blob_id stringlengths 40 40 | directory_id stringlengths 40 40 | path stringlengths 7 139 | content_id stringlengths 40 40 | detected_licenses listlengths 0 16 | license_type stringclasses 2
values | repo_name stringlengths 7 55 | snapshot_id stringlengths 40 40 | revision_id stringlengths 40 40 | branch_name stringclasses 6
values | visit_date int64 1,471B 1,694B | revision_date int64 1,378B 1,694B | committer_date int64 1,378B 1,694B | github_id float64 1.33M 604M ⌀ | star_events_count int64 0 43.5k | fork_events_count int64 0 1.5k | gha_license_id stringclasses 6
values | gha_event_created_at int64 1,402B 1,695B ⌀ | gha_created_at int64 1,359B 1,637B ⌀ | gha_language stringclasses 19
values | src_encoding stringclasses 2
values | language stringclasses 1
value | is_vendor bool 1
class | is_generated bool 1
class | length_bytes int64 3 6.4M | extension stringclasses 4
values | content stringlengths 3 6.12M |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
3375a7af539d92bb6ec23773e68a23fd7149cf18 | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/order/filter/lift.lean | 56a3f85869b3114b6632b9737622c4ca21e7a1f4 | [
"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 | 18,035 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Lift filters along filter and set functions.
-/
import order.filter.basic
open lattice set
local attribute [instance] classical.prop_decidable
namespace filter
varia... |
04f01b4d6df013d95ccaf4b3fa4834e33113218d | 54f4ad05b219d444b709f56c2f619dd87d14ec29 | /test.lean | 4a3d07c6678176bfa43a4c34f99482345fb7a4ef | [] | no_license | yizhou7/learning-lean | 8efcf838c7276e235a81bd291f467fa43ce56e0a | 91fb366c624df6e56e19555b2e482ce767cd8224 | refs/heads/master | 1,675,649,087,737 | 1,609,022,281,000 | 1,609,022,281,000 | 272,072,779 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,912 | lean | example (p q r : Prop) : p ∧ (q ∨ r) ↔ (p ∧ q) ∨ (p ∧ r) :=
begin
apply iff.intro,
intro h,
apply or.elim (and.right h),
intro hq,
apply or.inl,
apply and.intro,
apply and.left h,
exact hq,
intro hr,
apply or.inr,
apply and.intro,
apply a... |
f7c4e5abb59c79cb7936cf2ea050913c3be8b7ef | 3f48345ac9bbaa421714efc9872a0409379bb4ae | /src/examples/kripke_structure/Kripke_Structure.lean | 2e2cb0570297624f4d860c5284a88948c45fa949 | [] | no_license | QaisHamarneh/Coalgebra-in-Lean | b4318ee6d83780e5c734eb78fed98b1fe8016f7e | bd0452df98bc64b608e5dfd7babc42c301bb6a46 | refs/heads/master | 1,663,371,200,241 | 1,661,004,695,000 | 1,661,004,695,000 | 209,798,828 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,861 | lean | import coalgebra.Coalgebra
namespace Kripke_Structure
universes u v w
variable (Properties : Type u) -- Elementry properties
structure Kripke (Φ : Type u): Type (max u (v+1)) :=
(State : Type v)
(T : State → set State)
(v : State → set Φ)
instance Krip... |
0b7f1a685973f1d92838dd0a312a4010a9f564d6 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/reserve.lean | 143a2b57a09dca2136f25a5258220b98fe080d77 | [
"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 | 177 | lean | reserve infix `=?=`:50
reserve infixr `&&&`:25
notation a `=?=` b := eq a b
notation a `&&&` b := and a b
set_option pp.notation false
check λ a b : num, a =?= b &&& b =?= a
|
a05bbc52641fe181b59dee405e8665aaed6282dd | 9cb9db9d79fad57d80ca53543dc07efb7c4f3838 | /src/facts/nnreal.lean | f34b2997d21177ffea69ff9b4174ea2b3c0d9508 | [] | 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 | 2,752 | lean | import data.real.nnreal
open_locale nnreal
namespace nnreal
variables (r' k c c₁ c₂ c₃ : ℝ≥0)
instance fact_le_mul_of_one_le_left [hk : fact (1 ≤ k)] [hc : fact (c₁ ≤ c₂)] :
fact (c₁ ≤ k * c₂) :=
calc c₁ = 1 * c₁ : (one_mul _).symm
... ≤ k * c₂ : mul_le_mul' hk hc
instance fact_mul_le_of_le_one_left [hk : fa... |
fc47887dbe543796ff4fee1e854052e68880d649 | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /stage0/src/Lean/Data/Format.lean | d990bf2800f4fb9e8f361faf3e634a7d04aa3f02 | [
"Apache-2.0"
] | permissive | walterhu1015/lean4 | b2c71b688975177402758924eaa513475ed6ce72 | 2214d81e84646a905d0b20b032c89caf89c737ad | refs/heads/master | 1,671,342,096,906 | 1,599,695,985,000 | 1,599,695,985,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,832 | lean | /-
Copyright (c) 2018 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
import Lean.Data.Options
universes u v
namespace Lean
inductive Format
| nil : Format
| line : Format
| text ... |
27a89f78ceece03e7444cc8c49f0cbff3eb2168e | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/implicit_after_auto_param_bug.lean | 58462b60a463fe1abdf6ca703e40c94729aef189 | [
"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 | 670 | lean | meta def default_f_lt := `[apply has_lt.lt]
def f (α : Type) (lt : α → α → Prop . default_f_lt) [decidable_rel lt] : Type :=
α
example : id (f nat) = nat :=
rfl
example : f nat = nat :=
rfl
def mk {α : Type} (a : α) (lt : α → α → Prop . default_f_lt) [decidable_rel lt] : f α lt :=
a
def f.to_val {α : Type} {lt : α... |
e7df166474bd87349408955ba819a892d2620870 | aa5a655c05e5359a70646b7154e7cac59f0b4132 | /stage0/src/Init.lean | 8e850e3eb096668175009fb36ac6c12173c58be5 | [
"Apache-2.0"
] | permissive | lambdaxymox/lean4 | ae943c960a42247e06eff25c35338268d07454cb | 278d47c77270664ef29715faab467feac8a0f446 | refs/heads/master | 1,677,891,867,340 | 1,612,500,005,000 | 1,612,500,005,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 423 | 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
-/
prelude
import Init.Prelude
import Init.Notation
import Init.Core
import Init.Control
import Init.Data.Basic
import Init.WF
import Init.Data
import Init.Sys... |
2005388b0deb1eac1e6882da25fc2a198dd79df2 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/set_theory/surreal/basic.lean | fe4a17e045c3c2712f9f12d91ab1463543a7569e | [
"Apache-2.0"
] | permissive | hikari0108/mathlib | b7ea2b7350497ab1a0b87a09d093ecc025a50dfa | a9e7d333b0cfd45f13a20f7b96b7d52e19fa2901 | refs/heads/master | 1,690,483,608,260 | 1,631,541,580,000 | 1,631,541,580,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,149 | lean | /-
Copyright (c) 2019 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Scott Morrison
-/
import set_theory.game
/-!
# Surreal numbers
The basic theory of surreal numbers, built on top of the theory of combinatorial (pre-)games.
A pregam... |
bbcb4dc331cdea7e578aab42cad9166578acf984 | 853df553b1d6ca524e3f0a79aedd32dde5d27ec3 | /src/data/real/ennreal.lean | d4a304c5d4c440e68f7c836c86f779ddcf90eba3 | [
"Apache-2.0"
] | permissive | DanielFabian/mathlib | efc3a50b5dde303c59eeb6353ef4c35a345d7112 | f520d07eba0c852e96fe26da71d85bf6d40fcc2a | refs/heads/master | 1,668,739,922,971 | 1,595,201,756,000 | 1,595,201,756,000 | 279,469,476 | 0 | 0 | null | 1,594,696,604,000 | 1,594,696,604,000 | null | UTF-8 | Lean | false | false | 46,614 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl, Yury Kudryashov
Extended non-negative reals
-/
import data.real.nnreal
import data.set.intervals
noncomputable theory
open classical set
open_locale classical big_oper... |
01d621ff8a40a4b6369c3340dd1389085d89f7c6 | bb31430994044506fa42fd667e2d556327e18dfe | /src/data/real/cau_seq_completion.lean | 0769af1d4a5a53721f72c2e4c3b719e9f7251b03 | [
"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 | 12,776 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Robert Y. Lewis
-/
import data.real.cau_seq
/-!
