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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
6f64d6f7e656c2732e7940d33e7a05b6311df6fc | a338c3e75cecad4fb8d091bfe505f7399febfd2b | /src/data/equiv/basic.lean | b2acb84c4f4b71b0c0013c55cc9c11dc084f3d51 | [
"Apache-2.0"
] | permissive | bacaimano/mathlib | 88eb7911a9054874fba2a2b74ccd0627c90188af | f2edc5a3529d95699b43514d6feb7eb11608723f | refs/heads/master | 1,686,410,075,833 | 1,625,497,070,000 | 1,625,497,070,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 101,358 | 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.set.function
import data.sigma.basic
/-!
# Equivalence between types
In this file we define two types:
* `equiv α β` a.k.a. `... |
0216eb6f167c3861961a053789d17cdb77eac772 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/data/fintype/card.lean | cf47c0ac07658ae7aed8c8141315e0b5ee6ab75a | [
"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 | 15,509 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
-/
import data.fintype.basic
import algebra.big_operators.ring
/-!
Results about "big operations" over a `fintype`, and consequent
results about cardinalities of certain... |
24ac94b73f50987cbd30229edf577ebcc46cb386 | b2fe74b11b57d362c13326bc5651244f111fa6f4 | /src/analysis/special_functions/exp_log.lean | 57a90b7ef2be73c6a926585354650e2ccc5ab315 | [
"Apache-2.0"
] | permissive | midfield/mathlib | c4db5fa898b5ac8f2f80ae0d00c95eb6f745f4c7 | 775edc615ecec631d65b6180dbcc7bc26c3abc26 | refs/heads/master | 1,675,330,551,921 | 1,608,304,514,000 | 1,608,304,514,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 32,033 | 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 data.complex.exponential
import analysis.complex.basic
import analysis.calculus.mean_value
import measure_theory.bo... |
901cc4cee46010a101456493258a9850b0744f61 | 0af4d82083a01e7db9f2ed3f7d875a1de7745fce | /src/constructions.lean | 03e1557ad516f01fefe56d23562318262ef39cb9 | [] | no_license | johoelzl/lean-together | 2e2a0cfc36060bbffec864dca9468cdef52b4922 | b0ca0dbc8b971de50621ae67c2f0c2368fb72839 | refs/heads/master | 1,586,917,983,172 | 1,546,852,267,000 | 1,546,852,267,000 | 164,318,636 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 632 | lean | import algebra.ordered_field
import order.filter
/- Adjoin an element to α -/
#check with_top
#check with_bot
#check with_zero
/- Construct a ordered group or ring -/
#check nonneg_comm_group
#check nonneg_ring
#check linear_nonneg_ring
/- Lift along a Galois connection -/
#check galois_connection -- L x ≤ y ↔ x ... |
661c34bee770ddcc787ca757d047a14e479d91c2 | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /tests/lean/run/CoeNew.lean | 032140f73d532529c12d10f057de09d7fcfb26bf | [
"Apache-2.0"
] | permissive | dupuisf/lean4 | d082d13b01243e1de29ae680eefb476961221eef | 6a39c65bd28eb0e28c3870188f348c8914502718 | refs/heads/master | 1,676,948,755,391 | 1,610,665,114,000 | 1,610,665,114,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 738 | lean |
universes u v w
instance boolToNat : Coe Bool Nat :=
{ coe := fun b => cond b 1 0 }
instance natToBool : Coe Nat Bool :=
{ coe := fun n => match n with
| 0 => false
| _ => true }
structure ConstantFunction (α β : Type) :=
(f : α → β)
(h : ∀ a₁ a₂, f a₁ = f a₂)
instance constantFunctionCoe {α β : Type} : CoeFu... |
286167bec3d3f1e4bb5fa193e977c5bbf23ab009 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /tests/lean/run/csimp_type_error.lean | 3ffdc322acc5e1d8ad5e86549e8057c3e8b4a818 | [
"Apache-2.0"
] | permissive | mhuisi/lean4 | 28d35a4febc2e251c7f05492e13f3b05d6f9b7af | dda44bc47f3e5d024508060dac2bcb59fd12e4c0 | refs/heads/master | 1,621,225,489,283 | 1,585,142,689,000 | 1,585,142,689,000 | 250,590,438 | 0 | 2 | Apache-2.0 | 1,602,443,220,000 | 1,585,327,814,000 | C | UTF-8 | Lean | false | false | 303 | lean | namespace scratch
inductive type
| bv (w:Nat) : type
open type
def value : type -> Type
| bv w => {n // n < w}
def tester_fails : ∀ {tp : type}, value tp -> Bool
| bv _, v1 => decide (v1.val = 0)
def tester_ok : ∀ {tp : type}, value tp -> Prop
| bv _, v1 => v1.val = 0
end scratch
|
4a1b18cf910e19653ee7f88aeca0eb2664d848bc | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /src/Lean/Attributes.lean | 763dd88c0b78dd4c8c288d75653f56671eaa1a0c | [
"Apache-2.0"
] | permissive | williamdemeo/lean4 | 72161c58fe65c3ad955d6a3050bb7d37c04c0d54 | 6d00fcf1d6d873e195f9220c668ef9c58e9c4a35 | refs/heads/master | 1,678,305,356,877 | 1,614,708,995,000 | 1,614,708,995,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 18,820 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Syntax
import Lean.CoreM
import Lean.ResolveName
namespace Lean
inductive AttributeApplicationTime where
| afterTypeChecking | afterCompilat... |
8a308036c350a9ea5cc6d260a39d02be700b5f50 | f1b175e38ffc5cc1c7c5551a72d0dbaf70786f83 | /order/basic.lean | 4ffa0f7b905625fa50cef87854e1bd75339c1c02 | [
"Apache-2.0"
] | permissive | mjendrusch/mathlib | df3ae884dd5ce38c7edf452bcbfd3baf4e3a6214 | 5c209edb7eb616a26f64efe3500f2b1ba95b8d55 | refs/heads/master | 1,585,663,284,800 | 1,539,062,055,000 | 1,539,062,055,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 19,588 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Mario Carneiro
-/
import tactic.interactive logic.basic data.sum data.set.basic algebra.order
open function
/- TODO: automatic construction of dual definitions / theorem... |
b6f54b437d40b1030f128319f20fd60c8adf6c03 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/category_theory/abelian/exact.lean | c235f7dd92054e5c32653c1fb135cd4f4adc29e6 | [
"Apache-2.0"
] | permissive | agjftucker/mathlib | d634cd0d5256b6325e3c55bb7fb2403548371707 | 87fe50de17b00af533f72a102d0adefe4a2285e8 | refs/heads/master | 1,625,378,131,941 | 1,599,166,526,000 | 1,599,166,526,000 | 160,748,509 | 0 | 0 | Apache-2.0 | 1,544,141,789,000 | 1,544,141,789,000 | null | UTF-8 | Lean | false | false | 2,395 | lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import category_theory.abelian.basic
import algebra.homology.exact
/-!
# Exact sequences in abelian categories
We prove that in an abelian category, `(f, g)` is exact... |
c8baf04607f81bc500dcf00493013e0eccc6811b | 93c4ed09750233a3b114256e099d6a03939794b8 | /chapter3.lean | e6a4825d9ed378e8e6bb31d4cb4230c7ece62ca3 | [] | no_license | OwenGraves/TaoAnalysis | 1177c5772f3736b007f458b8817f6a25b13b5e77 | 695b149b5decdb6f8e46c883ea112f0a12082548 | refs/heads/master | 1,644,242,117,512 | 1,564,441,707,000 | 1,564,441,707,000 | 98,614,833 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,286 | lean | namespace chapter3
open nat
open classical
open set
-- Since sets are not exactly straightforward in type theory,
-- there will be some leniency with regards to the textbook
-- in order to define them type theoretically and
-- Lean's standard library will be employed
-- to express the properties of sets.
variable {α ... |
cc44596f14c06b35648873f9ff108c67010407aa | 137c667471a40116a7afd7261f030b30180468c2 | /src/data/complex/module.lean | 5ad4aa71df5e485afb17d4cd131e8eab679c0f5c | [
"Apache-2.0"
] | permissive | bragadeesh153/mathlib | 46bf814cfb1eecb34b5d1549b9117dc60f657792 | b577bb2cd1f96eb47031878256856020b76f73cd | refs/heads/master | 1,687,435,188,334 | 1,626,384,207,000 | 1,626,384,207,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,226 | lean | /-
Copyright (c) 2020 Alexander Bentkamp, Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, Sébastien Gouëzel, Eric Wieser
-/
import data.complex.basic
import algebra.algebra.ordered
import data.matrix.notation
import field_theory.to... |
54c615f506b719073f83dbe56bcaf1316be05c79 | 5749d8999a76f3a8fddceca1f6941981e33aaa96 | /src/topology/bounded_continuous_function.lean | 71eb6993ebf1237e8bdec9feea587d2227d6a844 | [
"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 | 23,606 | lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Mario Carneiro
Type of bounded continuous functions taking values in a metric space, with
the uniform distance.
