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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
9c49775657d0f41cdcdf2aebb475091aa5e69d21 | 8b9f17008684d796c8022dab552e42f0cb6fb347 | /tests/lean/hott/calc_auto_trans_eq.hlean | 205c439277f35e487d3c9aeb6562fda17437411d | [
"Apache-2.0"
] | permissive | chubbymaggie/lean | 0d06ae25f9dd396306fb02190e89422ea94afd7b | d2c7b5c31928c98f545b16420d37842c43b4ae9a | refs/heads/master | 1,611,313,622,901 | 1,430,266,839,000 | 1,430,267,083,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 558 | hlean | constant list : Type → Type
constant R.{l} : Π {A : Type.{l}}, A → A → Type.{l}
infix `~`:50 := R
example {A : Type} {a b c d : list nat} (H₁ : a ~ b) (H₂ : b = c) (H₃ : c = d) : a ~ d :=
calc a ~ b : H₁
... = c : H₂
... = d : H₃
example {A : Type} {a b c d : list nat} (H₁ : a = b) (H₂ : b = c) (H₃ : c ~ d) : a... |
2265f60a61a619c33cd8e9869b7bb41466b5ef9f | 5e42295de7f5bcdf224b94603a8ec29b17c2d367 | /proof_reconstruction.lean | b24ed1a02b333c76fb043b7a16b6fdb187716190 | [] | no_license | pnmadelaine/lean_polya | 9369e0d87dce773f91383bb58ac6fde0a00a1a40 | 1c62b0b3fa71044b0225ce28030627d251b08ebc | refs/heads/master | 1,590,161,172,243 | 1,515,010,019,000 | 1,515,010,019,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 49,384 | lean | import .datatypes .sum_form .reconstruction_theorems norm_num
namespace polya
open expr tactic diseq_proof
--#check mk_nat_val_ne_proof use something like this below?
theorem fake_ne_zero_pf (q : ℚ) : q ≠ 0 := sorry
theorem fake_gt_zero_pf (q : ℚ) : q > 0 := sorry
theorem fake_lt_zero_pf (q : ℚ) : q < 0 := sorry
theor... |
cc316d8c87291b380ec561fc5acf77e173194ebd | bb31430994044506fa42fd667e2d556327e18dfe | /src/analysis/inner_product_space/gram_schmidt_ortho.lean | 495227a7c37d009233830bb03ae6fc14d15eb6e2 | [
"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 | 17,637 | lean | /-
Copyright (c) 2022 Jiale Miao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jiale Miao, Kevin Buzzard, Alexander Bentkamp
-/
import analysis.inner_product_space.pi_L2
import linear_algebra.matrix.block
/-!
# Gram-Schmidt Orthogonalization and Orthonormalization
... |
dd3ccac099fac8ca31d8ff13bfe7cb932d28f98f | 4727251e0cd73359b15b664c3170e5d754078599 | /test/fin_cases.lean | 043d4585cc8e2f53b73f868c94a55d26b7780958 | [
"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 | 3,318 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import data.nat.interval
import data.nat.prime
import group_theory.perm.sign
import tactic.fin_cases
example (f : ℕ → Prop) (p : fin 3) (h0 : f 0) (h1 : f 1) (h2 : f... |
b1b7c2d974c21a94da913f73bf7d4eeb1c8dccaa | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/simpa.lean | 5f71a1d781d091a84c16bd6e8692cdd49674a49b | [] | 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 | 908 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.tactic.doc_commands
import Mathlib.PostPort
namespace Mathlib
namespace tactic
namespac... |
8b0e7f7727f2feba3156cab71fc0ecfe2353e074 | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/equiv/mul_add.lean | c57c1e91fa22c0067edf1b5b0dae5319274614b6 | [
"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 | 19,063 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Callum Sutton, Yury Kudryashov
-/
import algebra.group.hom
import algebra.group.type_tags
import algebra.group.units_hom
/-!
# Multiplicative and additive equivs
In t... |
230fc12de4509c039d46e5683aa7abfece241d38 | e9dbaaae490bc072444e3021634bf73664003760 | /src/Problems/2009/IMO_2009_P4.lean | 9cbd8eb735a737c0202e6a388b59e2e4360cf44a | [
"Apache-2.0"
] | permissive | liaofei1128/geometry | 566d8bfe095ce0c0113d36df90635306c60e975b | 3dd128e4eec8008764bb94e18b932f9ffd66e6b3 | refs/heads/master | 1,678,996,510,399 | 1,581,454,543,000 | 1,583,337,839,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 762 | lean | /-
IMO 2009 P4 is a determined problem. The problem statement is as follows:
"Find all possible values of <CAB."
This problem statement is replaced by the disjunctive witnesses in this formalization.
Solution: https://web.evanchen.cc/exams/IMO-2009-notes.pdf
-/
import Geo.Geo.Core
namespace Geo
open Analytic Angl... |
ae35789c4499f2785f8ccea858efc4d528df2b3a | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/algebra/field.lean | cb006f2ef751e12bd988049841124f741efebca2 | [
"Apache-2.0"
] | permissive | ayush1801/mathlib | 78949b9f789f488148142221606bf15c02b960d2 | ce164e28f262acbb3de6281b3b03660a9f744e3c | refs/heads/master | 1,692,886,907,941 | 1,635,270,866,000 | 1,635,270,866,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,014 | lean | /-
Copyright (c) 2014 Robert Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Lewis, Leonardo de Moura, Johannes Hölzl, Mario Carneiro
-/
import algebra.ring.basic
import algebra.group_with_zero
/-!
