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7bec99c290df9175f257c0e1895c8640ccc32fb1 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/ring_theory/witt_vector/discrete_valuation_ring.lean | f6301992373301e37421eb0851b10950d3d9d6ac | [
"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 | 6,092 | lean | /-
Copyright (c) 2022 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Heather Macbeth, Johan Commelin
-/
import ring_theory.witt_vector.domain
import ring_theory.witt_vector.mul_coeff
import ring_theory.discrete_valuation_ring
import t... |
d54466967856b885496301a8899b66c862f6da0d | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/simple.lean | 3c6233398ae18b2ef76400d02ebdc425c7c21ee5 | [
"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 | 592 | lean | prelude
definition Prop : Sort.{1} := Sort.{0}
section
parameter A : Sort*
definition Eq (a b : A) : Prop
:= βP : A β Prop, P a β P b
@[elab_simple]
theorem subst (P : A β Prop) (a b : A) (H1 : Eq a b) (H2 : P a) : P b
:= H1 P H2
theorem refl (a : A) : Eq a a
:= Ξ» (P : A β Prop) (H : P a), H
theore... |
862d412d68a5e89fcd1aa62a9977692911df94da | 4727251e0cd73359b15b664c3170e5d754078599 | /src/field_theory/intermediate_field.lean | cdb81f585706c19d20ff1dbf10f45e6c2cbf7026 | [
"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 | 18,367 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import field_theory.subfield
import field_theory.tower
import ring_theory.algebraic
/-!
# Intermediate fields
Let `L / K` be a field extension, given as an instance `alg... |
3d9029aa7e018b5f70c7bbf11bfbe319d6b899fa | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/implicit4.lean | a78b279897a91a2c984ef484b560a7c5fc3af229 | [
"Apache-2.0"
] | permissive | codyroux/lean0.1 | 1ce92751d664aacff0529e139083304a7bbc8a71 | 0dc6fb974aa85ed6f305a2f4b10a53a44ee5f0ef | refs/heads/master | 1,610,830,535,062 | 1,402,150,480,000 | 1,402,150,480,000 | 19,588,851 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 315 | lean | import Int.
variable f {A : Type} (a1 a2 : A) {B : Type} (b1 b2 : B) : A
variable g {A1 A2 : Type} (a1 : A1) (a2 : A2) {B : Type} (b : B) : A1
variable p (a1 a2 : Int) {B : Type} (b1 b2 b3 : B) : B
variable h {A1 A2 : Type} (a1 : A1) (a2 : A2) (a3 : A2) : A1
infix ++ : f
infix ++ : g
infix ++ : p
infix ++ : h |
62d4a38c16777505e7d3724944394cb7648b44f7 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/data/nat/modeq.lean | 7bc8f6ead6859d77ad672790e52ca5d1c14338ad | [
"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 | 20,822 | 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 data.int.gcd
import data.list.rotate
import tactic.abel
/-!
# Congruences modulo a natural number
This file defines the equivalence relation `a β‘ b [MOD n]` ... |
cdf55509b60925d2dc5a0fbb29aeefd02d786313 | efa51dd2edbbbbd6c34bd0ce436415eb405832e7 | /20160406_UW/ex3.lean | 12287a036fb567d6f204fb3a03bdbc1f6b373312 | [
"Apache-2.0"
] | permissive | leanprover/presentations | dd031a05bcb12c8855676c77e52ed84246bd889a | 3ce2d132d299409f1de269fa8e95afa1333d644e | refs/heads/master | 1,688,703,388,796 | 1,686,838,383,000 | 1,687,465,742,000 | 29,750,158 | 12 | 9 | Apache-2.0 | 1,540,211,670,000 | 1,422,042,683,000 | Lean | UTF-8 | Lean | false | false | 206 | lean | import data.prod data.list
open nat prod list
eval default (nat β nat Γ list nat Γ Prop)
definition myval [instance] : inhabited nat :=
inhabited.mk 10
eval default (nat β nat Γ list nat Γ Prop)
|
d3afc63a66a18df57ab16d7f458e6e0b7bd1edee | d061d5c7ed1e060bdd505484b3baf743f4d7ba42 | /src/mywork/practice_1.lean | 3f7330e13cc7ae5a42b88c162e3cb3676799da90 | [] | no_license | alexcatahan1/cs2120f21 | efbdaf901d29499a2726be966dc5f182823c5e10 | 40c15c5faa3e6c24244e41247c42d06ef74ce9d2 | refs/heads/main | 1,691,079,398,044 | 1,631,911,953,000 | 1,631,911,953,000 | 407,617,932 | 0 | 0 | null | 1,631,897,898,000 | 1,631,897,898,000 | null | UTF-8 | Lean | false | false | 6,788 | lean | /-
Giraffe
ctg8h@virginia.edu, https://github.com/ColeGinghina/cs2120f21.git
rac4sq@virginia.edu, https://github.com/alexcatahan1/cs2120f21.git
hl7zp@virginia.edu, https://github.com/hanyangli2/cs2120f21.git
-/
/-
EQUALITY
-/
/- #1
Suppose that x, y, z, and w are arbitrary objects of some type,
T; and suppose furth... |
86eb87f98bb1c17ee0ef12bc6f0db9fab8df3bb2 | 0f5090f82d527e0df5bf3adac9f9e2e1d81d71e2 | /src/kenji/scratch.lean | 9ed2509cb6bc9dff5096503bc47e338e4a9ea142 | [] | no_license | apurvanakade/mc2020-lean-projects | 36eb42c4baccc37183635c36f8e1b3afa4ec1230 | 02466225aa629ab1232043bcc0a053a099fdb939 | refs/heads/master | 1,688,791,717,534 | 1,597,874,092,000 | 1,597,874,092,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,295 | lean | import ring_theory.fractional_ideal
import ring_theory.discrete_valuation_ring
import linear_algebra.basic
import order.zorn
universes u v
variables (R : Type u) [comm_ring R] {A : Type v} [comm_ring A]
variables (K : Type u) [field K] (R' : Type u) [integral_domain R']
variables [algebra R A]
open function
open_loc... |
9ce0f5f4306d5eb6b779b3f94262daf4caa4c3a6 | 12dabd587ce2621d9a4eff9f16e354d02e206c8e | /world03/level08.lean | 9fa36241487cbaa1847f2c52e44acb6b79a0a972 | [] | no_license | abdelq/natural-number-game | a1b5b8f1d52625a7addcefc97c966d3f06a48263 | bbddadc6d2e78ece2e9acd40fa7702ecc2db75c2 | refs/heads/master | 1,668,606,478,691 | 1,594,175,058,000 | 1,594,175,058,000 | 278,673,209 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 152 | lean | lemma mul_comm (a b : mynat) : a * b = b * a :=
begin
induction a with h hd,
rw zero_mul,
rw mul_zero,
refl,
rw succ_mul,
rw mul_succ,
rw hd,
refl,
end
|
830c1b03e31b6e4b2bd58d02e481b79b8e2871cf | 690889011852559ee5ac4dfea77092de8c832e7e | /src/tactic/rcases.lean | ad91c1784dce742c8db86d5426c7cb869f787111 | [
"Apache-2.0"
] | permissive | williamdemeo/mathlib | f6df180148f8acc91de9ba5e558976ab40a872c7 | 1fa03c29f9f273203bbffb79d10d31f696b3d317 | refs/heads/master | 1,584,785,260,929 | 1,572,195,914,000 | 1,572,195,913,000 | 138,435,193 | 0 | 0 | Apache-2.0 | 1,529,789,739,000 | 1,529,789,739,000 | null | UTF-8 | Lean | false | false | 18,597 | 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 data.dlist tactic.core
open lean lean.parser
namespace tactic
/-
These synonyms for `list` are used to clarify the meanings of the many
usages of lists in t... |
5c0fd47830dbfc48d25a7f32c2daa85b1d526b2f | 38bf3fd2bb651ab70511408fcf70e2029e2ba310 | /src/topology/uniform_space/basic.lean | 8131e9773fd48bbabf8a104dcec48982c312ebe9 | [
"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 | 41,959 | lean | /-
Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl, Mario Carneiro, Patrick Massot
Theory of uniform spaces.