-/
import analysis.normed_space.basic topology.... |
63fef75d7a88728033de85b644a8d4c6732472fa | d6124c8dbe5661dcc5b8c9da0a56fbf1f0480ad6 | /Papyrus/Script/ParserUtil.lean | a3c84613ffe575e2b5e4ced4fb94beff22567d95 | [
"Apache-2.0"
] | permissive | xubaiw/lean4-papyrus | c3fbbf8ba162eb5f210155ae4e20feb2d32c8182 | 02e82973a5badda26fc0f9fd15b3d37e2eb309e0 | refs/heads/master | 1,691,425,756,824 | 1,632,122,825,000 | 1,632,123,075,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 362 | lean | import Lean.Parser
import Papyrus.Script.SyntaxUtil
open Lean Parser
namespace Papyrus.Script
@[runParserAttributeHooks]
def negNumLit := leading_parser
symbol "-" >> checkNoWsBefore >> numLit
def expandNegNumLit : (stx : Syntax) → MacroM Syntax
| `(negNumLit | -$n:numLit) => ``(-$n)
| stx => Macro.throwErrorAt st... |
e8eee3820a86241f8af9a65063d6332bc5ec766e | 4727251e0cd73359b15b664c3170e5d754078599 | /test/ring.lean | 04cef1e5ad9fae92565842707eb8dc978128334f | [
"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 | 2,998 | lean | import tactic.ring
import data.real.basic
import algebra.parity
example (x y : ℕ) : x + y = y + x := by ring
example (x y : ℕ) : x + y + y = 2 * y + x := by ring
example (x y : ℕ) : x + id y = y + id x := by ring!
example {α} [comm_ring α] (x y : α) : x + y + y - x = 2 * y := by ring
example (x y : ℚ) : x / 2 + x / 2 ... |
bbe7258d3b32bc445ecf449394d557e58debb386 | bb31430994044506fa42fd667e2d556327e18dfe | /src/data/nat/choose/sum.lean | fb9d4b7488df9aa99585cd3af755ba1f625fbf08 | [
"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 | 6,882 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Patrick Stevens
-/
import data.nat.choose.basic
import tactic.linarith
import algebra.big_operators.ring
import algebra.big_operators.intervals
import algebra.big_operators... |
5213cf904c26204cb97f445b63891376b4ebff63 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /stage0/src/Init/Util.lean | b4252d17feccea3376e6a087ae4b3c88424ced7d | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | EdAyers/lean4 | 57ac632d6b0789cb91fab2170e8c9e40441221bd | 37ba0df5841bde51dbc2329da81ac23d4f6a4de4 | refs/heads/master | 1,676,463,245,298 | 1,660,619,433,000 | 1,660,619,433,000 | 183,433,437 | 1 | 0 | Apache-2.0 | 1,657,612,672,000 | 1,556,196,574,000 | Lean | UTF-8 | Lean | false | false | 3,592 | 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
-/
prelude
import Init.Data.String.Basic
import Init.Data.ToString.Basic
universe u v
/-! # Debugging helper functions -/
set_option linter.unusedVariables.... |
1ab4499084525b16f1aa739f6ce49610959b3cef | 592ee40978ac7604005a4e0d35bbc4b467389241 | /Library/generated/mathscheme-lean/PointedInvolutiveMagma0Sig.lean | 412842ea47d45cba050e85e5bdcafcf766a5ed46 | [] | no_license | ysharoda/Deriving-Definitions | 3e149e6641fae440badd35ac110a0bd705a49ad2 | dfecb27572022de3d4aa702cae8db19957523a59 | refs/heads/master | 1,679,127,857,700 | 1,615,939,007,000 | 1,615,939,007,000 | 229,785,731 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,137 | lean | import init.data.nat.basic
import init.data.fin.basic
import data.vector
import .Prelude
open Staged
open nat
open fin
open vector
section PointedInvolutiveMagma0Sig
structure PointedInvolutiveMagma0Sig (A : Type) : Type :=
(times : (A → (A → A)))
(prim : (A → A))
(zero : A)
open Point... |
73f45ee0f647099ed65622ae40be68b9a32285d4 | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /stage0/src/Init/Control/Basic.lean | 7afc4908cfde915aef8a8879ada2c787ae3e5d86 | [
"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 | tobiasgrosser/lean4 | ce0fd9cca0feba1100656679bf41f0bffdbabb71 | ebdbdc10436a4d9d6b66acf78aae7a23f5bd073f | refs/heads/master | 1,673,103,412,948 | 1,664,930,501,000 | 1,664,930,501,000 | 186,870,185 | 0 | 0 | Apache-2.0 | 1,665,129,237,000 | 1,557,939,901,000 | Lean | UTF-8 | Lean | false | false | 9,574 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura, Sebastian Ullrich
-/
prelude
import Init.Core
universe u v w
@[reducible] def Functor.mapRev {f : Type u → Type v} [Functor f] {α β : Type u} : f α → (α → β)... |
3545f0b61d60c27fae83feb14b54bc147ddbead0 | 22e97a5d648fc451e25a06c668dc03ac7ed7bc25 | /src/algebra/group/with_one.lean | abd7c3ac9a8bd062fa850bf8d34271896fe0ac70 | [
"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 | 8,013 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johan Commelin
-/
import algebra.group.hom
import algebra.ring
universes u v
variable {α : Type u}
@[to_additive]
def with_one (α) := option α
namespace with_one
@[... |
162744f1825b2a34f157a5e23b7d1d90e6de48bb | 36c7a18fd72e5b57229bd8ba36493daf536a19ce | /library/theories/number_theory/irrational_roots.lean | 81c2268b9bb24f222b551f6284900603d9a889b5 | [
"Apache-2.0"
] | permissive | YHVHvx/lean | 732bf0fb7a298cd7fe0f15d82f8e248c11db49e9 | 038369533e0136dd395dc252084d3c1853accbf2 | refs/heads/master | 1,610,701,080,210 | 1,449,128,595,000 | 1,449,128,595,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,833 | lean | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
A proof that if n > 1 and a > 0, then the nth root of a is irrational, unless a is a perfect nth power.
-/
import data.rat .prime_factorization
open eq.ops
open algebra
/... |
acabc1e4e7122082491f1e3094a48625c0c8f64a | 3cb7d30bb276fa1e8fe9ca7b979f53cbfafb2dbb | /leanpkg/leanpkg/git.lean | e530042ede7aa7a2dc480216df878adc02bbb50c | [
"Apache-2.0"
] | permissive | andrejtokarcik/lean | e4148f69d020385c4fc07662b77792681b26c4d9 | ceacfa7445953cbc8860ddabc55407430a9ca5c3 | refs/heads/master | 1,584,800,445,031 | 1,529,598,225,000 | 1,529,598,469,000 | 138,652,902 | 0 | 0 | Apache-2.0 | 1,529,962,767,000 | 1,529,962,767,000 | null | UTF-8 | Lean | false | false | 1,300 | 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.lean_version system.io
namespace leanpkg
def upstream_git_branch :=
if lean.is_release then
"lean-" ++ lean_version_string_core
else
"ma... |
1708d28c401ea227d3db1c5d2798c552376f229a | bb31430994044506fa42fd667e2d556327e18dfe | /src/field_theory/intermediate_field.lean | 8d184914aea9c6aa6ef8f767c11f4690b945d7a5 | [
"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 | 21,922 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import field_theory.minpoly.field
import field_theory.subfield
import field_theory.tower
/-!