# Cauchy completion
This file generalizes the Cauchy completion of `(ℚ, abs)` to the completion of a ring
with absolut... |
a009c05764e292f0a5232165e583e23c639f715a | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/group_theory/index.lean | ce2d7fe11c1514dd225488ff4fe3c67ab117bfa9 | [
"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 | 18,694 | lean | /-
Copyright (c) 2021 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import data.finite.card
import group_theory.finiteness
import group_theory.group_action.quotient
/-!
# Index of a Subgroup
> THIS FILE IS SYNCHRONIZED WITH MATHL... |
3c5f84e955bb135563faf274331adba43aa42443 | 07c6143268cfb72beccd1cc35735d424ebcb187b | /src/category_theory/differential_object.lean | a0bd5f53fa83f2cdec4bf25d1157a0a57beb268d | [
"Apache-2.0"
] | permissive | khoek/mathlib | bc49a842910af13a3c372748310e86467d1dc766 | aa55f8b50354b3e11ba64792dcb06cccb2d8ee28 | refs/heads/master | 1,588,232,063,837 | 1,587,304,803,000 | 1,587,304,803,000 | 176,688,517 | 0 | 0 | Apache-2.0 | 1,553,070,585,000 | 1,553,070,585,000 | null | UTF-8 | Lean | false | false | 3,773 | 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
import category_theory.shift
import category_theory.concrete_category
/-!
# Differential objects in a category.
A differen... |
de2bf278698c1185569030e251838483a2686053 | 3ed5a65c1ab3ce5d1a094edce8fa3287980f197b | /src/herstein/ex2_5/Q_13.lean | 6baf96c84b69a1082d06656dc5664e4cc0e5841e | [] | no_license | group-study-group/herstein | 35d32e77158efa2cc303c84e1ee5e3bc80831137 | f5a1a72eb56fa19c19ece0cb3ab6cf7ffd161f66 | refs/heads/master | 1,586,202,191,519 | 1,548,969,759,000 | 1,548,969,759,000 | 157,746,953 | 0 | 0 | null | 1,542,412,901,000 | 1,542,302,366,000 | Lean | UTF-8 | Lean | false | false | 962 | lean | import algebra.group group_theory.subgroup
variables {G: Type*}
def normaliser (a: G) [group G]: set G :=
{ x: G | a * x = x * a }
theorem Q_13 (a: G) [group G]:
is_subgroup (normaliser a) := {
one_mem := calc
a * 1 = 1 * a: by rw [mul_one, one_mul],
mul_mem := λ g h hg hh, calc
a * (g * h) = (a * g... |
0e6c3a09bc23ed86efdd123955cfbba46b937475 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/bitvec/core.lean | 3053d766e754ebd176ec9531c8678e6fb24edb71 | [
"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 | 8,794 | lean | /-
Copyright (c) 2015 Joe Hendrix. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joe Hendrix, Sebastian Ullrich
-/
import data.vector.basic
import data.nat.basic
/-!
# Basic operations on bitvectors
This is a work-in-progress, and contains additions to other theori... |
3ba0b3ea3b87171688fe58ee0586d299d6c13c19 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/model_theory/syntax.lean | d93d18ac26b9a2f68cbab8623e21ed28f533052e | [
"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 | 38,809 | lean | /-
Copyright (c) 2021 Aaron Anderson, Jesse Michael Han, Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson, Jesse Michael Han, Floris van Doorn
-/
import data.set.prod
import logic.equiv.fin
import model_theory.language_map
/-!
# Basics o... |
5214a4cccab376e34fe0d6365d13c3b5f98ff3cc | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/ring_theory/is_tensor_product.lean | e2d58cab89499ba6b69c063ec6fe2ad1dcb08911 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 14,674 | lean | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import ring_theory.tensor_product
import algebra.module.ulift
import logic.equiv.transfer_instance
/-!
# The characteristice predicate of tensor product
## Main definiti... |
727146b8679ae171b6df108087ca6b1358c0376f | 5c7fe6c4a9d4079b5457ffa5f061797d42a1cd65 | /src/exercises/src_25_intersection_and_union.lean | 0a5145ae9418ddd53c1453b4dbbe463bb032dce6 | [] | no_license | gihanmarasingha/mth1001_tutorial | 8e0817feeb96e7c1bb3bac49b63e3c9a3a329061 | bb277eebd5013766e1418365b91416b406275130 | refs/heads/master | 1,675,008,746,310 | 1,607,993,443,000 | 1,607,993,443,000 | 321,511,270 | 3 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,159 | lean | import tactic
import data.set
import logic.basic
open set
namespace mth1001
section intersection_and_union
-- We'll deal with sets on a type `U`.
variable U : Type*
variables A B C : set U
/-
Typing set notation in Lean:
`∪` is `\cup`
`∩` is `\cap`
`∈` is `\in`
`∉` is `\notin`
`∅` is `\empty`
-/
/-
Throughout t... |
ae2207a4acb831f7da62d5908c8025d6d910c49d | b73bd2854495d87ad5ce4f247cfcd6faa7e71c7e | /src/game/world1/level1.lean | 4a4045c63074fec4f68743d45b5b979fb9706264 | [] | 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 | 1,547 | lean | import category_theory.category.default
universes v u -- The order in this declaration matters: v often needs to be explicitly specified while u often can be omitted
namespace category_theory
variables (C : Type u) [category.{v} C]
/-
# Category world
## Level 1: Definition of category
A category `C` consists of... |
722fb7e52e66e2716d38b727ee062cc754579540 | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /tests/lean/mvar1.lean | 85b43409187ede997f0c9254d73e7a30b111ae60 | [
"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 | 3,097 | lean | import Lean.MetavarContext
open Lean
def check (b : Bool) : IO Unit :=
«unless» b (throw $ IO.userError "error")
def f := mkConst `f []
def g := mkConst `g []
def a := mkConst `a []
def b := mkConst `b []
def c := mkConst `c []
def b0 := mkBVar 0
def b1 := mkBVar 1
def b2 := mkBVar 2
def u := mkLevelParam `u
def ... |
8247c2fdc47eccc3e0d8e11dfed1f2d93751a104 | 592ee40978ac7604005a4e0d35bbc4b467389241 | /Library/generated/mathscheme-lean/RightSpindle_ShelfSig.lean | 4f32d6b3a2d475dce777d7a4facceb1b4cc435f2 | [] | 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 | 9,620 | 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 RightSpindle_ShelfSig
structure RightSpindle_ShelfSig (A : Type) : Type :=
(rinv : (A → (A → A)))
(rightDistributive : (∀ {x y z : A} , (rinv (rinv y z) x) = (r... |
823b1d4d2b50e4fcc159cd4985bf475077ea6ae7 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/char_zero/infinite.lean | e204f5bbb4c8445b0d55a9934d10cea37a865027 | [
"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 | 587 | 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 algebra.char_zero.defs
import data.fintype.card
/-! # A characteristic-zero semiring is infinite
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to... |
0ba8255d55e331495c9947aaf767974629c08bd4 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/order/succ_pred/relation.lean | 5f1e0fc2b37a179ac40d2ebb47f66d3dde590d06 | [
"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 | 6,740 | lean | /-
Copyright (c) 2022 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import order.succ_pred.basic
/-!
# Relations on types with a `succ_order`
This file contains properties about relations on types with a `succ_order`
and their cl... |
d53ebb47741dbacd7b44a2c3c247f25c2837e7e3 | 76ce87faa6bc3c2aa9af5962009e01e04f2a074a | /HW/06_properties.lean | af81e15c7b00203e1a8a879ad134476fcc40b463 | [] | no_license | Mnormansell/Discrete-Notes | db423dd9206bbe7080aecb84b4c2d275b758af97 | 61f13b98be590269fc4822be7b47924a6ddc1261 | refs/heads/master | 1,585,412,435,424 | 1,540,919,483,000 | 1,540,919,483,000 | 148,684,638 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,090 | lean | /-
HOMEWORK: Read, complete, submit.