# Fields and division rings
This file introduces fields ... |
dd7d9c1fb9b30d0d3a312e1144c2f324660e4812 | 968e2f50b755d3048175f176376eff7139e9df70 | /examples/pred_logic/unnamed_493.lean | dc3f186881e400576f592b9a5c44c1a34d377b7b | [] | no_license | gihanmarasingha/mth1001_sphinx | 190a003269ba5e54717b448302a27ca26e31d491 | 05126586cbf5786e521be1ea2ef5b4ba3c44e74a | refs/heads/master | 1,672,913,933,677 | 1,604,516,583,000 | 1,604,516,583,000 | 309,245,750 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 67 | lean | example (h : 5 ≥ 3) : ∃ x, x ≥ 3 :=
by exact exists.intro 5 h |
6b4d9a8939a068c6b9033120737b9e5fb5a508c3 | d7189ea2ef694124821b033e533f18905b5e87ef | /galois/vector/zero_length_lemmas.lean | 9a2a92c40df6c0c60955f4ad0c0e5ae3a5a40f22 | [
"Apache-2.0"
] | permissive | digama0/lean-protocol-support | eaa7e6f8b8e0d5bbfff1f7f52bfb79a3b11b0f59 | cabfa3abedbdd6fdca6e2da6fbbf91a13ed48dda | refs/heads/master | 1,625,421,450,627 | 1,506,035,462,000 | 1,506,035,462,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 686 | lean | /- Lemmas for simplify terms involving zero-length vectors. -/
import data.vector
universe variables u
namespace vector
variable {α : Type u}
variable {n : ℕ}
local infix `++`:65 := vector.append
theorem length_zero_vector_is_nil (x : vector α 0) : x = nil :=
begin
apply vector.eq,
cases x with v p,
cases v,
... |
6e8b8286192a554c319cebcd0b5f8997bad94a35 | 82b86ba2ae0d5aed0f01f49c46db5afec0eb2bd7 | /src/Lean/Data/LBool.lean | 5bb3f32106ae109d1bf2eb47df2f40a3032aebc5 | [
"Apache-2.0"
] | permissive | banksonian/lean4 | 3a2e6b0f1eb63aa56ff95b8d07b2f851072d54dc | 78da6b3aa2840693eea354a41e89fc5b212a5011 | refs/heads/master | 1,673,703,624,165 | 1,605,123,551,000 | 1,605,123,551,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,015 | 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
-/
namespace Lean
inductive LBool
| false
| true
| undef
namespace LBool
instance : Inhabited LBool := ⟨false⟩
def neg : LBool → LBool
| true => ... |
9239d47ea26ca70515c5d18719f709520671b5ae | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/metric_space/emetric_space.lean | 983cb4e4990cef15af7169aa82dfa60e19a9cbc0 | [
"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 | 50,321 | lean | /-
Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
-/
import data.nat.interval
import data.real.ennreal
import topology.uniform_space.pi
import topo... |
5d1de7febddd351dc068e9dfe10d7395f44ae7a4 | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/implicit7.lean | b1f76468c1f2571428f84e71cc4db7d4a1f70384 | [
"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 | 360 | lean | variable f {A : Type} (a : A) {B : Type} : A -> B -> A
variable g {A B : Type} (a : A) {C : Type} : B -> C -> C
notation 100 _ ; _ ; _ : f
notation 100 _ ; _ ; _ : g
check 10 ; true ; false
check 10 ; 10 ; true
set_option pp::notation false
check 10 ; true ; false
check 10 ; 10 ; true
set_option pp::implicit true
check... |
26e41dff7ab683efca227b7954b33a436446a0aa | 5719a16e23dfc08cdea7a5bf035b81690f307965 | /stage0/src/Init/Lean/Compiler/IR/EmitC.lean | 1523dd3012d887deb53732337ac0e2d98de7eb25 | [
"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 | 24,458 | 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.Control.Conditional
import Init.Lean.Runtime
import Init.Lean.Compiler.NameMangling
import Init.Lean.Compiler.ExportAttr
import Init.Lea... |
20a0a1bdb63aeb0111053774bcbd50e93bc94e80 | 77c5b91fae1b966ddd1db969ba37b6f0e4901e88 | /src/data/polynomial/inductions.lean | 2c7efa041b9a7195875c6fa5745e020c89089732 | [
"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 | 5,022 | lean | /-
Copyright (c) 2021 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Damiano Testa, Jens Wagemaker
-/
import data.finset.intervals
import data.polynomial.degree.definitions
/-!
# Induction on polynomials
Th... |
ce59449589f6b8fe00af2e50eeb6394c6ac41dcf | 798dd332c1ad790518589a09bc82459fb12e5156 | /order/basic.lean | 4285fadf9a9ad118d561a9e0c50f76d53e8774c8 | [
"Apache-2.0"
] | permissive | tobiasgrosser/mathlib | b040b7eb42d5942206149371cf92c61404de3c31 | 120635628368ec261e031cefc6d30e0304088b03 | refs/heads/master | 1,644,803,442,937 | 1,536,663,752,000 | 1,536,663,907,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 15,242 | 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... |
f021a6bc33dd35a48850ad1e3c8c0a315f51dea3 | abd85493667895c57a7507870867b28124b3998f | /src/ring_theory/power_series.lean | e2b148ad2d6f9dd731dc7d92853f86bfdb5fa451 | [
"Apache-2.0"
] | permissive | pechersky/mathlib | d56eef16bddb0bfc8bc552b05b7270aff5944393 | f1df14c2214ee114c9738e733efd5de174deb95d | refs/heads/master | 1,666,714,392,571 | 1,591,747,567,000 | 1,591,747,567,000 | 270,557,274 | 0 | 0 | Apache-2.0 | 1,591,597,975,000 | 1,591,597,974,000 | null | UTF-8 | Lean | false | false | 57,819 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Kenny Lau
-/
import data.mv_polynomial
import ring_theory.ideal_operations
import tactic.linarith
/-!
# Formal power series
This file defines (multivariate) formal po... |
7a343c768b9ddefb3cb5551ae07f92a8fc338a46 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/inductive_type_whnf.lean | 941693e32b7a2099de1f756a2441959222d1418b | [
"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 | 62 | lean | def pred (α : Type) := α → Prop
inductive foo : pred ℕ
|
bb89095483bce4b323a3871e9361a94cbda00a4c | 65b579fba1b0b66add04cccd4529add645eff597 | /lambda/pure/src/parsing.lean | 77c2880b1c3695196d1347adeacf747b5651f674 | [] | no_license | teodorov/sf_lean | ba637ca8ecc538aece4d02c8442d03ef713485db | cd4832d6bee9c606014c977951f6aebc4c8d611b | refs/heads/master | 1,632,890,232,054 | 1,543,005,745,000 | 1,543,005,745,000 | 108,566,115 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,775 | lean | import data.buffer.parser
import .types
open parser lambda_types
namespace lambda_parser
def whitespaces := " \t\n\x0d".to_list
def reserved_chars := [' ', '.', 'λ', '(', ')']
def CHAR : parser char :=
sat (λ c, list.all (reserved_chars ++ whitespaces) (≠ c))
def LF := ch $ char.of_nat 10
def CR := ch $ char.of_... |
147ff1cb8b090bb12b0cf5fee1151996b444dbdd | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/analysis/convex/jensen.lean | 6dad2a1e76a823e7707ded4a4496d3417478b842 | [
"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 | 6,717 | lean | /-
Copyright (c) 2019 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, Yury Kudriashov
-/
import analysis.convex.combination
import analysis.convex.function
/-!
# Jensen's inequality and maximum principle for convex functions
In ... |
159e7eaa752ec8004d5f957ec67804fe993e140a | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/countable/defs.lean | c24a9c97eab72fa61d942f4f1264111b9c9a53a7 | [
"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 | 3,534 | lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import data.finite.defs
/-!
# Countable types
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
In th... |
c1997d221e52ef4218f455007b1a1fc08e90d9e6 | 9dd3f3912f7321eb58ee9aa8f21778ad6221f87c | /library/init/wf.lean | 1e6bbcf240233ab6a1e428d4d57b3d6b05c07e3b | [
"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 | 6,811 | 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
-/
prelude
import init.data.nat.basic init.data.prod
universes u v
inductive acc {α : Type u} (r : α → α → Prop) : α → Prop
| intro : ∀ x, (∀ y, r y x → acc y... |
6432744b331d39d27a59e25835c69f8ec2953c8f | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/algebra/ordered_group.lean | b0f529f2a4dfec1eb132fe7c7c3837a58d1d26ab | [
"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 | 67,734 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl
-/
import algebra.group.with_one
import algebra.group.type_tags
import order.bounded_lattice
set_option old_structure_c... |
c7247a38178b8be10c0d1a4791f6241b018ea34c | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/interactive/jumpMutual.lean | 141f9a7060c403d45983b35139c7a98eb4859508 | [
"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 | 564 | lean | mutual
def h (x : Nat) : Nat :=
match x with
| 0 => 1
--v textDocument/definition
--v textDocument/definition
| x+1 => f x + r x + h x
--^ textDocument/definition
where
r : Nat → Nat
| 0 => 1
--v textDocument/definition
| x + 1 => r x * h x
... |
cf6b7c981282b7cfea9bdd63bded693e0d3133d2 | 4fa118f6209450d4e8d058790e2967337811b2b5 | /src/sheaves/stalk_of_rings.lean | bd2eae537559aa5c73d5f039158ec34dca071cb1 | [
"Apache-2.0"
] | permissive | leanprover-community/lean-perfectoid-spaces | 16ab697a220ed3669bf76311daa8c466382207f7 | 95a6520ce578b30a80b4c36e36ab2d559a842690 | refs/heads/master | 1,639,557,829,139 | 1,638,797,866,000 | 1,638,797,866,000 | 135,769,296 | 96 | 10 | Apache-2.0 | 1,638,797,866,000 | 1,527,892,754,000 | Lean | UTF-8 | Lean | false | false | 14,370 | lean | /-
Stalk of rings.