# Intermediate fields
Let `L / K` be a field extension, given as an instance... |
31a87d5b1d09ea80369cd7395383831667c9257f | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/sigma_no_confusion.lean | 8894e45b074b3847456851cedd38f3b16ea115eb | [
"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 | 1,252 | lean | import data.sigma
namespace sigma
namespace manual
definition no_confusion_type {A : Type} {B : A → Type} (P : Type) (v₁ v₂ : sigma B) : Type :=
sigma.rec_on v₁
(λ (a₁ : A) (b₁ : B a₁), sigma.rec_on v₂
(λ (a₂ : A) (b₂ : B a₂),
(Π (eq₁ : a₁ = a₂), eq.rec_on eq₁ b₁ = b₂ → P) → P))
definition ... |
5221a1d13925551c1353bd28d288dffc5b466962 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /library/theories/group_theory/subgroup_to_group.lean | 52dad6c44540d9eb563bf50c3ee0f4b23168c65e | [
"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 | 3,855 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
Turn a subgroup into a group on the corresponding subtype. Given
variables {A : Type} [group A] (G : set A) [is_subgroup G]
we have:
group_of G := G, viewed a... |
3dbea8dd3c278b64f2aeebb8ec66b94fb1ae53c5 | 46125763b4dbf50619e8846a1371029346f4c3db | /src/algebra/direct_sum.lean | 159455a385ca6e6f64ca2ba380ace87c062e69da | [
"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 | 6,178 | lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
Direct sum of abelian groups, indexed by a discrete type.
-/
import data.dfinsupp
universes u v w u₁
variables (ι : Type v) [decidable_eq ι] (β : ι → Type w) [Π i, add_comm_gr... |
e81d9a3e6b31ee3463b855563b1f3bc41c01ff12 | 8e381650eb2c1c5361be64ff97e47d956bf2ab9f | /src/Kenny/sites/basic.lean | d6fe2603194ce232ef426bd8fe3865b72a8cb3f1 | [] | 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 | 3,698 | lean | import category_theory.limits.limits
universes v w u
namespace category_theory
inductive pullback_diagram : Type v
| base_left | base_right | target
namespace pullback_diagram
inductive hom : pullback_diagram → pullback_diagram → Type v
| id_base_left : hom base_left base_left
| id_base_right : hom base_right base... |
27202476918f54edb4266b9b745ca97acf0571fa | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/data/nat/interval.lean | 090809d0ea2056b20927e80fdc7ecd4ff2e73fb7 | [
"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 | 10,193 | 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
/-!
# Finite intervals of naturals
This file proves that `ℕ` is a `locally_finite_order` and calculates the cardinality of its
interva... |
34ec38386dc1145c03180fcaaf43cd81c99adcb7 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/category/Ring/instances.lean | b224997a96e495912c0e539f3d8d3c952be137a9 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 1,969 | lean | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import algebra.category.Ring.basic
import ring_theory.localization.away
import ring_theory.ideal.local_ring
/-!
# Ring-theoretic results in terms of categorical languages
... |
29c74a0ffb89967550fddd26178eb5eeddb5ffe5 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /tests/lean/run/backtrackable_estate.lean | b5a078807a8659cd4c0bb538e97b4de5d0776935 | [
"Apache-2.0"
] | permissive | mhuisi/lean4 | 28d35a4febc2e251c7f05492e13f3b05d6f9b7af | dda44bc47f3e5d024508060dac2bcb59fd12e4c0 | refs/heads/master | 1,621,225,489,283 | 1,585,142,689,000 | 1,585,142,689,000 | 250,590,438 | 0 | 2 | Apache-2.0 | 1,602,443,220,000 | 1,585,327,814,000 | C | UTF-8 | Lean | false | false | 684 | lean | import Init.System.IO
structure MyState :=
(bs : Nat := 0) -- backtrackable state
(ps : Nat := 0) -- non backtrackable state
instance : HasRepr MyState :=
⟨fun s => repr (s.bs, s.ps)⟩
instance : EStateM.Backtrackable Nat MyState :=
{ save := fun s => s.bs,
restore := fun s d => { bs := d, .. s } }
abbrev M :=... |
68528b7abcbbb5551a5d6c7a6f0a9733db22a09d | 07c76fbd96ea1786cc6392fa834be62643cea420 | /hott/types/int/hott.hlean | dcb718934fa2c7579ce8f939cdd507293c8ae979 | [
"Apache-2.0"
] | permissive | fpvandoorn/lean2 | 5a430a153b570bf70dc8526d06f18fc000a60ad9 | 0889cf65b7b3cebfb8831b8731d89c2453dd1e9f | refs/heads/master | 1,592,036,508,364 | 1,545,093,958,000 | 1,545,093,958,000 | 75,436,854 | 0 | 0 | null | 1,480,718,780,000 | 1,480,718,780,000 | null | UTF-8 | Lean | false | false | 7,051 | 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
Theorems about the integers specific to HoTT
-/
import .order types.eq arity algebra.bundled
open core eq is_equiv equiv algebra is_trunc
open nat (hiding pred)
na... |
dfeaafe6c3c8462832a8fcc1d31791f635cd4231 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/topology/category/Top/limits.lean | a0e6bd6a6f11653f84c26a9cdee4c0f3c4aa0e76 | [
"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 | 40,203 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Scott Morrison, Mario Carneiro, Andrew Yang
-/
import topology.category.Top.epi_mono
import category_theory.limits.preserves.limits
import category_theory.category.ulif... |
e346cafc0336e90e402750b6c2f9cc8ed5cd4810 | 97f752b44fd85ec3f635078a2dd125ddae7a82b6 | /tests/lean/run/class8.lean | 31d445358a3be1060bfe9176cfd06fff2315c294 | [
"Apache-2.0"
] | permissive | tectronics/lean | ab977ba6be0fcd46047ddbb3c8e16e7c26710701 | f38af35e0616f89c6e9d7e3eb1d48e47ee666efe | refs/heads/master | 1,532,358,526,384 | 1,456,276,623,000 | 1,456,276,623,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,063 | lean | import logic data.prod
open tactic prod
inductive inh [class] (A : Type) : Prop :=
intro : A -> inh A
attribute inh.intro [instance]
theorem inh_elim {A : Type} {B : Prop} (H1 : inh A) (H2 : A → B) : B
:= inh.rec H2 H1
theorem inh_exists {A : Type} {P : A → Prop} (H : ∃x, P x) : inh A
:= obtain w Hw, from H, inh.in... |
d8da7f2611e7d04d1a6cb0cfd86b961dc248d429 | 590f94277ab689acdc713c44e3bbca2e012fc074 | /Sequent Calculus (Lean)/src/list.lean | 97e39527a12dbfe0707715f68a7c24cbd7f9c68e | [] | no_license | Bpalkmim/iALC | bd3f882ad942c876d65c2d33cb50a36b2f8e5d16 | 9c2982ae916d01d9ebab9d58e0842292ed974876 | refs/heads/master | 1,689,527,062,560 | 1,631,502,537,000 | 1,631,502,537,000 | 108,029,498 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 507 | lean | -- Arquivo para definição do tipo indutivo de listas.
-- Autor: Bernardo Alkmim
-- bpalkmim@gmail.com
inductive list (A : Type) : Type :=
| nil {} : list A
| cons : A → list A → list A
namespace list
variable {A : Type}
notation h :: t := cons h t
definition append (s t : list A) : list A :=
list.rec t (λ x l u, ... |
44bb7c78267b7d96f2087c5eaeba3cb72e409af8 | b7b549d2cf38ac9d4e49372b7ad4d37f70449409 | /lean4_ffi/dump_llvm.lean | 108f28ccee961788022a13996b59e50f8cc53338 | [
"Apache-2.0"
] | permissive | GaloisInc/lean-llvm | 7cc196172fe02ff3554edba6cc82f333c30fdc2b | 36e2ec604ae22d8ec1b1b66eca0f8887880db6c6 | refs/heads/master | 1,637,359,020,356 | 1,629,332,114,000 | 1,629,402,464,000 | 146,700,234 | 29 | 1 | Apache-2.0 | 1,631,225,695,000 | 1,535,607,191,000 | Lean | UTF-8 | Lean | false | false | 1,375 | lean |
-- Type for pointers
--
-- USize compiles to a size_t when unboxed. Technically pointers
-- should map to intptr_t instead of size_t, but `size_t` is the
-- same size on x86_64.
structure Ptr :=
(val : USize)
namespace Ptr
protected def toString (x:Ptr) : String := "0x" ++ (Nat.toDigits 16 x.val.toNat).asString
in... |
dd9a7b5c66bdc3b414e167732dc216dd92f03814 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/ring_theory/mv_polynomial/basic.lean | bd06421d3908c021ea6fcd9cb5e1701626b63859 | [
"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 | 4,255 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import ring_theory.ideal.operations
import linear_algebra.finsupp_vector_space
import algebra.char_p.basic
/-!
