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4efc8d6aa091dbb0c6dded93633e810637e67766 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/list/chain_auto.lean | f91af5e36c90818b2a4b49e9ef9a406e585d501e | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,837 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kenny Lau, Yury Kudryashov
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.list.pairwise
import Mathlib.logic.relation
import Mathlib... |
4589371e5bf89e0b92752ee3078e26f73d226c4f | 4727251e0cd73359b15b664c3170e5d754078599 | /src/category_theory/monoidal/End.lean | f12b646e85e4cd11f98c4c6ccd3d85dad757f572 | [
"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 | 10,625 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Andrew Yang
-/
import category_theory.monoidal.functor
/-!
# Endofunctors as a monoidal category.
We give the monoidal category structure on `C ⥤ C`,
and show that wh... |
54b35e4a5e4cc24fe76e05d48fc95dad9c662603 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/group_theory/group_action/default_auto.lean | 972fbd6ab6d96f03c3ff9e3c10ad673a921cce57 | [] | 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 | 162 | lean | import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.group_theory.group_action.basic
import Mathlib.PostPort
namespace Mathlib
end Mathlib |
b7b7a23a7e35e12e8593e025d282c5c1d81f73df | 4727251e0cd73359b15b664c3170e5d754078599 | /src/measure_theory/measure/sub.lean | cb8d1b097292a7626dd224d7aef43f7b2b8a4b3d | [
"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 | 5,703 | lean | /-
Copyright (c) 2022 Martin Zinkevich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Martin Zinkevich
-/
import measure_theory.measure.measure_space
/-!
# Subtraction of measures
In this file we define `μ - ν` to be the least measure `τ` such that `μ ≤ τ + ν`.
It i... |
30f65041572e8c8debce95956e818e6f82dd6406 | 274748215b6d042f0d9c9a505f9551fa8e0c5f38 | /src/affine_algebraic_set/regular_function.lean | 20fa9a92818f8fa37e588a96f6928286bf39ba21 | [
"Apache-2.0"
] | permissive | ImperialCollegeLondon/M4P33 | 878ecb515c77d20cc799ff1ebd78f1bf4fd65c12 | 1a179372db71ad6802d11eacbc1f02f327d55f8f | refs/heads/master | 1,607,519,867,193 | 1,583,344,297,000 | 1,583,344,297,000 | 233,316,107 | 59 | 4 | Apache-2.0 | 1,579,285,778,000 | 1,578,788,367,000 | Lean | UTF-8 | Lean | false | false | 8,253 | lean | /-
Copyright (c) 2020 Kevin Buzzard
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, and whoever else wants to join in.
-/
-- need the definition of an affine alg set
import affine_algebraic_set.basic
-- need so I can state that the kernel of the evaluation map is 𝕀
impor... |
2c5647e2e6e558416442571e9b58d09e5b1d7072 | 1fbca480c1574e809ae95a3eda58188ff42a5e41 | /src/util/data/ordering.lean | 5fd22c92d17aa3f237099f5e793439951aeb1cdb | [] | no_license | unitb/lean-lib | 560eea0acf02b1fd4bcaac9986d3d7f1a4290e7e | 439b80e606b4ebe4909a08b1d77f4f5c0ee3dee9 | refs/heads/master | 1,610,706,025,400 | 1,570,144,245,000 | 1,570,144,245,000 | 99,579,229 | 5 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 223 | lean |
import algebra.order
universe u
variables {α : Type u}
variables [decidable_linear_order α]
lemma cmp_eq_eq (a b : α)
: cmp a b = ordering.eq = (a = b) :=
by { simp [cmp,cmp_using_eq_eq], rw ← le_antisymm_iff, cc }
|
476ddb90af1e89dc8db9567a27a7378cef5db0b6 | 8e2026ac8a0660b5a490dfb895599fb445bb77a0 | /tests/lean/field_access.lean | fb3344ef3566e1b3e8bc61b5781a95c44aa3c59e | [
"Apache-2.0"
] | permissive | pcmoritz/lean | 6a8575115a724af933678d829b4f791a0cb55beb | 35eba0107e4cc8a52778259bb5392300267bfc29 | refs/heads/master | 1,607,896,326,092 | 1,490,752,175,000 | 1,490,752,175,000 | 86,612,290 | 0 | 0 | null | 1,490,809,641,000 | 1,490,809,641,000 | null | UTF-8 | Lean | false | false | 536 | lean | #check list.map
variable l : list nat
#check l^.1 -- Error l is not a structure
#check (1, 2)^.5 -- Error insufficient fields
example (l : list nat) : list nat :=
l^.forr (λ x, x + 1) -- Error there is no list.forr
example (A : Type) (a : A) : A :=
a^.symm -- Error type of 'a' is not a constant application
exampl... |
5482aa408c4b5be9c96efbf0cf53000ccaea5cb0 | 3f7026ea8bef0825ca0339a275c03b911baef64d | /src/field_theory/finite_card.lean | 4400adfc6a31c9d63a1eaecc80a602938ad2a0ef | [
"Apache-2.0"
] | permissive | rspencer01/mathlib | b1e3afa5c121362ef0881012cc116513ab09f18c | c7d36292c6b9234dc40143c16288932ae38fdc12 | refs/heads/master | 1,595,010,346,708 | 1,567,511,503,000 | 1,567,511,503,000 | 206,071,681 | 0 | 0 | Apache-2.0 | 1,567,513,643,000 | 1,567,513,643,000 | null | UTF-8 | Lean | false | false | 1,119 | lean | /-
Copyright (c) 2019 Casper Putz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joey van Langen, Casper Putz
-/
import algebra.char_p data.zmod.basic linear_algebra.basis
universes u
variables (α : Type u) [discrete_field α] [fintype α]
namespace finite_field
the... |
6ff7dd66fe7f919a3d393f5845f6797c1a1ca0df | 1a61aba1b67cddccce19532a9596efe44be4285f | /hott/algebra/binary.hlean | a58114540a849673e2d406225266e353ffab7c97 | [
"Apache-2.0"
] | permissive | eigengrau/lean | 07986a0f2548688c13ba36231f6cdbee82abf4c6 | f8a773be1112015e2d232661ce616d23f12874d0 | refs/heads/master | 1,610,939,198,566 | 1,441,352,386,000 | 1,441,352,494,000 | 41,903,576 | 0 | 0 | null | 1,441,352,210,000 | 1,441,352,210,000 | null | UTF-8 | Lean | false | false | 4,789 | hlean | /-
Copyright (c) 2014-15 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad
General properties of binary operations.
-/
open eq.ops function equiv
namespace binary
section
variable {A : Type}
variables (o... |
c190f6dc1670078463099ea7c48cdf6fd16da082 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/testing/slim_check/functions.lean | f7948278aae72c314e7691223b26063230893f61 | [
"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 | 19,549 | lean | /-
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import data.list.sigma
import data.int.range
import data.finsupp.basic
import data.finsupp.to_dfinsupp
import tactic.pretty_cases
import testing.slim_check.sampleable
impor... |
5d971f64e61b22920ba8fedd1a6dec907764a29d | 947b78d97130d56365ae2ec264df196ce769371a | /tests/lean/run/matchArrayLit.lean | c25fb8f02451af64428c64ba9f2c1895bfb52586 | [
"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 | 3,097 | lean | new_frontend
universes u v
theorem eqLitOfSize0 {α : Type u} (a : Array α) (hsz : a.size = 0) : a = #[] :=
a.toArrayLitEq 0 hsz
theorem eqLitOfSize1 {α : Type u} (a : Array α) (hsz : a.size = 1) : a = #[a.getLit 0 hsz (ofDecideEqTrue rfl)] :=
a.toArrayLitEq 1 hsz
theorem eqLitOfSize2 {α : Type u} (a : Array α) (hsz ... |
ffca572d3f48dc34a49584081a7b66af4cd6b0f0 | f20db13587f4dd28a4b1fbd31953afd491691fa0 | /library/init/data/prod.lean | 9f3088e46bada5546391f8fab18ca55cc61e4f9f | [
"Apache-2.0"
] | permissive | AHartNtkn/lean | 9a971edfc6857c63edcbf96bea6841b9a84cf916 | 0d83a74b26541421fc1aa33044c35b03759710ed | refs/heads/master | 1,620,592,591,236 | 1,516,749,881,000 | 1,516,749,881,000 | 118,697,288 | 1 | 0 | null | 1,516,759,470,000 | 1,516,759,470,000 | null | UTF-8 | Lean | false | false | 1,566 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura, Jeremy Avigad
-/
prelude
import init.logic
universes u v
section
variables {α : Type u} {β : Type v}
instance [inhabited α] [inhabited β] : inhabited (prod α ... |
afa1332b160a8d8f870a5877ac1a4d57bb0b9769 | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/logic/function/basic.lean | 68d3d51cd9c82558ee78e845765c55b70d4781e1 | [
"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 | 26,984 | lean | /-
Copyright (c) 2016 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import logic.basic
import data.option.defs
/-!