https://stacks.math.columbia.edu/tag/007L
(just says that the category of rings is a type of algebraic structure)
Author -- Ramon Fernandez Mir
-/
import topology.basic
import sheaves.stalk
import sheaves.presheaf_of_rings
universes u v w
open topological_space
section stalk_of_rings
v... |
f94d52d54f0b0df425ecc6d02b3b6d90acdc6d71 | 618003631150032a5676f229d13a079ac875ff77 | /src/set_theory/game/domineering.lean | 528f9b444d09dc937f9029978b7cf1e2a33c84bd | [
"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 | 7,935 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import set_theory.game.state
/-!
# Domineering as a combinatorial game.
We define the game of Domineering, played on a chessboard of arbitrary shape
(possibly even ... |
c0aeb2db2dc46cb53bb30387a32039f7eeb49739 | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/group_theory/coset.lean | 399b04ff0351c4d2546128afb32808ac14be346f | [
"Apache-2.0"
] | permissive | ayush1801/mathlib | 78949b9f789f488148142221606bf15c02b960d2 | ce164e28f262acbb3de6281b3b03660a9f744e3c | refs/heads/master | 1,692,886,907,941 | 1,635,270,866,000 | 1,635,270,866,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 19,805 | lean | /-
Copyright (c) 2018 Mitchell Rowett. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Rowett, Scott Morrison
-/
import group_theory.subgroup.basic
/-!
# Cosets
This file develops the basic theory of left and right cosets.
## Main definitions
* `left_coset... |
9167fd3dc5a0627f0cf373ea9c7d9badc7bd5a24 | 799b5de27cebaa6eaa49ff982110d59bbd6c6693 | /mechanized/assumptions.lean | 0d0d02824a6bbb076669e7f0e274a4c712b60111 | [
"MIT"
] | permissive | philnguyen/soft-contract | 263efdbc9ca2f35234b03f0d99233a66accda78b | 13e7d99e061509f0a45605508dd1a27a51f4648e | refs/heads/master | 1,625,975,131,435 | 1,617,775,585,000 | 1,617,775,704,000 | 17,326,137 | 33 | 7 | MIT | 1,613,722,535,000 | 1,393,714,126,000 | Racket | UTF-8 | Lean | false | false | 1,533 | lean | import data.set definitions metafunctions
constant alloc (x: x) (σ: σ): a
-- The setup of this formalism is that the "concrete semantics" is just a sub-relation
-- of the full semantics with symbolic values, and there's one `alloc` function.
-- The assumption of `alloc_fresh` is only needed for the concrete side
-- t... |
9562644dc21c21f45fdc147dae1a0737c6e469eb | d1a52c3f208fa42c41df8278c3d280f075eb020c | /stage0/src/Init/Prelude.lean | 129aa4c04abbe4648fb49a18527a7e140beb4dae | [
"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 | 78,787 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
universe u v w
@[inline] def id {α : Sort u} (a : α) : α := a
@[inline] def Function.comp {α : Sort u} {β : Sort v} {δ : Sort w} (f : β → δ) (g :... |
d58b87dd394f07e1dfcdaff6459dce01c3cc8b25 | 367134ba5a65885e863bdc4507601606690974c1 | /src/algebra/lie/abelian.lean | b5f957d18e04cd5692533b65322b063405bdfa3d | [
"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 | 7,833 | lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import algebra.lie.of_associative
import algebra.lie.ideal_operations
/-!
# Trivial Lie modules and Abelian Lie algebras
The action of a Lie algebra `L` on a module `M` i... |
01b2a4ffe9028d9fb21ad170b7077dcaa46374a3 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /tests/lean/run/eq15.lean | 7e695acf9e92a3163b0c77984441810657807f07 | [
"Apache-2.0"
] | permissive | davidmueller13/lean | 65a3ed141b4088cd0a268e4de80eb6778b21a0e9 | c626e2e3c6f3771e07c32e82ee5b9e030de5b050 | refs/heads/master | 1,611,278,313,401 | 1,444,021,177,000 | 1,444,021,177,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 454 | lean | import data.list
open list
set_option pp.implicit true
definition append : Π {A : Type}, list A → list A → list A
| append nil l := l
| append (h :: t) l := h :: (append t l)
theorem append_nil {A : Type} (l : list A) : append nil l = l :=
rfl
theorem append_cons {A : Type} (h : A) (t l : list A) : append (h :... |
20f87ff9e943a0420dffc3c24371c580a3e31e1d | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/hott/congr_tac.hlean | af5b06da3cb20fcf01dc46630e001fa9375a3353 | [
"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 | 1,101 | hlean | example (f : nat → nat → nat) (a b c : nat) : b = c → f a b = f a c :=
begin
intro bc,
congruence,
assumption
end
example (f g : nat → nat → nat) (a b c : nat) : f = g → b = c → f a b = g a c :=
begin
intro fg bc,
congruence,
exact fg,
exact bc
end
example (f g : nat → nat → nat) (a b c : nat) : f = g →... |
62abc3d1e466c12a3df421713d9245fbff423ded | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /tests/lean/run/imp_curly.lean | 008aebd1c02d92a266907b6f8b4c21408f06d4de | [
"Apache-2.0"
] | permissive | davidmueller13/lean | 65a3ed141b4088cd0a268e4de80eb6778b21a0e9 | c626e2e3c6f3771e07c32e82ee5b9e030de5b050 | refs/heads/master | 1,611,278,313,401 | 1,444,021,177,000 | 1,444,021,177,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 251 | lean | import data.nat.basic
open nat
theorem zero_left (n : ℕ) : 0 + n = n :=
nat.induction_on n
!add_zero
(take m IH, show 0 + succ m = succ m, from
calc
0 + succ m = succ (0 + m) : add_succ
... = succ m : IH)
|
e6c50edb8bf9f6f52e5bc383a20959bb2d3068c3 | 37da0369b6c03e380e057bf680d81e6c9fdf9219 | /hott/init/trunc.hlean | bf504c0bb150f0ff9fc48cb7669505e7a96a5eb9 | [
"Apache-2.0"
] | permissive | kodyvajjha/lean2 | 72b120d95c3a1d77f54433fa90c9810e14a931a4 | 227fcad22ab2bc27bb7471be7911075d101ba3f9 | refs/heads/master | 1,627,157,512,295 | 1,501,855,676,000 | 1,504,809,427,000 | 109,317,326 | 0 | 0 | null | 1,509,839,253,000 | 1,509,655,713,000 | C++ | UTF-8 | Lean | false | false | 12,954 | 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.