# Multivariate polynomials over commutative rings
Th... |
306d3f3dc6e212f5b50df52ffa6cd9fd17e56eeb | c09f5945267fd905e23a77be83d9a78580e04a4a | /src/data/nat/basic.lean | 23652480556a0222cb883b3c3fc57cc3fe35c85d | [
"Apache-2.0"
] | permissive | OHIHIYA20/mathlib | 023a6df35355b5b6eb931c404f7dd7535dccfa89 | 1ec0a1f49db97d45e8666a3bf33217ff79ca1d87 | refs/heads/master | 1,587,964,529,965 | 1,551,819,319,000 | 1,551,819,319,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 35,258 | lean | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
Basic operations on the natural numbers.
-/
import logic.basic algebra.ordered_ring data.option.basic
universes u... |
bcc174121abb343b4ba51a818fb7b2ba5d98df0c | c31182a012eec69da0a1f6c05f42b0f0717d212d | /src/liquid.lean | e20c8fab7c2613bf9c8860ef8c542bd3242c74cb | [] | no_license | Ja1941/lean-liquid | fbec3ffc7fc67df1b5ca95b7ee225685ab9ffbdc | 8e80ed0cbdf5145d6814e833a674eaf05a1495c1 | refs/heads/master | 1,689,437,983,362 | 1,628,362,719,000 | 1,628,362,719,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,109 | lean | import thm95
import statement
/-!
# Liquid Tensor Experiment
This file is the entry point for this project.
The first goal of the Liquid Tensor Experiment
is to formalize a theorem by Clausen and Scholze stated below,
namely a mix of Theorem 9.4 and Theorem 9.5 of
[Analytic]: http://www.math.uni-bonn.de/people/scholz... |
04bf9428e77dcc7e6fa5653c83af195e9f53aa72 | b2c4bd81ed12cc14c20704365f094339d4c894a2 | /src/graph_theory/basic.lean | 8eec8030304440bad581af14bc58c81344c48f03 | [] | no_license | agusakov/graph_theory_2020 | 711639d9d9b25fd83899620da11ae1753d11d48b | 83a8afc31aa28dbec39a768d6042d3cb515f7a16 | refs/heads/master | 1,669,901,277,114 | 1,596,931,643,000 | 1,596,931,643,000 | 285,154,458 | 5 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 12,183 | lean | /-
Copyright (c) 2020 Aaron Anderson, Jalex Stark, Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Aaron Anderson, Jalex Stark, Kyle Miller.
-/
import data.fintype.basic
import ..sym2
import tactic
open finset
-- noncomputable theory
/-!
# Simple graphs
Th... |
4816b42b32f9b4455b5efe3dbb16651823cedc7b | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/conj.lean | d2baceff27987876b70cf16ecd120f45f9f5e27e | [
"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 | 5,475 | lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import algebra.hom.equiv.units.basic
import category_theory.endomorphism
/-!
# Conjugate morphisms by isomorphisms
An isomorphism `α : X ≅ Y` defines
- a monoid i... |
89b096a6a562abc5862fc8bad95f368d944014d3 | 737dc4b96c97368cb66b925eeea3ab633ec3d702 | /stage0/src/Lean/Meta/AppBuilder.lean | b6ad609875ee27f937e840ce786ec89a304157f8 | [
"Apache-2.0"
] | permissive | Bioye97/lean4 | 1ace34638efd9913dc5991443777b01a08983289 | bc3900cbb9adda83eed7e6affeaade7cfd07716d | refs/heads/master | 1,690,589,820,211 | 1,631,051,000,000 | 1,631,067,598,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 20,042 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Structure
import Lean.Util.Recognizers
import Lean.Meta.SynthInstance
import Lean.Meta.Check
namespace Lean.Meta
/-- Return `id e` -/
def mkId... |
cbf4c6afa2d8db59e39510ad78b66e2ccb03190e | 8f0ea954c1cc4f4cda83826954d6186c68fc9536 | /hott/homotopy/sphere.hlean | e89ce663e2ed32de26bab02859f1bc088931d6c4 | [
"Apache-2.0"
] | permissive | piyush-kurur/lean | fb3cbd339dfa8c70c49559fbea88ac0d3102b8ca | a8db8bc61a0b00379b3d0be8ecaf0d0858dc82ee | refs/heads/master | 1,594,387,140,961 | 1,457,548,608,000 | 1,457,909,538,000 | 53,615,930 | 0 | 0 | null | 1,457,642,939,000 | 1,457,642,939,000 | null | UTF-8 | Lean | false | false | 10,689 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
Declaration of the n-spheres
-/
import .susp types.trunc
open eq nat susp bool is_trunc unit pointed algebra
/-
We can define spheres with the following possib... |
40228011cdc0127ac19a89db577a6b609862aa29 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Meta/ACLt.lean | 122f1718d2bfa015d28f6a82a8ac2f18c50f5265 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 5,897 | lean | /-
Copyright (c) 2022 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.Basic
import Lean.Meta.FunInfo
import Lean.Meta.DiscrTree
namespace Lean
def Expr.ctorWeight : Expr → UInt8
| bvar .. => 0
| fvar ... |
4e8632a359ada063df881ffad737a0bd58b81292 | 367134ba5a65885e863bdc4507601606690974c1 | /src/order/well_founded_set.lean | 2e974b14f818a9954639560b8c634bb13639a24d | [
"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 | 16,800 | lean | /-
Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import data.set.finite
import data.fintype.basic
import order.well_founded
import order.order_iso_nat
import algebra.pointwise
/-!
# Well-founded sets
A well-founde... |
17f67ba09cb0eb88ab3e01e33e84bb0975b4bb4d | 38ee9024fb5974f555fb578fcf5a5a7b71e669b5 | /Mathlib/Init/Set.lean | 8b800c43bc5dc84b456ff9635159c995c7dc5810 | [
"Apache-2.0"
] | permissive | denayd/mathlib4 | 750e0dcd106554640a1ac701e51517501a574715 | 7f40a5c514066801ab3c6d431e9f405baa9b9c58 | refs/heads/master | 1,693,743,991,894 | 1,636,618,048,000 | 1,636,618,048,000 | 373,926,241 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,567 | 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.Init.SetNotation
/-!
# Sets
This file sets up the theory of sets whose elements have a given type.
## Main definitions
Given a type `X` a... |
6021d3acfaca8cb98118aea3cf2ee21b9b3a0814 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/topology/algebra/order/left_right_lim.lean | 0e3a0d1ca0e8dc9da91e844fb24f7b93833f2068 | [
"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 | 14,509 | lean | /-
Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import topology.algebra.order.basic
import topology.algebra.order.left_right
/-!
# Left and right limits
We define the (strict) left and right limits of a fun... |
d3ab93363425c2a45abf86bcf69a730c72230eb2 | 761d983a78bc025071bac14a3facced881cf5e53 | /affine/list_stuff.lean | bd47b1dcb182b7377edca3f77860e7fab719c70d | [] | no_license | rohanrajnair/affine_lib | bcf22ff892cf74ccb36a95bc9b7fff8e0adb2d0d | 83076864245ac547b9d615bc6a23804b1b4a8f70 | refs/heads/master | 1,673,320,928,343 | 1,603,036,653,000 | 1,603,036,653,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,133 | lean | import algebra.field tactic.ext
open list
universes u v
variables (K : Type u) [field K] [inhabited K] {α : Type v} [has_add α]
(x y : K) (xl yl : list K)
/-- addition function on `list α`, where `α` has an addition function -/
@[ext]
def ladd : list α → list α → list α := zip_with has_add.add
/-
Th... |
bc29746dda61fde4961385fad84b1a2c3b7a2371 | 437dc96105f48409c3981d46fb48e57c9ac3a3e4 | /src/order/boolean_algebra.lean | a1fb312fcb94cfaedf0e5dfba29e5d8687db85d2 | [
"Apache-2.0"
] | permissive | dan-c-k/mathlib | 08efec79bd7481ee6da9cc44c24a653bff4fbe0d | 96efc220f6225bc7a5ed8349900391a33a38cc56 | refs/heads/master | 1,658,082,847,093 | 1,589,013,201,000 | 1,589,013,201,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,263 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Type class hierarchy for Boolean algebras.
