Carneiro
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.tactic.ext
import Mathlib.PostPort
universes l
namespace Mathlib
namesp... |
a2c622a2d1bd592d463fc3e1f947edb40c616ddf | 42610cc2e5db9c90269470365e6056df0122eaa0 | /hott/homotopy/sphere2.hlean | e7ef858975c772a618bc826db7c9a90ccd255e8c | [
"Apache-2.0"
] | permissive | tomsib2001/lean | 2ab59bfaebd24a62109f800dcf4a7139ebd73858 | eb639a7d53fb40175bea5c8da86b51d14bb91f76 | refs/heads/master | 1,586,128,387,740 | 1,468,968,950,000 | 1,468,968,950,000 | 61,027,234 | 0 | 0 | null | 1,465,813,585,000 | 1,465,813,585,000 | null | UTF-8 | Lean | false | false | 5,044 | hlean | /-
Copyright (c) 2016 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
Calculating homotopy groups of spheres.
In this file we calculate
π₂(S²) = Z
πₙ(S²) = πₙ(S³) for n > 2
πₙ(Sⁿ) = Z for n > 0
π₂(S³) = Z
-/
import .homotopy_group .... |
f7c07852db0f4741a336780d9bf3739bea833dd6 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/tactic/lint/simp.lean | 18f00af9eb1c62e35cb3487f0bb6806a21f705d9 | [
"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 | 9,305 | lean | /-
Copyright (c) 2020 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner
-/
import tactic.lint.basic
/-!
# Linter for simplification lemmas
This files defines several linters that prevent common mistakes when declaring simp lemmas:
* `simp_... |
ea6d62c8bf26ddf65a0167eac0a1521b952eabd1 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/ind6.lean | 52faaf33efc06da42525332945257bf52ad51425 | [
"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 | 287 | lean | exit
inductive tree.{u} (A : Type.{u}) : Type.{max u 1} :=
| node : A → forest.{u} A → tree.{u} A
with forest : Type.{max u 1} :=
| nil : forest.{u} A
| cons : tree.{u} A → forest.{u} A → forest.{u} A
check tree.{1}
check forest.{1}
check tree.rec.{1 1}
check forest.rec.{1 1}
|
301107cbcc399a57415f270de5ea2ec7172e8dd7 | 0533ebfa09b11cf8a29da118dd1b86b94949511e | /src/riemann_zeta.lean | 20e4e3eaf646da535fd93927808901c44e60380e | [
"MIT"
] | permissive | wudcscheme/Lean-RH | 89e9055aac68703876e750c23fb5327979a09822 | 870f78cc7c0715d03466d1211b0f032b425ec984 | refs/heads/main | 1,679,188,429,923 | 1,602,701,790,000 | 1,602,701,790,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,227 | lean | /- ------------------------------------------------------------------------- -|
| @project: riemann_hypothesis |
| @file: riemann_zeta.lean |
| @author: Brandon H. Gomes and Alex Kontorovich ... |
1683d4bc36f710ccb31be0c5aaa9ce0bf7efcf8e | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/analysis/special_functions/trigonometric/chebyshev.lean | 78ddae6ca6b6f5046b29bc049dc27ff8f3a74b3e | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 3,396 | 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 analysis.complex.basic
import data.complex.exponential
import data.polynomial.algebra_map
import ring_theory.polynomial.chebyshev
/-!
# Multiple angle formula... |
9e35d36ee4d9431584c55a384fb7c0420ab9784e | 75db7e3219bba2fbf41bf5b905f34fcb3c6ca3f2 | /hott/init/trunc.hlean | d78e5953822f3ab5b3a5a647dcd5b89db1d9632d | [
"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 | 13,178 | hlean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Floris van Doorn
Definition of is_trunc (n-truncatedness)
Ported from Coq HoTT.