-/
prelude
import .nat .logic .equiv .pathover
open eq nat sigma unit sigma.ops... |
6a02e107bf1a90ee51c7889a08331d7a5d5de43d | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/ring_theory/polynomial/content_auto.lean | c46fea0f8fabe37552750a34e50839bf9117576c | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,283 | lean | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Aaron Anderson
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.finset.gcd
import Mathlib.data.polynomial.default
import Mathlib.data.polynomial.erase_... |
5d364fe294b159344a7dcaa282a338663a228b8f | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/1037.lean | df87681beb31d8ff44814ff5dbfd13fb2bffc825 | [
"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 | 410 | lean | example (p q r s: Prop) (h1: p -> s) (h2: q -> s) (h3: r -> s)
: ((p \/ q) -> s) /\ (r -> s) := by {
constructor <;> intro h <;>
(try (apply Or.elim h <;> intro h)) <;>
revert h <;> assumption;
}
example (p q r s: Prop) (h1: p -> s) (h2: q -> s) (h3: r -> s)
: ((p \/ q) -> s) /\ (r -> s) := by {
constr... |
e99b4726c30d4778368552e28755baf5e05ac0f9 | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /src/Lean/Util/MonadBacktrack.lean | d0532d5a83a402c3b01893327c30532693e19140 | [
"Apache-2.0"
] | permissive | WojciechKarpiel/lean4 | 7f89706b8e3c1f942b83a2c91a3a00b05da0e65b | f6e1314fa08293dea66a329e05b6c196a0189163 | refs/heads/master | 1,686,633,402,214 | 1,625,821,189,000 | 1,625,821,258,000 | 384,640,886 | 0 | 0 | Apache-2.0 | 1,625,903,617,000 | 1,625,903,026,000 | null | UTF-8 | Lean | false | false | 1,596 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
namespace Lean
/-- Similar to `MonadState`, but it retrieves/restores only the "backtrackable" part of the state -/
class MonadBacktrack (s : outParam Typ... |
e5336b649de9b38cea94e5e689903c797d4f1055 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/big_operators/ring.lean | 191ba358c799aa3e72e7051ac610fe71ba97abdc | [
"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 | 11,180 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import algebra.big_operators.basic
import algebra.field.defs
import data.finset.pi
import data.finset.powerset
/-!
# Results about big operators with values in a (s... |
166f583d2904d5d72e2d50e29e509ae612258689 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/algebra/module/submodule.lean | 6b1bd4f42e70543db4fb023bc9ed8c3f430960c1 | [
"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 | 11,468 | lean | /-
Copyright (c) 2015 Nathaniel Thomas. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nathaniel Thomas, Jeremy Avigad, Johannes Hölzl, Mario Carneiro
-/
import algebra.module.linear_map
import group_theory.group_action.sub_mul_action
/-!
# Submodules of a module
In ... |
635977d79a2f3e6eeef8abb9f62ea2b7cb33dabf | 2a70b774d16dbdf5a533432ee0ebab6838df0948 | /_target/deps/mathlib/src/category_theory/monoidal/Mon_.lean | 805be5b77e17a681afea41afd298ab9f9b1e5042 | [
"Apache-2.0"
] | permissive | hjvromen/lewis | 40b035973df7c77ebf927afab7878c76d05ff758 | 105b675f73630f028ad5d890897a51b3c1146fb0 | refs/heads/master | 1,677,944,636,343 | 1,676,555,301,000 | 1,676,555,301,000 | 327,553,599 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,409 | 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.monoidal.discrete
import category_theory.monoidal.unitors
import category_theory.limits.shapes.terminal
import algebra.punit_instances
/-!
# T... |
4e695d13f04c281e90a98fcc3f60a5e385b5795f | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/tcloop.lean | 9b95556de32ab1d2e11e7e0b977fd69a0a366e40 | [
"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 | 218 | lean | class A (α : Type u) where
a : Unit
class B (α : Type u) where
a : Unit
instance [s : B (Array α)] : A α where
a := ()
instance [s : A (Array α)] : B α where
a := ()
def f : B Nat :=
inferInstance
|
7fe30849aa17ad4c2ac8cff2ee35cefee515079d | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/algebra/category/default.lean | 7c35a9c4edcb5a1d40bd0b5ed7b2c91e7f369806 | [
"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 | 190 | lean | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Floris van Doorn
-/
import .morphism .constructions
|
e32de4c8d0028abac048558bbe93375a72b17e52 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/run/array1.lean | 74ccb3423eb476f9f3ffd852302a11d21c2b659c | [
"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 | 563 | lean | #check @array.mk
#eval mk_array 4 1
def v : array nat 10 :=
@array.mk nat 10 (λ ⟨i, _⟩, i)
#eval array.map (+10) v
def w : array nat 10 :=
(mk_array 9 1)^.push_back 3
def f : fin 10 → nat :=
array.cases_on w (λ f, f)
#eval f ⟨9, dec_trivial⟩
#eval f ⟨2, dec_trivial⟩
#eval (((mk_array 1 1)^.push_back 2)^.push_bac... |
e235ffab4448ecf2ed18b4e2f01b80b1c1d80eac | a206acf8ac244f25d5523b86bea8e677ea3c6b91 | /2.lean | 281e8d1e7c24c1d7ee3b200a0f73503bf258ecb9 | [] | no_license | quasimik/tp-lean | cebfd6adf1b7905a411fbb5e7dc3aec87a28e418 | bdf59f3d2fe22b95ed0944252a5019ca0081f96c | refs/heads/master | 1,615,744,339,038 | 1,584,612,369,000 | 1,584,682,398,000 | 246,781,014 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,419 | lean | /-
Exercise 1.
Define the function Do_Twice, as described in Section 2.4.
Exercise 2.
Define the functions curry and uncurry, as described in Section 2.4.
-/
def do_twice (f : ℕ → ℕ) (x : ℕ) : ℕ := f (f x)
def double (x : ℕ) : ℕ := x * 2
def quadruple (x : ℕ) : ℕ := do_twice double x
def octuple (x : ℕ) : ... |
fa5e9fe55c71fd4b626eca05cc480fc9292efd38 | ac89c256db07448984849346288e0eeffe8b20d0 | /src/Init/Notation.lean | 552dfe623e092264119ee66cc9071eedc9af815d | [
"Apache-2.0"
] | permissive | chepinzhang/lean4 | 002cc667f35417a418f0ebc9cb4a44559bb0ccac | 24fe2875c68549b5481f07c57eab4ad4a0ae5305 | refs/heads/master | 1,688,942,838,326 | 1,628,801,942,000 | 1,628,801,995,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 18,789 | 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
Notation for operators defined at Prelude.lean
-/
prelude
import Init.Prelude
-- DSL for specifying parser precedences and priorities
namespace Lean.Parser.... |
50810e96ade854ba4920658aad65bbafa0faded8 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/list/duplicate.lean | e142708891e1e2f5447c4c7d23846a24f7d62dd7 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 4,437 | lean | /-
Copyright (c) 2021 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky, Chris Hughes
-/
import data.list.nodup
/-!