# Miscellaneous function constructions and lemmas
-/
universes u v w
namespace function
section
var... |
67f38f1f5c8b0053b5ed572509baa6679d06c6e0 | 9cba98daa30c0804090f963f9024147a50292fa0 | /geom/geom1d.lean | dd46c080a7a02ecefa78c22394721c98130d4a1f | [] | no_license | kevinsullivan/phys | dcb192f7b3033797541b980f0b4a7e75d84cea1a | ebc2df3779d3605ff7a9b47eeda25c2a551e011f | refs/heads/master | 1,637,490,575,500 | 1,629,899,064,000 | 1,629,899,064,000 | 168,012,884 | 0 | 3 | null | 1,629,644,436,000 | 1,548,699,832,000 | Lean | UTF-8 | Lean | false | false | 17,620 | lean | import ..phys_dimensions
import linear_algebra.affine_space.basic
import ...math.euclidnK.euclidnK_definitions
import ..scalar
open_locale affine
section foo
universes u
abbreviation geom1d_frame := fm real_scalar 1 LENGTH
abbreviation geom1d_space (f : geom1d_frame) := spc real_scalar f
noncomputable def geom... |
56ab1ac13983cac1027b811f1c4341c5cb44e591 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/finset/option.lean | 88793ad39b3f3a698b0f379ceec887411a8d35a8 | [
"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 | 4,456 | lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Mario Carneiro, Sean Leather
-/
import data.finset.card
/-!
# Finite sets in `option α`
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file requir... |
721cf143ff9c851fa794f2112f24a0f91e579029 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/topology/separation.lean | 0dd1fcd92f90d9dfa7fbc4b6ddd611b9143fe2c7 | [
"Apache-2.0"
] | permissive | agjftucker/mathlib | d634cd0d5256b6325e3c55bb7fb2403548371707 | 87fe50de17b00af533f72a102d0adefe4a2285e8 | refs/heads/master | 1,625,378,131,941 | 1,599,166,526,000 | 1,599,166,526,000 | 160,748,509 | 0 | 0 | Apache-2.0 | 1,544,141,789,000 | 1,544,141,789,000 | null | UTF-8 | Lean | false | false | 21,995 | 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
Separation properties of topological spaces.
-/
import topology.subset_properties
open set filter
open_locale topological_space filter
local attribute ... |
f58a95c1e02a9eeab4190eb9b236d4d6677b8aa8 | 4d7079ae603c07560e99d1ce35876f769cbb3e24 | /src/pareto.lean | 410eb87dc03218f903974146afb4e906a5ca4dce | [] | no_license | chasenorman/Formalized-Voting | 72493a08aa09d98d0fb589731b842e2d08c991d0 | de04e630b83525b042db166670ba97f9952b5691 | refs/heads/main | 1,687,282,160,284 | 1,627,155,031,000 | 1,627,155,031,000 | 370,472,025 | 13 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,453 | lean | import main
import split_cycle
import algebra.linear_ordered_comm_group_with_zero
open_locale classical
variables {V X : Type}
def pareto (F : VSCC) (P : Prof V X ) : Prop := ∀ x y, ((∀ v, P v x y) → y ∉ F V X P)
lemma unanimous_margin [fintype V] [inhabited V] (P : Prof V X) [profile_asymmetric P] (x y : X) : (∀... |
0f0d2843d1845bbdd12604f95f36972060783dee | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/inlineLCNFIssue.lean | 3b2fd7df59e28468d5e16e9437608c61faffac0a | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 1,024 | lean | import Lean
def explode (x : Nat) : IO Unit := do
if x == 0 then IO.println "arg is 0"
if x == 1 then IO.println "arg is 1"
if x == 2 then IO.println "arg is 2"
if x == 3 then IO.println "arg is 3"
if x == 4 then IO.println "arg is 4"
if x == 5 then IO.println "arg is 5"
if x == 6 then IO.println ... |
8e8ee406e4c79f94f3f2460ec864fd04541354ea | 48f4f349e1bb919d14ab7e5921d0cfe825f4c423 | /fabstract/Bauer_A_InjBaireNat/categories.lean | 3b4a6bd6f58d7363ea9d1833816b48a0f1308eb0 | [] | no_license | thalesant/formalabstracts-2017 | fdf4ff90d30ab1dcb6d4cf16a068a997ea5ecc80 | c47181342c9e41954aa8d41f5049965b5f332bca | refs/heads/master | 1,584,610,453,925 | 1,528,277,508,000 | 1,528,277,508,000 | 136,299,625 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,261 | lean | -- a random and incomplete selection of notions in category theory
import meta_data
structure category :=
(obj : Type)
(hom : obj → obj → Type)
(id : Π (A : obj), hom A A)
(compose : Π {A B C : obj}, hom B C → hom A B → hom A C)
(id_left : Π {A B : obj} {f : hom A B}, compose (id B) f = f)
(id... |
0380937647a8c521a0ffb397ed8ab376c500ce72 | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/measure_theory/measurable_space.lean | 930dce376bc20df2e001d59b68f3eb78faa6aae1 | [
"Apache-2.0"
] | permissive | ayush1801/mathlib | 78949b9f789f488148142221606bf15c02b960d2 | ce164e28f262acbb3de6281b3b03660a9f744e3c | refs/heads/master | 1,692,886,907,941 | 1,635,270,866,000 | 1,635,270,866,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 48,700 | 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 measure_theory.measurable_space_def
import measure_theory.tactic
import data.tprod
import data.equiv.fin
/-!
# Measurable spaces and measurab... |
0fd2485c58ccc255c6bf5093c16873e9474b5e70 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/abelian/non_preadditive.lean | 457ca077e65ebf941bb4257665528338bd427b5f | [
"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 | 17,258 | lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import category_theory.limits.shapes.finite_products
import category_theory.limits.shapes.kernels
import category_theory.limits.shapes.normal_mono.equalizers
import cat... |
410b2aec5d5dc100ce7d3adfe2ba935f1e93637e | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/algebra/homology/homology.lean | eaedab2049c5d7aee1b0f890c1a7a57ffd6a230e | [
"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 | 4,978 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Markus Himmel
-/
import algebra.homology.chain_complex
import category_theory.limits.shapes.images
import category_theory.limits.shapes.kernels
/-!