-/
--TODO: can we replace some definitions with a hprop as codomain by theorems... |
154a16d1978a362d5c16b93f559c6a0ab60c3aab | 21c6ba3d88e3d63bc4dc2369086afcea71fdab70 | /.config.nor.lean | 2b80473b1a60326f89879414849a89f7383f70e4 | [
"MIT"
] | permissive | panda7887x2/OpenWrt_AR750S | a3b527a07c5d13001207658b965b5888907df36b | 178dfd579c661259a1fa4444c5274544cff3dd06 | refs/heads/main | 1,693,700,189,495 | 1,637,408,343,000 | 1,637,408,343,000 | 430,083,044 | 2 | 0 | MIT | 1,637,407,336,000 | 1,637,407,335,000 | null | UTF-8 | Lean | false | false | 250,326 | 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=y
# CONFIG_TARGET_ath79 is not set
# CONFIG_TARGET_bcm27xx is not set
# CONFIG_T... |
d1bdfb905ea0ba3d316e1aeee2be0a373b2f96e5 | cf39355caa609c0f33405126beee2739aa3cb77e | /library/init/meta/widget/tactic_component.lean | 0e667311bdde66bdd5c363d4aee8cb3511a43124 | [
"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 | 2,454 | lean | /-
Copyright (c) E.W.Ayers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: E.W.Ayers
-/
prelude
import init.meta.widget.basic
namespace widget
/-- A component that implicitly depends on tactic_state. For efficiency we always assume that the tactic_state is unchanged ... |
974bda87ebb81bd77fa5c68f04a94a6d1dbaaaf3 | 9cba98daa30c0804090f963f9024147a50292fa0 | /old/metrology/unit.lean | bd4d75624e9819fe4b5955791de2ba311fc8a3c3 | [] | no_license | kevinsullivan/phys | dcb192f7b3033797541b980f0b4a7e75d84cea1a | ebc2df3779d3605ff7a9b47eeda25c2a551e011f | refs/heads/master | 1,637,490,575,500 | 1,629,899,064,000 | 1,629,899,064,000 | 168,012,884 | 0 | 3 | null | 1,629,644,436,000 | 1,548,699,832,000 | Lean | UTF-8 | Lean | false | false | 313 | lean | namespace unit
inductive length : Type
| meter
| centimeter
| foot
inductive mass : Type
| kilogram
| pound
inductive time : Type
| second
inductive current : Type
| ampere
inductive temperature : Type
| kelvin
| fahrenheit
inductive quantity : Type
| mole
inductive intensity : Type
| candela
end unit |
7ff4368170b8b8e51e2a4a8ef6192929bb73cb5f | 88fb7558b0636ec6b181f2a548ac11ad3919f8a5 | /library/data/hash_map.lean | b4969259e1ab40a6380674101155406dbd804e22 | [
"Apache-2.0"
] | permissive | moritayasuaki/lean | 9f666c323cb6fa1f31ac597d777914aed41e3b7a | ae96ebf6ee953088c235ff7ae0e8c95066ba8001 | refs/heads/master | 1,611,135,440,814 | 1,493,852,869,000 | 1,493,852,869,000 | 90,269,903 | 0 | 0 | null | 1,493,906,291,000 | 1,493,906,291,000 | null | UTF-8 | Lean | false | false | 4,601 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
universes u v w
def bucket_array (α : Type u) (β : α → Type v) (n : nat) :=
array (list (Σ a, β a)) n
structure hash_map (α : Type u) [decidable_eq α] (β :... |
d7cfc52a0d3faebbaf18e625d4219956ff70fe63 | 6305b69bc7636a761e1a1947508bb5ebad93cb7e | /leanpkg/leanpkg/main.lean | 7024c203db3ea4abc84415429da4fed3d52dcc89 | [
"Apache-2.0"
] | permissive | HGldJ1966/lean | e7f0068f8a69fde3593b77d8a44609ae446d7738 | 049d940167c419cd5935d12b459c0695d8615ae9 | refs/heads/master | 1,611,340,395,700 | 1,503,103,829,000 | 1,503,103,829,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,699 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Gabriel Ebner
-/
import leanpkg.resolve
variable [io.interface]
namespace leanpkg
def write_file (fn : string) (cnts : string) (mode := io.mode.write) : io unit := do
h ← io.mk... |