Uniform spaces are a generalization of metric spaces and topological groups. Many concepts directly
generaliz... |
f4f42d4f0f529e2882f95c6ada8519800479160e | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/cast_sorry_bug.lean | a03e9610cb83d55968ba2d2b282d5e88954d0b49 | [
"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 | 358 | lean | open nat
inductive Fin : β β Type
| zero : Ξ {n : β}, Fin (succ n)
| succ : Ξ {n : β}, Fin n β Fin (succ n)
theorem foo (n m : β) (a : Fin n) (b : Fin m) (H : n = m) : cast (congr_arg Fin H) a = b :=
have eq : Fin n = Fin m, from congr_arg Fin H,
have ceq : cast eq a = b, from sorry, -- sorry implicit argument must ... |
a17fd857a69cf6f3674b58e2b0ce97039d86f6c6 | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /tests/lean/run/new_inductive2.lean | fd92c6be7cf8d91ad7be498f86170100a68e06ec | [
"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 | 344 | lean |
universes u v
inductive arrow (Ξ± : Type u) (Ξ² : Type v)
| mk : (Ξ± β Ξ²) β arrow Ξ± Ξ²
inductive foo
| mk : arrow Nat foo β foo
#print foo
#print foo.rec
set_option pp.all true
#print foo.below
mutual
inductive foo2 : Type
| mk : arrow2 β foo2
inductive arrow2 : Type
| mk : (Nat β foo2) β arrow2
end
#print foo2.b... |
84ae092572f32038e705d0635968678f43a65285 | fecda8e6b848337561d6467a1e30cf23176d6ad0 | /src/data/nat/parity.lean | dd2fe9231d2f705049f6ac4b5ef024a71bfd260a | [
"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 | 4,079 | lean | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
The `even` predicate on the natural numbers.
-/
import data.nat.modeq
namespace nat
@[simp] theorem mod_two_ne_one {n : nat} : Β¬ n % 2 = 1 β n % 2 = 0 :=
by cases mod_t... |
0cfea97cba4fbf531aec5ef1ddf763dbc38c2200 | 6b2a480f27775cba4f3ae191b1c1387a29de586e | /group_rep1/perm_action_matrix.lean | 82f3aa1a1af4f6698a43d47c25e5bf3e92551dc7 | [] | no_license | Or7ando/group_representation | a681de2e19d1930a1e1be573d6735a2f0b8356cb | 9b576984f17764ebf26c8caa2a542d248f1b50d2 | refs/heads/master | 1,662,413,107,324 | 1,590,302,389,000 | 1,590,302,389,000 | 258,130,829 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 2,282 | lean | import matrix_representation
import action_refondation
import matrix_representation_refondation
set_option trace.simplify.rewrite true
open is_basis linear_map character
--set_option trace.simplify true
universes u v w w'
open general classical_basis
variables (G : Type u) [group G]
(R : Type v) [comm_ring... |
5a3e97f1e2897fa89d4edfe9d772b6cf2f5789d0 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/topology/metric_space/hausdorff_dimension.lean | 976e0f419be16c7913de0975c82f71f95b49925f | [
"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 | 22,834 | 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 measure_theory.measure.hausdorff
/-!
# Hausdorff dimension
The Hausdorff dimension of a set `X` in an (extended) metric space is the unique number
`dimH s ... |
45e65d46dbc63ced82cab5973834d7aa0056ae7a | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/testing/slim_check/gen.lean | 2c031c925f0b4e9fac60f5ba8e49c0dc06b4f7cd | [
"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 | 5,698 | lean | /-
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author(s): Simon Hudon
-/
import control.uliftable
import system.random
import system.random.basic
/-!
# `gen` Monad
This monad is used to formulate randomized computations with a parameter
to ... |
4e29b999edb2bc0385209add66ef6077992cdb8b | 4727251e0cd73359b15b664c3170e5d754078599 | /src/tactic/reassoc_axiom.lean | 3f07919e3d73fb9c4c0382bfd203ba0fcb2bd5ee | [
"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 | 8,012 | lean | /-
Copyright (c) 2019 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import category_theory.category.basic
/-!
# Tools to reformulate category-theoretic axioms in a more associativity-friendly way
## The `reassoc` attribute
The `reassoc` ... |
b5a1e7f018caaa65cd524da33fe6ad0656ff1670 | 75db7e3219bba2fbf41bf5b905f34fcb3c6ca3f2 | /library/logic/examples/propositional/soundness.lean | 75fb9fad5837a8115e95a72321c6b06a138542dd | [
"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 | 6,375 | 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.
-/
import data.nat data.l... |
9d2095ef197a38354600a0a6315db2d97627237e | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/products/bifunctor_auto.lean | 9ba8f62b1c8642d4ec5c8e3076ea802616f7c4d6 | [] | 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 | 1,811 | 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
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.products.basic
import Mathlib.PostPort
universes vβ vβ vβ ... |
7d399fc91d60a7358a23cdd063287f70495eb668 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/data/string/defs.lean | ee89f6bf6a45a1aad96349b616bdbb3f25271477 | [
"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 | 1,025 | lean | import data.list.defs
namespace string
def map_tokens (c : char) (f : list string β list string) : string β string :=
intercalate (singleton c) β f β split (= c)
def over_list (f : list char β list char) : string β string :=
list.as_string β f β string.to_list
def split_on (c : char) (s : string) : list string :=
(... |
f4ab8f15cb239297d384c5da662ef75d9d4678eb | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/algebra/lie/basic.lean | a29c79666dcf7bb2ff8880d963df5af138370e5f | [
"Apache-2.0"
] | permissive | hamdysalah1/mathlib | b915f86b2503feeae268de369f1b16932321f097 | 95454452f6b3569bf967d35aab8d852b1ddf8017 | refs/heads/master | 1,677,154,116,545 | 1,611,797,994,000 | 1,611,797,994,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 80,822 | lean | /-
Copyright (c) 2019 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import data.bracket
import algebra.algebra.basic
import linear_algebra.bilinear_form
import linear_algebra.matrix
import order.preorder_hom
import order.compactly_generated... |
bcf43a9616c2e049486805881a235541c7afb78d | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/computability/turing_machine.lean | 1500d95d699313566eff6f7ddd8502e4a1a355f9 | [
"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 | 109,706 | 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 data.fintype.basic
import data.pfun
import logic.function.iterate
import order.basic
import tactic.apply_fun
/-!
# Turing machines
This file defines a sequen... |
f0d1f72488fa53cdbdbbf0e016756ddd77a46ba3 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/complex/orientation.lean | 074bfb08338d6a017b3e3012f7bff872d72a230f | [
"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 | 679 | 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 data.complex.module
import linear_algebra.orientation
/-!
# The standard orientation on `β`.
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to th... |
ff12cc77194609be6a2d7927645ade28b55fed49 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/complex/exponential.lean | 93f1c6224e39fedea437c80e3983ede1354becd6 | [
"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 | 65,814 | 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
-/
import algebra.geom_sum
import data.complex.basic
import data.nat.choose.sum
/-!