We've seen that equality is reflexive.
That is, everything is equal to itself.
It is also symmetric in the sense that
if any value, a, is equal to some other
value, b, i.e., if a = b, then b is also
equal to a, i.e., b = a.
What this means is we have an inference
rule that bot... |
73eef7507d0b3daa462e12fdb6f53973546b923a | 01ae0d022f2e2fefdaaa898938c1ac1fbce3b3ab | /categories/universal/types/default.lean | 7bab95315f85e2ffdec10505ad0f8c51b2b1ab8b | [] | no_license | PatrickMassot/lean-category-theory | 0f56a83464396a253c28a42dece16c93baf8ad74 | ef239978e91f2e1c3b8e88b6e9c64c155dc56c99 | refs/heads/master | 1,629,739,187,316 | 1,512,422,659,000 | 1,512,422,659,000 | 113,098,786 | 0 | 0 | null | 1,512,424,022,000 | 1,512,424,022,000 | null | UTF-8 | Lean | false | false | 1,640 | lean | import ...types
import ..instances
open categories.universal
open categories.isomorphism
namespace categories.types
definition {u} Types_has_Products : has_Products CategoryOfTypes.{u} := {
product := λ I φ, {
product := Π i : I, φ i,
projection := λ i x, x i,
map := λ Z f z i, f i z,... |
7905a58910d100bc443196b5c36a634a7b3a2d7d | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/measure_theory/constructions/pi.lean | 0495faa795381def0baf8ce421dad3adf158b0c1 | [
"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 | 32,886 | lean | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import measure_theory.constructions.prod
/-!
# Product measures
In this file we define and prove properties about finite products of measures
(and at some point... |
3ee0cf79bb62bb58b0650d2e46489ed07ae1d2ed | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/run/meta2.lean | 50dca8fb081be60f2987b39f953362fe91141984 | [
"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 | 18,281 | lean | import Lean.Meta
open Lean
open Lean.Meta
-- set_option trace.Meta true
--set_option trace.Meta.isDefEq.step false
-- set_option trace.Meta.isDefEq.delta false
set_option trace.Meta.debug true
def print (msg : MessageData) : MetaM Unit := do
trace[Meta.debug] msg
def checkM (x : MetaM Bool) : MetaM Unit :=
unless (←... |
8230e5563170e353ee87b90293c5db9f55a26a0d | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/measure_theory/decomposition/jordan.lean | e8d762e73b939b404f54db5b50d1a6dda0a9ceaa | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 25,172 | lean | /-
Copyright (c) 2021 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import measure_theory.decomposition.signed_hahn
import measure_theory.measure.mutually_singular
/-!
# Jordan decomposition
This file proves the existence and uniqueness o... |
bc1270fa3dc7db3e9ae51c634762d6eac4a736d1 | 2f8bf12144551bc7d8087a6320990c4621741f3d | /tests/playground/binarytrees.lean | d5bbabbdeedb968efd7208dee50a966c8e55f25f | [
"Apache-2.0"
] | permissive | jesse-michael-han/lean4 | eb63a12960e69823749edceb4f23fd33fa2253ce | fa16920a6a7700cabc567aa629ce4ae2478a2f40 | refs/heads/master | 1,589,935,810,594 | 1,557,177,860,000 | 1,557,177,860,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,626 | lean | inductive Tree
| Nil
| Node (l r : Tree) : Tree
open Tree
-- This Function has an extra argument to suppress the
-- Common Sub-expression Elimination optimization
def make' : UInt32 -> UInt32 -> Tree
| n d :=
if d = 0 then Node Nil Nil
else Node (make' n (d - 1)) (make' (n + 1) (d - 1))
-- build a tree
def make (... |
221df3475fa2f8c8f50cf388ea486200aa4255cc | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/star/module.lean | 3bc5edfa0e127c1e73a54f5a3de2512d2cf2bd16 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 5,962 | lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Frédéric Dupuis
-/
import algebra.star.self_adjoint
import algebra.module.equiv
import linear_algebra.prod
/-!
# The star operation, bundled as a star-linear equiv
> THIS F... |
3a06f4f62b35cdf762e2e2b9ad5b2e7ce0919446 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/tactic/omega/nat/neg_elim.lean | 8cc42923a421fe0fbca3e7bd2b3d8fbb1219c1ab | [
"Apache-2.0"
] | permissive | rmitta/mathlib | 8d90aee30b4db2b013e01f62c33f297d7e64a43d | 883d974b608845bad30ae19e27e33c285200bf84 | refs/heads/master | 1,585,776,832,544 | 1,576,874,096,000 | 1,576,874,096,000 | 153,663,165 | 0 | 2 | Apache-2.0 | 1,544,806,490,000 | 1,539,884,365,000 | Lean | UTF-8 | Lean | false | false | 3,818 | lean | /-
Copyright (c) 2019 Seul Baek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Seul Baek
Negation elimination.
-/
import tactic.omega.nat.form
namespace omega
namespace nat
open_locale omega.nat
@[simp] def push_neg : form → form
| (p ∨* q) := (push_neg p) ∧* (pus... |
7ac67768f01a5bf10c2d62073f40012cf361abbf | b147e1312077cdcfea8e6756207b3fa538982e12 | /tests/tactics.lean | 9e613b31e4b9f8534e113a367bee09303956318f | [
"Apache-2.0"
] | permissive | SzJS/mathlib | 07836ee708ca27cd18347e1e11ce7dd5afb3e926 | 23a5591fca0d43ee5d49d89f6f0ee07a24a6ca29 | refs/heads/master | 1,584,980,332,064 | 1,532,063,841,000 | 1,532,063,841,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,753 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import tactic data.set.lattice data.prod
section solve_by_elim
example {a b : Prop} (h₀ : a → b) (h₁ : a) : b :=
begin
apply_assumption,
apply_assumption,
end
example... |
85fc8bc73fd0146dc041ef951da9d31faf5850bb | 4fa118f6209450d4e8d058790e2967337811b2b5 | /src/examples/empty.lean | 95858f3eca515415761ae5c5dbfd7f7d2336a617 | [
"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 | 1,991 | lean | import data.padics.padic_numbers
import for_mathlib.punit_instances
import perfectoid_space
/-!
# An example of a perfectoid space
In this file we show that the empty space is perfectoid.
Every nonempty example requires a non-trivial amount of mathematical effort.
-/
/-- The structure presheaf on the empty space. ... |
7079a02b6de964b52fa3e1516f8b41bc4b03150a | ee8cdbabf07f77e7be63a449b8483ce308d37218 | /lean/src/test/mathd-algebra-156.lean | ebc531cd6cee50db145a9de6c158c53089d31da9 | [
"MIT",
"Apache-2.0"
] | permissive | zeta1999/miniF2F | 6d66c75d1c18152e224d07d5eed57624f731d4b7 | c1ba9629559c5273c92ec226894baa0c1ce27861 | refs/heads/main | 1,681,897,460,642 | 1,620,646,361,000 | 1,620,646,361,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 360 | lean | /-
Copyright (c) 2021 OpenAI. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kunhao Zheng
-/
import data.real.basic
example (x y : ℝ) (f g : ℝ → ℝ) (h₀ : ∀t, f t = t^4) (h₁ : ∀t, g t = 5 * t^2 - 6) (h₂ : f x = g x) (h₃ : f y = g y) (h₄ : x^2 < y^2) : y^2 - x^2 = 1 :=
... |
9610ef05f3005a38a4b10f39a120fcb65602c043 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/analysis/normed/group/add_torsor.lean | 0e1f3e2a565d97de69c42bf6dd7323af5897b0b3 | [
"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 | 10,793 | lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Yury Kudryashov
-/
import analysis.normed.group.basic
import linear_algebra.affine_space.affine_subspace
import linear_algebra.affine_space.midpoint
/-!
