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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
a0e09ba22e00e2c2b07dcd1789bb357da3bca57b | f5f7e6fae601a5fe3cac7cc3ed353ed781d62419 | /src/analysis/specific_limits.lean | 20eaeab6355585d3d2d6328c7d04bd729ce90839 | [
"Apache-2.0"
] | permissive | EdAyers/mathlib | 9ecfb2f14bd6caad748b64c9c131befbff0fb4e0 | ca5d4c1f16f9c451cf7170b10105d0051db79e1b | refs/heads/master | 1,626,189,395,845 | 1,555,284,396,000 | 1,555,284,396,000 | 144,004,030 | 0 | 0 | Apache-2.0 | 1,533,727,664,000 | 1,533,727,663,000 | null | UTF-8 | Lean | false | false | 7,352 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
A collection of specific limit computations.
-/
import analysis.normed_space.basic
import topology.instances.ennreal
noncomputable theory
local attribute [instance] cl... |
1d30f8db60655f06891b3069e9434c6a9dc8f02b | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/ring_theory/principal_ideal_domain.lean | 4f98208caaf3489b83b41ff7e9948cebde2c5d94 | [
"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 | 6,740 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Chris Hughes, Morenikeji Neri
-/
import algebra.euclidean_domain
import ring_theory.ideals ring_theory.noetherian ring_theory.unique_factorization_domain
variables {α : Type*}
open set... |
a64b70a7d1ab1a399f832300badea8926df89805 | 65b579fba1b0b66add04cccd4529add645eff597 | /lambda/pure/src/unicode.lean | 66c093e877b8b2184ba5bc1d5c7347a926e5a1af | [] | no_license | teodorov/sf_lean | ba637ca8ecc538aece4d02c8442d03ef713485db | cd4832d6bee9c606014c977951f6aebc4c8d611b | refs/heads/master | 1,632,890,232,054 | 1,543,005,745,000 | 1,543,005,745,000 | 108,566,115 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,650 | lean | import data.buffer system.io
import data.bitvec
namespace unicode
private def utf_8_convert_bitvec : list (bitvec 8) → option (list char)
-- 0xxxxxxx -- symbols from 0 to 7Fh
| (⟨ff :: tl₁, _⟩ :: chars) :=
list.cons (char.of_nat (bitvec.bits_to_nat tl₁)) <$> utf_8_convert_bitvec chars
-- 110xxxxx 10xxxxxx -- symbol... |
f3b540689d93383fa66f6a5d9fa8fbad4b741c6c | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/topology/sheaves/local_predicate.lean | 4acca6972ccd2412e72b62cf6ae38ef45897052d | [
"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 | 11,697 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Scott Morrison, Adam Topaz
-/
import topology.sheaves.sheaf_of_functions
import topology.sheaves.stalks
import topology.local_homeomorph
import topology.sheaves.sheaf_c... |
ec5cc144dfc47a271ce36eb1e9d19d24b1301ee7 | 3dc4623269159d02a444fe898d33e8c7e7e9461b | /.github/workflows/project_1_a_decrire/lean-scheme-submission/src/spectrum_of_a_ring/structure_sheaf.lean | 173368f11f1a97adac7cba15279572d524b71e98 | [] | no_license | Or7ando/lean | cc003e6c41048eae7c34aa6bada51c9e9add9e66 | d41169cf4e416a0d42092fb6bdc14131cee9dd15 | refs/heads/master | 1,650,600,589,722 | 1,587,262,906,000 | 1,587,262,906,000 | 255,387,160 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,125 | lean | /-
The structure presheaf is a sheaf of rings.
https://stacks.math.columbia.edu/tag/01HR
-/
import topology.basic
import to_mathlib.localization.localization_alt
import sheaves.sheaf_on_standard_basis
import spectrum_of_a_ring.induced_homeomorphism
import spectrum_of_a_ring.quasi_compact
import spectrum_of_a_ring... |
a7a624744791ac5ac69fe75194e5d3204bdbc49b | 969dbdfed67fda40a6f5a2b4f8c4a3c7dc01e0fb | /src/category_theory/sites/pretopology.lean | 2dc74b4d5ac36469a68fbd5b34fb8706fd034265 | [
"Apache-2.0"
] | permissive | SAAluthwela/mathlib | 62044349d72dd63983a8500214736aa7779634d3 | 83a4b8b990907291421de54a78988c024dc8a552 | refs/heads/master | 1,679,433,873,417 | 1,615,998,031,000 | 1,615,998,031,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,512 | 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.sites.grothendieck
/-!
# Grothendieck pretopologies
Definition and lemmas about Grothendieck pretopologies.
A Grothendieck pretopology for a cat... |
83e65720fc31a9bf9c0d8d907cc7cf18f0ba965c | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/basic.lean | 3bb228e2e5bd9def3531363e621272cdc8ce2a85 | [
"Apache-2.0"
] | permissive | leanprover-community/lean | 12b87f69d92e614daea8bcc9d4de9a9ace089d0e | cce7990ea86a78bdb383e38ed7f9b5ba93c60ce0 | refs/heads/master | 1,687,508,156,644 | 1,684,951,104,000 | 1,684,951,104,000 | 169,960,991 | 457 | 107 | Apache-2.0 | 1,686,744,372,000 | 1,549,790,268,000 | C++ | UTF-8 | Lean | false | false | 1,809 | lean | prelude
constant {l1 l2} A : Type l1 → Type l2
#check A
definition {l} tst (A : Type*) (B : Type*) (C : Type l) : Type* := A → B → C
#check tst
constant {l} group : Type (l+1)
constant {l} carrier : group.{l} → Type l
noncomputable definition to_carrier (g : group) := carrier g
#check to_carrier.{1}
section
variab... |
47018e1e453b319dde8595cc208b84ac88646d33 | 947b78d97130d56365ae2ec264df196ce769371a | /src/Lean/Util/CollectFVars.lean | f353cd80b2dbebe76e3b3151bf4b7fa016f73a5f | [
"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 | 1,178 | 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.Expr
namespace Lean
namespace CollectFVars
structure State :=
(visitedExpr : ExprSet := {})
(fvarSet : NameSet := {})
instance State... |
fea7c75497146837ad2a41193593d789aa472554 | 4aca55eba10c989f0d58647d3c2f371e7da44355 | /src/srg.lean | 493d889eaeebcdee209250110420d840cbced437 | [] | no_license | eric-wieser/l534zhan-my_project | f9fc75fb5454405e1a2fa9b56cf96c355f6f2336 | febc91e76b7b00fe2517f258ca04d27b7f35fcf3 | refs/heads/master | 1,689,218,910,420 | 1,630,439,440,000 | 1,630,439,440,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,255 | lean | import main2
import combinatorics.simple_graph.adj_matrix
import combinatorics.simple_graph.strongly_regular
/-!
# Strong regular graphs
This file attempts to construct strong regular graphs from
regular symmetric Hadamard matrices with constant diagonal (RSHCD).
-/
set_option pp.beta true
variables {α I R V : Typ... |
d6f0ed60e385ec308e09915cfb453383fd2ebb2a | 159fed64bfae88f3b6a6166836d6278f953bcbf9 | /Structure/UniverseFunctor.lean | 4769378cd17e9bd27d1df8f269fbd4c929df5377 | [
"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 | 14,328 | lean | -- An abstract formalization of "isomorphism is equality up to relabeling"
-- -------------------------------------------------------------------------
--
-- See `README.md` for more info.
--
-- Helpers for the construction of functors into `universeStructure`.
import Structure.Basic
import Structure.Forgetfulness
... |
4dbda01f9d44e65e1d7c1c6681762ce6c1c421a1 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/topology/uniform_space/uniform_convergence.lean | d6a61d1095bfc60599e9bcd9550a4a60d3acf0dc | [
"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 | 16,649 | lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import topology.uniform_space.basic
/-!