# Exponential, trigonometric and hyperbolic trigonometric func... |
5b8f370063ac7016f769ef4060e7b7a4dcb0da7b | 4727251e0cd73359b15b664c3170e5d754078599 | /src/ring_theory/localization/ideal.lean | 9ccf7028ff2bf0b38d1ac95912bfce388432d715 | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 9,018 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen
-/
import ring_theory.ideal.operations
import ring_theory.localization.basic
/-!
# Ideals in localizations of comm... |
774e4c46e70f0e7fc86ec614faaf986e25d26781 | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /library/classical.lean | 464f744fc470f39f902535513eda3a38f6e1fa9f | [
"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 | 183 | lean | -- Copyright (c) 2014 Jeremy Avigad. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Author: Jeremy Avigad
import standard logic.axioms |
7501e2df5866156641efec646e962b7fc3ad708e | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/group_theory/free_abelian_group.lean | 062b0a8839c5703514038cc1f00fdad0377c1c1c | [
"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 | 19,468 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import algebra.group.pi
import group_theory.free_group
import group_theory.abelianization
import algebra.module.basic -- we use the β€-module structure on an add_comm_group in ... |
40ad4eac07d347c2cb620c6cbfb656506ae10335 | 737dc4b96c97368cb66b925eeea3ab633ec3d702 | /stage0/src/Init/Control/Option.lean | 102dc14ff91595d480e89b0a50ac17e5c43842e5 | [
"Apache-2.0"
] | permissive | Bioye97/lean4 | 1ace34638efd9913dc5991443777b01a08983289 | bc3900cbb9adda83eed7e6affeaade7cfd07716d | refs/heads/master | 1,690,589,820,211 | 1,631,051,000,000 | 1,631,067,598,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,170 | 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, Sebastian Ullrich
-/
prelude
import Init.Data.Option.Basic
import Init.Control.Basic
import Init.Control.Except
universe u v
instance {Ξ±} : ToBool (Option Ξ±... |
94bace8bf60059cacb9f86c622a7b44a92c81491 | 6b02ce66658141f3e0aa3dfa88cd30bbbb24d17b | /tests/lean/match2.lean | 9097849e3d59567751360fef67a0e926211d06c5 | [
"Apache-2.0"
] | permissive | pbrinkmeier/lean4 | d31991fd64095e64490cb7157bcc6803f9c48af4 | 32fd82efc2eaf1232299e930ec16624b370eac39 | refs/heads/master | 1,681,364,001,662 | 1,618,425,427,000 | 1,618,425,427,000 | 358,314,562 | 0 | 0 | Apache-2.0 | 1,618,504,558,000 | 1,618,501,999,000 | null | UTF-8 | Lean | false | false | 1,589 | lean | #print "---- Op"
inductive Op : Nat β Nat β Type
| mk : β n, Op n n
structure Node : Type where
idβ : Nat
idβ : Nat
o : Op idβ idβ
def h1 (x : List Node) : Bool :=
match x with
| _ :: Node.mk _ _ (Op.mk 0) :: _ => true
| _ => false
def mkNode (n : Nat) : Node := { idβ... |
b7321706b78541d4eef34ae3aa2f26947def66b6 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/category_theory/limits/shapes/finite_limits.lean | b52b3f43df788b99a7eda5bc8f4a3a59c60a6f30 | [
"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 | 6,810 | 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 data.fintype.basic
import category_theory.fin_category
import category_theory.limits.shapes.products
import category_theory.limits.shapes.equalizers
import cat... |
b4c5ecbe5e2ae8eac12008b9a2f72ab891ac54d9 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/algebra/char_p/algebra.lean | feebf7234a3854359d3e35d4425e454e8c3d2297 | [
"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 | 4,021 | lean | /-
Copyright (c) 2021 Jon Eugster. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jon Eugster, Eric Wieser
-/
import algebra.char_p.basic
import ring_theory.localization.fraction_ring
import algebra.free_algebra
/-!
# Characteristics of algebras
In this file we desc... |
e2aaa3bcc522a682c219975d887bc1536d13bd3f | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/data/set/intervals/ord_connected.lean | 358937c1d2b2c41390a8a630a3f00adcba3b1dcf | [
"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 | 8,472 | 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.set.intervals.unordered_interval
import data.set.lattice
/-!
# Order-connected sets
We say that a set `s : set Ξ±` is `ord_connected` if for all ... |
35fca3572b75fd8cbb5153d978f3d3729323df3c | 9dd3f3912f7321eb58ee9aa8f21778ad6221f87c | /tests/lean/run/dep_coe_to_fn.lean | 10be2341f3a1105cec5e03cf712088864b33e2bb | [
"Apache-2.0"
] | permissive | bre7k30/lean | de893411bcfa7b3c5572e61b9e1c52951b310aa4 | 5a924699d076dab1bd5af23a8f910b433e598d7a | refs/heads/master | 1,610,900,145,817 | 1,488,006,845,000 | 1,488,006,845,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 252 | lean | universe variables u v
structure Func :=
(A : Type u) (B : Type v) (fn : A β B β A)
instance F_to_fn : has_coe_to_fun Func :=
{ F := Ξ» f, f^.A β f^.B β f^.A,
coe := Ξ» f, f^.fn }
variables (f : Func) (a : f^.A) (b : f^.B)
check (f a b)
|
93939c9c9976c51e1a9f52f74213022d4a6d0cb9 | f4bff2062c030df03d65e8b69c88f79b63a359d8 | /src/game/max/level03.lean | c70f2f4ee5719fba47d5dc651bb98b6d7bd58d71 | [
"Apache-2.0"
] | permissive | adastra7470/real-number-game | 776606961f52db0eb824555ed2f8e16f92216ea3 | f9dcb7d9255a79b57e62038228a23346c2dc301b | refs/heads/master | 1,669,221,575,893 | 1,594,669,800,000 | 1,594,669,800,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 802 | lean | import game.max.level02 -- hide
open_locale classical -- hide
noncomputable theory -- hide
namespace xena -- hide
/-
# Chapter ? : Max and abs
## Level 3
`le_max_left` is the statement that `a β€ max a b`.
Technical note: in contrast to the natural number game, the `rw` used
in the real number game is Lean's more... |
45869c98e63ee80b2331e00d6a428c54cc66dc8b | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /hott/algebra/precategory/basic.hlean | 2b9ba9e83dea2e6f750433f8b8b65cde7ef142e1 | [
"Apache-2.0"
] | permissive | tjiaqi/lean | 4634d729795c164664d10d093f3545287c76628f | d0ce4cf62f4246b0600c07e074d86e51f2195e30 | refs/heads/master | 1,622,323,796,480 | 1,422,643,069,000 | 1,422,643,069,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,201 | hlean | -- Copyright (c) 2014 Floris van Doorn. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Author: Floris van Doorn
open eq truncation
structure precategory [class] (ob : Type) : Type :=
(hom : ob β ob β Type)
(homH : Ξ {a b : ob}, is_hset (hom a b))
(comp : Ξ β¦a b c :... |
2b7eb9011bd6f261146c71fdfde589984c5a8902 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/rat/sqrt.lean | 82702e4ca6c037e32f854e7fd1008ad4082de493 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 1,307 | lean | /-
Copyright (c) 2019 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl, Mario Carneiro
-/
import data.rat.order
import data.rat.lemmas
import data.int.sqrt
/-!
# Square root on rational numbers
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
>... |
97cdcf8518087ba888e3776a50e55e4530dde91c | 4727251e0cd73359b15b664c3170e5d754078599 | /src/computability/DFA.lean | f369a88bf8dd17bcc36d42a21e44b21a595d32a0 | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 5,270 | lean | /-
Copyright (c) 2020 Fox Thomson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fox Thomson
-/
import data.fintype.basic
import computability.language
import tactic.norm_num
/-!