f28a8dc63d02c05a98d6d892da6c9e7592d6b093 | 076f5040b63237c6dd928c6401329ed5adcb0e44 | /instructor-notes/2019.10.14.prop_logic/semantic_validity.lean | 1250064ab1aea0aead7c8b51377dfb12e33f5c95 | [] | no_license | kevinsullivan/uva-cs-dm-f19 | 0f123689cf6cb078f263950b18382a7086bf30be | 09a950752884bd7ade4be33e9e89a2c4b1927167 | refs/heads/master | 1,594,771,841,541 | 1,575,853,850,000 | 1,575,853,850,000 | 205,433,890 | 4 | 9 | null | 1,571,592,121,000 | 1,567,188,539,000 | Lean | UTF-8 | Lean | false | false | 711 | lean | import .prop_logic
open prop_logic
open prop_logic.var
open prop_logic.unOp
open prop_logic.binOp
open prop_logic.pExp
def isModel (i: var → bool) (e : pExp) :=
pEval e i = tt
def valid (e : pExp) :=
∀ (i : var → bool),
isModel i e
def satisfiable (e : pExp) :=
∃ (i : var → bool),
isMo... |
fe29d45336be199f9f18ffa7902b002488e491a9 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/analysis/normed_space/spectrum.lean | cab94d955eebbf242a3f8b08c38ee9ca21dc8074 | [
"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 | 27,796 | lean | /-
Copyright (c) 2021 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import algebra.algebra.spectrum
import analysis.special_functions.pow
import analysis.complex.liouville
import analysis.complex.polynomial
import analysis.analytic.radi... |
5f1b0a9927ac6f5b675c2fedecdc8360021e6e86 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /test/matrix.lean | 2e8111d228b75d4450f501bda1f42c8c1cbd29ee | [
"Apache-2.0"
] | permissive | abentkamp/mathlib | d9a75d291ec09f4637b0f30cc3880ffb07549ee5 | 5360e476391508e092b5a1e5210bd0ed22dc0755 | refs/heads/master | 1,682,382,954,948 | 1,622,106,077,000 | 1,622,106,077,000 | 149,285,665 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,421 | lean | import data.matrix.notation
import linear_algebra.matrix.determinant
import group_theory.perm.fin
import tactic.norm_swap
variables {α β : Type} [semiring α] [ring β]
namespace matrix
open_locale matrix
example {a a' b b' c c' d d' : α} :
![![a, b], ![c, d]] + ![![a', b'], ![c', d']] = ![![a + a', b + b'], ![c + ... |
2455e45bf41696d494b42f5eaf5b81712461374d | 80746c6dba6a866de5431094bf9f8f841b043d77 | /src/algebra/order_functions.lean | 6fea01de1d334942d4269bc44a222ce1bca9335c | [
"Apache-2.0"
] | permissive | leanprover-fork/mathlib-backup | 8b5c95c535b148fca858f7e8db75a76252e32987 | 0eb9db6a1a8a605f0cf9e33873d0450f9f0ae9b0 | refs/heads/master | 1,585,156,056,139 | 1,548,864,430,000 | 1,548,864,438,000 | 143,964,213 | 0 | 0 | Apache-2.0 | 1,550,795,966,000 | 1,533,705,322,000 | Lean | UTF-8 | Lean | false | false | 8,116 | 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 algebra.ordered_group order.lattice
open lattice
universes u v
variables {α : Type u} {β : Type v}
attribute [simp] max_eq_left max_eq_right min_eq_left min... |
879fe5da703e177258baa06a9fcdcbbf1e0dcb0f | 88fb7558b0636ec6b181f2a548ac11ad3919f8a5 | /library/init/data/sigma/lex.lean | 5f8225223d1c5ecc0f7e58f1c6167ffe5c1153df | [
"Apache-2.0"
] | permissive | moritayasuaki/lean | 9f666c323cb6fa1f31ac597d777914aed41e3b7a | ae96ebf6ee953088c235ff7ae0e8c95066ba8001 | refs/heads/master | 1,611,135,440,814 | 1,493,852,869,000 | 1,493,852,869,000 | 90,269,903 | 0 | 0 | null | 1,493,906,291,000 | 1,493,906,291,000 | null | UTF-8 | Lean | false | false | 5,589 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import init.data.sigma.basic init.meta
universes u v
namespace sigma
section
variables {α : Type u} {β : α → Type v}
variable (r : α → α → Prop... |
4cbb4a25e5ee777dfdaeb88a56e6c05efe6f86f3 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/geometry/manifold/cont_mdiff.lean | 2c1c12497729721142e4efb76da944ee33044655 | [
"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 | 85,008 | 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 geometry.manifold.mfderiv
import geometry.manifold.local_invariant_properties
/-!