# List duplicates
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mat... |
92eb17f597edf710cd0825abe475701aa2790a53 | 94637389e03c919023691dcd05bd4411b1034aa5 | /src/inClassNotes/predicate_logic/true.lean | 1c6119aa408e901a5f27ae6bac35e39ff8409ba4 | [] | no_license | kevinsullivan/complogic-s21 | 7c4eef2105abad899e46502270d9829d913e8afc | 99039501b770248c8ceb39890be5dfe129dc1082 | refs/heads/master | 1,682,985,669,944 | 1,621,126,241,000 | 1,621,126,241,000 | 335,706,272 | 0 | 38 | null | 1,618,325,669,000 | 1,612,374,118,000 | Lean | UTF-8 | Lean | false | false | 456 | lean | /-
In Lean, true is a proposition that
is always true, in the sense that
there is a proof of it that doesn't
depend on anything else being true.
-/
#check true
/-
inductive true : Prop
| intro : true
-/
/-
Introduction rule for true
-/
lemma true_is_true : true := true.intro
/-
A function from true to true
-/
lem... |
97e5cbc0b827d662204e37dd18ea02e418616016 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/analysis/normed_space/point_reflection.lean | ecb340065255a74514230f62b47b54d0819e1a7e | [
"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 | 3,447 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Yury Kudryashov
-/
import algebra.midpoint
import topology.metric_space.isometry
/-!
# Point reflection in a point as an `isometric` homeomorphism
Given a `normed_group E` and `x : E... |
93e36604dee46e442f3df73690b7f6a521687090 | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/algebra/associated.lean | 0f745e302b2e165f89fbe4ffa33c55d651b7cbc8 | [
"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 | 25,505 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker
Associated and irreducible elements.
-/
import algebra.group data.multiset
variables {α : Type*} {β : Type*} {γ : Type*} {δ : Type*}
open lattice
/-- ... |
266e2f35a82ee8fa897bf91539eb1667413abd34 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/category_theory/monoidal/subcategory.lean | 8fef005cad002f024b4dfb79a9a64ba9b840a9b7 | [
"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 | 5,881 | lean | /-
Copyright (c) 2022 Antoine Labelle. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Labelle
-/
import category_theory.monoidal.braided
import category_theory.concrete_category.basic
/-!
# Full monoidal subcategories
Given a monidal category `C` and a monoid... |
375f8e493875de7942cd47db49aaacb9791fbdac | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/finset/fold.lean | 1f728224a9520abf7196e2f5a5e5a6815765b17c | [
"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 | 9,017 | 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.order.monoid.with_top
import data.finset.basic
import data.multiset.fold
/-!
# The fold operation for a commutative associative operation over a finse... |
0895b96f9378eaec0c01e78e72e3327668c816db | 4c630d016e43ace8c5f476a5070a471130c8a411 | /category/functor.lean | 09b84fecc0a7f8811e51d3b3f34856fbfe6488fe | [
"Apache-2.0"
] | permissive | ngamt/mathlib | 9a510c391694dc43eec969914e2a0e20b272d172 | 58909bd424209739a2214961eefaa012fb8a18d2 | refs/heads/master | 1,585,942,993,674 | 1,540,739,585,000 | 1,540,916,815,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,367 | lean | /-
Copyright (c) 2017 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Simon Hudon
Standard identity and composition functors
-/
import tactic.ext tactic.cache category.basic
universe variables u v w
section functor
variables {F : Type u → Type v}
variabl... |
e3b1a0b0b518931bcbcfb7aa4812927d5038e762 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/field/basic.lean | 51f74dd247549f391f6703c0a8da286d65a3e22a | [
"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 | 14,906 | lean | /-
Copyright (c) 2014 Robert Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Lewis, Leonardo de Moura, Johannes Hölzl, Mario Carneiro
-/
import algebra.ring.basic
/-!
# Fields and division rings
This file introduces fields and division rings (also known ... |
a002b3499156c346be68c7507da5e0fc427f22d4 | 592ee40978ac7604005a4e0d35bbc4b467389241 | /Library/generated/mathscheme-lean/CancellativeMagma.lean | 82ec736f0f02690bd7ad3ce5737b0596323d52c3 | [] | 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 | 6,427 | 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 CancellativeMagma
structure CancellativeMagma (A : Type) : Type :=
(op : (A → (A → A)))
(leftCancellative : (∀ {x y z : A} , ((op z x) = (op z y) → x = y)))
... |
be7d8d1f4bc45bc048ee40e893f6f26e1c373575 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/convPatternMatchIssue.lean | 8da8c6251a509ccf176a0d6ae31992e66078299a | [
"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 | 188 | lean | def test : (λ x => x)
=
(λ x : Nat =>
let_fun foo := λ y => id (id y)
foo x) := by
conv =>
pattern (id _)
trace_state
skip
|
ba7169a184e6aa67746b619616ce8120de89dfdc | 36c7a18fd72e5b57229bd8ba36493daf536a19ce | /library/theories/group_theory/action.lean | 5985aada4c9c0b9bfd69517bbbcb5eb5f17785d6 | [
"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 | 23,110 | lean | /-
Copyright (c) 2015 Haitao Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author : Haitao Zhang
-/
import algebra.group data .hom .perm .finsubg
namespace group
open finset algebra function
local attribute perm.f [coercion]
private lemma and_left_true {a b : Prop} ... |
09cfac0500ec83491e84199bf7417fb1c4a40537 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /11_Tactic-Style_Proofs.org.22.lean | 6f82a305a6291ce4326642f21461934ed4655926 | [] | no_license | cjmazey/lean-tutorial | ba559a49f82aa6c5848b9bf17b7389bf7f4ba645 | 381f61c9fcac56d01d959ae0fa6e376f2c4e3b34 | refs/heads/master | 1,610,286,098,832 | 1,447,124,923,000 | 1,447,124,923,000 | 43,082,433 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 392 | lean | import standard
example (p q : Prop) (H : p ∧ q) : p ∧ q ∧ p :=
assert Hp : p, from and.left H,
assert Hq : q, from and.right H,
begin
apply (and.intro Hp),
apply (and.intro Hq),
exact Hp
end
example (p q : Prop) (H : p ∧ q) : p ∧ q ∧ p :=
assert Hp : p, from and.left H,
assert Hq : q, from and.right H,
begin
apply an... |
8da91bbcd162b1f0edb5097dd38cbff20d4ed210 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/1766.lean | 6a0bca53286ed6333d26e063d09583f57fd8af9f | [
"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 | 738 | lean | inductive is_some (x : option nat) : Prop
| mk : ∀ value : nat, x = some value → is_some
def value_1 (x : option nat) (H : is_some x)
: nat :=
begin
destruct x; intros,
{destruct H, -- ERROR: `is_some` can only eliminate into Prop
intros, clear a_2, rw a at a_1, contradiction},
{assumption}
end
def ... |
af66c45dbaab5674b441a0450215414adb51fd94 | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /tests/lean/interactive/eq2.lean | 5000440e983c7d6c45718e5bf0e44c9bfcca7e98 | [
"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 | 7,033 | lean | -- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Leonardo de Moura, Jeremy Avigad, Floris van Doorn
-- logic.connectives.eq
-- ====================
-- Equality.