# Deterministic Finite Automata
This file contains the definition of a Deterministic Fi... |
791dff3f536996cc74f02a0f8c8c01a8c345e5f8 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/order/category/BddLat.lean | 9ba37c0bf28291951a27a326e4549cc2ac194c6e | [
"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 | 6,497 | lean | /-
Copyright (c) 2022 YaΓ«l Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: YaΓ«l Dillies
-/
import category_theory.adjunction.opposites
import order.category.BddOrd
import order.category.Lat
import order.category.Semilat
/-!
# The category of bounded lattices
... |
4bb11f1767a4f05594d698cba4f3a97e5f0b53c3 | 618003631150032a5676f229d13a079ac875ff77 | /src/order/copy.lean | 393548b0e4756eccda0aca700096e0f28580a25c | [
"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 | 4,599 | 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 order.conditionally_complete_lattice
/-!
# Tooling to make copies of lattice structures
Sometimes it is useful to make a copy of a lattice structure
where on... |
6288a41220d9255e215033fd90f97f1e26059730 | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/data/polynomial/monic.lean | 028441eae0058be39db35604b0d2c66411a0f71b | [
"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 | 9,367 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes HΓΆlzl, Scott Morrison, Jens Wagemaker
-/
import data.polynomial.degree
import algebra.associated
import tactic.omega
/-!
# Theory of monic polynomials
We give se... |
b78d31753914a0432f4e92a6e4e742564405b05b | f5f7e6fae601a5fe3cac7cc3ed353ed781d62419 | /src/topology/bounded_continuous_function.lean | c77d7c5df0d67e6180b908543e4b28424254953e | [
"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 | 23,570 | lean | /-
Copyright (c) 2018 SΓ©bastien GouΓ«zel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: SΓ©bastien GouΓ«zel, Mario Carneiro
Type of bounded continuous functions taking values in a metric space, with
the uniform distance.
-/
import analysis.normed_space.basic topology.... |
20706c896268d480a5ee1ebd7df78ed8046f3504 | 618003631150032a5676f229d13a079ac875ff77 | /src/analysis/normed_space/multilinear.lean | e7a482cd9a97ca1dd523f6d51d1e2f3f9884923b | [
"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 | 55,566 | lean | /-
Copyright (c) 2020 SΓ©bastien GouΓ«zel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: SΓ©bastien GouΓ«zel
-/
import analysis.normed_space.operator_norm
import topology.algebra.multilinear
/-!
# Operator norm on the space of continuous multilinear maps
When `f` is a c... |
9db9b0b7534ccdb724ddf856cab9e7587238da7a | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/topology/sheaves/sheaf_condition/pairwise_intersections.lean | 86c3402e535bca7a80fd4d68d24911b6c0b8bfcb | [] | 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 | 12,400 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.topology.sheaves.sheaf
import Mathlib.category_theory.limits.preserves.basic
import Mathlib... |
d0a9db475f34c1e9aa91da37557f80ecbf2e6ab7 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/category_theory/abelian/images.lean | 5e2d2a2bf1c46396d88d8778f45d10ac5364da30 | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 3,888 | lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Scott Morrison
-/
import category_theory.limits.shapes.kernels
/-!
# The abelian image and coimage.
In an abelian category we usually want the image of a morphism `f` t... |
1ec06f7f830d5e54acea03a86383783e51709cd7 | b147e1312077cdcfea8e6756207b3fa538982e12 | /data/equiv/basic.lean | 6bc7b8a0e52dc65f6003f16ea43b284706f4f8c6 | [
"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 | 24,500 | 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... |
96ea1fb417ef699e6390f517f512bb503e3bc518 | 3268ab3a126f0fef71459fbf170dc38efe5d0506 | /algebra/quotient_group.hlean | bdc433de2b6894e377d508526784ab008f4c7986 | [
"Apache-2.0"
] | permissive | soraismus/Spectral | f043fed1a4e02ddfeba531769b2980eb817471f4 | 32512bf47db3a1b932856e7ed7c7830b1fc07ef0 | refs/heads/master | 1,585,628,705,579 | 1,538,609,948,000 | 1,538,609,974,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 28,873 | 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, Egbert Rijke, Jeremy Avigad
Constructions with groups
-/
import hit.set_quotient .subgroup ..move_to_lib types.equiv
open eq algebra is_trunc set_quotient relati... |
d4459c16288ff0a677d82e2f9227a8018f1734b2 | 6b9565799c5c4b76978fc138a9aa7becedecd541 | /library/standard/list.lean | 4d8ccd5089fcfc69b2ef9d6f08e7a6c526a675b3 | [
"Apache-2.0"
] | permissive | leanparikshit/libraries | 657c9c09723523592b1d2021496f6f8041659130 | cbe08140e93fbde4cc81ef212fc65fbe357c5b59 | refs/heads/master | 1,586,305,043,220 | 1,401,535,624,000 | 1,401,535,624,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,246 | lean | ----------------------------------------------------------------------------------------------------
--
-- list.lean
--
-- Experimenting with lists.
--
-- authors: Jeremy Avigad, Parikshit Khanna
--
----------------------------------------------------------------------------------------------------
import macros
impor... |
b28a45bcba1e77140a21a58f9fcb38a0dfda6824 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/topology/compacts.lean | 32c0cb0103d6c8a3aa10bb792635dd8eeadda3fa | [] | 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 | 5,663 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.topology.homeomorph
import Mathlib.PostPort
universes u_1 u_2
namespace Mathlib
/-!... |
8e5cb29d044ff9fefd92cfb616cc2cf238d5e2a4 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/algebra/big_operators/intervals.lean | 2877c092ad5626411f6188de4a28505c80c01ac7 | [
"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 | 5,603 | lean | /-
Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl
-/
import algebra.big_operators.basic
import data.finset.intervals
/-!
# Results about big operators over intervals
We prove results about big operators over interva... |
d81c0e7e175160305897a64437ec22d621aa55a9 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/algebra/associated.lean | 0a0299ddbf6a9893974b4fed7837ba2f788f520c | [
"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 | 29,393 | lean | /-
Copyright (c) 2018 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl, Jens Wagemaker
-/
import algebra.big_operators.basic
import algebra.divisibility
import algebra.invertible
/-!
# Associated, prime, and irreducible elements.
-/
varia... |
9bba81a5b2f192b489485f757734e3ce07bd40be | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/data/nat/choose/basic.lean | 981a5eac18be6207ddf8cf845ea378b4daa55452 | [
"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 | 11,482 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Bhavik Mehta
-/
import data.nat.factorial
/-!
# Binomial coefficients
This file defines binomial coefficients and proves simple lemmas (i.e. those not
requiring more impo... |
d30d7f37fd2c8d8501627d6e4b38034932405e30 | eb9357a70318e50e095b58730bebfe0cffee457f | /lean/love07_metaprogramming_demo.lean | 984edcbd5d09ca0a225d5ca6aa6a60070ce58103 | [] | no_license | Vierkantor/logical_verification_2021 | 7485dd916953131d501760f023d5b30fbb74d36a | 9500b9c194e22a9ab4067321cfed7a1f445afcfc | refs/heads/main | 1,692,560,845,086 | 1,624,721,275,000 | 1,624,721,275,000 | 416,354,079 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,384 | lean | import .love05_inductive_predicates_demo
/-! # LoVe Demo 7: Metaprogramming
Users can extend Lean with custom tactics and tools. This kind of
programmingβprogramming the proverβis called metaprogramming.