-/
import order.bounded_lattice
import logic.function
set_option old_structure_cmd true
universes u
variables {α : Type u} {... |
14caa736eb2437bc0455385f8f98ee8515c0d7ce | c31182a012eec69da0a1f6c05f42b0f0717d212d | /src/for_mathlib/Gordan.lean | 91d31f4c5d703469dc2a5c3d40ef0f10d07beb85 | [] | no_license | Ja1941/lean-liquid | fbec3ffc7fc67df1b5ca95b7ee225685ab9ffbdc | 8e80ed0cbdf5145d6814e833a674eaf05a1495c1 | refs/heads/master | 1,689,437,983,362 | 1,628,362,719,000 | 1,628,362,719,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 22,114 | lean | import linear_algebra.dual
import topology.continuous_function.algebra
import analysis.normed_space.basic
import ring_theory.finiteness
import linear_algebra.free_module
import for_mathlib.nnrat
import for_mathlib.rational_cones
import for_mathlib.finite_free
/-
# Gordan's Lemma
The algebraic proof of Gordan's lemm... |
51a5899f0359c008e3fb912f1c521154becba7e6 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/multiset/sort_auto.lean | bdf3082e1a9f16a572ed14f83c48f89ebaf20acf | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,668 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.list.sort
import Mathlib.data.multiset.basic
import Mathlib.data.string.basic
import Ma... |
1f212cd5c897a7b80c708501736981982bcc9622 | cf39355caa609c0f33405126beee2739aa3cb77e | /library/init/data/list/qsort.lean | 75f28fa051fb387ea2600a28a0f8a135af075b63 | [
"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 | 1,631 | 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
-/
prelude
import init.data.list.lemmas init.wf
namespace list
-- Note: we can't use the equation compiler here because
-- init.meta.well_founded_tactics uses... |
797828281d9473f48a1af1d580225fe3490aed5d | 04fb7df3dddae0c07fba3e8f2ae375f52c857286 | /src/small_step.lean | cf4e4c21866d5b6f5e61b1e1589b41d2e6ff4147 | [] | no_license | ezrasitorus/ModelsOfComputation | 519137e30bb21ad406693c8f15455ffa516973eb | dfdfe9e3351b3bb01506b116fffb3ec017e9a89a | refs/heads/main | 1,679,797,496,030 | 1,616,435,697,000 | 1,616,435,697,000 | 308,993,502 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,398 | lean | import while
inductive w_exp_small : Type
| nat : ℕ → w_exp_small
| add : w_exp_small → w_exp_small → w_exp_small
open w_exp_small
inductive s_eval : w_exp_small → w_exp_small → Prop
| s_left : ∀ E1 E2 E1' : w_exp_small, s_eval E1 E1' → s_eval (add E1 E2) (add E1' E2)
| s_right : ∀ n : ℕ, ∀ E2 E2' : ... |
6aee9dedc0ce5cd09694aad6e784f91cbb2e243e | ea5678cc400c34ff95b661fa26d15024e27ea8cd | /padic_norm1.lean | 914d0573f5e11e9c3b399ee97eafeb7191890687 | [] | 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 | 30,434 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
Define the p-adic valuation on ℤ and ℚ, and the p-adic norm on ℚ
-/
import data.rat data.int.gcd algebra.field_power data.nat.enat
import ring_theory.unique_factoriz... |
24dead83d88190b7ba1f367696deaf16f34b2243 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/var2.lean | 9eec24b472a103ee0341ac071018be0cc47b2aa2 | [
"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 | 177 | lean | --
section
universe l
variable A : Type.{l}
variable a : A
parameter B : Type.{l}
parameter b : B
definition foo := fun (H : A = B), cast H a = b
end
#check foo
|
99a55e17752346c097a836e0c904fb57701024f9 | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/algebra/euclidean_domain.lean | 7e5a9d75eddfa0b6171fa842abe217ddbee4b8f8 | [
"Apache-2.0"
] | permissive | vaibhavkarve/mathlib | a574aaf68c0a431a47fa82ce0637f0f769826bfe | 17f8340912468f49bdc30acdb9a9fa02eeb0473a | refs/heads/master | 1,621,263,802,637 | 1,585,399,588,000 | 1,585,399,588,000 | 250,833,447 | 0 | 0 | Apache-2.0 | 1,585,410,341,000 | 1,585,410,341,000 | null | UTF-8 | Lean | false | false | 13,887 | lean | /-
Copyright (c) 2018 Louis Carlin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Louis Carlin, Mario Carneiro
Euclidean domains and Euclidean algorithm (extended to come)
A lot is based on pre-existing code in mathlib for natural number gcds
-/
import data.int.basic... |
1d5c1c366a12589cddb8ae2f51e043542cda1e60 | 9a0b1b3a653ea926b03d1495fef64da1d14b3174 | /tidy/rwing.lean | 0f79568fd0996abd649f66f2c4eac99f1f8bde62 | [
"Apache-2.0"
] | permissive | khoek/mathlib-tidy | 8623b27b4e04e7d598164e7eaf248610d58f768b | 866afa6ab597c47f1b72e8fe2b82b97fff5b980f | refs/heads/master | 1,585,598,975,772 | 1,538,659,544,000 | 1,538,659,544,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 854 | lean | -- Copyright (c) 2018 Keeley Hoek. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Keeley Hoek
import tactic.ring
-- import tactic.interactive
open lean
open lean.parser
open tactic
open ring
open interactive interactive.types expr
meta def rwing (q : parse in... |
4d99221e9b15dc965ab08c73d38c003e78277857 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /stage0/src/Init/Data/Format/Syntax.lean | 2dd3ada2cf73f4b8da85ee15ed32a1963d1949bd | [
"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 | 1,822 | lean | /-
Copyright (c) 2021 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.Format.Macro
import Init.Data.Format.Instances
import Init.Meta
namespace Lean.Syntax
open Std
open Std.Format
private def format... |
15f269b4f15c30981a903b3ab5bb54bc105f2bea | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/algebraic_geometry/prime_spectrum.lean | 5421fb5aa9370e139096f39356ee1859980c616a | [
"Apache-2.0"
] | permissive | hamdysalah1/mathlib | b915f86b2503feeae268de369f1b16932321f097 | 95454452f6b3569bf967d35aab8d852b1ddf8017 | refs/heads/master | 1,677,154,116,545 | 1,611,797,994,000 | 1,611,797,994,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,605 | 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 topology.opens
import ring_theory.ideal.prod
import linear_algebra.finsupp
import algebra.punit_instances
/-!
# Prime spectrum of a commutative ring
The prim... |
64e0ef1a3c23f413b0473680f3d672002b74d30a | 392d28f7e76ae84b38b6424255b29b4a4af0d129 | /zzz_junk/dependentTypes.lean | 93d6e3dcdb789a79c45d5832d789200abde956b6 | [] | no_license | dg-1225/complogic-s21 | dd7349fd5288ec6c7bad3b0fe27987cfe176dc67 | f46b0bce48bbefbfbcdbc3da904a85c5f643ef58 | refs/heads/master | 1,678,017,116,497 | 1,613,794,266,000 | 1,613,794,266,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,750 | lean | /- A FAMILY OF TYPES ("INDUCTIVE FAMILY")
efine a family of types, *tuple n*, indexed
by natural numbers. For any (n : nat), tuple n
is the type of tuples (of natural numbers) of
length n.
-/
/-
Reminder: prod is a type builder. Given
types, α and β, prod α β (or α × β) is the
the *type* of ordered α-β pairs. We c... |
3240990e199533ee66153d044ff5d98d7da85af9 | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /tests/lean/uintCtors.lean | a885508cb81fbc3c6806186ad1e0fb22cc22e115 | [
"Apache-2.0"
] | permissive | williamdemeo/lean4 | 72161c58fe65c3ad955d6a3050bb7d37c04c0d54 | 6d00fcf1d6d873e195f9220c668ef9c58e9c4a35 | refs/heads/master | 1,678,305,356,877 | 1,614,708,995,000 | 1,614,708,995,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,341 | lean | def UInt32.ofNatCore' (n : Nat) (h : Less n UInt32.size) : UInt32 := {
val := { val := n, isLt := h }
}
#eval UInt32.ofNatCore' 10 decide!
def UInt64.ofNatCore' (n : Nat) (h : Less n UInt64.size) : UInt64 := {
val := { val := n, isLt := h }
}
#eval UInt64.ofNatCore' 3 decide!