# Torsors of addit... |
9cf1139df4bb7af0dd2b71370fa965c17d38e7f4 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/category_theory/category/preorder.lean | 3055687f8ece27f7b9c7d58d17767fdd9b34359f | [
"Apache-2.0"
] | permissive | hikari0108/mathlib | b7ea2b7350497ab1a0b87a09d093ecc025a50dfa | a9e7d333b0cfd45f13a20f7b96b7d52e19fa2901 | refs/heads/master | 1,690,483,608,260 | 1,631,541,580,000 | 1,631,541,580,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,903 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stephen Morgan, Scott Morrison, Johannes Hölzl, Reid Barton
-/
import category_theory.category.Cat
import category_theory.category.default
import category_theory.opposites
import orde... |
e2ff6718c254f3b4690aaedad6a56caeeafd583e | 1a61aba1b67cddccce19532a9596efe44be4285f | /hott/core.hlean | dfaa9b191823cd23bf08048f0dc4aa4b66c2be63 | [
"Apache-2.0"
] | permissive | eigengrau/lean | 07986a0f2548688c13ba36231f6cdbee82abf4c6 | f8a773be1112015e2d232661ce616d23f12874d0 | refs/heads/master | 1,610,939,198,566 | 1,441,352,386,000 | 1,441,352,494,000 | 41,903,576 | 0 | 0 | null | 1,441,352,210,000 | 1,441,352,210,000 | null | UTF-8 | Lean | false | false | 255 | 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
The core of the HoTT library
-/
import types
import cubical
import hit.circle
import algebra.hott
|
63b13f086c277ee7b07cafb3dd74dbc625df1532 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/analysis/normed_space/affine_isometry.lean | 859a7d258b3b726fba8cbe863935e5bc65611b66 | [
"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 | 21,954 | lean | /-
Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import analysis.normed_space.add_torsor
import analysis.normed_space.linear_isometry
/-!
# Affine isometries
In this file we define `affine_isometry 𝕜 P P₂` to b... |
ec701e94e3e2cd3fcc117c9c27dd4ef9fbbc0483 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /src/Lean/Compiler/ImplementedByAttr.lean | cc017e309d35eca9d8da3ed32243019745bc6fb0 | [
"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 | 2,052 | 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.Attributes
import Lean.Declaration
import Lean.MonadEnv
import Lean.Elab.InfoTree
namespace Lean.Compiler
builtin_initialize implementedByAttr... |
23a728ed85725f2e6e14eb842fedf78405b17bd6 | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/topology/Top/opens.lean | 57e8869b2fc47edf47ca9c57998f2e84ffde6fcc | [
"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 | 3,944 | 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 topology.Top.basic
import category_theory.natural_isomorphism
import category_theory.opposites
import category_theory.eq_to_hom
import topology.opens
open cat... |
96726a4d7b7816ef1eabb505c5a27e8c1bc01325 | 853df553b1d6ca524e3f0a79aedd32dde5d27ec3 | /src/data/quot.lean | 374ab2920a20e8c384d8f5f277dfe1d171f74e88 | [
"Apache-2.0"
] | permissive | DanielFabian/mathlib | efc3a50b5dde303c59eeb6353ef4c35a345d7112 | f520d07eba0c852e96fe26da71d85bf6d40fcc2a | refs/heads/master | 1,668,739,922,971 | 1,595,201,756,000 | 1,595,201,756,000 | 279,469,476 | 0 | 0 | null | 1,594,696,604,000 | 1,594,696,604,000 | null | UTF-8 | Lean | false | false | 16,160 | 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 logic.relator
/-!
# Quotients -- extends the core library
-/
variables {α : Sort*} {β : Sort*}
namespace setoid
lemma ext {α : Sort*} :
∀{s t : setoid α}... |
9c5c204dd18f7c0e35bcf9acf574296b66571623 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/order/conditionally_complete_lattice.lean | 254f3e7ce670c856a9ccedc9de3ac66edd3bfa02 | [
"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 | 50,064 | lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import data.set.intervals.ord_connected
/-!
# Theory of conditionally complete lattices.
A conditionally complete lattice is a lattice in which every non-empt... |
fc44fba508bcfd63eb811eccd4d2793e975eabba | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/tactic/omega/find_ees.lean | 83968c777d89856f5e8728ef1e4f02ca9ad19dbb | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 5,568 | lean | /-
Copyright (c) 2019 Seul Baek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Seul Baek
-/
/-
A tactic for finding a sequence of equality
elimination rules for a given set of constraints.
-/
import tactic.omega.eq_elim
variables {α β : Type}
open tactic
namespac... |
69b86af4cd3f7403a31833af147b35eba3642d1e | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/order/with_zero.lean | 33eba665df98db3271bfa1ba42fd3f71a87c2faf | [
"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 | 12,922 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Johan Commelin, Patrick Massot
-/
import algebra.order.group
import tactic.abel
/-!
# Linearly ordered commutative groups and monoids with a zero element adjoined
This file se... |
34c4f6e7a9fab6cee39bce0e8077eb8357013d55 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/list/func_auto.lean | 81a67a6e69af13ec8da519fda9ee9bd7c20dbd8c | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,554 | lean | /-
Copyright (c) 2019 Seul Baek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Seul Baek
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.nat.basic
import Mathlib.PostPort
universes u v w
namespace Mathlib
namespace list
namespa... |
0079335e814b77ff6fe5a49eeb6357714d6a65ef | b3fced0f3ff82d577384fe81653e47df68bb2fa1 | /src/measure_theory/measurable_space.lean | c2b53de9234062096219ed48c6bf98f191147cdc | [
"Apache-2.0"
] | permissive | ratmice/mathlib | 93b251ef5df08b6fd55074650ff47fdcc41a4c75 | 3a948a6a4cd5968d60e15ed914b1ad2f4423af8d | refs/heads/master | 1,599,240,104,318 | 1,572,981,183,000 | 1,572,981,183,000 | 219,830,178 | 0 | 0 | Apache-2.0 | 1,572,980,897,000 | 1,572,980,896,000 | null | UTF-8 | Lean | false | false | 42,876 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
Measurable spaces -- σ-algberas
-/
import data.set.disjointed order.galois_connection data.set.countable
/-!
# Measurable spaces and measurable functio... |
233b9ce75ef2da9ad5bc14c28ec1556ac73c9896 | b815abf92ce063fe0d1fabf5b42da483552aa3e8 | /library/init/algebra/ordered_ring.lean | 42beca9c0df3a6a944db85b381e0111ebc28d25f | [
"Apache-2.0"
] | permissive | yodalee/lean | a368d842df12c63e9f79414ed7bbee805b9001ef | 317989bf9ef6ae1dec7488c2363dbfcdc16e0756 | refs/heads/master | 1,610,551,176,860 | 1,481,430,138,000 | 1,481,646,441,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,705 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
-/
prelude
import init.algebra.ordered_group init.algebra.ring
/- Make sure instances defined in this file have lower priority than the ones
... |
9ada85f1715912d7b454004277a00c60b6461beb | d642a6b1261b2cbe691e53561ac777b924751b63 | /src/category_theory/endomorphism.lean | d505bbdad6622a635db87b91d26043912bcb8330 | [
"Apache-2.0"
] | permissive | cipher1024/mathlib | fee56b9954e969721715e45fea8bcb95f9dc03fe | d077887141000fefa5a264e30fa57520e9f03522 | refs/heads/master | 1,651,806,490,504 | 1,573,508,694,000 | 1,573,508,694,000 | 107,216,176 | 0 | 0 | Apache-2.0 | 1,647,363,136,000 | 1,508,213,014,000 | Lean | UTF-8 | Lean | false | false | 2,805 | lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Scott Morrison, Simon Hudon
Definition and basic properties of endomorphisms and automorphisms of an object in a category.