# Uniform convergence
A sequence of functions `Fₙ` (with values in a metric space) converges uniformly on a set `s` to... |
7397caf9b52a1a398699341a1438cbc50311c570 | 222111140d2023e142b07e9cd5119ac2829b36f5 | /src/finset_sum.lean | ab71f2cfa50de98b77de74ce15aa9b02ef5f9a28 | [] | no_license | jjcrawford/lean-gaussian-elimination | 740dfdf2de89dc99c088c53e5221d9dfad3c0b92 | c473d33c07fa6f141d17d9dc42ad07956c33dd03 | refs/heads/master | 1,585,793,867,436 | 1,540,443,865,000 | 1,540,443,865,000 | 153,901,939 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,483 | lean | import data.finsupp
universes u v
variable (α : Type u)
variable [ring α]
variable [decidable_eq α]
@[simp] lemma ite.map (P : Prop) [decidable P] {β γ : Type*} (a b : β) (f : β → γ) :
f (ite P a b) = ite P (f a) (f b) :=
begin
split_ifs; refl
end
@[simp] lemma ite.mul_right (P : Prop) [decidable P]... |
bf43f749ff4e12c0dabbd83c6c26792636e6c4a2 | b70031c8e2c5337b91d7e70f1e0c5f528f7b0e77 | /src/algebra/group_with_zero/defs.lean | 943f63e50c16df0f938ee597529cce1d1cc0b4ac | [
"Apache-2.0"
] | permissive | molodiuc/mathlib | cae2ba3ef1601c1f42ca0b625c79b061b63fef5b | 98ebe5a6739fbe254f9ee9d401882d4388f91035 | refs/heads/master | 1,674,237,127,059 | 1,606,353,533,000 | 1,606,353,533,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,305 | 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.defs
import logic.nontrivial
/-!
# Typeclasses for groups with an adjoined zero element
This file provides just the typeclass definitions, and ... |
8e959833de575da17b3075789c0dc7cb10778ee0 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /library/init/meta/backward.lean | 8781719616decdd292dc913737f445d54258cdb7 | [
"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 | 3,018 | 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.meta.set_get_option_tactics
namespace tactic
meta constant back_lemmas : Type
/- Create a datastructure containing al... |
b5bcc36e7c5b4bf9dc7bb7198bd9bb4fca9e0c20 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/topology/instances/rat.lean | 766fc107b595d13a90f4a7860e63a24fb9c7fd32 | [
"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 | 4,063 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import topology.metric_space.basic
import topology.algebra.order.archimedean
import topology.instances.int
import topology.instances.nat
import topolo... |
63202ae15e260940ac63f8c503eba94f80515dbe | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/set/intervals/infinite.lean | cdca43d3557a78957c0a7add1b2b8a7b9547013e | [
"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 | 1,883 | lean | /-
Copyright (c) 2020 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton
-/
import data.set.finite
/-!
# Infinitude of intervals
Bounded intervals in dense orders are infinite, as are unbounded intervals
in orders that are unbounded on the approp... |
8e250ec1d34b9af7942a7d28f86af30e77f91253 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/algebraic_topology/simplex_category.lean | 984d5cd0b9f3acfe44bcf84e4173941b24ee9cf7 | [
"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 | 17,695 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Scott Morrison, Adam Topaz
-/
import order.category.NonemptyFinLinOrd
import category_theory.skeletal
import data.finset.sort
import tactic.linarith
/-! # The simplex... |
579f03d36c9cee67180960f7a080413777108911 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/cc1.lean | 2a393cd981790e7a41986ba5ba0e345f3efb46fd | [
"Apache-2.0"
] | permissive | leanprover-community/lean | 12b87f69d92e614daea8bcc9d4de9a9ace089d0e | cce7990ea86a78bdb383e38ed7f9b5ba93c60ce0 | refs/heads/master | 1,687,508,156,644 | 1,684,951,104,000 | 1,684,951,104,000 | 169,960,991 | 457 | 107 | Apache-2.0 | 1,686,744,372,000 | 1,549,790,268,000 | C++ | UTF-8 | Lean | false | false | 2,155 | lean | open tactic
set_option pp.implicit true
example (a b c d : nat) (f : nat → nat → nat) : a = b → b = c → d + (if b > 0 then a else b) = 0 → f (b + b) b ≠ f (a + c) c → false :=
by do intros,
s ← cc_state.mk_using_hs,
trace s,
t₁ ← to_expr ```(f (b + b) b),
t₂ ← to_expr ```(f (a + c) c),
b... |
3bfb41737b6623188bb061f76e1f658c832781a7 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /archive/sensitivity.lean | 408a2291020aaa9294e164ac0e8ece10798591a2 | [
"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 | 15,505 | lean | /-
Copyright (c) 2019 Reid Barton, Johan Commelin, Jesse Han, Chris Hughes, Robert Y. Lewis, and
Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Johan Commelin, Jesse Han, Chris Hughes, Robert Y. Lewis, and Patrick Massot
-/
import tactic.f... |
a745d21ab9deaa3b3f6052ff6fa402f158bed950 | 03577f7aaac416af2e8f734149669af300dc499c | /lean_exercises/lcp_lcpo.lean | 042877392c5d8bf10879ba0180b42a3bbae4c765 | [] | no_license | nymarya/algorithms | b4dc73389de588e6934da15b0e0b67ae354907aa | 1df987f82273a8ffe2b2042552bbb1428bf165bf | refs/heads/master | 1,609,629,118,479 | 1,600,087,537,000 | 1,600,087,537,000 | 99,489,969 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 1,242 | lean | variables ( A B C D P Q : Prop )
variable R: Prop → Prop
-- LCP-003
example ( h1: A→(B→C)) (h2 : A→B) : (A→C) :=
assume h3: A,
show C, from h1 (h3) (h2 (h3))
-- LCP-007
example ( h: A→(B→(C→D))) : (C→(B→(A→D))) :=
assume hc: C,
assume hb: B,
assume ha: A,
show D , from h (ha) (hb) (hc)
-- LCP-032
example (h : ... |
1e5ef012f685b72045c575318639104e63e5466a | 8cb37a089cdb4af3af9d8bf1002b417e407a8e9e | /library/init/data/int/comp_lemmas.lean | 762ec3e734fb5d407d551cb1d4470289f8724bc8 | [
"Apache-2.0"
] | permissive | kbuzzard/lean | ae3c3db4bb462d750dbf7419b28bafb3ec983ef7 | ed1788fd674bb8991acffc8fca585ec746711928 | refs/heads/master | 1,620,983,366,617 | 1,618,937,600,000 | 1,618,937,600,000 | 359,886,396 | 1 | 0 | Apache-2.0 | 1,618,936,987,000 | 1,618,936,987,000 | null | UTF-8 | Lean | false | false | 5,041 | 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
Auxiliary lemmas used to compare int numerals.
-/
prelude
import init.data.int.order
namespace int
/- Auxiliary lemmas for proving that to int numerals are d... |
039e1003a61bec057347059c05be0e77f162ba75 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/combinatorics/simple_graph/finsubgraph.lean | dc13b8d50a0a56e591e63bd4542eb375a24ca55c | [
"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 | 6,006 | lean | /-
Copyright (c) 2022 Joanna Choules. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joanna Choules
-/
import category_theory.cofiltered_system
import combinatorics.simple_graph.subgraph
/-!
# Homomorphisms from finite subgraphs
> THIS FILE IS SYNCHRONIZED WITH MATHL... |
937820da112e33374145caa01067acfee0c276be | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /hott/algebra/category/functor/default.hlean | 8274c00c1c4d40d48b3d116c49ef3d60867377cc | [
"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 | 173 | 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
-/
import .basic
|
0daeffa21105275864b90f2f2cf50943e9a91c28 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/data/nat/factorial/cast.lean | 0340d3652207fe4708461d450ec0805ded8a19b1 | [
"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 | 2,239 | lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import ring_theory.polynomial.pochhammer
/-!
# Cast of factorials
This file allows calculating factorials (including ascending and descending ones) as elements of a
sem... |
639a2e9abba50decf3ed6c8ecbe14d57cdee2cdc | 4727251e0cd73359b15b664c3170e5d754078599 | /src/ring_theory/power_series/well_known.lean | 0e1ee81f3f6fdc4b8c3d644c9b7faf84be4e9e05 | [
"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 | 4,968 | lean | /-
Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import ring_theory.power_series.basic
import data.nat.parity
import algebra.big_operators.nat_antidiagonal
/-!
# Definition of well-known power series
In th... |
aedd4e0d87aeda36e81548797da566f27c93f602 | b2fe74b11b57d362c13326bc5651244f111fa6f4 | /src/number_theory/pythagorean_triples.lean | c447e0d93b4545c7f34e84bf86394be1834d71d8 | [
"Apache-2.0"
] | permissive | midfield/mathlib | c4db5fa898b5ac8f2f80ae0d00c95eb6f745f4c7 | 775edc615ecec631d65b6180dbcc7bc26c3abc26 | refs/heads/master | 1,675,330,551,921 | 1,608,304,514,000 | 1,608,304,514,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 26,067 | lean | /-
Copyright (c) 2020 Paul van Wamelen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Paul van Wamelen.