prelude
definition Prop := Type.{0}
-- eq
-- --
inductiv... |
873250e563e37365a8dcf72299dcaeeeab940d45 | 91b8df3b248df89472cc0b753fbe2bac750aefea | /experiments/lean/src/ddl/host/default.lean | 545ae7042cec8f88d84751b0d6ad1bc630b0a150 | [
"Apache-2.0",
"LicenseRef-scancode-unknown-license-reference"
] | permissive | yeslogic/fathom | eabe5c4112d3b4d5ec9096a57bb502254ddbdf15 | 3960a9466150d392c2cb103c5cb5fcffa0200814 | refs/heads/main | 1,685,349,769,736 | 1,675,998,621,000 | 1,675,998,621,000 | 28,993,871 | 214 | 11 | Apache-2.0 | 1,694,044,276,000 | 1,420,764,938,000 | Rust | UTF-8 | Lean | false | false | 95 | lean | import ddl.host.basic
import ddl.host.evaluation
import ddl.host.typing
import ddl.host.lemmas
|
b46f3d6be03df4b17d037575bd5636c139aff42a | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/measure_theory/integral/set_integral.lean | 37eb88792a7d123db4bcc5d0a901dc21ea9d57b1 | [
"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 | 50,163 | lean | /-
Copyright (c) 2020 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Yury Kudryashov
-/
import measure_theory.integral.integrable_on
import measure_theory.integral.bochner
import order.filter.indicator_function
import topology.metric_space... |
cd0ffc18412f0270dbd7c8696f5bc3cee1d1c3b2 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/category_theory/monad/adjunction.lean | acf56216ef6604f6292a6492ed55044506b1c00d | [
"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 | 8,124 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Bhavik Mehta
-/
import category_theory.monad.algebra
import category_theory.adjunction
namespace category_theory
open category
universes v₁ v₂ u₁ u₂ -- morphism level... |
ff54752ec2a369b3667f21f302e90b7f3027d2d9 | c062f1c97fdef9ac746f08754e7d766fd6789aa9 | /tools/auto/mk_inhabitant.lean | 9027cee3214451a24daefc8e63681da55f5be741 | [] | no_license | emberian/library_dev | 00c7a985b21bdebe912f4127a363f2874e1e7555 | f3abd7db0238edc18a397540e361a1da2f51503c | refs/heads/master | 1,624,153,474,804 | 1,490,147,180,000 | 1,490,147,180,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 533 | lean | open tactic
/- mk_inthabitant_using A t assumes A is an expression denoting a type. It creates
a goal with type A, applies t, and returns the expression that results. -/
meta def mk_inhabitant_using (A : expr) (t : tactic unit) : tactic expr :=
do m ← mk_meta_var A,
gs ← get_goals,
set_goals [m],
t,
r ←... |
b790880865c1d9a3e84ff3497f5869b71f399716 | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /tests/playground/lazylist.lean | 46b0ac90ea8a9144878b68c99e6449676a16e261 | [
"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 | 5,623 | lean | /-
Copyright (c) 2019 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
inductive LazyList (α : Type u)
| nil {} : LazyList
| cons (hd : α) (tl : LazyList) : LazyList
| delayed (t : Thunk L... |
243bdc236028100f21f3b6c633fbd9a2f7520229 | 9b9a16fa2cb737daee6b2785474678b6fa91d6d4 | /src/category_theory/natural_isomorphism.lean | 6e544304e41de1dda7b27f2b98b241ff3f3f6053 | [
"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 | 5,516 | 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.isomorphism
import category_theory.functor_category
open category_theory
namespace category_theory.nat_iso
... |
fa43c8a8a822c51caa1ab51b9629f6f8bbde2134 | 5d166a16ae129621cb54ca9dde86c275d7d2b483 | /tests/lean/run/cases_nested.lean | 4d1daa0360caf478b17a4894be41fc279c415d0c | [
"Apache-2.0"
] | permissive | jcarlson23/lean | b00098763291397e0ac76b37a2dd96bc013bd247 | 8de88701247f54d325edd46c0eed57aeacb64baf | refs/heads/master | 1,611,571,813,719 | 1,497,020,963,000 | 1,497,021,515,000 | 93,882,536 | 1 | 0 | null | 1,497,029,896,000 | 1,497,029,896,000 | null | UTF-8 | Lean | false | false | 511 | lean | inductive term : Type
| var : string → term
| app : string → list term → term
def cidx : term → nat
| (term.var _) := 1
| (term.app _ _) := 2
def to_list : term → list term
| (term.app _ ts) := ts
| (term.var _) := []
def tid : term → string
| (term.var id) := id
| (term.app id _) := id
lemma ex (t : term) (... |
babd72a39981d287cd303fce10dbdf0ef9839b1f | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/deprecated/group.lean | 0b8fb17c1af4ac149f107b3f25da8c55899a73cb | [
"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 | 13,133 | 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.group.type_tags
import algebra.group.units_hom
import algebra.ring.basic
import data.equiv.mul_add
/-!
# Unbundled monoid and group homomorphisms
T... |
97c20de6251e847553da3d42878cc2baec17e0af | 9d2e3d5a2e2342a283affd97eead310c3b528a24 | /src/hints/thursday/afternoon/category_theory/exercise2/hint6.lean | 5b7f9f4849eaf5ff69513116d94bb68b3b296c2b | [] | permissive | Vtec234/lftcm2020 | ad2610ab614beefe44acc5622bb4a7fff9a5ea46 | bbbd4c8162f8c2ef602300ab8fdeca231886375d | refs/heads/master | 1,668,808,098,623 | 1,594,989,081,000 | 1,594,990,079,000 | 280,423,039 | 0 | 0 | MIT | 1,594,990,209,000 | 1,594,990,209,000 | null | UTF-8 | Lean | false | false | 898 | lean | import algebra.category.CommRing.basic
import data.polynomial
noncomputable theory -- the default implementation of polynomials is noncomputable
local attribute [irreducible] polynomial.eval₂
def Ring.polynomial : Ring ⥤ Ring :=
{ obj := λ R, Ring.of (polynomial R),
map := λ R S f, ring_hom.of (polynomial.map f), ... |
a6f4ea6b658c9ad6db4869174184f07a8353c775 | ce6917c5bacabee346655160b74a307b4a5ab620 | /src/ch4/ex0502.lean | 26df9706122226494c7b6c176f0fb9f2dbe4b9d3 | [] | 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 | 238 | lean | variable f : ℕ → ℕ
variable h : ∀ x : ℕ, f x ≤ f (x + 1)
example : f 0 ≤ f 3 :=
have f 0 ≤ f 1, from h 0,
have f 0 ≤ f 2, from le_trans (by assumption) (h 1),
show f 0 ≤ f 3, from le_trans (by assumption) (h 2)
|
de9b1df3d9fd588743751a5703c517507f8e7e34 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/order/bounded_lattice.lean | a4d1287b22baead5a16f9b52cf68beb1ed8cecfe | [
"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 | 46,934 | 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.lattice
import data.option.basic
import tactic.pi_instances
import logic.nontrivial
/-!
# ⊤ and ⊥, bounded lattices and variants
This file defines top ... |
377a46280291927da9fe3c11691d8500409f3736 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/control/traversable/lemmas.lean | 2a4134ddcbfdc3a48dab2603bbdaaab32c01e443 | [
"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 | 3,857 | 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 control.applicative
import control.traversable.basic
/-!
# Traversing collections
This file proves basic properties of traversable and applicative functors and def... |
53d2c613a5e410f35d212fe624c82b6ad0944f9a | 94e33a31faa76775069b071adea97e86e218a8ee | /src/category_theory/essentially_small.lean | 82779c2c980b960f62fb9219792a17014f0a8a73 | [
"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 | 7,376 | lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import logic.small
import category_theory.skeletal
/-!