#eval toString $ { val := { val := ... |
877337e628f33813bb7919d3054c6db5d1f34cbd | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/tactic/linarith.lean | 241e19724913b889f8fe9f859c35e94c362aa4f8 | [
"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 | 32,838 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Robert Y. Lewis
A tactic for discharging linear arithmetic goals using Fourier-Motzkin elimination.
`linarith` is (in principle) complete for ℚ and ℝ. It is not complete for n... |
09d61d1addc9c40758315b6270f032fc7cb94d0f | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/order/basic.lean | aab452458023ff0bf3457f119b4565abd82762df | [
"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 | 24,897 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Mario Carneiro
-/
import data.subtype
import data.prod
/-!
# Basic definitions about `≤` and `<`
## Definitions
### Predicates on functions
- `monotone f`: A function... |
b2e65d42cb6a321db6ede0b45f292857123f3e82 | da3a76c514d38801bae19e8a9e496dc31f8e5866 | /library/init/data/int/order.lean | 11aac6cfec965a49ce214fcdb3577d3742ea85b8 | [
"Apache-2.0"
] | permissive | cipher1024/lean | 270c1ac5781e6aee12f5c8d720d267563a164beb | f5cbdff8932dd30c6dd8eec68f3059393b4f8b3a | refs/heads/master | 1,611,223,459,029 | 1,487,566,573,000 | 1,487,566,573,000 | 83,356,543 | 0 | 0 | null | 1,488,229,336,000 | 1,488,229,336,000 | null | UTF-8 | Lean | false | false | 8,597 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
The order relation on the integers.
-/
prelude
import init.data.int.basic
namespace int
private def nonneg (a : ℤ) : Prop := int.cases_on a (take n, true) (take n, fals... |
ce710755dcf649ef39c9066fbca53dd54add758c | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/linear_algebra/special_linear_group.lean | f5592209d74599302ca9412d81890df470b62b62 | [
"Apache-2.0"
] | permissive | waynemunro/mathlib | e3fd4ff49f4cb43d4a8ded59d17be407bc5ee552 | 065a70810b5480d584033f7bbf8e0409480c2118 | refs/heads/master | 1,693,417,182,397 | 1,634,644,781,000 | 1,634,644,781,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,023 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import linear_algebra.matrix.nonsingular_inverse
import linear_algebra.matrix.to_lin
/-!
# The Special Linear group $SL(n, R)$
This file defines the elements of the Speci... |
b0c82d0d97d50476aa80271fc6ab38281f54eb4e | 9dd3f3912f7321eb58ee9aa8f21778ad6221f87c | /tests/lean/pp.lean | 957952858e914f03d75e51003347bac88389c5bf | [
"Apache-2.0"
] | permissive | bre7k30/lean | de893411bcfa7b3c5572e61b9e1c52951b310aa4 | 5a924699d076dab1bd5af23a8f910b433e598d7a | refs/heads/master | 1,610,900,145,817 | 1,488,006,845,000 | 1,488,006,845,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 389 | lean | prelude set_option pp.beta false check λ {A : Type} (B : Type) (a : A) (b : B), a
check λ {A : Type} {B : Type} (a : A) (b : B), a
check λ (A : Type) {B : Type} (a : A) (b : B), a
check λ (A : Type) (B : Type) (a : A) (b : B), a
check λ [A : Type] (B : Type) (a : A) (b : B), a
check λ {{A : Type}} {B : Type} (a : A) (b... |
8fa1f57918543bda1ab7dc04c04a453df89030d3 | 22e97a5d648fc451e25a06c668dc03ac7ed7bc25 | /src/category_theory/natural_isomorphism.lean | cb91bf90afe62c31aebe86c062b7b2f54cc07a7f | [
"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 | 5,353 | 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, Floris van Doorn
-/
import category_theory.functor_category
import category_theory.isomorphism
open category_theory
universes v₁ v₂ v₃ v₄... |
983f2dfc4512f13e8b6ada538d9af167e482a908 | fcf3ffa92a3847189ca669cb18b34ef6b2ec2859 | /src/world3/level2.lean | 6cc9ba751b8c177d73ee40f65fed4bee3ca12169 | [
"Apache-2.0"
] | permissive | nomoid/lean-proofs | 4a80a97888699dee42b092b7b959b22d9aa0c066 | b9f03a24623d1a1d111d6c2bbf53c617e2596d6a | refs/heads/master | 1,674,955,317,080 | 1,607,475,706,000 | 1,607,475,706,000 | 314,104,281 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 242 | lean | import mynat.definition
import mynat.mul
import world2.level1
namespace mynat
lemma mul_one (m : mynat) : m * 1 = m :=
begin [nat_num_game]
rw one_eq_succ_zero,
rw mul_succ,
rw mul_zero,
rw zero_add,
refl,
end
end mynat |
099abaf1e1b386391d122d056aaa16515e2b402d | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/tactic5.lean | b5c70ff242fbf48118923b18a742582b168b95bd | [
"Apache-2.0"
] | permissive | codyroux/lean0.1 | 1ce92751d664aacff0529e139083304a7bbc8a71 | 0dc6fb974aa85ed6f305a2f4b10a53a44ee5f0ef | refs/heads/master | 1,610,830,535,062 | 1,402,150,480,000 | 1,402,150,480,000 | 19,588,851 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 168 | lean | (*
simple_tac = Repeat(conj_tac()) .. assumption_tac()
*)
theorem T4 (a b : Bool) : a → b → a /\ b /\ a := _.
simple_tac
done
print environment 1. |
2134236d059993ebfa9b4ad550d6e2de23960124 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/511a.lean | 00077163d0974c2c76b17000f2ff9abbffb4e396 | [
"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 | 370 | lean | import data.nat
open nat
example (a b : nat) (f : nat → nat) (h : f (succ a) = 0) : f (a+1) = 0 :=
by rewrite [add_one, h]
example (a b : nat) (f : nat → nat) (h : f (succ a) = 0) : f (a+1) = 0 :=
by krewrite h
definition g (a : nat) := a + 1
definition h (a : nat) := a
example (a b : nat) (f : nat → nat) (h : f (g... |
c0611b1d35929c9f94ee79f9cf0d214bcfe92e85 | 9cb9db9d79fad57d80ca53543dc07efb7c4f3838 | /src/for_mathlib/extend_from_nat.lean | fb161b8cfb5b11aa50a6d253d54da87a03ccb582 | [] | no_license | mr-infty/lean-liquid | 3ff89d1f66244b434654c59bdbd6b77cb7de0109 | a8db559073d2101173775ccbd85729d3a4f1ed4d | refs/heads/master | 1,678,465,145,334 | 1,614,565,310,000 | 1,614,565,310,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 923 | lean | namespace int
/-!
### extend from nat
A helper function to define a function on the integers
by extending a function from the naturals.
We use this to define a complex indexed by `ℤ` by extending a complex indexed by `ℕ`
with zeros on negative indices.
-/
variables {X : ℤ → Sort*} (x : Π i, X i) (f : Π i : ℕ, X i)
... |
1b78bbe5b8e4d3ab23cc2d8ba29efc962828fb46 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/algebra/order/archimedean.lean | 1019ab4fe0c0aac13c6e7dfeb61da2fd7f476d2c | [
"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 | 14,860 | 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.field_power
import data.rat
import data.int.least_greatest
/-!
# Archimedean groups and fields.
This file defines the archimedean property for ordere... |
343c4302f47836581b30e3e4ec13e6207d49f4db | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/data/polynomial/basic.lean | 848965f374573d0ed15e76260e6545022626295a | [
"Apache-2.0"
] | permissive | ramonfmir/mathlib | c5dc8b33155473fab97c38bd3aa6723dc289beaa | 14c52e990c17f5a00c0cc9e09847af16fabbed25 | refs/heads/master | 1,661,979,343,526 | 1,660,830,384,000 | 1,660,830,384,000 | 182,072,989 | 0 | 0 | null | 1,555,585,876,000 | 1,555,585,876,000 | null | UTF-8 | Lean | false | false | 32,508 | 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 algebra.monoid_algebra.basic
/-!