Lean's metaprogramming framework uses mostly the same notions and syntax as
Lean's input language itself. Abstra... |
a48edcb8741cb48de58e5309abc7f4a6ccf718cd | 1717bcbca047a0d25d687e7e9cd482fba00d058f | /src/algebra/field.lean | 1f1bea341b8bbb830aac2aa348330d12212a56ae | [
"Apache-2.0"
] | permissive | swapnilkapoor22/mathlib | 51ad5804e6a0635ed5c7611cee73e089ab271060 | 3e7efd4ecd5d379932a89212eebd362beb01309e | refs/heads/master | 1,676,467,741,465 | 1,610,301,556,000 | 1,610,301,556,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,955 | lean | /-
Copyright (c) 2014 Robert Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Lewis, Leonardo de Moura, Johannes HΓΆlzl, Mario Carneiro
-/
import algebra.ring.basic
import algebra.group_with_zero
open set
set_option old_structure_cmd true
universe u
variab... |
c2b5c00a7a803cecbe5cd9cb098d14a9e70c6641 | d718c3849c9ac45bd482d671f56c3831e5f2e699 | /src/tactic/local_cache.lean | 481487f6618c6e0cdcaa8add34935a700c810651 | [] | no_license | khoek/lean-local-cache | a4089ed9a6bdc21254b22b387b2dd4d0fb79659c | 4cd64e20628be2a33d138a31dcc5b64ec57d13b7 | refs/heads/master | 1,588,230,294,496 | 1,553,071,246,000 | 1,553,071,246,000 | 176,673,783 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,107 | lean | import tactic.basic
namespace name
private def from_components_aux : name β list string β name
| n [] := n
| n (s :: rest) := from_components_aux (name.mk_string s n) rest
def from_components (l : list string) : name :=
from_components_aux name.anonymous l
end name
namespace tactic
namespace local_cache
section i... |
02d7de895edf233fa1228d02f40fc3fba4112727 | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /tests/lean/substlet.lean | 53bf8c374c189a0ff758951f5a1ec2ce4de22c87 | [
"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 | 526 | lean | theorem ex1 (n : Nat) : 0 + n = n := by
let m := n
have h : β k, id k = m := β¨m, rflβ©
cases h with
| intro a e =>
traceState
subst e
traceState
apply Nat.zero_add
theorem ex2 (n : Nat) : 0 + n = n := by
let m := n
have h : β k, m = id k := β¨m, rflβ©
cases h with
| intro a e =>
traceS... |
9c61f5e7ed8b527fec60779d351f8b3f6c2843ea | 43390109ab88557e6090f3245c47479c123ee500 | /src/M1F/problem_bank/0103/Q0103.lean | 592acc443a99a695f38b3d0685c0845926bf40f9 | [
"Apache-2.0"
] | permissive | Ja1941/xena-UROP-2018 | 41f0956519f94d56b8bf6834a8d39473f4923200 | b111fb87f343cf79eca3b886f99ee15c1dd9884b | refs/heads/master | 1,662,355,955,139 | 1,590,577,325,000 | 1,590,577,325,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 984 | lean | /-
M1F 2017-18 Sheet 1 Question 1
Author : Kevin Buzzard
This file should work with any version of lean -- whether you installed it yourself
or are running the version on https://leanprover.github.io/live/latest/
-/
-- We probably need the "law of the excluded middle" for this question -- every
-- proposition is eith... |
77966ed84288480a4cb6384abdf118a870576e7d | 947b78d97130d56365ae2ec264df196ce769371a | /stage0/src/Lean/Elab/Inductive.lean | 71c85c117c5c2fdd66541ab1ad1295da001954ed | [
"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 | 22,060 | 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.Elab.Command
impor... |
2486e96d4cc69b081958ff236820fd323a287bda | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/algebraic_geometry/locally_ringed_space/has_colimits.lean | 914c360cfb4d05723d6f71d614f103e18b1e0279 | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 12,783 | lean | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import algebraic_geometry.locally_ringed_space
import algebra.category.CommRing.constructions
import algebraic_geometry.open_immersion
import category_theory.limits.constru... |
035852e165e21cbef1d6f1da6ffc542cc545e865 | 75db7e3219bba2fbf41bf5b905f34fcb3c6ca3f2 | /hott/algebra/category/constructions/initial.hlean | 0cf3dfcb0cbc76d94897805e88c1d081c7f3dcff | [
"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 | 1,382 | 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
Initial category
-/
import .indiscrete
open functor is_trunc eq
namespace category
definition initial_precategory [constructor] : precategory empty :=
indi... |
fcef462588912db49acb2fbcd75b7e268ff4fb0a | 94e33a31faa76775069b071adea97e86e218a8ee | /src/topology/continuous_function/weierstrass.lean | 665260cde375daa05f4baace277ef303eb0bec3b | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 5,409 | lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import analysis.special_functions.bernstein
import topology.algebra.algebra
/-!
# The Weierstrass approximation theorem for continuous functions on `[a,b]`
We've al... |
9a17ac42b18d0a8f8106e7dacda4b8f85d60758f | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/geometry/euclidean/default.lean | 92f3395b0c2a14881e3fbc9ef396c841532531c4 | [] | 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 | 280 | lean | import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.geometry.euclidean.basic
import Mathlib.geometry.euclidean.circumcenter
import Mathlib.geometry.euclidean.monge_point
import Mathlib.geometry.euclidean.triangle
import Mathlib.PostPort
namespace Mathlib
|
29219343842bf8d1964c16229a718efc62a84234 | 859855170b866e395d328ebb28c4e060aa5559e8 | /src/solutions/tuto_lib.lean | 11375fc69ffc3c2e85eb64534816e3aaba427805 | [
"Apache-2.0"
] | permissive | bradheintz/tutorials | 1be40c9e97a484441f268ea8504c3d74534162cf | 02f15b400478de7278f4baa08935befd0f3986ef | refs/heads/master | 1,688,028,802,367 | 1,627,863,284,000 | 1,627,863,284,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,817 | lean | import analysis.specific_limits
import data.int.parity
import topology.sequences
attribute [instance] classical.prop_decidable
/-
Lemmas from that file were hidden in my course, or restating things which
were proved without name in previous files.
-/
notation `|`x`|` := abs x
-- The mathlib version is unusable bec... |
5b90a4d1a132b79f303017426a2c1196e9b2ac1c | 88892181780ff536a81e794003fe058062f06758 | /src/positive_nat/basic.lean | f0bb3d761d6185060eab34b001404e7cee250f54 | [] | no_license | AtnNn/lean-sandbox | fe2c44280444e8bb8146ab8ac391c82b480c0a2e | 8c68afbdc09213173aef1be195da7a9a86060a97 | refs/heads/master | 1,623,004,395,876 | 1,579,969,507,000 | 1,579,969,507,000 | 146,666,368 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 123 | lean | import positive_nat.def
import positive_nat.lemmas
import positive_nat.mod
import positive_nat.gcd
import positive_nat.div
|
1c5078bb5c7b5848c121feb1cb561270a1a4611d | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/set_theory/game/winner_auto.lean | fa8c890e92a2a4dcb9bc4185e091b8026ec725de | [] | 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 | 3,486 | lean | /-
Copyright (c) 2020 Fox Thomson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fox Thomson
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.set_theory.pgame
import Mathlib.PostPort
universes u_1
namespace Mathlib
/-!
# Basic definiti... |
aefcc42b2a09da5e6f6b29cdc73dd99d2d9cc58b | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/number_theory/padics/padic_numbers.lean | 83f1fca5f7df03dc796b72b5949b1cdc9f8b566d | [
"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 | 40,465 | 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
-/
import analysis.normed_space.basic
import number_theory.padics.padic_norm
/-!