-/
import category_theory.category catego... |
fa99661a34d663f3a6892f0e5d022e32fcfd875d | a7dd8b83f933e72c40845fd168dde330f050b1c9 | /src/data/nat/enat.lean | 32c0c7150826c7eb25bf9485ff121c12cadc8aff | [
"Apache-2.0"
] | permissive | NeilStrickland/mathlib | 10420e92ee5cb7aba1163c9a01dea2f04652ed67 | 3efbd6f6dff0fb9b0946849b43b39948560a1ffe | refs/heads/master | 1,589,043,046,346 | 1,558,938,706,000 | 1,558,938,706,000 | 181,285,984 | 0 | 0 | Apache-2.0 | 1,568,941,848,000 | 1,555,233,833,000 | Lean | UTF-8 | Lean | false | false | 7,886 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
Natural numbers with infinity, represented as roption ℕ.
-/
import data.pfun algebra.ordered_group
import tactic.norm_cast
open roption lattice
def enat : Type := roption... |
e2277ea9d907bf8f96ea9f60b1874eb0b450f456 | efce24474b28579aba3272fdb77177dc2b11d7aa | /src/homotopy_theory/formal/cofibrations/track.lean | e2ae9af2e0b6347725cd29dd73f3650529fafe02 | [
"Apache-2.0"
] | permissive | rwbarton/lean-homotopy-theory | cff499f24268d60e1c546e7c86c33f58c62888ed | 39e1b4ea1ed1b0eca2f68bc64162dde6a6396dee | refs/heads/lean-3.4.2 | 1,622,711,883,224 | 1,598,550,958,000 | 1,598,550,958,000 | 136,023,667 | 12 | 6 | Apache-2.0 | 1,573,187,573,000 | 1,528,116,262,000 | Lean | UTF-8 | Lean | false | false | 26,209 | lean | import category_theory.assoc_pushouts
import category_theory.eq_to_hom
import category_theory.groupoid
import category_theory.transport
import .homotopy
universes v u
open category_theory
open category_theory.category
local notation f ` ∘ `:80 g:80 := g ≫ f
namespace homotopy_theory.cofibrations
open homotopy_theory... |
dc93b59824d22018112d585d8ba6040aa8d5678c | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/module/default_auto.lean | b7c6c8a35165650f14e6528d674811fb6c5dbf7c | [] | 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 | 341 | lean | /-
Copyright (c) 2020 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.algebra.module.basic
import Mathlib.algebra.module.submodule
import Mathlib.PostPort
namespace... |
7da348de536dd3ddf9a779b8e57bab81a15f7c0a | 6fca17f8d5025f89be1b2d9d15c9e0c4b4900cbf | /src/game/world5/level3.lean | e2cf5e9240bbdd024753647f58681da5369fd2b1 | [
"Apache-2.0"
] | permissive | arolihas/natural_number_game | 4f0c93feefec93b8824b2b96adff8b702b8b43ce | 8e4f7b4b42888a3b77429f90cce16292bd288138 | refs/heads/master | 1,621,872,426,808 | 1,586,270,467,000 | 1,586,270,467,000 | 253,648,466 | 0 | 0 | null | 1,586,219,694,000 | 1,586,219,694,000 | null | UTF-8 | Lean | false | false | 3,713 | lean | /- Tactic : have
## Summary
`have h : P,` will create a new goal of creating a term of type `P`,
and will add `h : P` to the hypotheses for the goal you were working on.
## Details
If you want to name a term of some type (because you want it
in your local context for some reason), and if you have the
formula for th... |
9e006922a0498e0c1f964ab58812fc37f39ac011 | fecda8e6b848337561d6467a1e30cf23176d6ad0 | /src/ring_theory/ideal/basic.lean | 4469f485973aa99d3a8ce2f211ef6600d35f459b | [
"Apache-2.0"
] | permissive | spolu/mathlib | bacf18c3d2a561d00ecdc9413187729dd1f705ed | 480c92cdfe1cf3c2d083abded87e82162e8814f4 | refs/heads/master | 1,671,684,094,325 | 1,600,736,045,000 | 1,600,736,045,000 | 297,564,749 | 1 | 0 | null | 1,600,758,368,000 | 1,600,758,367,000 | null | UTF-8 | Lean | false | false | 31,677 | 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 algebra.associated
import linear_algebra.basic
import order.zorn
/-!
# Ideals over a ring
This file defines `ideal R`, the type of ideals... |
3e043c5fce474e5e3735b854d7c1dc8e9d420f78 | 947b78d97130d56365ae2ec264df196ce769371a | /src/Lean/Elab/DeclModifiers.lean | 0bab18eabd1d5fc27db863db78abeadf6569438e | [
"Apache-2.0"
] | permissive | shyamalschandra/lean4 | 27044812be8698f0c79147615b1d5090b9f4b037 | 6e7a883b21eaf62831e8111b251dc9b18f40e604 | refs/heads/master | 1,671,417,126,371 | 1,601,859,995,000 | 1,601,860,020,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,633 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
import Lean.Modifiers
import Lean.Elab.Attributes
import Lean.Elab.Exception
import Lean.Elab.DeclUtil
namespace Lean
namespace Elab
de... |
3fa076b712d9f71d59e5033f885a44a47d49ab4f | a721fe7446524f18ba361625fc01033d9c8b7a78 | /elaborate/add_comm_2.lean | 5113d5434a7cbbecf5e7709c737b3911a0637b69 | [] | no_license | Sterrs/leaning | 8fd80d1f0a6117a220bb2e57ece639b9a63deadc | 3901cc953694b33adda86cb88ca30ba99594db31 | refs/heads/master | 1,627,023,822,744 | 1,616,515,221,000 | 1,616,515,221,000 | 245,512,190 | 2 | 0 | null | 1,616,429,050,000 | 1,583,527,118,000 | Lean | UTF-8 | Lean | false | false | 2,343 | lean | λ (m n : mynat),
(mynat.rec
⟨λ (m : mynat),
eq.rec (eq.refl m)
(eq.rec (eq.refl (m = add zero m))
(eq.rec (eq.refl (m = add zero m))
((mynat.rec ⟨eq.refl zero, punit.star⟩
(λ (n : mynat)
(ih :
pprod (ad... |
92c9e3d48a0c3068bc226c8a160d0104a7869720 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/category_theory/monad/monadicity.lean | be665e374b78a211c241074abd8e994f3d0fb9ee | [
"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 | 14,985 | 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.reflexive
import category_theory.limits.preserves.limits
import category_theory.monad.limits
import category_theory.monad.coequalize... |
35119052860df7a7a10943fb92270b01413c2a29 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/errorOnInductionForNested.lean | fc7d5dfc429afe22e5a9b7307ccf8edb7a68145d | [
"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 | 209 | lean | inductive LazyList (α : Type u)
| nil : LazyList α
| cons (hd : α) (tl : LazyList α) : LazyList α
| delayed (t : Thunk (LazyList α)) : LazyList α
example (as : LazyList α) : True := by
induction as
|
5d20052f015d166bcd6a552a82bb138c774dafa5 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/group_theory/abelianization.lean | c2915d7a3684051efa4c7164d0b2925dc1aed5b5 | [
"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 | 10,559 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Michael Howes
-/
import data.finite.card
import group_theory.commutator
import group_theory.finiteness
/-!
# The abelianization of a group
> THIS FILE IS SYNCHRONIZED WITH MATH... |
f95ca3e7532af416c51833108b81dcbd899129c8 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /library/theories/number_theory/irrational_roots.lean | 11ad148bd7ec82b10b82fe9045d1590fd8a6da8d | [
"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 | 7,174 | 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
/- First, a te... |
b44356a18285bc978e984a321923ec8298bc1f91 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/free_algebra.lean | fc2e81ca3a5b327992dafc87418f02a15c4347df | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,107 | lean | /-
Copyright (c) 2020 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Scott Morrison, Adam Topaz.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.algebra.subalgebra
import Mathlib.algebra.monoid_algebra
import Mathlib.lin... |
46d69e3487ec781e3e5fb00c6badb14bd7cb0618 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/real/ereal.lean | 0e7f0f8f7d11269f7cec71297db11623119850b9 | [
"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 | 40,906 | lean | /-
Copyright (c) 2019 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard
-/
import data.real.basic
import data.real.ennreal
import data.sign
/-!