# Smooth functions between smooth manifolds
We define `Cⁿ` functions... |
e1d5c658642a1c39d21e68e0e96c05c87d643504 | 271e26e338b0c14544a889c31c30b39c989f2e0f | /tests/lean/run/expr_maps.lean | d098bc0dd2c8e845ebd5451ba2047d511e76df5c | [
"Apache-2.0"
] | permissive | dgorokho/lean4 | 805f99b0b60c545b64ac34ab8237a8504f89d7d4 | e949a052bad59b1c7b54a82d24d516a656487d8a | refs/heads/master | 1,607,061,363,851 | 1,578,006,086,000 | 1,578,006,086,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,919 | lean | import Init.Lean.Expr
open Lean
def exprType : Expr := mkSort levelOne
def biDef := BinderInfo.default
def exprNat := mkConst `Nat []
-- Type -> Type
def TypeArrowType := mkForall `α biDef exprType exprType
-- Type -> Type
def TypeArrowType2 := mkForall `β biDef exprType exprType
-- fun (x : Nat) ... |
926f144f5a70f6c06f4c13f30a55cbd0d60271f1 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/number_theory/pell.lean | b8eae0615add60667ff66848e7f5404eaf0fcc65 | [
"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 | 29,355 | lean | /-
Copyright (c) 2023 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Geißer, Michael Stoll
-/
import tactic.qify
import data.zmod.basic
import number_theory.diophantine_approximation
import number_theory.zsqrtd.basic
/-!
# Pell's Equation
*Pel... |
e050edb8eb1ef6be67bade8ae59991f65bd47404 | 77c5b91fae1b966ddd1db969ba37b6f0e4901e88 | /src/data/list/perm.lean | 21c02102f2ce988a2a4295d313667d0478cbac16 | [
"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 | 54,122 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
import data.list.bag_inter
import data.list.erase_dup
import data.list.zip
import logic.relation
/-!
# List Permutations
Th... |
a673e72ce475925ea8d90447b7d4b02e2de16197 | 7fc0ec5c526f706107537a6e2e34ac4cdf88d232 | /src/group_theory/representation/bilinear_form.lean | 9d0a79fd6a829ff2cd6f2a28e33d91868707c8e8 | [
"Apache-2.0"
] | permissive | fpvandoorn/group-representations | 7440a81f2ac9e0d2defa44dc1643c3167f7a2d99 | bd9d72311749187d3bd4f542d5eab83e8341856c | refs/heads/master | 1,684,128,141,684 | 1,623,338,135,000 | 1,623,338,135,000 | 256,117,709 | 0 | 2 | null | null | null | null | UTF-8 | Lean | false | false | 6,159 | lean | /- Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Douglas, Floris van Doorn
-/
import .basic
/- everything we have done that uses bilinear forms-/
universe variables u v w w' w''
open linear_map
variables {G : Type u} {R :... |
bf8e8af005974cd063983b8815f39c084f64e249 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/linear_algebra/bilinear_form.lean | aee58fb963f49105022a5f23c59d2c91827c4f36 | [
"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 | 63,014 | lean | /-
Copyright (c) 2018 Andreas Swerdlow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andreas Swerdlow, Kexing Ying
-/
import linear_algebra.dual
import linear_algebra.matrix.nonsingular_inverse
import linear_algebra.matrix.to_lin
import linear_algebra.tensor_product... |
2d97702c7f77b40c5207beedd4a143fd2db374c4 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/order/galois_connection.lean | dc208135463b37626b2d448705976124e0e6f5e5 | [
"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 | 31,286 | 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 order.complete_lattice
import order.synonym
/-!