# Theory of univariate polynomials
This file defines `polynomial R`, the type of... |
911b6e75bb921dda22a333e86519108752b04771 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/dynamics/minimal.lean | fbe3a23715fe8644b4a55c9dbec3d13d52a2653b | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 3,930 | lean | /-
Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import topology.algebra.mul_action
import group_theory.group_action.basic
/-!
# Minimal action of a group
In this file we define an action of a monoid `M` o... |
37d1682730d2f69583c23716ef96ec17b87afde4 | 4767244035cdd124e1ce3d0c81128f8929df6163 | /data/multiset.lean | 9c47e8d4fb32646a6ce63f5d6d4e9722099571fb | [
"Apache-2.0"
] | permissive | 5HT/mathlib | b941fecacd31a9c5dd0abad58770084b8a1e56b1 | 40fa9ade2f5649569639608db5e621e5fad0cc02 | refs/heads/master | 1,586,978,681,358 | 1,546,681,764,000 | 1,546,681,764,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 121,673 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
Multisets.
-/
import logic.function order.boolean_algebra
data.list.basic data.list.perm data.list.sort data.quot data.string
algebra.order_functions algebra.... |
d523a864e88d162e5fc89cc398e6c6bd6c38949a | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/squarefree.lean | 8f7611aa8d9a4155e918cf065c9ae835443503b2 | [
"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 | 8,602 | lean | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import ring_theory.unique_factorization_domain
/-!
# Squarefree elements of monoids
An element of a monoid is squarefree when it is not divisible by any squares
exce... |
6915e9be28fda47d4515ba851c2d65ad4b739264 | 98beff2e97d91a54bdcee52f922c4e1866a6c9b9 | /src/category/kernel_pair.lean | 74f9766ae5bd22b3d7a4c323e5171c7cb3bffdfa | [] | no_license | b-mehta/topos | c3fc43fb04ba16bae1965ce5c26c6461172e5bc6 | c9032b11789e36038bc841a1e2b486972421b983 | refs/heads/master | 1,629,609,492,867 | 1,609,907,263,000 | 1,609,907,263,000 | 240,943,034 | 43 | 3 | null | 1,598,210,062,000 | 1,581,877,668,000 | Lean | UTF-8 | Lean | false | false | 5,222 | lean | import category_theory.limits.shapes.equalizers
import category_theory.limits.shapes.pullbacks
import category_theory.limits.shapes.regular_mono
universes v u u₂
namespace category_theory
open category_theory category_theory.category category_theory.limits
variables {C : Type u} [category.{v} C]
variables {R X Y Z... |
f3f732e9deecd370a660a5b1923750dc86b817c0 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/tropical/lattice.lean | cf81c638bf8065865e0c96424d557b9433f638fd | [
"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 | 2,393 | 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 algebra.tropical.basic
import order.conditionally_complete_lattice
/-!
# Order on tropical algebraic structure
This file defines the orders induced on tro... |
52b93688a759e72906e234b88f4a5b8c83456355 | 42c01158c2730cc6ac3e058c1339c18cb90366e2 | /M1S/probability_example.lean | 938734c857e948ef81855dc3f3f1c5520ea56132 | [] | no_license | ChrisHughes24/xena | c80d94355d0c2ae8deddda9d01e6d31bc21c30ae | 337a0d7c9f0e255e08d6d0a383e303c080c6ec0c | refs/heads/master | 1,631,059,898,392 | 1,511,200,551,000 | 1,511,200,551,000 | 111,468,589 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,967 | lean | import .probability_axioms
-- "minimalistic" example
definition my_space : set (set ℕ) := {{},set.univ} -- no pun intended
instance my_field : sigma_field my_space :=
begin
constructor,
right, left, refl,
intros A H,
cases H with H H,
rw ←comp_univ at H,
rw H,
rw comp_co... |
06ebbd2fd89e229c1717ba8bf8f7a0d5bd577cc4 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/category_theory/closed/functor.lean | 3c6005f0c45a2d76e5d169a38c0614ba500fcdce | [
"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 | 6,611 | 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.closed.cartesian
import category_theory.limits.preserves.shapes.binary_products
import category_theory.adjunction.fully_faithful
/-!
# Cartesian ... |
87fdc5680f7e19c5d513e2b217d3785ffdee581d | c777c32c8e484e195053731103c5e52af26a25d1 | /src/algebra/category/Module/monoidal.lean | 20dd4ea2f8fc4a699e3d482e3effbee4c5674260 | [
"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 | 13,535 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Scott Morrison, Jakob von Raumer
-/
import category_theory.monoidal.braided
import category_theory.closed.monoidal
import algebra.category.Module.basic
import linear_alg... |
82abd80aeb629170e6bb0df3b80309cf7fff988c | 4b846d8dabdc64e7ea03552bad8f7fa74763fc67 | /library/tools/super/selection.lean | ba3819616e4631362e3a0bdabb028cfda70d3080 | [
"Apache-2.0"
] | permissive | pacchiano/lean | 9324b33f3ac3b5c5647285160f9f6ea8d0d767dc | fdadada3a970377a6df8afcd629a6f2eab6e84e8 | refs/heads/master | 1,611,357,380,399 | 1,489,870,101,000 | 1,489,870,101,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,005 | lean | /-
Copyright (c) 2016 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner
-/
import .prover_state
namespace super
meta def simple_selection_strategy (f : (expr → expr → bool) → clause → list ℕ) : selection_strategy :=
take dc, do gt ← get_term... |
12c46954ce2936c1807b06d72428396ae302cd9f | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/algebra/commute.lean | 6223ef81c562f3250d27a6c117425a5bf183616d | [
"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 | 15,023 | lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Neil Strickland, Yury Kudryashov
-/
import algebra.semiconj group_theory.submonoid group_theory.subgroup ring_theory.subring
/-!
# Commuting pairs of elements in monoids
## Main de... |
cd9750c46c3ceb4c3885a4893b74ebe452e23b4a | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/run/imp3.lean | c413200b8d2430c96d0e70bfe617474d09a86cc8 | [
"Apache-2.0"
] | permissive | GaloisInc/lean | aa1e64d604051e602fcf4610061314b9a37ab8cd | f1ec117a24459b59c6ff9e56a1d09d9e9e60a6c0 | refs/heads/master | 1,592,202,909,807 | 1,504,624,387,000 | 1,504,624,387,000 | 75,319,626 | 2 | 1 | Apache-2.0 | 1,539,290,164,000 | 1,480,616,104,000 | C++ | UTF-8 | Lean | false | false | 225 | lean | class is_equiv {A B : Type} (f : A → B) :=
(inv : B → A)
#check @is_equiv.inv
namespace is_equiv
section
parameters A B : Type
parameter f : A → B
parameter c : is_equiv f
#check inv f
end
end is_equiv
|
b5294fdac76cd23b5e0aea578551508604550f6a | f1a12d4db0f46eee317d703e3336d33950a2fe7e | /common/nnf.lean | 0e66075bc750dff951ca22446f38ad649a079708 | [
"Apache-2.0"
] | permissive | avigad/qelim | bce89b79c717b7649860d41a41a37e37c982624f | b7d22864f1f0a2d21adad0f4fb3fc7ba665f8e60 | refs/heads/master | 1,584,548,938,232 | 1,526,773,708,000 | 1,526,773,708,000 | 134,967,693 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,198 | lean | import .atom
variables {α β : Type}
/-
Requires : qfree arg0
Ensures : nqfree ret
-/
def nnf (β) [@atom_type α β] : fm α → fm α
| (fm.true α) := ⊤'
| (fm.false α) := ⊥'
| (fm.atom a) := A' a
| (fm.not (fm.true α)) := ⊥'
| (fm.not (fm.false α)) := ⊤'
| (fm.not (fm.atom a)) := atom_type.neg β a
| (fm.not (fm.not... |
75ebd3b41ac1c2a517832525af5056ab8aaafb84 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/run/cc_ac2.lean | 97f989f066f66593cecf37f47ddb89460c942a05 | [
"Apache-2.0"
] | permissive | GaloisInc/lean | aa1e64d604051e602fcf4610061314b9a37ab8cd | f1ec117a24459b59c6ff9e56a1d09d9e9e60a6c0 | refs/heads/master | 1,592,202,909,807 | 1,504,624,387,000 | 1,504,624,387,000 | 75,319,626 | 2 | 1 | Apache-2.0 | 1,539,290,164,000 | 1,480,616,104,000 | C++ | UTF-8 | Lean | false | false | 118 | lean | open tactic
example (a b c d : nat) (f : nat → nat → nat) : b + a = d → f (a + b + c) a = f (c + d) a :=
by cc
|
ac48af4e1ac64442dcac97b65b5229138c4257ec | 037dba89703a79cd4a4aec5e959818147f97635d | /src/2022/logic/sheet4.lean | aad48b5c4ea4bb6c33af966121f082bc51b063f3 | [] | 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 | 1,415 | lean | /-
Copyright (c) 2022 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
/-!