# The extended reals [-∞, ∞].
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this fi... |
81844f2c27bc0a47604952d32495206c266ee6f2 | cf39355caa609c0f33405126beee2739aa3cb77e | /library/init/meta/constructor_tactic.lean | 28d07ab5944b052220c6ac478c5c0762754c70bd | [
"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 | 3,281 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.meta.tactic init.function
namespace tactic
/-- Return target after instantiating metavars and whnf -/
private meta def target' : tacti... |
669b99eb00a266a389ad6f4a680d10880218c9c4 | 86ee6b815fda4c9a5aa42e17b61336a913552e60 | /src/tactics/equality.lean | 4a8e54f125312ed7d63c0e87073ea2ff5438a38a | [
"Apache-2.0"
] | permissive | fgdorais/lean-groupoids | 6487f6d84427a757708fd4e795038ab159cc4f2c | 54d1582f8d6ae642fc818e7672ac1c49fe7733e5 | refs/heads/master | 1,587,778,056,386 | 1,551,055,383,000 | 1,551,055,383,000 | 172,408,995 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,249 | lean | /-
Copyright © 2019 François G. Dorais. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
-/
import .groupoids.paths
namespace tactic
meta def match_ne' : expr → tactic (expr × expr)
| `(%%a ≠ %%b) := return (a,b)
| `(¬ %%a = %%b) := return (a,b)
| _ := failed
meta def eq_grou... |
a4da74f1a0f1eede3cefb28b790058c1c2a9a97f | 5bf112cf7101c6c6303dc3fd0b3179c860e61e56 | /lean/background/util.lean | ccbbc63a0aea1424b47b9fd770f2314b381bd40e | [
"Apache-2.0"
] | permissive | fredfeng/formal-encoding | 7ab645f49a553dfad2af03fcb4289e40fc679759 | 024efcf58672ac6b817caa10dfe8cd9708b07f1b | refs/heads/master | 1,597,236,551,123 | 1,568,832,149,000 | 1,568,832,149,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,254 | lean | axiom SKIP {X : Type} : X
axiom SORRY {P : Prop} : P
namespace Nat
def fact : Nat -> Nat
| 0 => 1
| 1 => 1
| n+1 => (n+1) * fact n
def choose (n : Nat) (k : Fin n) : Nat :=
n.fact / (k.val.fact * (n-k.val).fact)
end Nat
namespace Fin
def cadd {n : Nat} {k₁ k₂ : Fin n} : Fin n :=
⟨(k₁.val + k₂.val) % n, SORRY⟩
no... |
1a7611f775f8dd4fa2f7d3fed42dd0585a2f6843 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/order/category/omega_complete_partial_order.lean | 65d74186c9172b46ea0e6090c17f30d87fc2de7d | [
"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 | 4,223 | lean | /-
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import order.omega_complete_partial_order
import category_theory.limits.shapes.products
import category_theory.limits.shapes.equalizers
import category_theory.limits.const... |
112dee5d8a80bb860df773eef1a7e98c9949d0d7 | ee8cdbabf07f77e7be63a449b8483ce308d37218 | /lean/src/test/amc12-2000-p6.lean | 1e18df28e574630ac6df7d43b0ff013ca961943e | [
"MIT",
"Apache-2.0"
] | permissive | zeta1999/miniF2F | 6d66c75d1c18152e224d07d5eed57624f731d4b7 | c1ba9629559c5273c92ec226894baa0c1ce27861 | refs/heads/main | 1,681,897,460,642 | 1,620,646,361,000 | 1,620,646,361,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 333 | lean | /-
Copyright (c) 2021 OpenAI. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kunhao Zheng
-/
import data.nat.prime
example (p q : ℕ) (h₀ : nat.prime p ∧ nat.prime q) (h₁ : 4 ≤ p ∧ p ≤ 18) (h₂ : 4 ≤ q ∧ q ≤ 18) : p * q - ( p + q ) ≠ 194 :=
begin
sorry
end
|
cadd55482c0359d8c91dd0a0875d8f35b543d605 | 8d65764a9e5f0923a67fc435eb1a5a1d02fd80e3 | /src/algebra/module/submodule_lattice.lean | 5701c0062d2ab7bcff285f02e200bbbe53dc677a | [
"Apache-2.0"
] | permissive | troyjlee/mathlib | e18d4b8026e32062ab9e89bc3b003a5d1cfec3f5 | 45e7eb8447555247246e3fe91c87066506c14875 | refs/heads/master | 1,689,248,035,046 | 1,629,470,528,000 | 1,629,470,528,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,174 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov
-/
import algebra.module.submodule
import algebra.punit_instances
/-!
# The lattice structure on `submodule`s
This file... |
2c6e723934a08e457a0dcf7d027a8bf6661874ff | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebraic_geometry/AffineScheme.lean | 827f2d0f8852ba930573a8779d5263cd60b1ba2a | [
"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 | 32,256 | lean | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import algebraic_geometry.Gamma_Spec_adjunction
import algebraic_geometry.open_immersion.Scheme
import category_theory.limits.opposites
import ring_theory.localization.inv_... |
c678d1160145cbc77737be484ae0a3a509b9646c | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/t6.lean | 2729808e0a2044351354907ad49a733c4424a05e | [
"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 | 343 | lean | prelude definition Prop : Type.{1} := Type.{0}
section
variable {A : Type*} -- Mark A as implicit parameter
variable R : A → A → Prop
definition id (a : A) : A := a
definition refl : Prop := forall (a : A), R a a
definition symm : Prop := forall (a b : A), R a b -> R b a
end
check id.{2}
check refl.... |
883a9945e5802a032425d93eb7bbb336b0936245 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/analysis/mean_inequalities.lean | 4da258c008edf41b99704c5eed82dcff5a413ea5 | [
"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 | 33,112 | lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne
-/
import analysis.convex.specific_functions
import data.real.conjugate_exponents
/-!
# Mean value inequalities
In this file we prov... |
2bf48166e5261af31d4c51b04edb8bc8a390e3c5 | 6f510b1ed724f95a55b7d26a8dcd13e1264123dd | /src/help.lean | ae75786763b57ae588f24ffce23f4a20482cc569 | [] | no_license | jcommelin/oberharmersbach2019 | adaf2e54ba4eff7c178c933978055ff4d6b0593b | d2cdf780a10baa8502a9b0cae01c7efa318649a6 | refs/heads/master | 1,587,558,516,731 | 1,550,558,213,000 | 1,550,558,213,000 | 170,372,753 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 881 | lean | import tactic.interactive tactic.tidy
namespace nat
lemma dvd_add_iff_right_of_left (k m n : ℕ) (h : k ∣ m) :
k ∣ n ↔ k ∣ m + n :=
nat.dvd_add_iff_right h
lemma dvd_right_of_dvd_add_of_dvd_left (k m n : ℕ) (h : k ∣ m) :
k ∣ m + n → k ∣ n :=
(dvd_add_iff_right_of_left _ _ _ h).mpr
end nat
namespace tactic
names... |
702def3de3793431a919000c0c22a2fe5bf71d66 | 46125763b4dbf50619e8846a1371029346f4c3db | /src/set_theory/cardinal.lean | b750ab7bd894315ca579337d0dbe49918cbd0b30 | [
"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 | 45,226 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl, Mario Carneiro
-/
import data.set.countable data.quot logic.function set_theory.schroeder_bernstein
import data.fintype.card
/-!
# Cardinal Numbers
We define cardinal... |
eca900c78e2c83ca4d962db454420d7b0c97bc72 | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/measure_theory/measure/hausdorff.lean | c6278be73ab7048ca36a85a886e6101e94f546dd | [
"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 | 43,618 | 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 topology.metric_space.metric_separated
import measure_theory.constructions.borel_space
import measure_theory.measure.lebesgue
import analysis.special_functio... |
a24e5d3b994ab50ecf3a149aa1143685db36ab96 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/algebra/big_operators/intervals.lean | baf2ae60a8fafa6eaf6c4fd8f47a5d6753f15612 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 10,559 | 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.module.basic
import data.nat.interval
import tactic.linarith
import tactic.abel
/-!