# p-adic numbers
This file defines the p-adic numbers (rationals) `β_p` as
the compl... |
8fd1a1859cff5bacbd989e6a95cf8ad7e22359c6 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /hott/types/int/default.hlean | 10147301ea70794fe8df9fcd1298bee69662ed2a | [
"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 | 179 | hlean | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import .basic .hott
|
ce5cab2412acf65dc4b1bd12d19e46ab91cc6c06 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/order/antichain.lean | 5ed338257ddd69e41dcd6e3c1e115b0b28513e89 | [
"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 | 11,045 | lean | /-
Copyright (c) 2021 YaΓ«l Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: YaΓ«l Dillies
-/
import data.set.pairwise
/-!
# Antichains
This file defines antichains. An antichain is a set where any two distinct elements are not related.
If the relation is `(β€)`,... |
f7e4718d955701fd3b6b7ef5a8d601a43b9ebf86 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/interactive/run.lean | 56d7a9bd7c1677499d22e1413d753a9ac8276ec5 | [
"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 | 3,912 | lean | import Lean.Data.Lsp
open Lean
open Lean.Lsp
open Lean.JsonRpc
partial def main (args : List String) : IO Unit := do
let uri := s!"file://{args.head!}"
Ipc.runWith (βIO.appPath) #["--server"] do
let hIn β Ipc.stdin
Ipc.writeRequest β¨0, "initialize", { capabilities := β¨β© : InitializeParams }β©
let _ β Ip... |
099946e32cb6917646c2c01f1226806e9ee9a1ae | 097294e9b80f0d9893ac160b9c7219aa135b51b9 | /instructor/predicate_logic/intro_and_elim_rules/exists.lean | 3999d82b63153277e174a59c54b98c0fa9de7087 | [] | no_license | AbigailCastro17/CS2102-Discrete-Math | cf296251be9418ce90206f5e66bde9163e21abf9 | d741e4d2d6a9b2e0c8380e51706218b8f608cee4 | refs/heads/main | 1,682,891,087,358 | 1,621,401,341,000 | 1,621,401,341,000 | 368,749,959 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,785 | lean | /-
To prove that (β (p : P), Q) we show that there
is a specific value, p, in the context of which
we can prove Q.
-/
/-
Here's a silly example. We want to show that
we can pick some natural number in the context
of which we can construct a proof of 1=1. Of
course it doesn't matter what number we pick
because 1=1 is ... |
b98f99d3069f9c5531359477d0d7078e97ee75e3 | f313d4982feee650661f61ed73f0cb6635326350 | /Mathlib/Tactic/NoMatch.lean | 0496671a9b5fd4e71b319601335ab3467a962e3b | [
"Apache-2.0"
] | permissive | shingtaklam1324/mathlib4 | 38c6e172eec1385944db5a70a3b5545c924980ee | 50610c343b7065e8eec056d641f859ceed608e69 | refs/heads/master | 1,683,032,333,313 | 1,621,942,699,000 | 1,621,942,699,000 | 371,130,608 | 0 | 0 | Apache-2.0 | 1,622,053,166,000 | 1,622,053,166,000 | null | UTF-8 | Lean | false | false | 1,981 | lean | /-
Copyright (c) 2021 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
-/
import Mathlib.Tactic.OpenPrivate
import Lean.Elab.Match
import Lean.Elab.Syntax
/-
This adds support for the alternative syntax `match x with.` instead of `nomatch x... |
9dcbbdc5c2b9220349a7a4585367abbcf9d63124 | 4fa161becb8ce7378a709f5992a594764699e268 | /src/ring_theory/algebra.lean | 6695c7766abfebb881627bb685f8bf01dedeae60 | [
"Apache-2.0"
] | permissive | laughinggas/mathlib | e4aa4565ae34e46e834434284cb26bd9d67bc373 | 86dcd5cda7a5017c8b3c8876c89a510a19d49aad | refs/heads/master | 1,669,496,232,688 | 1,592,831,995,000 | 1,592,831,995,000 | 274,155,979 | 0 | 0 | Apache-2.0 | 1,592,835,190,000 | 1,592,835,189,000 | null | UTF-8 | Lean | false | false | 34,455 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov
-/
import data.matrix.basic
import linear_algebra.tensor_product
import data.equiv.ring
/-!
# Algebra over Commutative Semiring (under category)
In this file we... |
01f0ded76b9b33b1c824ad5974a0ba32bf32f2ed | 94e33a31faa76775069b071adea97e86e218a8ee | /src/dynamics/flow.lean | ca3dcf4650506bdee89263af94175c7ad4c95e93 | [
"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 | 6,172 | lean | /-
Copyright (c) 2020 Jean Lo. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean Lo
-/
import topology.algebra.group
import logic.function.iterate
/-!
# Flows and invariant sets
This file defines a flow on a topological space `Ξ±` by a topological
monoid `Ο` as a c... |
c8d5aa854547094d7d76c5dc546bc8744c9880b5 | 95dcf8dea2baf2b4b0a60d438f27c35ae3dd3990 | /src/topology/metric_space/gluing.lean | 8c397c0c99250552470ca7f3a5bf7a317c50be20 | [
"Apache-2.0"
] | permissive | uniformity1/mathlib | 829341bad9dfa6d6be9adaacb8086a8a492e85a4 | dd0e9bd8f2e5ec267f68e72336f6973311909105 | refs/heads/master | 1,588,592,015,670 | 1,554,219,842,000 | 1,554,219,842,000 | 179,110,702 | 0 | 0 | Apache-2.0 | 1,554,220,076,000 | 1,554,220,076,000 | null | UTF-8 | Lean | false | false | 18,013 | lean | /-
Copyright (c) 2019 SΓ©bastien GouΓ«zel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Gluing metric spaces
Authors: SΓ©bastien GouΓ«zel
Gluing two metric spaces along a common subset. Formally, we are given
Ξ¦
Ξ³ ---> Ξ±
|
|Ξ¨
v
Ξ²
where hΦ : isometry Φ and hΨ : isom... |
c111af15b6ff03dc830572fa78ed695067883281 | 3d2a7f1582fe5bae4d0bdc2fe86e997521239a65 | /cs-lib/src/tiny.lean | 6b65d1f59cde67e266e1ee4c4a5752668d057f13 | [] | no_license | own-pt/common-sense-lean | e4fa643ae010459de3d1bf673be7cbc7062563c9 | f672210aecb4172f5bae265e43e6867397e13b1c | refs/heads/master | 1,622,065,660,261 | 1,589,487,533,000 | 1,589,487,533,000 | 254,167,782 | 3 | 2 | null | 1,589,487,535,000 | 1,586,370,214,000 | Lean | UTF-8 | Lean | false | false | 1,721 | lean | /- everithing derives from an universal type U -/
constant U : Type
constant ins : U β U β Prop
constant subclass : U β U β Prop
constant orientation : U β U β U β Prop
constant OppositeDirection : U β U β Prop
/- axioms and definitions from tiny+spatial transformation -/
/- the reference can be found at: tiny+spati... |
f6cf65757997a9967d81770b3403977c0601fea3 | 5df84495ec6c281df6d26411cc20aac5c941e745 | /src/formal_ml/finset.lean | beeb50e918c3f06ac551c119f541da3f0a0d8df1 | [
"Apache-2.0"
] | permissive | eric-wieser/formal-ml | e278df5a8df78aa3947bc8376650419e1b2b0a14 | 630011d19fdd9539c8d6493a69fe70af5d193590 | refs/heads/master | 1,681,491,589,256 | 1,612,642,743,000 | 1,612,642,743,000 | 360,114,136 | 0 | 0 | Apache-2.0 | 1,618,998,189,000 | 1,618,998,188,000 | null | UTF-8 | Lean | false | false | 17,967 | 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... |
8a5530dba3b7c6c002c46af5cace94e0e490449f | 7b66d83f3b69dae0a3dfb684d7ebe5e9e3f3c913 | /src/exercises_sources/thursday/afternoon/category_theory/exercise4.lean | 35da6c421c71786721b89216761f29b6fbf3360d | [] | permissive | dpochekutov/lftcm2020 | 58a09e10f0e638075b97884d3c2612eb90296adb | cdfbf1ac089f21058e523db73f2476c9c98ed16a | refs/heads/master | 1,669,226,265,076 | 1,594,629,725,000 | 1,594,629,725,000 | 279,213,346 | 1 | 0 | MIT | 1,594,622,757,000 | 1,594,615,843,000 | null | UTF-8 | Lean | false | false | 914 | lean | import category_theory.monoidal.category
/-!