# Essentially small categories.
A category given by `(C : Type u) [category.{v} C]` is `w`-essentially small
... |
0ad169546f1cadbc38df6c11b536bd5c711f16e2 | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/data/pnat/basic.lean | ccfc98b7bab7d5c97c1d19698cadf0feec137aa8 | [
"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 | 14,267 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro, Neil Strickland
-/
import data.nat.basic
/-!
# The positive natural numbers
This file defines the type `ℕ+` or `pnat`, the subtype of natural numbers that are p... |
4d27f845e12d361cb15f569fb4e2162ab5ef7785 | a4673261e60b025e2c8c825dfa4ab9108246c32e | /stage0/src/Lean/Elab/PreDefinition/Structural.lean | 34f503434b3f7f183701418fa196d6911f5e620f | [
"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 | 22,351 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Util.ForEachExpr
import Lean.Meta.ForEachExpr
import Lean.Meta.RecursorInfo
import Lean.Meta.Match.Match
import Lean.Elab.PreDefinition.Basic
na... |
974aec3df6e91ec78e68a6fe2f13e9e382ddc0d2 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/run/simpPrio.lean | d005414fbb86085623a64a2ecbdd98d033ca65c8 | [
"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 | 183 | lean | constant n : Nat
@[simp] axiom prio_1000 : n = 1000
@[simp 10] axiom prio_10 : n = 10
-- simp should prefer the prio_1000 lemma with the higher priority
example : n = 1000 := by simp
|
89fa822929c90a57263cc287b2cbfc055726de5c | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/order/filter/ultrafilter.lean | d845c9350166e07f5d8fb828daa8a02aac50b9d0 | [
"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 | 12,822 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jeremy Avigad, Yury Kudryashov
-/
import order.filter.cofinite
/-!
# Ultrafilters
An ultrafilter is a minimal (maximal in the set order) proper filter.
In this file w... |
7c9bcbf038eb1466223363d85c6a29abb48d8a2f | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/analysis/inner_product_space/euclidean_dist.lean | 40ca085e11c73c9071c8107e16b03e6a8f4d0117 | [
"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 | 4,691 | lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import analysis.inner_product_space.calculus
import analysis.inner_product_space.pi_L2
/-!
# Euclidean distance on a finite dimensional space
When we define a smo... |
686fe7735ed99172787ef5e1e79fd7bef66735d9 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/order/hom/basic.lean | 26cdd079ec5f599c00ae8c687874e6212a8626ec | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 13,014 | lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import algebra.group_power.order
/-!
# Algebraic order homomorphism classes
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a correspondin... |
4b999ae69ae81399625603d8f2be25c6c495a5b6 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /src/Lean/Meta/Tactic/Assert.lean | 512c711eb5c5cd6ad993a057203d9770bda44c0e | [
"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 | 5,800 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.Tactic.Util
import Lean.Meta.Tactic.FVarSubst
import Lean.Meta.Tactic.Intro
import Lean.Meta.Tactic.Revert
namespace Lean.Meta
/--
Conv... |
a2184561e7ee9432af2c435b89ab45cf2be1c07d | c777c32c8e484e195053731103c5e52af26a25d1 | /src/analysis/inner_product_space/lax_milgram.lean | c6f4f84191f2aab6fa769dfacfe1cf8d9ece23d9 | [
"Apache-2.0"
] | permissive | kbuzzard/mathlib | 2ff9e85dfe2a46f4b291927f983afec17e946eb8 | 58537299e922f9c77df76cb613910914a479c1f7 | refs/heads/master | 1,685,313,702,744 | 1,683,974,212,000 | 1,683,974,212,000 | 128,185,277 | 1 | 0 | null | 1,522,920,600,000 | 1,522,920,600,000 | null | UTF-8 | Lean | false | false | 4,683 | lean | /-
Copyright (c) 2022 Daniel Roca González. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Roca González
-/
import analysis.inner_product_space.projection
import analysis.inner_product_space.dual
import analysis.normed_space.banach
import analysis.normed_space.o... |
a1fa430f13901420babaec8a6b8f36fceefbf8c7 | 3268ab3a126f0fef71459fbf170dc38efe5d0506 | /cohomology/basic.hlean | 5ce09d20126d5867822a2545052248213a4db29a | [
"Apache-2.0"
] | permissive | soraismus/Spectral | f043fed1a4e02ddfeba531769b2980eb817471f4 | 32512bf47db3a1b932856e7ed7c7830b1fc07ef0 | refs/heads/master | 1,585,628,705,579 | 1,538,609,948,000 | 1,538,609,974,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 24,876 | 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, Ulrik Buchholtz
Reduced cohomology of spectra and cohomology theories
-/
import ..spectrum.basic ..algebra.arrow_group ..algebra.product_group ..choice
..h... |
2537c9deb4adb06223ddb6eccbb8adcf2c6f71b6 | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/number_theory/quadratic_reciprocity.lean | 3b7f9214cf0f4661353596813cfd1136b7d1ab30 | [
"Apache-2.0"
] | permissive | jumpy4/mathlib | d3829e75173012833e9f15ac16e481e17596de0f | af36f1a35f279f0e5b3c2a77647c6bf2cfd51a13 | refs/heads/master | 1,693,508,842,818 | 1,636,203,271,000 | 1,636,203,271,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 24,984 | 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 field_theory.finite.basic
import data.zmod.basic
import data.nat.parity
/-!
# Quadratic reciprocity.
This file contains results about quadratic residues modulo ... |
182e022ff7ac8c107d92e0e68e4190a4c7fbd3ef | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/nat/enat_auto.lean | 5126fca1be03125d515388ec25f5d6f4e0748bc4 | [] | 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 | 16,527 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.pfun
import Mathlib.tactic.norm_num
import Mathlib.data.equiv.mul_add
import Mathlib.PostP... |
a0c1b4b5804a350b88ba198f6f335d534f6aeef7 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/number_theory/zsqrtd/to_real.lean | aeb45b6ec98a8404f313f4a393d4e26cc898e99a | [
"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 | 855 | lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import data.real.sqrt
import number_theory.zsqrtd.basic
/-!
# Image of `zsqrtd` in `ℝ`
This file defines `zsqrtd.to_real` and related lemmas.
It is in a separate file to ... |
f1755a21ab3e557c84a95991f8e24054f0f861d3 | 159fed64bfae88f3b6a6166836d6278f953bcbf9 | /Structure/Generic/Axioms/GeneralizedProperties.lean | bea514a43d41026cc6177240c6003b8ce798e919 | [
"MIT"
] | permissive | SReichelt/lean4-experiments | 3e56830c8b2fbe3814eda071c48e3c8810d254a8 | ff55357a01a34a91bf670d712637480089085ee4 | refs/heads/main | 1,683,977,454,907 | 1,622,991,121,000 | 1,622,991,121,000 | 340,765,677 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,642 | lean | import Structure.Generic.Axioms.Universes
import Structure.Generic.Axioms.AbstractFunctors
import Structure.Generic.Axioms.AbstractEquivalences
import Structure.Generic.Lemmas.DerivedFunctors
import Structure.Generic.Notation
set_option autoBoundImplicitLocal false
--set_option pp.universes true
universes u v
de... |
5ec0261854c2a47175c3b1378d85e9db6695f881 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/linear_algebra/linear_independent_auto.lean | be673e708a4232c63d6cd8791cda66400c2ae688 | [] | 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 | 32,927 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Alexander Bentkamp, Anne Baanen
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.linear_algebra.finsupp
import Mathlib.order.z... |
2a6d4fd7792fe29c6b92a42e9d2d6dd49b9d0f8b | 94e33a31faa76775069b071adea97e86e218a8ee | /src/analysis/specific_limits/basic.lean | db98954d6e8a048e079a4a2e3b6073bc4d0dd645 | [
"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 | 24,564 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Johannes Hölzl, Yury G. Kudryashov, Patrick Massot
-/
import algebra.geom_sum
import order.filter.archimedean
import order.iterate
import topology.instances.ennreal
... |
239d4741442a14f0868b3a623270f81c2d2daeae | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/data/nat/prime.lean | f075322bf4dcfb8de1cea4e787a24b1c69247895 | [
"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 | 24,311 | 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.nat.sqrt
import data.nat.gcd
import algebra.group_power
import tactic.wlog
/-!