# Galois connections, insertions and coinsertions
Galois connections are order theoretic adjoints, i.e. a pai... |
531348768287d38e5af13389d1501f95ca073b5d | 26ac254ecb57ffcb886ff709cf018390161a9225 | /src/ring_theory/localization.lean | 440733d20775a2284bf65b6d0c934245a38ee490 | [
"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 | 49,262 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston
-/
import data.equiv.ring
import tactic.ring_exp
import ring_theory.ideal_operations
import group_theory.monoid_localization
im... |
f2cda7109523b77d683c102e6f4916f037b7a579 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/data/finset/interval.lean | 7fee4058a7f0bd44ac2ba8e08ef935177823e902 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 3,611 | 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.finset.locally_finite
/-!
# Intervals of finsets as finsets
This file provides the `locally_finite_order` instance for `finset α` and calculates the cardina... |
e1ae2d678a531d3c83272fd04088620cfcfdd4d5 | 5749d8999a76f3a8fddceca1f6941981e33aaa96 | /src/group_theory/perm/sign.lean | c64a896e877cbd7ec9de52772d775fea549f497e | [
"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 | 32,921 | 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
universes u v
open equiv function fintype finset
variables {α : Type u} {β : Type v}
namespace equiv.perm
def subtype_perm (f : perm α) {p : α → Pr... |
ec297cbcb7dfa28d9417de1fbaae39b002396907 | ce6917c5bacabee346655160b74a307b4a5ab620 | /src/ch5/ex0413.lean | f0a24f6879c94b55e8f551686cda72c04e373326 | [] | 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 | 490 | lean | example (p q r : Prop) : p ∧ (q ∨ r) ↔ (p ∧ q) ∨ (p ∧ r) :=
begin
apply iff.intro,
{ intro h,
cases h.right with hq hr,
{ show (p ∧ q) ∨ (p ∧ r),
exact or.inl ⟨h.left, hq⟩ },
show (p ∧ q) ∨ (p ∧ r),
exact or.inr ⟨h.left, hr⟩ },
intro h,
cases h with hpq hpr,
{ show p ∧ (q ∨... |
2d2568bac8fef2d052bd80eb0480829e4126003c | c777c32c8e484e195053731103c5e52af26a25d1 | /src/order/lattice.lean | e3877be97db81ad80c49397865cfe9d744c14d61 | [
"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 | 44,920 | 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 order.monotone.basic
import tactic.simps
import tactic.pi_instances
/-!
# (Semi-)lattices
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this fi... |
242e85e58c8cc4420fa869e7598ca4570a0ac0fd | 8e381650eb2c1c5361be64ff97e47d956bf2ab9f | /src/spectrum_of_a_ring/spec.lean | 8fe699d416446f367ed44cfaf851aa8bbeb48eb7 | [] | no_license | alreadydone/lean-scheme | 04c51ab08eca7ccf6c21344d45d202780fa667af | 52d7624f57415eea27ed4dfa916cd94189221a1c | refs/heads/master | 1,599,418,221,423 | 1,562,248,559,000 | 1,562,248,559,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 746 | lean | /-
Definition of Spec(R).
https://stacks.math.columbia.edu/tag/00DZ
-/
import topology.opens
import ring_theory.ideals
universe u
section spectrum
parameters (α : Type u) [comm_ring α]
-- Spec(R).
def Spec := {P : ideal α // ideal.is_prime P}
parameter {α}
-- General definitions.
def Spec.V : set α → set ... |
bc7c762b99f6ce063614714af5da92897c7fd4bd | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/list/count.lean | e918fc3ef6aa917655ae27e988c22570503f3947 | [
"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 | 7,602 | lean | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
import data.list.big_operators
/-!
# Counting in lists
This file proves basic properties of ... |
e66305212d96a61a492525e854294210065a803f | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/topology/sets/closeds.lean | 4ca4f1b2c2ff5e669ea188bae7fdbe41a28915ed | [
"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 | 7,039 | lean | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Yaël Dillies
-/
import topology.sets.opens
/-!