# Non-functorial co... |
0aeebc506b188f02d0f09a893641f68451c895de | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /src/Lean/Meta/Tactic/Simp.lean | 1a80748a75749f65f7d50c0fea5e236844e5e6c3 | [
"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 | 533 | 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.Simp.SimpLemmas
import Lean.Meta.Tactic.Simp.CongrLemmas
import Lean.Meta.Tactic.Simp.Types
import Lean.Meta.Tactic.Simp.Main
import... |
ac38b8c3c5be6d30f652181483ba4f4830d1a331 | 82b86ba2ae0d5aed0f01f49c46db5afec0eb2bd7 | /src/Lean/Meta/ForEachExpr.lean | b972155116a6abbe062d4a6d758182b704b8d0f5 | [
"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 | 2,244 | 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
import Lean.Util.MonadCache
import Lean.Meta.Basic
namespace Lean.Meta
namespace ForEachExpr
abbrev M := MonadCacheT Expr Unit MetaM
mut... |
86669238197d0c7cde65deaa17181abc4fcfcdc2 | 6e9cd8d58e550c481a3b45806bd34a3514c6b3e0 | /src/data/complex/exponential.lean | 7a24dafefb0ecbb71e4ff3fc88eeb67b7a891d7a | [
"Apache-2.0"
] | permissive | sflicht/mathlib | 220fd16e463928110e7b0a50bbed7b731979407f | 1b2048d7195314a7e34e06770948ee00f0ac3545 | refs/heads/master | 1,665,934,056,043 | 1,591,373,803,000 | 1,591,373,803,000 | 269,815,267 | 0 | 0 | Apache-2.0 | 1,591,402,068,000 | 1,591,402,067,000 | null | UTF-8 | Lean | false | false | 47,766 | 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.nat.choose
import data.complex.basic
local notation `abs'` := _root_.abs
open is_absolute_value
open_locale... |
119ffc5dca43cda67d1a05a14b0665e643fc71cb | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/fun_like/fintype.lean | 64f0b9e8732f8c63c5cae164418593c36a68ed89 | [
"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 | 2,549 | lean | /-
Copyright (c) 2022 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import data.finite.basic
import data.fintype.basic
import data.fun_like.basic
/-!
# Finiteness of `fun_like` types
We show a type `F` with a `fun_like F α β` is finite i... |
f5f54e2e94252a0debadddaefe3fdc92aa3f9baf | df7bb3acd9623e489e95e85d0bc55590ab0bc393 | /lean/love08_operational_semantics_exercise_solution.lean | d20f9beccb8997f188d1d442ba803966c51d5763 | [] | no_license | MaschavanderMarel/logical_verification_2020 | a41c210b9237c56cb35f6cd399e3ac2fe42e775d | 7d562ef174cc6578ca6013f74db336480470b708 | refs/heads/master | 1,692,144,223,196 | 1,634,661,675,000 | 1,634,661,675,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,418 | lean | import .love08_operational_semantics_demo
/- # LoVe Exercise 8: Operational Semantics -/
set_option pp.beta true
set_option pp.generalized_field_notation false
namespace LoVe
/- ## Question 1: Program Equivalence
For this question, we introduce the notion of program equivalence: `S₁ ≈ S₂`. -/
def big_step_equi... |
d645fdded5ee692abd7f7982b8cabec0ff0381ea | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/analysis/normed_space/add_torsor_auto.lean | e5aa51acab416309140494623de32843c73a1158 | [] | 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 | 20,380 | lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Yury Kudryashov.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.linear_algebra.affine_space.midpoint
import Mathlib.topology.metric_space.iso... |
9ddcfb44efd3a770fc42ddc9b0796202d072bea3 | c03e95bc725cd3f471d8655b0b5c3557f82c289b | /writing a tactic/refine.lean | 90976ace2019e6d0214741d527a02c9578140ef6 | [] | no_license | unitb/lean-tutorials | 7ee8983438c64e5efc08682f6f7ca7957ee5b534 | 95ea03ebbd7b7162285e6971ef9728377afdca9c | refs/heads/master | 1,631,165,521,602 | 1,520,991,342,000 | 1,520,991,342,000 | 125,005,853 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,345 | lean |
import data.dlist
/- We want to write a set of tactics to automate the construction of
instances. One approach might be to automate the specific instances
that we are interested in. Instead, we will try to build reusable
components and aim for wide applicability.
Our first example of application is the c... |
9fa7d7f7c02bb21c80d99d12eddb367a3bb6102e | a523fc1740c8cb84cd0fa0f4b52a760da4e32a5c | /src/missing_mathlib/data/polynomial.lean | 4c1906e3f44b6bd981e348f317db0242223317e2 | [] | no_license | abentkamp/spectral | a1aff51e85d30b296a81d256ced1d382345d3396 | 751645679ef1cb6266316349de9e492eff85484c | refs/heads/master | 1,669,994,798,064 | 1,597,591,646,000 | 1,597,591,646,000 | 287,544,072 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,433 | lean | import data.polynomial
import missing_mathlib.ring_theory.algebra
universe variables u v w
namespace polynomial
variables {α : Type u} {β : Type v}
open polynomial
lemma leading_coeff_X_add_C {α : Type v} [integral_domain α] [decidable_eq α] (a b : α) (ha : a ≠ 0):
leading_coeff (C a * X + C b) = a :=
begin
rw... |
3b75d6ab419dda385068ae44a32864410a2810ae | b6f0d4562078d09b2d51c6aa5216cf0e07e8090f | /LeanRanges/NatRange.lean | feadb9c266114bacbbc923aff79c0d3bbc14af06 | [
"Apache-2.0"
] | permissive | pnwamk/lean4-ranges | 206a46e0ded663f546927f598549efacc36492f2 | 6c6a7e21edc1c2ad319749b75a222d77b1340f7d | refs/heads/master | 1,680,233,414,507 | 1,617,384,186,000 | 1,617,384,186,000 | 349,486,531 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,055 | lean | import LeanRanges.ToRange
namespace Nat
instance : HasMin Nat where
minOf _ := 0
end Nat
structure NatRange where
start : Nat
stop : Nat
step : Nat
ascending : Bool
/-- An exclusive range `[start,stop)` of `Nat` values separated by `step`. -/
def Nat.range (start stop : Nat) (step : Nat := 1) (ascendi... |
9af7dd0bc0f2a06882b32b1ca2ea9805b2e7057c | 43390109ab88557e6090f3245c47479c123ee500 | /src/vector_space.lean | 0f7fe99a47249e5da4ad8cc00db2723e165551db | [
"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 | 5,476 | lean | structure vector (R : Type) :=
vec :: (x : R) (y : R) (z : R)
namespace vector
variables {R : Type} [comm_ring R]
def zero : vector R := vec 0 0 0
def add (a b : vector R) :=
vec (a.x + b.x) (a.y + b.y) (a.z + b.z)
def neg (a : vector R) :=
vec (-a.x) (-a.y) (-a.z)
def cross_prod (a b : vector R)... |
bda6ee19f3d0ab93d50459e2b8324eac041f648f | e21db629d2e37a833531fdcb0b37ce4d71825408 | /src/mcl/compute_list.lean | 0776a1dec553b10bd9800a05b522b29dde2375fc | [] | no_license | fischerman/GPU-transformation-verifier | 614a28cb4606a05a0eb27e8d4eab999f4f5ea60c | 75a5016f05382738ff93ce5859c4cfa47ccb63c1 | refs/heads/master | 1,586,985,789,300 | 1,579,290,514,000 | 1,579,290,514,000 | 165,031,073 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,144 | lean | import parlang.defs
import mcl.defs
open parlang
open parlang.state
open parlang.thread_state
open mcl
def compute_list {σ ι : Type} {τ : ι → Type} [decidable_eq ι] : list (σ → σ) → (thread_state σ τ → thread_state σ τ)
| (f :: tl) := compute_list tl ∘ @compute σ ι τ _ f
| [] := id
lemma compute_to_compute_list {σ ι... |
425c1f9a84876e5122efc77a2ec6831839802e01 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/euclidean_domain.lean | 804a774569455d0437b0e22fea176feb5d9a0fa5 | [] | 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 | 13,045 | lean | /-
Copyright (c) 2018 Louis Carlin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Louis Carlin, Mario Carneiro
Euclidean domains and Euclidean algorithm (extended to come)
A lot is based on pre-existing code in mathlib for natural number gcds
-/