# Logic in Lean, example sheet 4 : "and" (`∧`)
We learn about how to manipulate `P ∧ Q` in Lean.
## Tactics
You'... |
f8416d1eea4214fd670d8cd2e2927b5a4ab7ae11 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/ring_theory/ideal/basic_auto.lean | d9819737d44ddc95aa2379cbdf7c887ae82cad35 | [] | 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 | 28,907 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Chris Hughes, Mario Carneiro
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.associated
import Mathlib.linear_algebra.basic
import Mathlib.o... |
6285e43831ac09f54227e67ba924b2c6d65928ba | 8cd4726d66eec7673bcc0325fed07d5ba5bf17c4 | /hw2.lean | a649821292e175f8e91ec1238b60e04e849308bc | [] | no_license | justinqcai/CS2102 | 8c5fddedffa6147fedd4b6ee7d5d39fc21f0ddab | d309f0db3f1df52eb77206ee1e8665a3b49d7a0c | refs/heads/master | 1,590,108,991,894 | 1,557,610,044,000 | 1,557,610,044,000 | 186,064,169 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,167 | lean | /-
This is the second homework assignment for UVa CS2101, Spring 2019.
If you are in Professor Sullivan's class, you are to complete problems 1 - 8.
If you are in Prof. Hocking's class, you are to complete problems 9 - 13.
The first eight problems require that you carefully read the updated class
notes on relatio... |
7a540470896071b8479c298d81863dd34b747737 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/topology/partition_of_unity.lean | e84f667a353657950acf5f53eaa8fcf6c04f7dd1 | [
"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 | 20,680 | 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 algebra.big_operators.finprod
import set_theory.ordinal.basic
import topology.continuous_function.algebra
import topology.paracompact
import topology.shrinki... |
0532ca3932f811fa9de42d8f3d5e835343ee4680 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/452.lean | 157e7d0a0ff0f711d9dce43dce61439f66840f70 | [
"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 | 332 | lean | example (h : x ∨ y) : y ∨ x := by
cases h with
| inl hx => first
| apply Or.inr; assumption
| apply Or.inl; assumption
| inr hy => exact Or.inl hy
example (h : x ∨ y) : y ∨ x := by
cases h with
| inl hx => first
| apply Or.inl; assumption
| apply Or.inr; assumption
| inr hy => exact Or.inl... |
f4d7fe8d9fef539d9802cc40d09649b82fd01992 | 5fbbd711f9bfc21ee168f46a4be146603ece8835 | /lean/natural_number_game/power/8.lean | f6b6a252c6b9decfe8547b0d65466ac2dd8a74b9 | [
"LicenseRef-scancode-warranty-disclaimer"
] | no_license | goedel-gang/maths | 22596f71e3fde9c088e59931f128a3b5efb73a2c | a20a6f6a8ce800427afd595c598a5ad43da1408d | refs/heads/master | 1,623,055,941,960 | 1,621,599,441,000 | 1,621,599,441,000 | 169,335,840 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 259 | lean | lemma add_squared (a b : mynat) :
(a + b) ^ (2 : mynat) = a ^ (2 : mynat) + b ^ (2 : mynat) + 2 * a * b :=
rw two_eq_succ_one,
rw one_eq_succ_zero,
repeat {rw pow_succ},
repeat {rw pow_zero},
ring, -- instead of lots of comm-ing and assoc-ing
end
|
5cd693c262b2f9a7ca351feccef6c1c4cb29281c | a7eef317ddec01b9fc6cfbb876fe7ac00f205ac7 | /src/ring_theory/matrix_algebra.lean | 5e5a0e9bb5968a1f507310b1ba36c28d14e54c27 | [
"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 | 6,579 | 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 ring_theory.tensor_product
import data.matrix.basic
/-!
We provide the `R`-algebra structure on `matrix n n A` when `A` is an `R`-algebra,
and show `matrix n ... |
c249eaf070d3848d1b2a379a2e7039d96ad3875a | f3849be5d845a1cb97680f0bbbe03b85518312f0 | /old_library/init/to_string.lean | 7a34e396da18f95c1d8801a5cccc93b54b43249d | [
"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 | 3,771 | 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.string init.bool init.subtype init.unsigned init.prod init.sum
open bool list sum prod sigma subtype nat
universe variables u v
stru... |
122b09fd5e22bbe6f3b274337573cb2b04f06de4 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/category_theory/shift.lean | 298831216618ecb2e70b86684eb101fb56c80d4d | [
"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 | 1,411 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.limits.shapes.zero
/-!
# Shift
A `shift` on a category is nothing more than an automorphism of the category. An example to
keep in mind might... |
4807c4e203cd406b8c4d533bc33c4ffc229087c0 | 75db7e3219bba2fbf41bf5b905f34fcb3c6ca3f2 | /hott/algebra/category/functor/equivalence.hlean | 8b7e520efce3b4c652f880e1c154430a024a8fae | [
"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 | 16,010 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
Functors which are equivalences or isomorphisms
-/
import .adjoint
open eq functor iso prod nat_trans is_equiv equiv is_trunc
namespace category
variables {C D... |
990657074ab4619f993f79ee39b4d02a8cd4c885 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Data/Format.lean | ebc31b72e18291f84ead565073625d8f2db75382 | [
"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 | 1,753 | 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
universe u v
namespace Std
namespace Format
open Lean
def getWidth (o : Options) : Nat := o.get `format.width defWidth
def get... |
9b9ed2a6faa6fdcbefed0e4dfb7593e748296c5d | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/infoFromFailure.lean | 7a6ca625e57de07edf5b5f845c712a2f98c5b6df | [
"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 | 427 | lean |
def A.foo {α : Type} [Add α] (a : α) : α × α :=
(a, a + a)
def B.foo {α : Type} (a : α) : α × α :=
(a, a)
open A
open B
set_option trace.Meta.synthInstance true
-- `foo` is overloaded, the case `A.foo` is discarded because we don't have an instance `[Add String]`.
-- However, we still want to see the trace since w... |
515baff514534bded5197a2a9154a99552946089 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/limits/preserves/shapes/equalizers.lean | 0fa7a3b6f92b677ee3a9da0284594fca96ecea76 | [
"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 | 9,342 | 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
> THIS FILE IS SYNCHRONIZED WITH MA... |
30a07c5bba07da488619708c057500179aa148ea | d450724ba99f5b50b57d244eb41fef9f6789db81 | /src/mywork/lectures/lecture_13.lean | edcf7136ce64359eaed48ac53bc9f01e61ec5f7b | [] | no_license | jakekauff/CS2120F21 | 4f009adeb4ce4a148442b562196d66cc6c04530c | e69529ec6f5d47a554291c4241a3d8ec4fe8f5ad | refs/heads/main | 1,693,841,880,030 | 1,637,604,848,000 | 1,637,604,848,000 | 399,946,698 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,272 | lean | /-
UPDATE: Test distributed after class on
Monday. Monday will be a review day. The
test is due back Wednesday before class.
In class Wednesday we will have at least
a short quiz to sanity check what you will
have submitted for the test. We reserve the
right to do follow-on in-person testing if
the results indicate a ... |
c9cce7bcb5a0ee8d145a51a1922bc5a8cef28b24 | aa2345b30d710f7e75f13157a35845ee6d48c017 | /category_theory/functor_category.lean | e9f395d3c7567fa4afd14e2691101d864d94c21a | [
"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 | 2,196 | 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.natural_transformation
namespace category_theory
universes u₁ v₁ u₂ v₂ u₃ v₃
open nat_trans
/--
`functor.c... |
c615b7b601feab942b29a04526663ed6cf75ee3a | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/nat/choose/bounds.lean | 3d9e5a32dd7781c54d9bcb1bae18653e0caf8857 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 1,391 | lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Eric Rodriguez
-/
import algebra.group_power.lemmas
import algebra.order.field.basic
import data.nat.choose.basic
/-!
# Inequalities for binomial coefficients
> THIS FIL... |
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