-/
import algebra.field
import ring_theory.int.basic
import algebra.group_with_zero.power
import tactic.ring
import tactic.ring_exp
/-!
# Pythagorean Triples
The ma... |
af94e7ab9e36466114df2d4051f919045a463631 | a3db153d66921f9d5a199b60b52ab3c21cf0e023 | /src/ordered_field.lean | d4bc5eb0e25e49d2a20b0ec1293969ef9cd9ec04 | [
"MIT"
] | permissive | metalogical/sia-lean | 3bd87a76b3ee6d910cbf182eb2a0e6d9eca3c056 | f8e354dd2ff6c09c4e001c1f80f6112c62da8592 | refs/heads/master | 1,629,775,811,523 | 1,512,684,874,000 | 1,512,684,874,000 | 106,763,566 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,190 | lean | import .util
universe u
variable {R : Type u}
class st_order R extends has_lt R := -- strict total order
(lt_irrefl : forall a : R, not (a < a))
(lt_trans : forall {a b c : R}, a < b -> b < c -> a < c)
(ne_lt : forall {a b : R}, a != b -> a < b \/ b < a)
-- Bell 1.2, but we use it as an axiom for... |
a8cbefa69c4e1c82d59d8cfe68f26464ecc18161 | e2fc96178628c7451e998a0db2b73877d0648be5 | /src/classes/unrestricted/closure_properties/concatenation.lean | a731e28a9fa9662da3491bdf4617e087cfae66fb | [
"BSD-2-Clause"
] | permissive | madvorak/grammars | cd324ae19b28f7b8be9c3ad010ef7bf0fabe5df2 | 1447343a45fcb7821070f1e20b57288d437323a6 | refs/heads/main | 1,692,383,644,884 | 1,692,032,429,000 | 1,692,032,429,000 | 453,948,141 | 7 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 93,156 | lean | import classes.unrestricted.basics.toolbox
import utilities.list_utils
section list_technicalities
variables {α β : Type}
lemma list_take_one_drop {l : list α} {i : ℕ} (hil : i < l.length) :
list.take 1 (list.drop i l) = [l.nth_le i hil] :=
begin
have l_split : l = list.take i l ++ list.drop i l,
{
rw list... |
48f3575f57c8802dab38ceed77bbe5bda3b78a57 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/big_operators/basic.lean | 4c941cb016542e88cb80f11eacfdfa8fddcb77be | [
"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 | 70,837 | 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.group.pi
import algebra.hom.equiv
import algebra.ring.opposite
import data.finset.fold
import data.fintype.basic
import data.set.pairwise
/-!
# Big o... |
f6bf8cc0e76d84aa26ab60059470869052932383 | 07c76fbd96ea1786cc6392fa834be62643cea420 | /hott/hit/pushout.hlean | a21df3f4d8a8b55cdc71ca8773efb9876cba2dd3 | [
"Apache-2.0"
] | permissive | fpvandoorn/lean2 | 5a430a153b570bf70dc8526d06f18fc000a60ad9 | 0889cf65b7b3cebfb8831b8731d89c2453dd1e9f | refs/heads/master | 1,592,036,508,364 | 1,545,093,958,000 | 1,545,093,958,000 | 75,436,854 | 0 | 0 | null | 1,480,718,780,000 | 1,480,718,780,000 | null | UTF-8 | Lean | false | false | 14,456 | hlean | /-
Copyright (c) 2015-16 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Ulrik Buchholtz, Jakob von Raumer
Declaration and properties of the pushout
-/
import .quotient types.sigma types.arrow_2
open quotient eq sum equiv is_trunc ... |
1d3cd1ca5d72f3bfbedbaaf2147ad54dbce4c0de | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/topology/order.lean | cd8b6cbe65cc36af1117184831d7cda3725e3ec3 | [
"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 | 27,489 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import topology.basic
/-!
# Ordering on topologies and (co)induced topologies
Topologies on a fixed type `α` are ordered, by reverse inclusion.
That... |
63c5704b5992350e72cfa91e909ee0610d8d940c | bb31430994044506fa42fd667e2d556327e18dfe | /src/ring_theory/adjoin_root.lean | d3f088f947c3ce660b4eb1963c7d7614595fd948 | [
"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 | 29,545 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Chris Hughes
-/
import algebra.algebra.basic
import data.polynomial.field_division
import field_theory.minpoly.basic
import ring_theory.adjoin.basic
import ring_theory.... |
615c16a0a262b57b215ca6740b5f688b625ea78e | ee8cdbabf07f77e7be63a449b8483ce308d37218 | /lean/src/test/amc12a-2003-p5.lean | 8dc6117ef4cc3cc76974f54231ff0a6301fdbd16 | [
"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 | 363 | 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.basic
example (a m c : ℕ) (h₀ : a ≤ 9 ∧ m ≤ 9 ∧ c ≤ 9) ( h₁ : 10*(10*(10*(10*a + m) + c) + 1) + 0 + (10*(10*(10*(10*a + m) + c) + 1) + 2) = 123422) : a + m + c... |
33433390bece6ac5535924f7b345e338c91ea3f6 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/handthen.lean | c73939cc544ecb39fc37e765dc2efdeebd872945 | [
"Apache-2.0"
] | permissive | leanprover-community/lean | 12b87f69d92e614daea8bcc9d4de9a9ace089d0e | cce7990ea86a78bdb383e38ed7f9b5ba93c60ce0 | refs/heads/master | 1,687,508,156,644 | 1,684,951,104,000 | 1,684,951,104,000 | 169,960,991 | 457 | 107 | Apache-2.0 | 1,686,744,372,000 | 1,549,790,268,000 | C++ | UTF-8 | Lean | false | false | 1,009 | lean | open tactic
local attribute [simp] nat.add_zero nat.zero_add
lemma ex1 (a b c : nat) : a + 0 = 0 + a ∧ b = b :=
begin
-- We use `(` to go to regular tactic mode.
constructor; [skip, constructor],
-- Remaining goal is
-- |- a + 0 = 0 + a
simp
end
lemma ex2 (a b c : nat) : a + 0 = 0 + a ∧ b = b :=
begin
co... |
212172fbe3ddc452113cd90749881cd91c120a8d | 947b78d97130d56365ae2ec264df196ce769371a | /stage0/src/Lean/Level.lean | 3589a3c6b85620f67412485dd2995197ce114604 | [
"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 | 16,481 | lean | /-
Copyright (c) 2018 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Std.Data.HashMap
import Std.Data.HashSet
import Std.Data.PersistentHashMap
import Std.Data.PersistentHashSet
import Lean.Data.Name
import Lean.Data.F... |
9bdd7ea58b04097c5de22bc3f9644cddaa31d0a3 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/order/monoid/min_max.lean | eebcdd00179a03ebb740506a83dcb673373c3602 | [
"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 | 4,020 | 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 order.min_max
import algebra.order.monoid.lemmas
/-!
# Lemmas about `min` and `max` in an ordered monoid.
> ... |
08059983907c31a0d1e5a37c73301f00726f83c5 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/analysis/calculus/deriv.lean | 88f8f56871c0ff7e616aea5dae8c446b39b09205 | [
"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 | 70,702 | lean | /-
Copyright (c) 2019 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner, Sébastien Gouëzel
-/
import analysis.calculus.fderiv
import data.polynomial.derivative
/-!
# One-dimensional derivatives
This file defines the derivative of a function... |
d7ec14524a47958e6d4ca9b95f89f2077da749fc | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/topology/category/Compactum.lean | 2a85ae47f544b8466af164b544619246a6b07b0f | [
"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 | 17,836 | lean | /-
Copyright (c) 2020 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import category_theory.monad.types
import category_theory.monad.limits
import category_theory.equivalence
import topology.category.CompHaus
import topology.category.Profinit... |
09782c71ed5ab8f24d161bcde4ae0faac44676c4 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/topology/algebra/uniform_mul_action.lean | e8efe7c86821f8f6ff1a9cb3425682d6f0759cd3 | [
"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 | 7,301 | lean | /-
Copyright (c) 2022 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import topology.algebra.uniform_group
import topology.uniform_space.completion
/-!