Let's construct the category of monoid objects in a monoidal category.
-/
universes v u
open category_theory
variables (C : Type u) [category.{v} C] [monoidal_category C]
structure Mon_in :=
(X : C)
(ΞΉ : π_ C βΆ X)
(ΞΌ : X β X βΆ X)
-- There are three missing axioms here!... |
ef9f89af2f77c52c52a55922cd2f7f8ab42bf666 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/tactic/interval_cases.lean | f1277b61e2e9d518519e082c073fd5ff824662f8 | [
"Apache-2.0"
] | permissive | AntoineChambert-Loir/mathlib | 64aabb896129885f12296a799818061bc90da1ff | 07be904260ab6e36a5769680b6012f03a4727134 | refs/heads/master | 1,693,187,631,771 | 1,636,719,886,000 | 1,636,719,886,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,037 | 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 data.fin.interval
import data.int.interval
import data.pnat.interval
import tactic.fin_cases
/-!
# Case bash on variables in finite intervals
This file provi... |
7535f1ed045b391774b5c0259b487a1ce8f630e1 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/order/filter/ennreal.lean | 7a9f03cf5b16634c5faad1175d1c6cd79b51e099 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 3,955 | lean | /-
Copyright (c) 2021 RΓ©my Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: RΓ©my Degenne
-/
import topology.instances.ennreal
/-!
# Order properties of extended non-negative reals
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a ... |
211e9daf735ea6992a3fb05dcb68abd1160261f8 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/584b.lean | 15d54110f8711bd9aa416558380a158a96adb316 | [
"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 | 402 | lean | section
universe variable u variable (A : Type u)
section
variables (a b : A)
variable (H : a = b)
definition tstβ := a
#check @tstβ
variable {A}
definition tstβ := a
#check @tstβ -- A is implicit
lemma symmβ : b = a := eq.symm H
#check @symmβ
end
variable (a : A)
... |
7bbf6a83ba012f5400c763bcb86a604835178749 | bb31430994044506fa42fd667e2d556327e18dfe | /src/linear_algebra/determinant.lean | b670bd9a2e84376139fb9e585ba102f1cf22396c | [
"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 | 25,831 | lean | /-
Copyright (c) 2019 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl, Patrick Massot, Casper Putz, Anne Baanen
-/
import linear_algebra.matrix.reindex
import tactic.field_simp
import linear_algebra.matrix.nonsingular_inverse
import linear... |
97cdd269fabc7e8ec03fa88b6f49800f5712df26 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/category_theory/limits/filtered_colimit_commutes_finite_limit.lean | 35e023f296b088485348242caf24cb06781fcef0 | [
"Apache-2.0"
] | permissive | AntoineChambert-Loir/mathlib | 64aabb896129885f12296a799818061bc90da1ff | 07be904260ab6e36a5769680b6012f03a4727134 | refs/heads/master | 1,693,187,631,771 | 1,636,719,886,000 | 1,636,719,886,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,150 | 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.colimit_limit
import category_theory.limits.shapes.finite_limits
/-!
# Filtered colimits commute with finite limits.
We show that for ... |
60830e76d17368d29ef14ea7907e163278463df6 | c777c32c8e484e195053731103c5e52af26a25d1 | /counterexamples/sorgenfrey_line.lean | f96879bbd74c9dbac3c180c7c537f11d93314ae4 | [
"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 | 14,233 | lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import topology.instances.irrational
import topology.algebra.order.archimedean
import topology.paracompact
import topology.metric_space.metrizable
import topology.m... |
af2f9059a7c42275730943037c7308d9d9e831f9 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/measure_theory/measurable_space_def.lean | 6606ed0fa1a5af8dd3b20d42be9b58e6bb3f5596 | [
"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 | 19,551 | lean | /-
Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl, Mario Carneiro
-/
import data.set.countable
import logic.encodable.lattice
import order.conditionally_complete_lattice
import order.disjointed
import order.symm_diff
/... |
64007eec46ec0d189a292b8e11fbdf20f91ef7de | 856e2e1615a12f95b551ed48fa5b03b245abba44 | /src/algebraic_geometry/stalks.lean | cae964b42a7d261e06eff4f7be0ded0c4342526d | [
"Apache-2.0"
] | permissive | pimsp/mathlib | 8b77e1ccfab21703ba8fbe65988c7de7765aa0e5 | 913318ca9d6979686996e8d9b5ebf7e74aae1c63 | refs/heads/master | 1,669,812,465,182 | 1,597,133,610,000 | 1,597,133,610,000 | 281,890,685 | 1 | 0 | null | 1,595,491,577,000 | 1,595,491,576,000 | null | UTF-8 | Lean | false | false | 2,090 | 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 algebraic_geometry.presheafed_space
import topology.sheaves.stalks
/-!
# Stalks for presheaved spaces
This file lifts constructions of stalks and pushforward... |
de272ac595e64d6cafd49ae79327c36c049fc51f | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/category_theory/limits/shapes/pullbacks.lean | 38464064f372889259a8a54e63430b3d48db7fcb | [
"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 | 7,541 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.eq_to_hom
import category_theory.limits.cones
import category_theory.sparse
open category_theory
namespace category_theory.limits
universes ... |
51595068bc87efd631b67e926367db2c8a086003 | 4fa161becb8ce7378a709f5992a594764699e268 | /src/data/dfinsupp.lean | 5dc30d75caa7aaa53dff9efe4ae699c6098c708f | [
"Apache-2.0"
] | permissive | laughinggas/mathlib | e4aa4565ae34e46e834434284cb26bd9d67bc373 | 86dcd5cda7a5017c8b3c8876c89a510a19d49aad | refs/heads/master | 1,669,496,232,688 | 1,592,831,995,000 | 1,592,831,995,000 | 274,155,979 | 0 | 0 | Apache-2.0 | 1,592,835,190,000 | 1,592,835,189,000 | null | UTF-8 | Lean | false | false | 32,979 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl, Kenny Lau
-/
import algebra.pi_instances
/-!
# Dependent functions with finite support
For a non-dependent version see `data/finsupp.lean`.