import Mathlib.PrePor... |
f74996f797c8e6fb2862f5738353cce9a4f4e5da | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/ring_theory/hahn_series.lean | 05899a5c64965624d08cf58725db845df02cdedd | [
"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 | 61,486 | lean | /-
Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import order.well_founded_set
import algebra.big_operators.finprod
import ring_theory.valuation.basic
import ring_theory.power_series.basic
import data.finsupp.pwo
im... |
7121e7bcc413a05ef76921ccd736c3487f84ce25 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/quote1.lean | 97139db658f4ae6a3014fe3a5ccfee85bf993a12 | [
"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 | 315 | lean | open tactic list
meta definition foo (a : pexpr) : pexpr :=
```(%%a + %%a + %%a + b)
example (a b : nat) : a = a :=
by do
a ← get_local `a,
t1 ← mk_app ``has_add.add [a, a],
t2 ← to_expr (foo (to_pexpr t1)),
trace t2,
r ← mk_app (`eq.refl) [a],
exact r
private def f := unit
#check ``f
|
2ea05b1464d8dbf16e5da266b5e051145f092679 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/ring_theory/polynomial/basic.lean | dff704c08562ab38c7d9b7a7c5aa861706920fdd | [
"Apache-2.0"
] | permissive | ramonfmir/mathlib | c5dc8b33155473fab97c38bd3aa6723dc289beaa | 14c52e990c17f5a00c0cc9e09847af16fabbed25 | refs/heads/master | 1,661,979,343,526 | 1,660,830,384,000 | 1,660,830,384,000 | 182,072,989 | 0 | 0 | null | 1,555,585,876,000 | 1,555,585,876,000 | null | UTF-8 | Lean | false | false | 50,677 | lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import algebra.char_p.basic
import data.mv_polynomial.comm_ring
import data.mv_polynomial.equiv
import ring_theory.polynomial.content
import ring_theory.unique_factorization_d... |
fe1c598359986ec78d3abcb0920800e534e3008d | 2a70b774d16dbdf5a533432ee0ebab6838df0948 | /_target/deps/mathlib/src/ring_theory/polynomial/cyclotomic.lean | 8378d4d011563789eeae601414cfe3e374fe62d4 | [
"Apache-2.0"
] | permissive | hjvromen/lewis | 40b035973df7c77ebf927afab7878c76d05ff758 | 105b675f73630f028ad5d890897a51b3c1146fb0 | refs/heads/master | 1,677,944,636,343 | 1,676,555,301,000 | 1,676,555,301,000 | 327,553,599 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 30,971 | lean | /-
Copyright (c) 2020 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Riccardo Brasca
-/
import field_theory.splitting_field
import ring_theory.roots_of_unity
import algebra.polynomial.big_operators
import number_theory.arithmetic_function
import data.p... |
e02e7b0d5378f8b19f20db4f42bed86c16d92813 | ce89339993655da64b6ccb555c837ce6c10f9ef4 | /bluejam/chap4_exercise2.lean | beb9d36adc7877892a97aebac779c2ce86c9f21b | [] | no_license | zeptometer/LearnLean | ef32dc36a22119f18d843f548d0bb42f907bff5d | bb84d5dbe521127ba134d4dbf9559b294a80b9f7 | refs/heads/master | 1,625,710,824,322 | 1,601,382,570,000 | 1,601,382,570,000 | 195,228,870 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,117 | lean | variables (α : Type) (p q : α → Prop)
variable r : Prop
example : α → ((∀ x : α, r) ↔ r) :=
assume y: α,
iff.intro
(
assume h: (∀ x: α, r),
show r, from h y
)
(
assume h: r,
assume x: α,
h
)
-- example : (∀ x, p x ∨ r)... |
57ce0c84081ffed88015698538e170f747a046ee | bb31430994044506fa42fd667e2d556327e18dfe | /src/algebra/order/monoid/with_top.lean | c40041e3a9e031550594e9a45a8d385ac60dee86 | [
"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 | 20,877 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl
-/
import algebra.hom.group
import algebra.order.monoid.order_dual
import algebra.order.monoid.with_zero.basic
import da... |
7c36b450cc4ee44e33a9689997ecce267ef25ced | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/order/lattice.lean | 8ac6ff0f7c318c3042caaf044dba3afa84e58d9f | [
"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 | 17,633 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Defines the inf/sup (semi)-lattice with optionally top/bot type class hierarchy.
-/
import order.rel_classes
set_option old_structure_cmd true
universes u v w
variab... |
432d2eaa7e485bda0901fd53e7da607a19cf6457 | 01ae0d022f2e2fefdaaa898938c1ac1fbce3b3ab | /categories/products/bifunctors.lean | c3f43a44f057f08f160aa4bda6a7a71dcdef4e86 | [] | no_license | PatrickMassot/lean-category-theory | 0f56a83464396a253c28a42dece16c93baf8ad74 | ef239978e91f2e1c3b8e88b6e9c64c155dc56c99 | refs/heads/master | 1,629,739,187,316 | 1,512,422,659,000 | 1,512,422,659,000 | 113,098,786 | 0 | 0 | null | 1,512,424,022,000 | 1,512,424,022,000 | null | UTF-8 | Lean | false | false | 3,283 | 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 ..products
open categories
open categories.functor
open categories.natural_transformation
namespace categories.products
@[simp] lemma {u1... |
8302b92186ec03f508a31f5eaf70ac74c87bb0bb | f57749ca63d6416f807b770f67559503fdb21001 | /hott/hit/susp.hlean | c06c9abcdad6972c90a8900b1be5e050b3a63dd6 | [
"Apache-2.0"
] | permissive | aliassaf/lean | bd54e85bed07b1ff6f01396551867b2677cbc6ac | f9b069b6a50756588b309b3d716c447004203152 | refs/heads/master | 1,610,982,152,948 | 1,438,916,029,000 | 1,438,916,029,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,574 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
Declaration of suspension
-/
import .pushout types.pointed types.cubical.square
open pushout unit eq equiv equiv.ops
definition susp (A : Type) : Type := pushout... |
d6c10d3f6fa3cf8d8ec1ea73736ca2af7e3ab57e | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/interactive/catHover.lean | 7c3f523fa652f47c03fbc9628cebb8f8a66dc965 | [
"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 | 497 | lean | /-- Index syntax categoy -/
declare_syntax_cat index
--v textDocument/hover
syntax "foo " term prio index : term
--^ textDocument/hover
--^ textDocument/hover
namespace Foo
/-- Value syntax category -/
declare_syntax_cat value
syntax "bla " value : te... |
817dbf961486201c1273170033ba1ee67be817e2 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/linear_algebra/bilinear_form/tensor_product.lean | 97fdc9fcd996fe1d7696e5be11abd8dc2b19df46 | [
"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 | 3,066 | lean | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import linear_algebra.bilinear_form
import linear_algebra.tensor_product
/-!
# The bilinear form on a tensor product
## Main definitions
* `bilin_form.tensor_distrib (B₁... |
8b71037b6be1cad2ca6f89beb9ba7177a0897653 | 367134ba5a65885e863bdc4507601606690974c1 | /src/category_theory/monad/adjunction.lean | 66c33af29f3aa9a1225ae38e86bcd333c3777234 | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 6,330 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Bhavik Mehta
-/
import category_theory.monad.algebra
import category_theory.adjunction
namespace category_theory
open category
universes v₁ v₂ u₁ u₂ -- declare the `v... |
87d7ac935cec612ad6d2632255f3276e9fcb35dc | 19cc34575500ee2e3d4586c15544632aa07a8e66 | /src/algebra/group_power/basic.lean | 66ef70e5c96af2856b44c642f343f87ac97c54ad | [
"Apache-2.0"
] | permissive | LibertasSpZ/mathlib | b9fcd46625eb940611adb5e719a4b554138dade6 | 33f7870a49d7cc06d2f3036e22543e6ec5046e68 | refs/heads/master | 1,672,066,539,347 | 1,602,429,158,000 | 1,602,429,158,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 21,774 | lean | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis
-/
import algebra.order_functions
import deprecated.group
/-!