# Multiplicative action on the completion of a uniform space
In this file... |
ccc7ea665249b795b7669693b571c36047ed1ad3 | 98beff2e97d91a54bdcee52f922c4e1866a6c9b9 | /src/category/images.lean | 7db30561f20e4f1f23a8567bf6b410f594e4d0fc | [] | no_license | b-mehta/topos | c3fc43fb04ba16bae1965ce5c26c6461172e5bc6 | c9032b11789e36038bc841a1e2b486972421b983 | refs/heads/master | 1,629,609,492,867 | 1,609,907,263,000 | 1,609,907,263,000 | 240,943,034 | 43 | 3 | null | 1,598,210,062,000 | 1,581,877,668,000 | Lean | UTF-8 | Lean | false | false | 1,286 | lean | import category_theory.limits.shapes.images
universes v u
noncomputable theory
open category_theory category_theory.limits
namespace category_theory.limits
variables {C : Type u} [category.{v} C] [has_strong_epi_mono_factorisations.{v} C]
variables {X Y : C} (f : X ⟶ Y)
@[simps]
def unique_factorise (I' : C) (e ... |
113a0524b52004c5528ec947081d4855edf31bc2 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /hott/hit/prop_trunc.hlean | 84e6f2f82ea343489f1152ffe7741010ed5d84ec | [
"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 | 14,843 | hlean | import function types.trunc hit.colimit homotopy.connectedness --types.nat.hott hit.trunc cubical.square
open eq is_trunc unit quotient seq_colim pi nat equiv sum algebra is_conn function
/-
In this file we define the propositional truncation, which, given (X : Type)
has constructors
* tr : X → trun... |
bf6d5e58141a119595e63dc4b2254e2a5ec71394 | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /library/standard/data/list/basic.lean | 091123f292d7ce9e349a35f5fe911daa941fe3ff | [
"Apache-2.0"
] | permissive | codyroux/lean | 7f8dff750722c5382bdd0a9a9275dc4bb2c58dd3 | 0cca265db19f7296531e339192e9b9bae4a31f8b | refs/heads/master | 1,610,909,964,159 | 1,407,084,399,000 | 1,416,857,075,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,853 | lean | ----------------------------------------------------------------------------------------------------
--- Copyright (c) 2014 Parikshit Khanna. All rights reserved.
--- Released under Apache 2.0 license as described in the file LICENSE.
--- Authors: Parikshit Khanna, Jeremy Avigad
----------------------------------------... |
89961abaefca66f928932b3f017cf19cd74a912e | 53f7fd7840fe4979de24f9611c89f2ee1b4fc5dc | /src/zipper.lean | 27d9fa05397cf9a3882b9bd4628792425428a268 | [] | no_license | cipher1024/search-trees | 6d1925283c6ce47d84bdf41ca40d8317ff2e64d7 | 0e0ea0ee59f0b0499ebad1ef6f34f09ec9666cde | refs/heads/master | 1,673,300,158,759 | 1,603,984,112,000 | 1,603,984,112,000 | 308,132,998 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,634 | lean |
import .basic .backtrack
universes u v
variables (α : Type u) (β : Type v)
namespace two_three.tree
open two_three
inductive zipper
| nil : zipper
| node2_0 : zipper → α → tree α β → zipper
| node2_1 : tree α β → α → zipper → zipper
| node3_0 : zipper → α → tree α β → α → tree α β → zipper
| node3_1 : tree α β → α ... |
ed19edb9181cff465c589b6596feac7ec2789193 | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /stage0/src/Lean/Elab/Inductive.lean | 83699abf8fa8dc5ac8470d61d87f11769db0f295 | [
"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 | 24,893 | 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.ReplaceLevel
import Lean.Util.ReplaceExpr
import Lean.Util.CollectLevelParams
import Lean.Util.Constructions
import Lean.Meta.CollectFVars
... |
89c2649b2d86dc5405130ef57bcb39349615dd7c | 4727251e0cd73359b15b664c3170e5d754078599 | /src/logic/nontrivial.lean | cb91c974cceec74687fdeeae2056d001bde12e42 | [
"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 | 10,792 | lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import data.prod
import data.subtype
import logic.function.basic
import logic.unique
/-!
# Nontrivial types
A type is *nontrivial* if it contains at least two... |
5ebb1b5dfc4748ee7d6db9f842b856cf66e29925 | 5e3548e65f2c037cb94cd5524c90c623fbd6d46a | /src_icannos_totilas/aops/2005_IMO_Shortlist_Problems_A3.lean | c91261b0637cde841e1f04369e4ba114709f0668 | [] | no_license | ahayat16/lean_exos | d4f08c30adb601a06511a71b5ffb4d22d12ef77f | 682f2552d5b04a8c8eb9e4ab15f875a91b03845c | refs/heads/main | 1,693,101,073,585 | 1,636,479,336,000 | 1,636,479,336,000 | 415,000,441 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 295 | lean | import data.matrix.notation
import data.real.basic
import data.finmap
theorem IMO_Shortlist_Problems_A3_2005 (v : fin 4 -> ℝ) :
(v 0 + v 1 + v 2 + v 4 = 9) ∧ ((v 0)^2 + (v 1)^2 + (v 2)^2 + (v 3)^2=21)
→ ∃ p : (equiv.perm (fin 4)), v (p 0) * v (p 1) - v (p 2) * v (p 3) ≥ 2 := sorry |
2f63cc72f3c46ae88f206e2b8f1eea2681682b1d | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/convex/krein_milman.lean | 8ae0817cf2298c22537931de95f565a2fbaf8157 | [
"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 | 5,384 | 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 analysis.convex.exposed
import analysis.normed_space.hahn_banach.separation
/-!
# The Krein-Milman theorem
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any chang... |
53143d0a7a5a19623bdbf8adb23623468ce39d70 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/analysis/complex/basic.lean | 8e2f096e22ee520363e76b6cc7dda4e7e2a72b4a | [
"Apache-2.0"
] | permissive | gebner/mathlib | eab0150cc4f79ec45d2016a8c21750244a2e7ff0 | cc6a6edc397c55118df62831e23bfbd6e6c6b4ab | refs/heads/master | 1,625,574,853,976 | 1,586,712,827,000 | 1,586,712,827,000 | 99,101,412 | 1 | 0 | Apache-2.0 | 1,586,716,389,000 | 1,501,667,958,000 | Lean | UTF-8 | Lean | false | false | 7,976 | lean | /-
Copyright (c) Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import analysis.calculus.deriv analysis.normed_space.finite_dimension
/-!
# Normed space structure on `ℂ`.
This file gathers basic facts on complex numbers of an a... |
1511b7ec3cfde055b3cda2a4a94a284d1bec18ad | b70447c014d9e71cf619ebc9f539b262c19c2e0b | /hott/algebra/homotopy_group.hlean | ccae578598d36d6e44e91a43d3018c1912a7da53 | [
"Apache-2.0"
] | permissive | ia0/lean2 | c20d8da69657f94b1d161f9590a4c635f8dc87f3 | d86284da630acb78fa5dc3b0b106153c50ffccd0 | refs/heads/master | 1,611,399,322,751 | 1,495,751,007,000 | 1,495,751,007,000 | 93,104,167 | 0 | 0 | null | 1,496,355,488,000 | 1,496,355,487,000 | null | UTF-8 | Lean | false | false | 11,081 | 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
homotopy groups of a pointed space
-/
import .trunc_group types.trunc .group_theory types.nat.hott
open nat eq pointed trunc is_trunc algebra group function equiv... |
3a3e02a97d7a679f86d4da1f8fa7e8d45d3dc1ac | c5b07d17b3c9fb19e4b302465d237fd1d988c14f | /src/natural_model.lean | 5894ca1342b67c6f73698030fd32ac0164bf77c9 | [
"MIT"
] | permissive | skaslev/papers | acaec61602b28c33d6115e53913b2002136aa29b | f15b379f3c43bbd0a37ac7bb75f4278f7e901389 | refs/heads/master | 1,665,505,770,318 | 1,660,378,602,000 | 1,660,378,602,000 | 14,101,547 | 0 | 1 | MIT | 1,595,414,522,000 | 1,383,542,702,000 | Lean | UTF-8 | Lean | false | false | 2,573 | lean | -- This is based on the talk "Polynomial Functors and Natural Models of Type Theory"
-- by Steve Awodey on the Polynomial Functor Workshop
-- https://youtu.be/RDuNIP4icKI?list=PLhgq-BqyZ7i7R-fGcAmNyWmJBQg1wzex-&t=10765
import functors.family
open fam
abbreviation U := Type*
abbreviation Ω := Prop
abbreviation P := f... |
fd44bf882dd780826c91749bbbb777a0b68b0c5f | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/data/complex/is_R_or_C.lean | ebdc0c738fd2ade6bb4efba674c29f3e893e32b1 | [
"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 | 32,332 | lean | /-
Copyright (c) 2020 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import data.real.sqrt
import field_theory.tower
import analysis.normed_space.finite_dimension
/-!