# Closed sets
We define a few types of closed sets in a topological space.
## Main Definitions
For a topological ... |
88e332f64588c0589b2318fc601e7114ce923064 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/hint.lean | 691ae5fdc3b9b234b567f098ac606d58bc64f447 | [] | 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 | 998 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.tactic.solve_by_elim
import Mathlib.tactic.interactive
import Mathlib.PostPort
namespace M... |
49ea5366dc42612c6b0c142a68655fb9b4e34d98 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/calc_assistant.lean | d3cd41b4d52275bb521f4a69113e729a65edba5b | [
"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 | 800 | lean | import logic
open eq.ops
set_option elaborator.calc_assistant false
theorem tst1 (a b c : num) (H₁ : ∀ x, b = x) (H₂ : c = b) : a = c :=
calc a = b : H₁ -- error because calc assistant is off
... = c : H₂
theorem tst2 (a b c : num) (H₁ : ∀ x, b = x) (H₂ : c = b) : a = c :=
calc a = b : !H₁⁻¹
... = c : H₂ ... |
3de50ec4c2ae80cfc3f6b506a5b0d179d78e4e6e | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/number_theory/class_number/admissible_abs.lean | b93949539f36993a17d8e56de520c5ad49d2a014 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 2,677 | 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.algebra.basic
import number_theory.class_number.admissible_absolute_value
/-!
# Admissible absolute value on the integers
> THIS FILE IS SYNCHRONIZED WITH ... |
161fd7091d38df505d622a4086d3914e65780205 | fe84e287c662151bb313504482b218a503b972f3 | /src/poset/subdiv.lean | 73bb752a3cce1f1b7dca688a9c362b87d66d8e44 | [] | 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 | 19,561 | lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Neil Strickland
Given a poset `P`, we define `subdiv P` to be the poset of
finite nonempty chains `s ⊆ P`. Any such `s` has a largest
element, and the map `max : (subdiv P) → P` i... |
d6669ff340f03906c9b9b604f1a19cdcb276354c | 4727251e0cd73359b15b664c3170e5d754078599 | /src/dynamics/fixed_points/basic.lean | 27623adab88023f091d1f8968be7d1f732e1bd63 | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 5,655 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import data.set.function
import logic.function.iterate
/-!
# Fixed points of a self-map
In this file we define
* the predicate `is_fixed_pt f x := f x = x`;
* th... |
d969402989fa39352d0c7c5ef5b5c4a8f8bbe8d3 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/category_theory/limits/limits.lean | 182a5ef204cda94b6b9dd942f6c4a030d82af634 | [
"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 | 36,891 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Mario Carneiro, Scott Morrison, Floris van Doorn
-/
import category_theory.whiskering
import category_theory.yoneda
import category_theory.limits.cones
import category_the... |
6785a8411b7aff226f1517d1180fc87f2a80c3b7 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/data/sum/instances.lean | e8f746bf2a16c7ce77b227df22a4a422075e74ca | [] | 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 | 985 | 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
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.meta.mk_dec_eq_instance
universes u v
namespace Mathlib
protected instance sum.decidable_eq {α : T... |
43340c6072455e4114a8eae343cedde5e8558ca1 | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /tests/lean/run/class_coe.lean | 52151aa59d0c88a86590870d5034ed4ed1175612 | [
"Apache-2.0"
] | permissive | codyroux/lean | 7f8dff750722c5382bdd0a9a9275dc4bb2c58dd3 | 0cca265db19f7296531e339192e9b9bae4a31f8b | refs/heads/master | 1,610,909,964,159 | 1,407,084,399,000 | 1,416,857,075,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,299 | lean | import data.num
constants int nat real : Type.{1}
constant nat_add : nat → nat → nat
constant int_add : int → int → int
constant real_add : real → real → real
inductive add_struct [class] (A : Type) :=
mk : (A → A → A) → add_struct A
definition add {A : Type} {S : add_struct A} (a b : A) : A :=
add_struct.rec (λ ... |
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