# Power operations on monoids and groups
The power operation on monoids and groups.
We sep... |
74ff0edf9f88020637f189eaa3d27382503dbe83 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/pack_unpack1.lean | 01e3191c00590553438a07a00dab64b6319152ef | [
"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 | 2,295 | lean | inductive {u} tree_core (A : Type u) : bool → (Type u)
| leaf' : A → tree_core ff
| node' : tree_core tt → tree_core ff
| nil' {} : tree_core tt
| cons' : tree_core ff → tree_core tt → tree_core tt
attribute [reducible]
definition tree (A : Sort*) := tree_core A ff
attribute [reducible]
definition tree_list... |
eeea646226dc6bc3d943b9dde1f2d67c6640eac2 | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/data/complex/exponential.lean | 7ff1c9de3b19a33f210e6e6aaa1ae50d392121a0 | [
"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 | 47,448 | 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.archimedean
import data.nat.choose data.complex.basic
import tactic.linarith
local attribute [instance, priority 0] cla... |
10ae63fef252b6cb959ceccad573a33b7e4e7063 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/ring_theory/polynomial/scale_roots.lean | 81f1f9a01c64484f54dd2bc6f37307d9e76ba593 | [
"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 | 5,693 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Devon Tuma
-/
import ring_theory.non_zero_divisors
import data.polynomial.algebra_map
/-!
# Scaling the roots of a polynomial
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> ... |
eb546ed5ac2e74eec4a4d308a68b0d52105a3d12 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/category/default.lean | 2b74e64f59d233482c21f43af63b142404d0b2f4 | [] | 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 | 10,849 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stephen Morgan, Scott Morrison, Johannes Hölzl, Reid Barton
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.tactic.basic
import Mathlib.PostPort
universe... |
9ab1435cf7eca75b7c0c3b2d888d93cc3eb14c84 | 8d65764a9e5f0923a67fc435eb1a5a1d02fd80e3 | /src/measure_theory/decomposition/jordan.lean | dcaae29fdc4ee89d6a829c5caf9a6185ba7e192f | [
"Apache-2.0"
] | permissive | troyjlee/mathlib | e18d4b8026e32062ab9e89bc3b003a5d1cfec3f5 | 45e7eb8447555247246e3fe91c87066506c14875 | refs/heads/master | 1,689,248,035,046 | 1,629,470,528,000 | 1,629,470,528,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 16,591 | lean | /-
Copyright (c) 2021 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import measure_theory.decomposition.signed_hahn
/-!
# Jordan decomposition
This file proves the existence and uniqueness of the Jordan decomposition for signed measures.
... |
58759286e01147dcf9dde0e67a9ec837f5b8a2db | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /archive/imo/imo1987_q1.lean | b4809852dd33bd83006d1d75368574708980818a | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 4,179 | 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 data.fintype.big_operators
import data.fintype.perm
import data.fintype.prod
import dynamics.fixed_points.basic
/-!
# Formalization of IMO 1987, Q1
Let $p_... |
edd08d67bd8075a419710894f58d35869cbd5dd6 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/order/filter/cofinite.lean | 38f8908f2dec682cfd833ab1bbd035385dfdfd14 | [
"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 | 7,269 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jeremy Avigad, Yury Kudryashov
-/
import order.filter.at_top_bot
import order.filter.pi
/-!
# The cofinite filter
In this file we define
`cofinite`: the filter of se... |
c798411cd58f7def223a033cf3b990c64b82236a | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /tests/lean/run/optParam.lean | 818d3c26232f31ee4e5dea884bb02356f4096c0e | [
"Apache-2.0"
] | permissive | williamdemeo/lean4 | 72161c58fe65c3ad955d6a3050bb7d37c04c0d54 | 6d00fcf1d6d873e195f9220c668ef9c58e9c4a35 | refs/heads/master | 1,678,305,356,877 | 1,614,708,995,000 | 1,614,708,995,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 325 | lean | def p (x : Nat := 0) : Nat × Nat :=
(x, x)
theorem ex1 : p.1 = 0 :=
rfl
theorem ex2 : p (x := 1) |>.2 = 1 :=
rfl
def c {α : Type} [Inhabited α] : α × α :=
(arbitrary, arbitrary)
theorem ex3 {α} [Inhabited α] : c.1 = arbitrary (α := α) :=
rfl
theorem ex4 {α} [Inhabited α] : c.2 = arbitrary (α := α) :=
rfl
|
3e744053858c490dafae3d229b460a207a5319aa | 8e381650eb2c1c5361be64ff97e47d956bf2ab9f | /src/Kenny/sheaf_of_rings_on_opens.lean | f069c9f5e019e21bf76f3b10e7a34041cd95d1b0 | [] | no_license | alreadydone/lean-scheme | 04c51ab08eca7ccf6c21344d45d202780fa667af | 52d7624f57415eea27ed4dfa916cd94189221a1c | refs/heads/master | 1,599,418,221,423 | 1,562,248,559,000 | 1,562,248,559,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 22,643 | lean | import sheaves.sheaf_of_rings Kenny.sheaf_on_opens ring_theory.subring
universes v w u₁ v₁ u
open topological_space lattice
def sheaf_of_rings_on_opens (X : Type u) [topological_space X] (U : opens X) : Type (max u (v+1)) :=
sheaf_of_rings.{u v} X
namespace sheaf_of_rings_on_opens
variables {X : Type u} [topologic... |
c407c2be8e71c18b01b0fa59a7b1c88db17f2890 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/section4.lean | 5a4f427deff9f1372f8a664cfc8327a02ae863b7 | [
"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 | 648 | lean | import logic
set_option pp.universes true
set_option pp.implicit true
section
universe k
parameter A : Type
section
universe variable l
universe variable u
parameter B : Type
definition foo (a : A) (b : B) := b
inductive mypair :=
mk : A → B → mypair
definition pr1' (p : mypai... |
adcb8bc3a7696ac57e7ee467547e370f15006a8b | 359199d7253811b032ab92108191da7336eba86e | /src/instructor/lectures/lecture_5.lean | 1368bc7298b70c9e7bc8991861617ecbc6718d89 | [] | no_license | arte-et-marte/my_cs2120f21 | 0bc6215cb5018a3b7c90d9d399a173233f587064 | 91609c3609ad81fda895bee8b97cc76813241e17 | refs/heads/main | 1,693,298,928,348 | 1,634,931,202,000 | 1,634,931,202,000 | 399,946,705 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,005 | lean | /-
INTRODUCTION and ELIMINATION RULES
-/
/-
For ∀ x, P x (every x has property P)
- introduction rule: assume arbitrary x, then show P x
- elimination rule: *apply* a proof of ∀ x, P x, as a
kind of function to a specific value of x, say k, to
produce a proof of P k.
-/
/-
Now we need a short detour, so as ... |
c4f3855d933f621e81ea2555cb5625d1f96fb0e9 | 0f54cce53cdd7d43dc5b0017dfb0a3eaf09ba18a | /src/simp_loop/exists_one_point_elim.lean | 45b87bdbb21b0ae85bf74e73c6ad70edd11a9dd4 | [] | no_license | johoelzl/lean-simp-loop | dabc7629b21e319fa0b9c45639c82f9bea57a18a | c1ad8c34be7c6fd323fc5eff5ce337fd23a72e04 | refs/heads/master | 1,618,774,503,904 | 1,525,883,646,000 | 1,525,883,646,000 | 126,789,660 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,586 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
1-point elimination for ∃.
This implements a conversion transforming
`∃x, t[x, x = a] ~> t[a, rfl]`
where `t` is an expression consiting of existentials and conjunct... |
fcc3c6747eb0fcc41ccbda092b924e7e128fe65b | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/number_theory/pell.lean | ffdd65bd0783a75cd1786202cd01541b00ab3cba | [
"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 | 37,733 | 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.nat.modeq
import number_theory.zsqrtd.basic
/-!