# `is_R_or_C`: a typeclass for ℝ or ℂ
This file defines the type... |
9b8d550569cc00b82eca0291d2d08edfc3143622 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/elab_error_recovery.lean | 6bfb9d213c170265dbe9557fe9b559dc96e0167e | [
"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 | 454 | lean | def half_baked : ℕ → ℕ
| 3 := 2
-- type mismatches
| 0 := 1 + ""
-- placeholders
| 5 := _ + 4
-- missing typeclass instances
| 42 := if 2 ∈ 3 then 3 else _
-- exceptions during tactic evaluation
| 7 := by do undefined
-- nested elaboration errors
| 10 := begin exact [] end
-- missing cases
#print half_baked._main
... |
5f409221e271dfb69a9e2a5da9517151cc7f9116 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/order/complete_lattice.lean | a61730a6820896d5fe2402e4cf0b3cd0b62d00e1 | [
"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 | 38,187 | 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.bounds
/-!
# Theory of complete lattices
## Main definitions
* `Sup` and `Inf` are the supremum and the infimum of a set;
* `supr (f : ι → α)` and `in... |
ef798cdf4b334db300cefae9c59f495d6188debc | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/topology/subset_properties.lean | f50c9161ead9a8b820125133f56144ef1c0a1fe5 | [
"Apache-2.0"
] | permissive | gebner/mathlib | eab0150cc4f79ec45d2016a8c21750244a2e7ff0 | cc6a6edc397c55118df62831e23bfbd6e6c6b4ab | refs/heads/master | 1,625,574,853,976 | 1,586,712,827,000 | 1,586,712,827,000 | 99,101,412 | 1 | 0 | Apache-2.0 | 1,586,716,389,000 | 1,501,667,958,000 | Lean | UTF-8 | Lean | false | false | 54,731 | 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, Yury Kudryashov
-/
import topology.continuous_on
/-!
# Properties of subsets of topological spaces
## Main definitions
`compact`, `is_clopen`, `is_i... |
e7a1be13af3cbb6acb593140e34670ae7b81a589 | 75db7e3219bba2fbf41bf5b905f34fcb3c6ca3f2 | /library/logic/examples/colog88.lean | 55e4502838227abcbcc2a17b7ce98d9ac0fbe2a1 | [
"Apache-2.0"
] | permissive | jroesch/lean | 30ef0860fa905d35b9ad6f76de1a4f65c9af6871 | 3de4ec1a6ce9a960feb2a48eeea8b53246fa34f2 | refs/heads/master | 1,586,090,835,348 | 1,455,142,203,000 | 1,455,142,277,000 | 51,536,958 | 1 | 0 | null | 1,455,215,811,000 | 1,455,215,811,000 | null | UTF-8 | Lean | false | false | 2,741 | lean | /-
Example from "Inductively defined types",
from Thierry Coquand and Christine Paulin,
COLOG-88.
It shows it is inconsistent to allow inductive datatypes such as
inductive A : Type :=
| intro : ((A → Prop) → Prop) → A
-/
/- Phi is a positive, but not strictly positive, operator. -/
definition Phi (A : Type) := (A ... |
2738fde293d77b601b36bce1fcb99c36f85b6e17 | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/data/nat/multiplicity.lean | 1598dd1289cb0597c7862dc67d10568e3aad61b6 | [
"Apache-2.0"
] | permissive | ilitzroth/mathlib | ea647e67f1fdfd19a0f7bdc5504e8acec6180011 | 5254ef14e3465f6504306132fe3ba9cec9ffff16 | refs/heads/master | 1,680,086,661,182 | 1,617,715,647,000 | 1,617,715,647,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,118 | lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import data.nat.bitwise
import data.nat.parity
import data.nat.log
import ring_theory.int.basic
import algebra.big_operators.intervals
/-!
# Natural number multiplicity... |
89bd1932e75d255c9f22c112cf8257edb5c1847c | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/tactic/cache.lean | de1b5bc995ad5d96e5965699ed4b4891f82fa217 | [
"Apache-2.0"
] | permissive | vaibhavkarve/mathlib | a574aaf68c0a431a47fa82ce0637f0f769826bfe | 17f8340912468f49bdc30acdb9a9fa02eeb0473a | refs/heads/master | 1,621,263,802,637 | 1,585,399,588,000 | 1,585,399,588,000 | 250,833,447 | 0 | 0 | Apache-2.0 | 1,585,410,341,000 | 1,585,410,341,000 | null | UTF-8 | Lean | false | false | 4,702 | 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 tactic.doc_commands
/-!
# Instance cache tactics
For performance reasons, Lean does not automatically update its database
of class instances during a proof. T... |
683cfed0ae15a177175bd9ccc4b729ff423eb955 | c46a17c860913da8a635099f06be3a2416f6cdab | /dhs_islanders_n2.lean | aa480fedbb60d32267cf65ba1a84ea56f3024648 | [] | no_license | vladfi1/vfds | 4ed0b7fd810218c74eef933364b9aa6be4cc2551 | 664b0d1c8126c93b379115ffe5da7b943f3375d5 | refs/heads/master | 1,585,024,431,435 | 1,535,567,828,000 | 1,535,567,828,000 | 142,457,395 | 0 | 1 | null | 1,532,805,351,000 | 1,532,617,692,000 | Lean | UTF-8 | Lean | false | false | 5,370 | lean | inductive person : Type
| dan, tina
open person
@[reducible] def timestep := ℕ
constant is_marked : person → Prop
constant knows (t : timestep) (n : person) (p : Prop) : Prop
@[reducible] def mk_prec (p : timestep → person → Prop) : ℕ → timestep → person → Prop
| 0 t n := p t n
| (d+1) t₁ n₁ := ∀ {t₂ : timest... |
e6f7dadb32cf852cd6d469368e64e252107f44f7 | 618003631150032a5676f229d13a079ac875ff77 | /test/solve_by_elim.lean | 07c8f733a139ebeb1a8013ecd7c58d3a0c20d73b | [
"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 | 4,168 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Scott Morrison
-/
import tactic.solve_by_elim
example {a b : Prop} (h₀ : a → b) (h₁ : a) : b :=
begin
apply_assumption,
apply_assumption,
end
example {X : Type} (x : X)... |
bf2b2b7f91506ad3e082d15e1444cda01d5303ff | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/auto_include.lean | 77ec231fd2a4f2b3ef08deac0452af413073f346 | [
"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 | 438 | lean | import algebra.group
open algebra
section
variables {A : Type} [group A]
variables {B : Type} [group B]
definition foo (a b : A) : a * b = b * a :=
sorry
definition bla (b : B) : b * 1 = b :=
sorry
print foo
print bla
end
section
variable {A : Type}
variable [group A]
variable {B : Type}
variable [group B]
defini... |
f4af835466b8ba932545caf0f531b5acb52ca6d5 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/group_theory/archimedean.lean | 1e6c89f7fea43f96ac2ff136fe4b19c72c073985 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,071 | lean | /-
Copyright (c) 2020 Heather Macbeth, Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth, Patrick Massot
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.group_theory.subgroup
import Mathlib.algebra.archimedean
... |
ed973331af0482f0878e0357b8ab570b6e21d88b | 82b86ba2ae0d5aed0f01f49c46db5afec0eb2bd7 | /stage0/src/Std/Data/PersistentHashMap.lean | c013a97f9ecae34418ea736296f03f1ddba68b76 | [
"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 | 13,364 | 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 Std
universes u v w w'
namespace PersistentHashMap
inductive Entry (α : Type u) (β : Type v) (σ : Type w)
| entry (key : α) (val : β) : Entry ... |
89bfd7bc01b1e974c503ad39f1e579e4cec915e8 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/category/Module/change_of_rings.lean | 327a5e779e98a6a9c3de53fc937d4e4470f0f7fa | [
"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 | 22,698 | lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
import algebra.category.Module.basic
import ring_theory.tensor_product
/-!