# Results about big operators ... |
700baf024d7911dad55e599b2554784af069fb96 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/lake/Lake/Config/Workspace.lean | 8bbba8fc14a351ed37c0987493d985cb5908d99f | [
"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 | 8,038 | lean | /-
Copyright (c) 2021 Mac Malone. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mac Malone
-/
import Lean.Util.Paths
import Lake.Config.FacetConfig
import Lake.Config.TargetConfig
import Lake.Config.Env
import Lake.Util.Log
open System
namespace Lake
/-- A Lake wor... |
96948a656b233dc5c39a701c061409a9d1f5a74c | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /stage0/src/Lean/Elab/PatternVar.lean | 3dabeae54c5b26e692b47ea4ed81482a25b650bd | [
"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 | 13,894 | 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
-/
import Lean.Meta.Match.MatchPatternAttr
import Lean.Elab.Arg
import Lean.Elab.MatchAltView
namespace Lean.Elab.Term
open Meta
abbrev PatternVar := Syntax... |
360fc1a3326025af1ebfb4e02666fd9fa6687d1a | 618003631150032a5676f229d13a079ac875ff77 | /src/category_theory/limits/shapes/finite_products.lean | 7b29e557f98c385b3fb01a3b42f99dcd6bfcd85b | [
"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 | 1,619 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.limits.shapes.finite_limits
universes v u
open category_theory
namespace category_theory.limits
variables (C : Type u) [category.{v} C]
cla... |
14894c1b17c4c90d0854bde7ea54a33bd526bb86 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/group_theory/free_product.lean | a20b6ee73241f4d2a915bf5cd2eee86b95afe91a | [
"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 | 33,850 | lean | /-
Copyright (c) 2021 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn, Joachim Breitner
-/
import algebra.free_monoid
import group_theory.congruence
import group_theory.is_free_group
import group_theory.subgroup.pointwise
import data.list.chain
im... |
8f6500f4a204bb2bce9fb057c6ff392e416dc042 | 947b78d97130d56365ae2ec264df196ce769371a | /src/Lean/Elab/Import.lean | f30c0fc9728753859edbcc7d966a3d2c34706be8 | [
"Apache-2.0"
] | permissive | shyamalschandra/lean4 | 27044812be8698f0c79147615b1d5090b9f4b037 | 6e7a883b21eaf62831e8111b251dc9b18f40e604 | refs/heads/master | 1,671,417,126,371 | 1,601,859,995,000 | 1,601,860,020,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,970 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
import Lean.Parser.Module
namespace Lean
namespace Elab
def headerToImports (header : Syntax) : List Import :=
let header := header.as... |
bea81113fc6447e168825dc23be3722f810c1a46 | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/linear_algebra/exterior_algebra.lean | 351d9230a7e6f97400e2cdbfa3ef3b2e86817824 | [
"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 | 4,547 | lean | /-
Copyright (c) 2020 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhangir Azerbayev, Adam Topaz, Eric Wieser.
-/
import algebra.ring_quot
import linear_algebra.tensor_algebra
import group_theory.perm.sign
/-!
# Exterior Algebras
We construct the exter... |
3fa4b5a442a770b53a3cdcc4dad9f94cd2e147b2 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /stage0/src/Lean/Elab/Deriving/Repr.lean | 3e15d5e996cf3702116d48324e2dad12c13df923 | [
"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 | 5,130 | 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.Transform
import Lean.Meta.Inductive
import Lean.Elab.Deriving.Basic
import Lean.Elab.Deriving.Util
namespace Lean.Elab.Deriving.Repr
open... |
55e8fbcd4f2fd1b8895f89aebf3cd5a5649fdc2b | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/field_theory/mv_polynomial.lean | 7a34d1b8629116cc4726162cfa9b34fc89d7a835 | [
"Apache-2.0"
] | permissive | dupuisf/mathlib | 62de4ec6544bf3b79086afd27b6529acfaf2c1bb | 8582b06b0a5d06c33ee07d0bdf7c646cae22cf36 | refs/heads/master | 1,669,494,854,016 | 1,595,692,409,000 | 1,595,692,409,000 | 272,046,630 | 0 | 0 | Apache-2.0 | 1,592,066,143,000 | 1,592,066,142,000 | null | UTF-8 | Lean | false | false | 9,571 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
Multivariate functions of the form `α^n → α` are isomorphic to multivariate polynomials in
`n` variables.
-/
import linear_algebra.finsupp_vector_space
import field_theo... |
f22f2353e9de7a7556057ba678fff1fb64ac098b | c777c32c8e484e195053731103c5e52af26a25d1 | /src/measure_theory/integral/divergence_theorem.lean | 17ecec3e87575b25f8daa8883fcce3e1465da404 | [
"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 | 30,101 | 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.box_integral.divergence_theorem
import analysis.box_integral.integrability
import measure_theory.integral.interval_integral
/-!
# Divergence theore... |
c5a0740eacbd6d6109c138e646f8249941264a4f | 137c667471a40116a7afd7261f030b30180468c2 | /src/analysis/special_functions/exp_log.lean | 8b5426b0b91fe7037f9d8109fa03bef5876e77c6 | [
"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 | 34,879 | 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.calculus.inverse
import analysis.complex.real_deriv
/-!
# Complex and rea... |
006c34e11881a69742658afedcaa0f01f00c79bb | 5719a16e23dfc08cdea7a5bf035b81690f307965 | /src/Init/Control/Lift.lean | 1b7549edbb724b10f7e7a6b7172c8337be0a819c | [
"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 | 4,416 | lean | /-
Copyright (c) 2016 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner, Sebastian Ullrich
Classy functions for lifting monadic actions of different shapes.
This theory is roughly modeled after the Haskell 'layers' package https://hackage.ha... |
b89f566845f6d515d2bf19b37c75fc04933a6509 | ebf7140a9ea507409ff4c994124fa36e79b4ae35 | /src/hints/category_theory/exercise3/hint8.lean | f64f783e3f0a4afdbc53849b90bd2072600f5127 | [] | no_license | fundou/lftcm2020 | 3e88d58a92755ea5dd49f19c36239c35286ecf5e | 99d11bf3bcd71ffeaef0250caa08ecc46e69b55b | refs/heads/master | 1,685,610,799,304 | 1,624,070,416,000 | 1,624,070,416,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 444 | lean | import category_theory.equivalence
open category_theory
variables {C : Type*} [category C]
variables {D : Type*} [category D]
lemma equiv_preserves_mono {X Y : C} (f : X ⟶ Y) [mono f] (e : C ≌ D) :
mono (e.functor.map f) :=
begin
tidy,
replace w := congr_arg (λ k, e.inverse.map k) w,
simp at w,
rw [←catego... |
399ad3ceb59af55aa3927012b4863c80cffa1d21 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /library/init/meta/hole_command.lean | dfbbe190b45938693a26f320c3f41e72b5ae4066 | [
"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 | 1,970 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.meta.tactic
/--
The front-end (e.g., Emacs, VS Code) can invoke commands for holes {! ... !} in
a declaration. A command is a tactic th... |
811a73ebb334d951529491dd7cdb6fb82e7f8a6d | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/group_with_zero/basic.lean | bc47e022764d61d6acd458db55d289ef3933622d | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 13,169 | 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 algebra.group.basic
import algebra.group_with_zero.defs
import algebra.group.order_synonym
/-!