# Pell's equation and Matiyasevic's theorem
This file solves Pell's equation, i.e. integer solutions to... |
6b752cb9c45f65c91e0826bcbfb30b0dd2792a41 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/1852.lean | 970ca3c2555cc4e1740c1360ce5880801b7ed587 | [
"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 | 473 | lean | class foo (F : Type) where
foo : F
class foobar (F : outParam Type) [foo F] where
bar : F
class C (α : Type) where
val : α
class D (α : Type) (β : outParam Type) [C β] where
val1 : α
val2 : β := C.val
instance : C String where
val := "hello"
instance : C Nat where
val := 42
instance : D Nat String w... |
bd1faf5166cd38379d36f72e916b8bd1c26222be | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/blast_simp_sum.lean | 289e2aa9422d77cd9f3b5237eeaee7b994eecc26 | [
"Apache-2.0"
] | permissive | soonhokong/lean | cb8aa01055ffe2af0fb99a16b4cda8463b882cd1 | 38607e3eb57f57f77c0ac114ad169e9e4262e24f | refs/heads/master | 1,611,187,284,081 | 1,450,766,737,000 | 1,476,122,547,000 | 11,513,992 | 2 | 0 | null | 1,401,763,102,000 | 1,374,182,235,000 | C++ | UTF-8 | Lean | false | false | 1,102 | lean | import data.nat
open - [simp] nat
definition Sum : nat → (nat → nat) → nat :=
sorry
notation `Σ` binders ` < ` n `, ` r:(scoped f, Sum n f) := r
lemma Sum_const [simp] (n : nat) (c : nat) : (Σ x < n, c) = n * c :=
sorry
lemma Sum_add [simp] (f g : nat → nat) (n : nat) : (Σ x < n, f x + g x) = (Σ x < n, f x) + (Σ x ... |
0939261022bc37f1fb6d64b7d0ffb5dff00baa70 | bb31430994044506fa42fd667e2d556327e18dfe | /src/topology/metric_space/pi_nat.lean | ba35f8bb48a1a0c474e2222bd8702f209bd81a9f | [
"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 | 41,448 | lean | /-
Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import tactic.ring_exp
import topology.metric_space.hausdorff_distance
/-!
# Topological study of spaces `Π (n : ℕ), E n`
When `E n` are topological spaces, t... |
5bb90486d0edb62569e7d445d895fd356efa7b97 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/measure_theory/function/l2_space.lean | c9e52cd5a9fc9780b2c1d497805e5adffc127a86 | [
"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 | 10,950 | lean | /-
Copyright (c) 2021 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import analysis.inner_product_space.basic
import measure_theory.integral.set_integral
/-! # `L^2` space
If `E` is an inner product space over `𝕜` (`ℝ` or `ℂ`), then `L... |
cf5761a4997861db39e7a35b3547d21a30129b42 | 2469dcaa81734b4823dbd29f4534010be87e60ea | /library/system/io.lean | 75138b2facfccb651161971680126536807e37a8 | [
"Apache-2.0"
] | permissive | elefthei/lean | d43213fee34f1d971121d872ad9bfcae684c354c | 6e02ce9b345bc9263272668ead709d3d24c2a1fa | refs/heads/master | 1,630,434,764,528 | 1,513,935,338,000 | 1,513,940,069,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,179 | 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 and Leonardo de Moura
-/
import data.buffer
inductive io.error
| other : string → io.error
| sys : nat → io.error
structure io.terminal (m ... |
7815811fed734db745175b47c85f25be95dca07c | d642a6b1261b2cbe691e53561ac777b924751b63 | /src/data/fin.lean | b6de34d5a70c7f1a523c732e456b8fa3e39bae7e | [
"Apache-2.0"
] | permissive | cipher1024/mathlib | fee56b9954e969721715e45fea8bcb95f9dc03fe | d077887141000fefa5a264e30fa57520e9f03522 | refs/heads/master | 1,651,806,490,504 | 1,573,508,694,000 | 1,573,508,694,000 | 107,216,176 | 0 | 0 | Apache-2.0 | 1,647,363,136,000 | 1,508,213,014,000 | Lean | UTF-8 | Lean | false | false | 14,249 | lean | /-
Copyright (c) 2017 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Keeley Hoek
More about finite numbers.
-/
import data.nat.basic
open fin nat function
/-- `fin 0` is empty -/
def fin_zero_elim {C : Sort*} : fin 0 → C :=
λ x, fal... |
de4fabf0ab6a09aa8a23dba95414fa1cd7c32169 | bb31430994044506fa42fd667e2d556327e18dfe | /src/data/finset/pointwise.lean | b73271640aefe84fb397993eb3d5b7ace6fbd59b | [
"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 | 49,504 | 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, Yaël Dillies
-/
import data.finset.n_ary
import data.finset.preimage
import data.set.pointwise.smul
import data.set.pointwise.list_of_fn
/-!
# Pointwise operations... |
424f10697382aa469407d5ee90c7e574e42cd60e | d29d82a0af640c937e499f6be79fc552eae0aa13 | /src/linear_algebra/matrix/to_lin.lean | 2164c0bc14645dd62d49790b7da1b9cfc45ccde3 | [
"Apache-2.0"
] | permissive | AbdulMajeedkhurasani/mathlib | 835f8a5c5cf3075b250b3737172043ab4fa1edf6 | 79bc7323b164aebd000524ebafd198eb0e17f956 | refs/heads/master | 1,688,003,895,660 | 1,627,788,521,000 | 1,627,788,521,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 27,608 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-/
import data.matrix.block
import linear_algebra.matrix.finite_dimensional
import linear_algebra.std_basis
import ring_theory.... |
c4dc7a67c54da6da167aac4aacbf58c448e56f81 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/fin_category.lean | e297f2ce5e26d2965a065d88f0abe9a8b8e872b8 | [] | 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 | 2,384 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.fintype.basic
import Mathlib.category_theory.discrete_category
import Mathlib.PostPort... |
20c19552ca203f869c38127a1d641593c0b79fb7 | 159fed64bfae88f3b6a6166836d6278f953bcbf9 | /Structure/Generic/Axioms/AbstractProducts.lean | 663fbbf4f7720af9f953fe19f8be09f0c1cd31a7 | [
"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 | 1,369 | lean | import Structure.Generic.Axioms.Universes
import Structure.Generic.Axioms.AbstractFunctors
import mathlib4_experiments.Data.Equiv.Basic
set_option autoBoundImplicitLocal false
--set_option pp.universes true
def ExternalProduct {U V : Universe} (α : U) (β : V) := PProd ⌈α⌉ ⌈β⌉
namespace ExternalProduct
infixr... |
ca4a7da1ee8bd669a7c05e7587dcb190f2b89a46 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/blast_simp_subsingleton.lean | f6eb70d6b1abbf7700fc5bbdb4a5912dddf247a5 | [
"Apache-2.0"
] | permissive | soonhokong/lean | cb8aa01055ffe2af0fb99a16b4cda8463b882cd1 | 38607e3eb57f57f77c0ac114ad169e9e4262e24f | refs/heads/master | 1,611,187,284,081 | 1,450,766,737,000 | 1,476,122,547,000 | 11,513,992 | 2 | 0 | null | 1,401,763,102,000 | 1,374,182,235,000 | C++ | UTF-8 | Lean | false | false | 1,036 | lean | import data.unit
open nat unit
constant f {A : Type} (a : A) {B : Type} (b : B) : nat
constant g : unit → nat
example (a b : unit) : g a = g b :=
by simp
example (a c : unit) (b d : nat) : b = d → f a b = f c d :=
by simp
constant h {A B : Type} : A → B → nat
example (a b c d : unit) : h a b = h c d :=
by simp
d... |
60de56488eb5003d054bc9728f11898583516d60 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/match1.lean | 4e973b2a1596f372e43c0fd8793bff49420cbf07 | [
"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 | 3,855 | lean | --
#print "---- h1"
def h1 (b : Bool) : Nat :=
match b with
| true => 0
| false => 10
#eval h1 false
#print "---- h2"
def h2 (x : List Nat) : Nat :=
match x with
| [x1, x2] => x1 + x2
| x::xs => x
| _ => 0
#eval h2 [1, 2]
#eval h2 [10, 4, 5]
#eval h2 []
#print "---- h3"
def h3 (x : Array Nat) : Nat :... |
8f593a75df15defaf4dcd56be47ca06c9ec40205 | fcf3ffa92a3847189ca669cb18b34ef6b2ec2859 | /src/world1/level1.lean | 7a77edcb50edf89af325508bc2b2a81e4788567b | [
"Apache-2.0"
] | permissive | nomoid/lean-proofs | 4a80a97888699dee42b092b7b959b22d9aa0c066 | b9f03a24623d1a1d111d6c2bbf53c617e2596d6a | refs/heads/master | 1,674,955,317,080 | 1,607,475,706,000 | 1,607,475,706,000 | 314,104,281 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 178 | lean | import mynat.definition
import mynat.add
import mynat.mul
namespace mynat
lemma example1 (x y z : mynat) : x * y + z = x * y + z :=
begin [nat_num_game]
refl
end
end mynat |
efc923b88c144b9e29ee371ca85cc7fdac41ff4f | e151e9053bfd6d71740066474fc500a087837323 | /src/hott/types/pointed2.lean | 7cf22e35915caaf430888b2c5b047e5b7209a00a | [
"Apache-2.0"
] | permissive | daniel-carranza/hott3 | 15bac2d90589dbb952ef15e74b2837722491963d | 913811e8a1371d3a5751d7d32ff9dec8aa6815d9 | refs/heads/master | 1,610,091,349,670 | 1,596,222,336,000 | 1,596,222,336,000 | 241,957,822 | 0 | 0 | Apache-2.0 | 1,582,222,839,000 | 1,582,222,838,000 | null | UTF-8 | Lean | false | false | 43,752 | lean | /-
Copyright (c) 2017 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
More results about pointed types.