# Change Of Rings
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file requi... |
dc37c5ebc7404b454b3219151aea9441d3aaccde | 271e26e338b0c14544a889c31c30b39c989f2e0f | /stage0/src/Init/System/IO.lean | e21ba6f2fc4f1f4807975e889593e2cff4a0880b | [
"Apache-2.0"
] | permissive | dgorokho/lean4 | 805f99b0b60c545b64ac34ab8237a8504f89d7d4 | e949a052bad59b1c7b54a82d24d516a656487d8a | refs/heads/master | 1,607,061,363,851 | 1,578,006,086,000 | 1,578,006,086,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,568 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Luke Nelson, Jared Roesch, Leonardo de Moura, Sebastian Ullrich
-/
prelude
import Init.Control.EState
import Init.Data.String.Basic
import Init.System.FilePath
/-- Like https:/... |
7465988a5497b02c6b12fec4d22810e826770c81 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/list/nodup_equiv_fin.lean | 9ea0ba982d781f3b610a95a23bf2f0d870959c2c | [
"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 | 8,520 | lean | /-
Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import data.fin.basic
import data.list.sort
import data.list.duplicate
/-!
# Equivalence between `fin (length l)` and elements of a list
> THIS FILE IS SYNC... |
40dd83538762fc0e3130e84487149d788a62904c | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/combinatorics/derangements/basic.lean | 6d0cce36db9ec479d4073cd961c8a5cc0b8994f4 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 8,321 | lean | /-
Copyright (c) 2021 Henry Swanson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Henry Swanson
-/
import dynamics.fixed_points.basic
import group_theory.perm.option
import logic.equiv.defs
import logic.equiv.option
/-!
# Derangements on types
In this file we defin... |
aebbb33cfcfe08d70b2c70c4fb68d8a1bb5da759 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/doNotation3.lean | ccccf9151b49623f3005627dc583ef7fa1cf768d | [
"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 | 2,685 | lean | theorem zero_lt_of_lt : {a b : Nat} → a < b → 0 < b
| 0, _, h => h
| a+1, b, h =>
have : a < b := Nat.lt_trans (Nat.lt_succ_self _) h
zero_lt_of_lt this
def fold {m α β} [Monad m] (as : Array α) (b : β) (f : α → β → m β) : m β := do
let rec loop : (i : Nat) → i ≤ as.size → β → m β
| 0, h, b => pure b
| i+1... |
e9765857946b184c58894784f832a2066dde6ff4 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/geometry/manifold/local_invariant_properties_auto.lean | 0cdb83efe842e54182b0b01bc1a644f9e1d4e96e | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 28,535 | lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.geometry.manifold.smooth_manifold_with_corners
import Mathlib.PostPort
universes u_1... |
c566d2461477ce01c906dad6eec02f8250c041ce | 076f5040b63237c6dd928c6401329ed5adcb0e44 | /instructor-notes/2019.09.17.notes.lean | 9fd04ec0792ebfd318baa0da1146ee2033e1ce1a | [] | no_license | kevinsullivan/uva-cs-dm-f19 | 0f123689cf6cb078f263950b18382a7086bf30be | 09a950752884bd7ade4be33e9e89a2c4b1927167 | refs/heads/master | 1,594,771,841,541 | 1,575,853,850,000 | 1,575,853,850,000 | 205,433,890 | 4 | 9 | null | 1,571,592,121,000 | 1,567,188,539,000 | Lean | UTF-8 | Lean | false | false | 2,367 | lean | -- Namespaces
-- Here is the global namespace
-- first namespace nested within global
namespace cs
def x := 1
#check x
#eval x
end cs
-- second namespace
namespace oc
def x := "Hi!"
#check x
#eval x
end oc
-- namespaces are closed by default
#eval cs.x
#eval oc.x
#eval x -- x not visible in global ns
open cs -- ... |
78e243bbb5953a512b9f5607bb4c9e60192cf917 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/algebra/tower.lean | 093a1ef2bb23d0e09bf2f4d61368a84f271b68b2 | [
"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 | 11,159 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Anne Baanen
-/
import algebra.algebra.basic
/-!
# Towers of algebras
In this file we prove basic facts about towers of algebra.
An algebra tower A/S/R is expressed by having ... |
3e6a56fb0592f655786bbac8a49f1d0a12e440af | bb31430994044506fa42fd667e2d556327e18dfe | /src/algebra/hom/non_unital_alg.lean | c60ff8177307c534a1e3e6c06b79011f9c7b95fd | [
"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 | 12,429 | 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.algebra.hom
/-!
# Morphisms of non-unital algebras
This file defines morphisms between two types, each of which carries:
* an addition,
* an additive zer... |
1fb8c01b50e3b10de3100ca2d61af0795a91dc77 | f083c4ed5d443659f3ed9b43b1ca5bb037ddeb58 | /linear_algebra/quotient_module.lean | ed4dec1b2a42e24418e6215e237f6905b7961f27 | [
"Apache-2.0"
] | permissive | semorrison/mathlib | 1be6f11086e0d24180fec4b9696d3ec58b439d10 | 20b4143976dad48e664c4847b75a85237dca0a89 | refs/heads/master | 1,583,799,212,170 | 1,535,634,130,000 | 1,535,730,505,000 | 129,076,205 | 0 | 0 | Apache-2.0 | 1,551,697,998,000 | 1,523,442,265,000 | Lean | UTF-8 | Lean | false | false | 4,333 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
Quotient construction on modules
-/
import linear_algebra.basic
namespace is_submodule
universes u v w
variables {α : Type u} {β : Type v} {γ : Type w}
variables [rin... |
dea755cc630dff252d8a47ab4cae996832c06b07 | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /tests/lean/run/inductive1.lean | ed52ba27f883266d80169c487a0112062d8595d3 | [
"Apache-2.0"
] | permissive | collares/lean4 | 861a9269c4592bce49b71059e232ff0bfe4594cc | 52a4f535d853a2c7c7eea5fee8a4fa04c682c1ee | refs/heads/master | 1,691,419,031,324 | 1,618,678,138,000 | 1,618,678,138,000 | 358,989,750 | 0 | 0 | Apache-2.0 | 1,618,696,333,000 | 1,618,696,333,000 | null | UTF-8 | Lean | false | false | 1,636 | lean |
inductive L1.{u} (α : Type u)
| nil
| cons : α → L1 α → L1 α
#check L1
#check @L1.cons
inductive L2.{u} (α : Type u)
| nil
| cons (head : α) (tail : L2 α)
#check @L2.cons
universes u v
variable (α : Type u)
inductive A (β : Type v)
| nil {}
| protected cons : α → β → A β → A β
#check @A.cons
#check A.nil Nat Bo... |
6d8ba5e5e92a664a5b07bda8726ec7054da1a012 | e9078bde91465351e1b354b353c9f9d8b8a9c8c2 | /helper_lemmas.hlean | 3250ffa2aaee6e75f79cd58f9276c8068f2fe711 | [
"Apache-2.0"
] | permissive | EgbertRijke/leansnippets | 09fb7a9813477471532fbdd50c99be8d8fe3e6c4 | 1d9a7059784c92c0281fcc7ce66ac7b3619c8661 | refs/heads/master | 1,610,743,957,626 | 1,442,532,603,000 | 1,442,532,603,000 | 41,563,379 | 0 | 0 | null | 1,440,787,514,000 | 1,440,787,514,000 | null | UTF-8 | Lean | false | false | 3,110 | hlean | /- NOT FOR BLESSED REPOSITORY -/
import types.eq types.pi hit.colimit cubical.square
open eq is_trunc unit quotient seq_colim is_equiv funext pi nat equiv
definition eq_of_homotopy_tr {A : Type} {B : A → Type} {C : Πa, B a → Type}
{f g : Πa, B a} {H : f ~ g} {a : A} (c : C a (f a)) :
eq_of_homotopy H ▸ c... |
46e5c111ef3c59f0940825880192232de8afaea3 | ce6917c5bacabee346655160b74a307b4a5ab620 | /src/ch4/ex0606.lean | 40306c52f9b58788f47681e1ebdc44e350fa3c90 | [] | 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 | 731 | lean | variables (real : Type) [ordered_ring real]
variables (log exp : real → real)
variable log_exp_eq : ∀ x, log (exp x) = x
variable exp_log_eq : ∀ {x}, x > 0 → exp (log x) = x
variable exp_pos : ∀ x, exp x > 0
variable exp_add : ∀ x y, exp (x + y) = exp x * exp y
-- this ensures the assumptions are available in tactic p... |
4dce9636c8b678cce98b64577f6be95b98f16340 | 761d983a78bc025071bac14a3facced881cf5e53 | /affine/eucl_norm.lean | 0707744c5a84d9fcd20f673ab0d71745e1ada7ef | [] | no_license | rohanrajnair/affine_lib | bcf22ff892cf74ccb36a95bc9b7fff8e0adb2d0d | 83076864245ac547b9d615bc6a23804b1b4a8f70 | refs/heads/master | 1,673,320,928,343 | 1,603,036,653,000 | 1,603,036,653,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 777 | lean | import analysis.normed_space.real_inner_product
import ..affine.aff_coord_space
variable n : ℕ
/-! ### rfl lemmas and prerequisite lemmas -/
/-! ### lemmas necessary to show type class instances -/
/-! ### type class instances -/
--first implement inner product (dot product)
instance : has_... |
ee7b8fedde2188be9ac6e415f07d441beb3633a6 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/data/pi/lex.lean | c6ac718a57a907a378679a82c27fb6e78507e746 | [
"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 | 5,194 | lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import order.well_founded
import algebra.group.pi
import order.min_max
/-!