-/
universes u uβ uβ v vβ vβ v... |
80a2bb8e582ad8ea26a00c7aaf8e80af9d94b44f | da2388aff16df48b4a928b575bcec678b8e7f2cf | /src/main.lean | 856144bbe8a561ae1c3f614cecd2623878a3f1cc | [] | no_license | ADedecker/series | 1d0d282d4333c7599f07cc705a35cf5edfb87a3b | 12fbcdd16b3cdeda4476165a4645fcccc0fb3234 | refs/heads/master | 1,674,828,739,868 | 1,607,618,619,000 | 1,607,618,619,000 | 304,379,894 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,247 | lean | import analysis.specific_limits
open set finset filter
open_locale big_operators topological_space
noncomputable theory
def series (u : β β β) := Ξ» n, (β i in range n, u i)
def converges {Ξ± : Type*} [topological_space Ξ±] (u : β β Ξ±) := β l, tendsto u at_top (π l)
lemma tendsto_geom_series_at_top_of_nonneg_of_lt_o... |
16f94d492c8726fc31d7a189f4af0f950036463f | 4727251e0cd73359b15b664c3170e5d754078599 | /src/group_theory/quotient_group.lean | dd609fcf3ccd6eb03bf54fb868de13e90a4e59aa | [
"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 | 21,147 | lean | /-
Copyright (c) 2018 Kevin Buzzard, Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Patrick Massot
This file is to a certain extent based on `quotient_module.lean` by Johannes HΓΆlzl.
-/
import group_theory.coset
import group_theory.congr... |
5cf590a7c8906da62d98fcda6f08d884e8d53833 | f3be49eddff7edf577d3d3666e314d995f7a6357 | /TBA/Eulerian/List.lean | 5da56ae60679a4f5ef444519592b35e5392d5ae7 | [] | no_license | IPDSnelting/tba-2021 | 8b930bcd2f4aae44a2ddc86e72b77f84e6d46e82 | b6390e55b768423d3266969e81d19290129c5914 | refs/heads/master | 1,686,754,693,583 | 1,625,135,602,000 | 1,625,136,365,000 | 355,124,341 | 50 | 7 | null | 1,625,133,762,000 | 1,617,699,824,000 | Lean | UTF-8 | Lean | false | false | 16,777 | lean | import TBA.Eulerian.Nat
open BEq Nat List Decidable
namespace Eq
protected theorem symm_iff {a b : Ξ±} : b = a β a = b := β¨Eq.symm, Eq.symmβ©
end Eq
namespace List
@[simp] theorem length_append {as bs : List Ξ±} :
length (as ++ bs) = length as + length bs :=
match as with
| [] => by simp
| a :: as => by... |
9565398b06b9a1439ab27eefa578467b93dc67bc | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /tests/lean/run/struct_instance_in_eqn.lean | 61cd87a036f61e86879e5750d846c2be892d7e79 | [
"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 | 152 | lean | structure S :=
(x : Nat) (y : Bool) (z : Nat) (w : Nat)
set_option trace.compiler.stage1 true
def g : S β S
| s@{ x := x, ..} => { x := x + 1, ..s}
|
752866490ad168ccc27ca87183398db9bb764c94 | bdb33f8b7ea65f7705fc342a178508e2722eb851 | /group_theory/coset.lean | f8970ebd789b8bf8e67bd6d0810e2937604d954f | [
"Apache-2.0"
] | permissive | rwbarton/mathlib | 939ae09bf8d6eb1331fc2f7e067d39567e10e33d | c13c5ea701bb1eec057e0a242d9f480a079105e9 | refs/heads/master | 1,584,015,335,862 | 1,524,142,167,000 | 1,524,142,167,000 | 130,614,171 | 0 | 0 | Apache-2.0 | 1,548,902,667,000 | 1,524,437,371,000 | Lean | UTF-8 | Lean | false | false | 5,543 | lean | /-
Copyright (c) 2018 Mitchell Rowett. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Rowett, Scott Morrison
-/
import group_theory.subgroup data.equiv data.quot
open set function
variable {Ξ± : Type*}
def left_coset [has_mul Ξ±] (a : Ξ±) (s : set Ξ±) : set Ξ± :=... |
d074b59baf26b3c8028f07bf8dfc3e2cb07479f2 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/order/filter/pointwise_auto.lean | 6cc13c235ef7bda08c05b2c24d0409dbeb8943ca | [] | 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 | 3,932 | lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.pointwise
import Mathlib.order.filter.basic
import Mathlib.PostPort
universes u v
... |
598a5658087c1612a33f1dcbfb51668748791fe1 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/at_at_bug.lean | b9af3f9ea5337d69526fabbe05d31ed7c1b5e89a | [
"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 | 383 | lean |
example (a b : nat) (p : nat β nat β Prop) (hβ : p a b) (hβ : a = b) : p b b :=
@@eq.subst (Ξ» x, p x b) hβ hβ
set_option pp.all true
variable my_has_add : has_add nat
check @@add my_has_add 0 1
local notation h1 `βΈ[` m `]` h2 := @@eq.subst m h1 h2
example (a b : nat) (p : nat β nat β Prop) (hβ : p a b) (hβ : a = b... |
8c0407ead23d96b85735b43e90c9b24889fd9108 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/163c.lean | 0fb33067bac3529a1ba4bf297506f55ac335bcea | [
"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 | 475 | lean | @[simp] lemma subsingleton.eq {Ξ±} [subsingleton Ξ±] (a b : Ξ±) : a = b β true := by cc
example {Ξ±} [subsingleton Ξ±] (a b : Ξ±) : a = b := by simp -- works
-- let's generalize this to unique
class unique (Ξ± : Sort*) extends inhabited Ξ± := [ss : subsingleton Ξ±]
attribute [instance] unique.ss
@[simp] lemma unique.eq {Ξ±} ... |
a59bfdd45278cf1bc13887711aa9473573c583c1 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/simple.lean | 623851345e990aca0308200a171c01d8817b70e5 | [
"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 | 571 | lean | prelude
definition Prop : Type.{1} := Type.{0}
section
parameter A : Type
definition eq (a b : A) : Prop
:= βP : A β Prop, P a β P b
theorem subst (P : A β Prop) (a b : A) (H1 : eq a b) (H2 : P a) : P b
:= H1 P H2
theorem refl (a : A) : eq a a
:= Ξ» (P : A β Prop) (H : P a), H
theorem symm (a b : A) ... |
e91d84ebc0c15c05ee7432e77c8ba19c9cfede68 | 947b78d97130d56365ae2ec264df196ce769371a | /tests/lean/mvar1.lean | f79fe379e8a2e9dfc547213896a1a286dda2c9f5 | [
"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 | 3,109 | lean | import Lean.MetavarContext
new_frontend
open Lean
def check (b : Bool) : IO Unit :=
Β«unlessΒ» 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 := mkLevelPa... |
5b769f50f2dfc33648b3186829452da276589409 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /src/Init/Data/PersistentHashSet.lean | c1ae1bb15a9eeb279e36b21635688efd4a37e8fb | [
"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 | 1,608 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import Init.Data.PersistentHashMap
universes u v
structure PersistentHashSet (Ξ± : Type u) [HasBeq Ξ±] [Hashable Ξ±] :=
(set : PersistentHashMap Ξ± Uni... |
fc0c5238c0106c06a5ef051ee6d57cb02805da31 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/order/lattice.lean | a36c0bf74920e698626ebabba3a8810f31bbe4ea | [] | 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 | 22,076 | lean | /-
Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl
Defines the inf/sup (semi)-lattice with optionally top/bot type class hierarchy.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.order.rel... |
9b40b5e1c02eba9cbd734143cd38b91947531a8d | 5c7fe6c4a9d4079b5457ffa5f061797d42a1cd65 | /src/exercises/src_38_further_upper_bounds_sup_inf.lean | 89193a9bebdd5f33e50e37c63caf95df9a31c84b | [] | 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 | 4,182 | lean | import ..library.src_real_field_lemmas
import ..library.src_ordered_field_lemmas
import data.set.basic
import tactic
namespace mth1001
namespace myreal
section upper_bound_of_subset
open myreal_field classical myordered_field
open_locale classical
variables {R : Type} [myreal_field R]
theorem upper_bound_of_subs... |
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