# Prime numbers
This file deals... |
abf5f87d58bd4ef02d67d46480baa5cd293df9ce | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/category_theory/preadditive/schur.lean | 97eba89df7dadafd3d619341d8a4a35cfae30774 | [
"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 | 6,979 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Scott Morrison
-/
import algebra.group.ext
import category_theory.simple
import category_theory.linear
import category_theory.endomorphism
import algebra.algebra.spectru... |
fa6bf1d66a1528bd63ea5497c32f340294d10acd | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/inlineIssue.lean | eb5067532b895e2fc232d2982f29d6dac8bfa21d | [
"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 | 376 | lean | import Lean
def f (x : Nat) :=
let g (y z : Nat) := match y with | 0 => x * z * x * y * y | .succ y => y + z
let h (x : Nat) := g x x
h (x+1) +
h (x+2) +
h (x+3) +
h (x+4) +
h (x+5) +
h (x+6) +
h (x+7) +
h (x+8) +
h (x+9)
#eval Lean.Compiler.compile #[``f]
-- set_option trace.Compiler.simp tru... |
59b5be58f48d3478a8775255a03c055233a4b5f9 | b73bd2854495d87ad5ce4f247cfcd6faa7e71c7e | /src/game/intro.lean | c4d3991d81dd002c1be5a9540869afaf6f5e9999 | [] | no_license | agusakov/category-theory-game | 20db0b26270e0c95a3d5605498570273d72f731d | 652dd7e90ae706643b2a597e2c938403653e167d | refs/heads/master | 1,669,201,216,310 | 1,595,740,057,000 | 1,595,740,057,000 | 280,895,295 | 12 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,745 | lean | /-
# The Category Theory Game, version 0.1
## By Alena Gusakov
# What is this game?
Welcome to the category theory game -- a game to help undergraduates learn category theory
through Lean, a formal proof verification system. Starting from the definition of categories,
we develop the theory of functors, natural tran... |
da74cace5fd30608a64b8ac8d26b8d47d785aafb | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/simpAtDefIssue.lean | e82f81f901b91473d9e85e6990bc4e5ab404b12d | [
"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 | 194 | lean | @[simp] def g (x y : Nat) : Nat :=
match x, y with
| 0, 0 => 1
| 0, y => y
| x+1, 5 => 2 * g x 0
| x+1, y => 2 * g x y
#check g._eq_1
#check g._eq_2
#check g._eq_3
#check g._eq_4
|
4279d0f2351cff704d549edd614e3e5c1dbfe13d | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/ring_theory/jacobson.lean | 3a03bc503546cc4170de3fffee5628be7d1729cc | [
"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 | 10,818 | lean | /-
Copyright (c) 2020 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Devon Tuma
-/
import data.mv_polynomial
import ring_theory.ideal.basic
import ring_theory.ideal.operations
import ring_theory.jacobson_ideal
import ring_theory.localization
/-!
# Jacobson... |
1e739ef46b651c44f696fe9230fbb8d8f1e0e993 | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/category_theory/isomorphism.lean | 554338d66b68690121a462b0c197ac98460ec27b | [
"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 | 9,379 | 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
universes v u -- declare the `v`'s first; see `category_theory.category` for an explana... |
93210858973c19d2f5702ad312f67c6ea696d3a5 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/topology/dense_embedding.lean | 22f27d6a90f94576fc98a849fe4346b7d13d12c4 | [
"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 | 14,407 | lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot
-/
import topology.separation
/-!
# Dense embeddings
This file defines three properties of functions:
* `dense_range f` means `f` ha... |
9816dc3ae6ac044155d81127198b43c4d5f6c9ca | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/set_theory/game/short.lean | b346fb5ad07e847139623b81a8617539608b77f7 | [] | 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 | 11,948 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.set_theory.game
import Mathlib.data.fintype.basic
import Mathlib.PostPort
universes u l u_... |
e4e7a8b24def5283928bdf8fc7fec915abcacc23 | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/category_theory/limits/shapes/equalizers.lean | fced6ad619e51f66e781e205de9a1b15e26f9ebd | [
"Apache-2.0"
] | permissive | mcncm/mathlib | 8d25099344d9d2bee62822cb9ed43aa3e09fa05e | fde3d78cadeec5ef827b16ae55664ef115e66f57 | refs/heads/master | 1,672,743,316,277 | 1,602,618,514,000 | 1,602,618,514,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 30,338 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Markus Himmel
-/
import category_theory.epi_mono
import category_theory.limits.limits
/-!
# Equalizers and coequalizers
This file defines (co)equalizers as special ca... |
3df592c08acf86880a0456351e3dab56287163cc | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/group_theory/submonoid/basic.lean | d4ba45e82042a1dcec90bac3612e94eeb4431e5c | [
"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 | 15,958 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard,
Amelia Livingston, Yury Kudryashov
-/
import data.set.lattice
/-!
# Submonoids: definition and `complete_latt... |
7a7854097e7dcc248babe0496db0396bce7d1025 | 82b86ba2ae0d5aed0f01f49c46db5afec0eb2bd7 | /tests/lean/run/meta7.lean | 728877e644ff85ac4bd853bef01fa1b947448b94 | [
"Apache-2.0"
] | permissive | banksonian/lean4 | 3a2e6b0f1eb63aa56ff95b8d07b2f851072d54dc | 78da6b3aa2840693eea354a41e89fc5b212a5011 | refs/heads/master | 1,673,703,624,165 | 1,605,123,551,000 | 1,605,123,551,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,724 | lean | import Lean.Meta
open Lean
open Lean.Meta
partial def fact : Nat → Nat
| 0 => 1
| n+1 => (n+1)*fact n
set_option trace.Meta.debug true
set_option trace.Meta.check false
def print (msg : MessageData) : MetaM Unit :=
trace! `Meta.debug msg
def checkM (x : MetaM Bool) : MetaM Unit :=
unless (← x) do throwError "check... |
54b3ff2928c24b4085cb342f966de59288c0510d | 4727251e0cd73359b15b664c3170e5d754078599 | /src/order/cover.lean | bcb6c46c22f2aa769df47c0c9d2e1cb9bb3f94f2 | [
"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 | 9,271 | lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Violeta Hernández Palacios, Grayson Burton, Floris van Doorn
-/
import data.set.intervals.ord_connected
/-!
# The covering relation
This file defines the covering relatio... |
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