# Lexicographic order on Pi types
This file defines the lexicographic order for Pi types. `a`... |
51e47e219c4973fcf1f693675aab84ce6bd2aba1 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /tests/lean/run/rewrite12.lean | 45dacfeb57445c4345b7c46f9ecb19ba6b3516bc | [
"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 | 305 | lean | import data.nat
open nat
variables (f : nat → nat → nat → nat) (a b c : nat)
example (H₁ : a = b) (H₂ : f b a b = 0) : f a a a = 0 :=
by rewrite [H₁ at -{2}, H₂]
example (H₁ : a = b) (H₂ : f b a b = 0) (H₃ : c = f a a a) : c = 0 :=
by rewrite [H₁ at H₃ -{2}, H₂ at H₃, H₃]
|
5f457dff5f24c2672b9fd22547707091518b9016 | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /stage0/src/Lean/Compiler/LCNF/ToLCNF.lean | 5c321fdf6c936d2f9b281566281f5a787e6cd794 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | tobiasgrosser/lean4 | ce0fd9cca0feba1100656679bf41f0bffdbabb71 | ebdbdc10436a4d9d6b66acf78aae7a23f5bd073f | refs/heads/master | 1,673,103,412,948 | 1,664,930,501,000 | 1,664,930,501,000 | 186,870,185 | 0 | 0 | Apache-2.0 | 1,665,129,237,000 | 1,557,939,901,000 | Lean | UTF-8 | Lean | false | false | 26,737 | lean | /-
Copyright (c) 2022 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.ProjFns
import Lean.Compiler.BorrowedAnnotation
import Lean.Compiler.LCNF.Types
import Lean.Compiler.LCNF.Bind
import Lean.Compiler.LCNF.InferTy... |
9adfeb561fe035fde3a410d62472a68b50795902 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /src/Init/Lean/Meta/Tactic/Assumption.lean | d874b4415e16d8f95eb4369c31237e11f91e2527 | [
"Apache-2.0"
] | permissive | mhuisi/lean4 | 28d35a4febc2e251c7f05492e13f3b05d6f9b7af | dda44bc47f3e5d024508060dac2bcb59fd12e4c0 | refs/heads/master | 1,621,225,489,283 | 1,585,142,689,000 | 1,585,142,689,000 | 250,590,438 | 0 | 2 | Apache-2.0 | 1,602,443,220,000 | 1,585,327,814,000 | C | UTF-8 | Lean | false | false | 791 | 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.Lean.Meta.ExprDefEq
import Init.Lean.Meta.Tactic.Util
namespace Lean
namespace Meta
def assumptionAux (mvarId : MVarId) : MetaM Bool :... |
78ebb58a6bf625e00e9314b9243273c2416e80db | 3dd1b66af77106badae6edb1c4dea91a146ead30 | /tests/lean/run/univ2.lean | 786d1a8c980e4e5ea74291c184e899e3cc417df3 | [
"Apache-2.0"
] | permissive | silky/lean | 79c20c15c93feef47bb659a2cc139b26f3614642 | df8b88dca2f8da1a422cb618cd476ef5be730546 | refs/heads/master | 1,610,737,587,697 | 1,406,574,534,000 | 1,406,574,534,000 | 22,362,176 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 278 | lean | import standard
hypothesis I : Type
definition F (X : Type) : Type := (X → Prop) → Prop
hypothesis unfold : I → F I
hypothesis fold : F I → I
hypothesis iso1 : ∀x, fold (unfold x) = x
variable sorry {A : Type} : A
theorem iso2 : ∀x, fold (unfold x) = x
:= sorry
|
6e63b65be164489fb78b30a8577861eab351b485 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/analysis/normed_space/multilinear.lean | 215cdacd8b096b4ab4ccbd068ceef5d89a680403 | [
"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 | 54,472 | lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import analysis.normed_space.operator_norm
import topology.algebra.multilinear
/-!
# Operator norm on the space of continuous multilinear maps
When `f` is a c... |
d9379e19bcec7babbf150fecd757c084fb18ecbf | 9a0b1b3a653ea926b03d1495fef64da1d14b3174 | /tidy/rewrite_search/discovery/screening.lean | 48dd2e190af7715932f3d4d5697e4800a072d38f | [
"Apache-2.0"
] | permissive | khoek/mathlib-tidy | 8623b27b4e04e7d598164e7eaf248610d58f768b | 866afa6ab597c47f1b72e8fe2b82b97fff5b980f | refs/heads/master | 1,585,598,975,772 | 1,538,659,544,000 | 1,538,659,544,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,320 | lean | import tidy.lib.list
import tidy.lib.env
import tidy.lib.tactic
import tidy.lib.pretty_print
open tactic tactic.interactive
open interactive
namespace tidy.rewrite_search.discovery
-- TODO make sure this didn't break anything
meta def is_acceptable_rewrite (t : expr) : bool :=
is_eq_or_iff_after_binders t
meta de... |
c0f6b63aecfc1fc4d09bff215baa3f1e2175627c | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/ring_theory/henselian.lean | 90b788067f64ec371e8095bdddf710b309c5a6c5 | [
"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 | 11,812 | lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import data.polynomial.taylor
import ring_theory.ideal.local_ring
import linear_algebra.adic_completion
/-!
# Henselian rings
In this file we set up the basic theo... |
59c164b4932da45f7e3fea850827efdc9cc65a0b | 38bf3fd2bb651ab70511408fcf70e2029e2ba310 | /src/ring_theory/multiplicity.lean | b12ef016f3971dd0a219bbf50ff3f4e5450b53c0 | [
"Apache-2.0"
] | permissive | JaredCorduan/mathlib | 130392594844f15dad65a9308c242551bae6cd2e | d5de80376088954d592a59326c14404f538050a1 | refs/heads/master | 1,595,862,206,333 | 1,570,816,457,000 | 1,570,816,457,000 | 209,134,499 | 0 | 0 | Apache-2.0 | 1,568,746,811,000 | 1,568,746,811,000 | null | UTF-8 | Lean | false | false | 17,301 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Chris Hughes
-/
import algebra.associated data.int.gcd algebra.big_operators
import tactic.converter.interactive
variables {α : Type*}
open nat roption
theorem nat... |
5c7d803551cf346b298883b5c6dbcae6cbfc8cc7 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/analysis/mean_inequalities_pow.lean | ea49f3cc8f0c267ede09070b85c21ad77fc97d18 | [
"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 | 12,868 | 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
/-!
# Mean value inequalities
In this file we prove several mean inequalities for finit... |
9f5b6d2e11e5272892f19ba27e6bf5aeb18374de | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/category_theory/limits/shapes/binary_products.lean | 31fa5a5992a07bc149e36bcb2d91a4cf28cb7c43 | [
"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 | 25,998 | 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.limits.limits
import category_theory.discrete_category
import category_theory.epi_mono
/-!
# Binary (co)products
We define a ca... |
6a9d238b9af5bfc9be20be0f927a2797c3d64cc2 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/topology/dense_embedding.lean | cb8bba18d0a98639e07e582609d6f4dfc69b8037 | [
"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 | 15,300 | 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
import topology.bases
/-!