Contains
- squares of pointed maps,
- equalities between pointed homotopies and
- squares between pointed homotopies
- pointed ma... |
343693d21510f8ee1cdeca4f092a3585c639f92d | 36938939954e91f23dec66a02728db08a7acfcf9 | /lean/deps/sexpr/src/galois/sexpr.lean | 16d8a143e11304a9ccc5b40cb64fb2ddf9143688 | [
"Apache-2.0"
] | permissive | pnwamk/reopt-vcg | f8b56dd0279392a5e1c6aee721be8138e6b558d3 | c9f9f185fbefc25c36c4b506bbc85fd1a03c3b6d | refs/heads/master | 1,631,145,017,772 | 1,593,549,019,000 | 1,593,549,143,000 | 254,191,418 | 0 | 0 | null | 1,586,377,077,000 | 1,586,377,077,000 | null | UTF-8 | Lean | false | false | 5,887 | lean | /-
This declares an s-expression datatype for generating
expressions and reasoning about their interpretation.
-/
import system.io
import galois.category.except
import galois.data.array
import galois.data.buffer
import galois.data.list
import galois.data.nat
import .char_reader
universes u v w
namespace sexpr
class... |
b903457f509af52250adc9576bda59cdd1f43075 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/topology/algebra/module.lean | d3fa6b4ebca3aee5f659d9a9e616328e6d922b41 | [
"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 | 26,040 | 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
-/
import topology.algebra.ring linear_algebra.basic ring_theory.algebra
/-!
# Theory of topological modules and continuous linear m... |
f43db0cae60d7e5104ff0753e691d6f6fcc3d460 | 8cb37a089cdb4af3af9d8bf1002b417e407a8e9e | /library/init/meta/declaration.lean | 22361c54e11bdcafde5ca4ebb647616cab7df92f | [
"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 | 5,495 | 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.expr init.meta.name init.meta.task
/--
Reducibility hints are used in the convertibility checker.
When trying to solve a constrain... |
88426d9f7792509b76815892120e1020e265a770 | 38bf3fd2bb651ab70511408fcf70e2029e2ba310 | /src/measure_theory/l1_space.lean | e19feab1a237fc3144af21e1b1bbcebf340ff7b5 | [
"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 | 6,540 | lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
Integrable functions and L¹ space
-/
import measure_theory.ae_eq_fun
noncomputable theory
open_locale classical
set_option class.instance_max_depth 100
namespace meas... |
ff1a015e157fb4ec36caec4cc0bea4bd2de01513 | 5e3548e65f2c037cb94cd5524c90c623fbd6d46a | /src_icannos_totilas/reduction/cpge_reduction_012_b.lean | 23e72ae4c0a32f10a65a136e1293896cf940f0cb | [] | 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 | 1,049 | lean | import data.real.basic
import data.polynomial.derivative
import linear_algebra.basic
import linear_algebra.finite_dimensional
-- On se place dans le R -espace vectoriel E = R[X] .
-- (a) Soit H un sous-espace vectoriel de dimension finie et f un endomorphisme de H. Montrer qu'il existe p ∈ N tel que
-- ∀k ≥ p, Ke... |
438bde0d8fbbab21e926e268a15b4ef6fb085b1b | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/mv_polynomial/invertible.lean | e7ba6f0675eaf222003a2dbb809901a133a0f4c4 | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 1,034 | lean | /-
Copyright (c) 2020 Johan Commelin and Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin and Robert Y. Lewis
-/
import data.mv_polynomial.basic
import ring_theory.algebra_tower
/-!
# Invertible polynomials
This file is a stub containin... |
64bb404e24ef6af52d1cb33e27ad976ddccc7ba4 | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/finsupp/lattice.lean | fe6beb9bea6fe47f0cb631846f528b6a74d2e28c | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 3,163 | lean | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import data.finsupp.basic
import algebra.ordered_group
/-!
# Lattice structure on finsupps
This file provides instances of ordered structures on finsupps.
-/
open... |
ffdc633d314aa954da32257f3fb0e9cef0ebb743 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /library/data/nat/examples/fib.lean | 53dd3a58d8dfd6d01908a08575ceca55e88771b6 | [
"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 | 1,292 | 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
-/
import data.nat
open nat
definition fib : nat → nat
| 0 := 1
| 1 := 1
| (n+2) := fib (n+1) + fib n
private definition fib_fast_aux : nat → (nat × n... |
d795e5152676a682c2c1f7b89d5bc2283a472883 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/list/tfae_auto.lean | 16d92c0a4dc2922cef5a9259a4a4797229699ef1 | [] | 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 | 2,321 | lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Simon Hudon
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.list.basic
import Mathlib.PostPort
namespace Mathlib
namespace list
/... |
177d021041be0ffb807eb1b6fb831470c344267e | 6fbf10071e62af7238f2de8f9aa83d55d8763907 | /hw/hw8.lean | 5442c5a2f571f518c0c3dceb907670931e29955c | [] | no_license | HasanMukati/uva-cs-dm-s19 | ee5aad4568a3ca330c2738ed579c30e1308b03b0 | 3e7177682acdb56a2d16914e0344c10335583dcf | refs/heads/master | 1,596,946,213,130 | 1,568,221,949,000 | 1,568,221,949,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,762 | lean | /- 1a. [10 points]
Implement a function, bool_implies, that takes
two bool values, b1 and b2 (not propositions),
and that returns the the value of b1 → b2.