# Groups with an adjoined zero element
> THIS FILE IS SYNCHRON... |
856971284935466c98b941e3d68d6c19cce50f58 | eb798737e855f3521e075272ed9781f5a67ff135 | /src/hello_world.lean | 87acf4381891827286a6bdae3dfa3fe0538cc4c0 | [] | no_license | BarinderBanwait/integrally_closedness | cd611ef1ff47eea950a6ebcc1220ddc920d3e7e1 | f3b45be4f8b1ac64a2f0a48f0b9f3b281947bcd1 | refs/heads/master | 1,669,515,621,453 | 1,596,147,374,000 | 1,596,147,374,000 | 267,625,375 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,739 | lean | /-
Copyright (c) 2020 Barinder Singh Banwait. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Barinder Singh Banwait, with lots of help from the good folk on the Leanprover Zulip chat :)
-/
import ring_theory.noetherian
import ring_theory.integral_closure
import ring_th... |
e770f3777821ffe3d73480b57b517240290cc2dd | 98000ddc36f1ec26addea0df1853c69fa0e71d67 | /reckless.lean | 9ba46aa32df421d48478cf525ff076a2991e9e5e | [] | no_license | SCRK16/Intuitionism | 50b7b5ed780a75c4ff1339c3d36f1133b8acdfe3 | a3d9920ae056b39a66e37d1d0e03d246bca1e961 | refs/heads/master | 1,670,199,869,808 | 1,598,045,061,000 | 1,598,045,061,000 | 254,657,585 | 1 | 0 | null | 1,590,754,909,000 | 1,586,529,604,000 | Lean | UTF-8 | Lean | false | false | 28,631 | lean | /-
This file captures the notion of a statement being reckless
Meaning: A statement that cannot be proven, and whose negation also cannot be proven
The most important example of recklessness is the law of exluded middle: ∀ P : Prop, P ∨ ¬ P,
also called "the principle of omniscience"
-/
import ..Intuitionism.na... |
ee31201e22ecc0c7dba36cb51cb9696bfd81de23 | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/data/rat/order.lean | dc44806d1c01289a7ff43c02e8043a6798da72c6 | [
"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 | 9,024 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import data.rat.basic
/-!
# Order for Rational Numbers
## Summary
We define the order on `ℚ`, prove that `ℚ` is a discrete, linearly ordered field, ... |
3d8831fcfb76dbabffbc52dedd404b19838f254a | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/data/list/big_operators.lean | e9ed34eb77b50629809d4589c7728c95f956c351 | [
"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 | 16,764 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Floris van Doorn, Sébastien Gouëzel
-/
import data.list.basic
/-!
# Sums and products from lists
This file provides basic results about `list.prod` and `list.sum`, wh... |
f21ebd04fe39c4601dbc8a43f596dfc00b8a6982 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /archive/imo/imo1972_q5.lean | 21178464e58dd0691fe95e82073bbcae524148d7 | [
"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 | 4,244 | lean | /-
Copyright (c) 2020 Ruben Van de Velde, Stanislas Polu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ruben Van de Velde, Stanislas Polu
-/
import data.real.basic
import analysis.normed_space.basic
/-!
# IMO 1972 Q5
Problem: `f` and `g` are real-valued functions ... |
30de73645e53b614b17aba69acb076ee921d5b71 | ae9f8bf05de0928a4374adc7d6b36af3411d3400 | /src/formal_ml/measurable_space.lean | 3a8e59e49a5155f17992e5c5a44f16000cdcea8f | [
"Apache-2.0"
] | permissive | NeoTim/formal-ml | bc42cf6beba9cd2ed56c1cd054ab4eb5402ed445 | c9cbad2837104160a9832a29245471468748bb8d | refs/heads/master | 1,671,549,160,900 | 1,601,362,989,000 | 1,601,362,989,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 18,235 | lean | /-
Copyright 2020 Google LLC
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
di... |
b2c8583c31e18da29b7cf302242c31c09ccb3850 | 853df553b1d6ca524e3f0a79aedd32dde5d27ec3 | /src/data/equiv/basic.lean | a7f5894f52c73d3fb4c4a0cd6fab274d5a3d0c3b | [
"Apache-2.0"
] | permissive | DanielFabian/mathlib | efc3a50b5dde303c59eeb6353ef4c35a345d7112 | f520d07eba0c852e96fe26da71d85bf6d40fcc2a | refs/heads/master | 1,668,739,922,971 | 1,595,201,756,000 | 1,595,201,756,000 | 279,469,476 | 0 | 0 | null | 1,594,696,604,000 | 1,594,696,604,000 | null | UTF-8 | Lean | false | false | 68,904 | 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
In the standard library we cannot assume the univalence axiom.
We say two types are equivalent if they are isomorphic.
Two equivalent types h... |
cc2a60b08dc467f58c6e0ed7672a964b0ca4c059 | 5ca7b1b12d14c4742e29366312ba2c2ef8201b21 | /levels/idea_subtraction.lean | bbcaebe8c69bf4aa53f669b890c86bd9347d624e | [
"Apache-2.0"
] | permissive | MatthiasHu/natural_number_game | 2e464482ef3001863430b0336133b6697b275ba3 | 2d764f72669ae30861f6a1057fce0257f3e466c4 | refs/heads/master | 1,609,719,110,419 | 1,576,345,737,000 | 1,576,345,737,000 | 240,296,314 | 0 | 0 | Apache-2.0 | 1,581,608,357,000 | 1,581,608,356,000 | null | UTF-8 | Lean | false | false | 645 | lean | /- to be written
(feel free to write it, anyone!)
The natural numbers has this hideous "computer science natural number `subtraction`" which is far less well behaved than integer subtraction -- they define it so that `2 - 7 = 0` and more generally all negative numbers are mapped to zero. There are inqualities eveyyw... |
27bd28f5a4a8f9e005f3ecd0f6b0af2deca1710d | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/limits/shapes/zero.lean | 00e02e2b6ffd7ded3f924b25f55001e420f6b4fd | [] | 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 | 16,377 | 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.category_theory.limits.shapes.terminal
import Mathlib.category_theory.limits.shapes.binary_... |
969d21d48ac0c2b6eea96a96319e3e7b90f74839 | 35c41e824c38dc6aa7f0b1467f4d5bc33d61f260 | /Build_Maths/build_maths.lean | b8c534099ebc16818b5030a3687cbb5826eadaec | [] | no_license | kckennylau/xena | 697eb8f55a8f1ce456a241e8b8e4e8a27b91438e | 7dc03dc9588d30d7d36b6904b59ca63a72096229 | refs/heads/master | 1,627,104,810,584 | 1,509,486,416,000 | 1,509,486,416,000 | 107,829,951 | 0 | 0 | null | 1,509,486,381,000 | 1,508,637,567,000 | Lean | UTF-8 | Lean | false | false | 2,705 | lean | namespace xena
inductive xnat
| zero : xnat
| succ : xnat → xnat
open xnat
definition plus : xnat → xnat → xnat
| n zero := n
| n (succ p) := succ (plus n p)
notation a + b := plus a b
definition one := succ zero
definition two := succ one
example : one + one = two :=
begin
refl
end
theorem plus_assoc (a b c :... |
6faafbc576f9627b446a1518a384801da81f1a23 | 33340b3a23ca62ef3c8a7f6a2d4e14c07c6d3354 | /lia/eval_sqe.lean | d716daebbb9fe1b2958ad5eee7b23696f8322f1f | [] | no_license | lclem/cooper | 79554e72ced343c64fed24b2d892d24bf9447dfe | 812afc6b158821f2e7dac9c91d3b6123c7a19faf | refs/heads/master | 1,607,554,257,488 | 1,578,694,133,000 | 1,578,694,133,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 12,744 | lean | import .eval_sqe_core .qfree_sqe .wf_sqe
open list
lemma hco_le_eq_of_ne_zero {m i k ks} :
k ≠ 0 → atom.unify m (atom.le i (k::ks)) =
let m' := (m / (abs k)) in
atom.le (m' * i) (znum.sign k :: map_mul m' ks) :=
begin intro h, simp [atom.unify], rw if_neg, apply h end
lemma hco_dvd_eq_of_ne_zero {m d i k ks} :
k... |
3e5395837f8fb91014c78ace25c87ccb2aa2055c | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /src/Init/LeanInit.lean | 790759176bc3a8099f22024e14b255b3e8d072e7 | [
"Apache-2.0"
] | permissive | walterhu1015/lean4 | b2c71b688975177402758924eaa513475ed6ce72 | 2214d81e84646a905d0b20b032c89caf89c737ad | refs/heads/master | 1,671,342,096,906 | 1,599,695,985,000 | 1,599,695,985,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 28,767 | 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 and Sebastian Ullrich
-/
prelude
import Init.Data.Option.BasicAux
import Init.Data.String.Basic
import Init.Data.Array.Basic
import Init.Data.UInt
import Init.... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.