# Dense embeddings
This file defines three properties of functions:
* `dense_rang... |
ac82182efd64348de1f3be75228deef26ea0fd59 | 75db7e3219bba2fbf41bf5b905f34fcb3c6ca3f2 | /library/theories/group_theory/perm.lean | 4ff686b6e6a941b563f86a83972234e7137d1871 | [
"Apache-2.0"
] | permissive | jroesch/lean | 30ef0860fa905d35b9ad6f76de1a4f65c9af6871 | 3de4ec1a6ce9a960feb2a48eeea8b53246fa34f2 | refs/heads/master | 1,586,090,835,348 | 1,455,142,203,000 | 1,455,142,277,000 | 51,536,958 | 1 | 0 | null | 1,455,215,811,000 | 1,455,215,811,000 | null | UTF-8 | Lean | false | false | 4,039 | 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 data.fintype.function
open nat list function
namespace group_theory
open fintype
section perm
variables {A : Type} [fintype A] [decidable_eq... |
e34b911765540b2e10ea58c5ed49f1ece16f9b36 | e0f9ba56b7fedc16ef8697f6caeef5898b435143 | /src/topology/algebra/module.lean | 8de3c4f6193f523a215b3b5aff0818fc01cccf21 | [
"Apache-2.0"
] | permissive | anrddh/mathlib | 6a374da53c7e3a35cb0298b0cd67824efef362b4 | a4266a01d2dcb10de19369307c986d038c7bb6a6 | refs/heads/master | 1,656,710,827,909 | 1,589,560,456,000 | 1,589,560,456,000 | 264,271,800 | 0 | 0 | Apache-2.0 | 1,589,568,062,000 | 1,589,568,061,000 | null | UTF-8 | Lean | false | false | 33,907 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo, Yury Kudryashov
-/
import topology.algebra.ring
import ring_theory.algebra
/-!
# Theory of topological modules and continuous linear ... |
2e8613cec2577be47aa97f5a43057e2eb9995826 | 82b86ba2ae0d5aed0f01f49c46db5afec0eb2bd7 | /stage0/src/Lean/Meta/Match/CaseArraySizes.lean | 1307da144bc3d30fdc0707befe685417686640e0 | [
"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 | 3,754 | 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.Assert
import Lean.Meta.Match.CaseValues
namespace Lean.Meta
structure CaseArraySizesSubgoal :=
(mvarId : MVarId)
(elems : Ar... |
392594af15812a6a30d7ef8b8d3d42d2f81a886c | 93b17e1ec33b7fd9fb0d8f958cdc9f2214b131a2 | /src/sep/rel_extra.lean | 01753929536c13285bbd3eedeb92a330bf708551 | [] | no_license | intoverflow/timesink | 93f8535cd504bc128ba1b57ce1eda4efc74e5136 | c25be4a2edb866ad0a9a87ee79e209afad6ab303 | refs/heads/master | 1,620,033,920,087 | 1,524,995,105,000 | 1,524,995,105,000 | 120,576,102 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,411 | lean | /- Extra stuff about relations
-
-/
import .rel
namespace Sep
universes ℓ₁ ℓ₂
-- More ways of writing up/down closed
def Rel.DownClosed' {A₁ : Alg.{ℓ₁}} {A₂ : Alg.{ℓ₂}} (r : Rel A₁ A₂) : Prop
:= ∀ m₃ n₁ n₂
, (∃ m₁ m₂, r n₁ m₁ ∧ r n₂ m₂ ∧ A₂.join m₁ m₂ m₃)
→ (∃ n₃, r n₃ m₃ ∧ A₁.join n₁ n₂ n₃)
def Rel.UpClo... |
afb9357c0ccdc592d5ff2d0126da9953694e2ecf | 4b846d8dabdc64e7ea03552bad8f7fa74763fc67 | /tests/lean/run/soundness.lean | 3b82199b94aeb71e0f01d83d67af9ce48054f75f | [
"Apache-2.0"
] | permissive | pacchiano/lean | 9324b33f3ac3b5c5647285160f9f6ea8d0d767dc | fdadada3a970377a6df8afcd629a6f2eab6e84e8 | refs/heads/master | 1,611,357,380,399 | 1,489,870,101,000 | 1,489,870,101,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,713 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
Define propositional calculus, valuation, provability, validity, prove soundness.
This file is based on Floris van Doorn Coq files.
Similar to soundness.lea... |
926f0cd074060a854c3a73b9ed7e4098171830d4 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/int/char_zero.lean | d23a772c2dc7d56c7075f3c5ff7152077973c418 | [] | 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 | 1,026 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.int.cast
import Mathlib.algebra.char_zero
import Mathlib.PostPort
universes u_1
nam... |
7041705eec00b7d110e4ce5be834094c86ac063c | d450724ba99f5b50b57d244eb41fef9f6789db81 | /src/homework/hw5.lean | 933e05fa68a08410802b2628661ef1f312377166 | [] | no_license | jakekauff/CS2120F21 | 4f009adeb4ce4a148442b562196d66cc6c04530c | e69529ec6f5d47a554291c4241a3d8ec4fe8f5ad | refs/heads/main | 1,693,841,880,030 | 1,637,604,848,000 | 1,637,604,848,000 | 399,946,698 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,138 | lean | import data.set
/-
CS2120 F21 HW5
The goals of this assignment are to give you
practice with proofs of propositions that use
existential quantificaton, and to develop your
understanding of formal and informal proofs in
set theory.
-/
/-
PART I: EXISTENTIAL QUANTIFICATION.
-/
/-
To start, suppose that α and β are ar... |
0f402c65a211fccae066a442bb6bb1d7064124ac | d450724ba99f5b50b57d244eb41fef9f6789db81 | /src/Submissions/practice_2.lean | 2d2973fd7b3547ca9c23de0c09339a53cd7cb2aa | [] | no_license | jakekauff/CS2120F21 | 4f009adeb4ce4a148442b562196d66cc6c04530c | e69529ec6f5d47a554291c4241a3d8ec4fe8f5ad | refs/heads/main | 1,693,841,880,030 | 1,637,604,848,000 | 1,637,604,848,000 | 399,946,698 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 15,103 | lean | /-
Group: Earth, Wind, and Fire
Jakob Kauffmann, jgk2qq@virginia.edu, https://github.com/jakekauff/CS2120F21.git
Jumi Hall, jah5py@virginia.edu, https://github.com/hubdaha/cs2120f21.git
Connor McCaffrey, cam7qp@virginia.edu, https://github.com/camccaffrey/cs2120.git
-/
/-
Prove the following simple logical conjectures.... |
05a5a139d4aeb436490357ef838dc5bbef4fa028 | 7a097aab717143b13a4a4f8824fe9cfe670a7883 | /src/smt2/lol.lean | 1bcc945aef14d0f3bde472412885944ef3a1cb9c | [
"Apache-2.0"
] | permissive | digama0/smt2_interface | 6b3bbc12cb90bd4bc70b07ca86918c1e9ff4ed97 | cf516ae4142f33adcf4b272758d63fee37ec9f7d | refs/heads/master | 1,611,266,770,453 | 1,498,177,713,000 | 1,498,177,713,000 | 95,167,865 | 0 | 0 | null | 1,498,177,813,000 | 1,498,177,813,000 | null | UTF-8 | Lean | false | false | 6,782 | lean | import smt2.syntax
import smt2.builder
import .except
-- instance {α : Type} [decidable_eq α] : decidable_eq (list α)
-- | [] [] := is_true rfl
-- | (a::l) [] := is_false (λh, list.no_confusion h)
-- | [] (b::l') := is_false (λh, list.no_confusion h)
-- | (a::l) (b::l') :=
-- begin
-- refine (if ... |
b3b029ed060736e342bc5b0c0432ac6f7cd8c6a0 | 4b846d8dabdc64e7ea03552bad8f7fa74763fc67 | /library/init/meta/vm.lean | cb1b02f0859912d1f84ac8c6b7cac673ff761616 | [
"Apache-2.0"
] | permissive | pacchiano/lean | 9324b33f3ac3b5c5647285160f9f6ea8d0d767dc | fdadada3a970377a6df8afcd629a6f2eab6e84e8 | refs/heads/master | 1,611,357,380,399 | 1,489,870,101,000 | 1,489,870,101,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,515 | 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.data.option.basic
import init.meta.mk_dec_eq_instance
meta constant vm_obj : Type
inductive vm_obj_kind
| simple | co... |
1e527b4b6f8d8058860f8ad9777654bd2ced1ec0 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/topology/sheaves/sheaf_condition/unique_gluing.lean | f12c4adc4668dceb835d3fffe14f139bf15a780f | [
"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 | 10,765 | lean | /-
Copyright (c) 2021 Justus Springer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Justus Springer
-/
import topology.sheaves.forget
import category_theory.limits.shapes.types
import topology.sheaves.sheaf
import category_theory.types
/-!
# The sheaf condition in t... |
00a7e443b315140c609d5823dc3ec9ae5953f831 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/linear_algebra/linear_independent.lean | 7242efa4e225652e70ba877053e2b99573933114 | [
"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 | 57,634 | 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 algebra.big_operators.fin
import linear_algebra.finsupp
import linear_algebra.prod
import set_theory.cardinal.bas... |
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