Here the → operator means implication in Boolean
algebra. To know what your function should do,
write out the truth table for implication. You
may not use Lean's ... |
dd81338259838e1ff75355607e0f875d74c1ddfb | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/let3.lean | 87315a552461c7632ed142e45ea6fd82677abd9d | [
"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 | 900 | lean | definition p1 := (10, 20, 30)
definition v1 : nat :=
let (a, b, c) := p1 in
a + b + c
definition v2 : nat :=
let ⟨a, b, c⟩ := p1 in
a + b + c
example : v2 = 60 :=
rfl
/-
let with patterns is just syntax sugar for the match convoy pattern.
let (a, b, c) := p1 in
a + b + c
is encoded as
match p1 with
(... |
1c864572a74aaa2d3472b7e7e4edfda6aa06c943 | 649957717d58c43b5d8d200da34bf374293fe739 | /src/category_theory/limits/functor_category.lean | eb8da8bf5a65b56b243336328346b4da7596e94f | [
"Apache-2.0"
] | permissive | Vtec234/mathlib | b50c7b21edea438df7497e5ed6a45f61527f0370 | fb1848bbbfce46152f58e219dc0712f3289d2b20 | refs/heads/master | 1,592,463,095,113 | 1,562,737,749,000 | 1,562,737,749,000 | 196,202,858 | 0 | 0 | Apache-2.0 | 1,562,762,338,000 | 1,562,762,337,000 | null | UTF-8 | Lean | false | false | 4,863 | 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.products
import category_theory.limits.preserves
open category_theory category_theory.category
namespace category_theory.limits
universe... |
8a694ea84e1a4e3806a287fe29f3d1a935f25d5a | 3f7026ea8bef0825ca0339a275c03b911baef64d | /src/topology/uniform_space/basic.lean | fd233bd8ac647bc49db60538c5ff8a821a306846 | [
"Apache-2.0"
] | permissive | rspencer01/mathlib | b1e3afa5c121362ef0881012cc116513ab09f18c | c7d36292c6b9234dc40143c16288932ae38fdc12 | refs/heads/master | 1,595,010,346,708 | 1,567,511,503,000 | 1,567,511,503,000 | 206,071,681 | 0 | 0 | Apache-2.0 | 1,567,513,643,000 | 1,567,513,643,000 | null | UTF-8 | Lean | false | false | 42,459 | 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, Patrick Massot
Theory of uniform spaces.
Uniform spaces are a generalization of metric spaces and topological groups. Many concepts directly
generaliz... |
ddcae87ce1a88f47d79bdad4681c62fbceef515e | 4e39e38e0c2134eafdc7ab6e0f8ca5c27795f7a2 | /test.lean | 1b5fc0e5882cdbf239b3231c12720a56d5e32391 | [] | no_license | tcmch/cs-dm | a33c4169b8282b54653be72b9600e83ad329953c | 4d9e45e398d7ec12538fe0335c007b98f0b32403 | refs/heads/master | 1,585,694,000,689 | 1,544,118,938,000 | 1,544,118,938,000 | 152,622,502 | 0 | 0 | null | 1,539,275,269,000 | 1,539,275,269,000 | null | UTF-8 | Lean | false | false | 4,972 | lean | /-
This exam focuses on assessing your
ability to write and prove propositions
in predicate logic, with an emphasis on
predicates, disjunctions, and existentially
quantified propositions. There are three
parts:
A: Predicates [20 points in 4 parts]
B: Disjuctions [40 points in 2 parts]
C. Existentials [40 point i... |
9fe6dd4020acbb4e7fea438715f7a8110dacd31e | 1ce2e14f78a7f514bae439fbbb1f7fa2932dd7dd | /src/common.lean | 34e08b0e2f6f71e3385060f863714e5c8d056921 | [
"MIT"
] | permissive | wudcscheme/lean-mathgirls | b88faf76d12e5ca07b83d6e5580663380b0bb45c | 95b64a33ffb34f3c45e212c4adff3cc988dcbc60 | refs/heads/master | 1,678,994,115,961 | 1,585,127,877,000 | 1,585,127,877,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,219 | lean | import data.list.basic data.list.perm init.data.int.order
import tactic.omega tactic.basic tactic.tidy
notation `ℙ` := nat.primes
meta def by_eval (typ: Type*) [reflected typ]: tactic unit := do
e <- tactic.target,
match expr.is_eq e with
| (some (e1, e2)) := tactic.eval_expr' typ e1 >> tactic.reflexivity
| ... |
a12783363e337f1e2e6dd761f85979d14fde902e | d7c0dac4019ec4c77a89fd6d3e672674a3cad8f8 | /ANT.lean | ecbe3f0dfdd17b90cb47f297354e9d9769fa4e47 | [] | no_license | TudorTitan/Lean_ElementaryNT | 97fb78afaa07822c9ee0f563e263e16536b28638 | e9fa9e1db315fa7aca88666aee9910d5d9d34a11 | refs/heads/master | 1,630,895,651,127 | 1,517,510,995,000 | 1,517,510,995,000 | 108,649,763 | 0 | 1 | null | 1,509,757,816,000 | 1,509,195,975,000 | Lean | UTF-8 | Lean | false | false | 9,529 | lean | -- Needed for sheaves temporarily
import analysis.topology.topological_space
-- Auxiliary lemmas
lemma exists_and_commute {α : Type} {p q r: α → Prop} :
(∃! a : α, r a ∧ p a ∧ q a) → ∃! a : α, r a ∧ q a ∧ p a :=
λ ⟨a, ⟨b, c ⟩⟩,
begin
existsi a,
simp at *,
exact ⟨b.symm.2,... |
d0882374363a8436a3a3078db8f3ed4b7d380b06 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/topology/algebra/multilinear.lean | 7ac860de6d656aaa7dc1779a734870b9d605104a | [
"Apache-2.0"
] | permissive | stjordanis/mathlib | 51e286d19140e3788ef2c470bc7b953e4991f0c9 | 2568d41bca08f5d6bf39d915434c8447e21f42ee | refs/heads/master | 1,631,748,053,501 | 1,627,938,886,000 | 1,627,938,886,000 | 228,728,358 | 0 | 0 | Apache-2.0 | 1,576,630,588,000 | 1,576,630,587,000 | null | UTF-8 | Lean | false | false | 17,198 | 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.algebra.module
import linear_algebra.multilinear
/-!
# Continuous multilinear maps
We define continuous multilinear maps as maps from `Π(i : ι... |
04acac95a0c3a5f6b617ca2fad459f7d7994e269 | e91b0bc0bcf14cf6e1bfc20ad1f00ad7cfa5fa76 | /src/sheaves/stalk_on_basis.lean | b418b8a3515dc2c66ff735c64175bcbdba6fbfb0 | [] | no_license | kckennylau/lean-scheme | b2de50025289a0339d97798466ef777e1899b0f8 | 8dc513ef9606d2988227490e915b7c7e173a2791 | refs/heads/master | 1,587,165,137,978 | 1,548,172,249,000 | 1,548,172,249,000 | 167,025,881 | 0 | 0 | null | 1,548,173,930,000 | 1,548,173,924,000 | Lean | UTF-8 | Lean | false | false | 2,564 | lean | -- stuff mentioned in section "Bases and sheaves" (6.30; tag 009H)
-- but not in any definition etc
import sheaves.presheaf_of_types_on_basis
universe u
-- definition after 6.30.1 and before 6.30.2
section presheaf_on_basis_stalk
parameters {α : Type u} [TX : topological_space α]
{B : set (set α )}
{HB : topo... |
2dbd56268f0effad5750bd0c4fc90fc566b70494 | 5c7fe6c4a9d4079b5457ffa5f061797d42a1cd65 | /src/exercises/src_33_identity_and_inverse_functions.lean | 896ddf9097088010abbdd245f43324258160dbd8 | [] | 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 | 10,222 | lean | import data.set.function
import tactic.linarith
import tactic.norm_num
open function
namespace mth1001
section identity
/-
For a given type `α`, there is a special function, the identity function `id : α → α` defined so
that `id a = a`, for every `a : α`.
-/
def p₁ (x : ℕ) : ℤ := 3 * x
/-
For every function `f :... |
1d40530df671787856804b940372cb3889f46c9a | 969dbdfed67fda40a6f5a2b4f8c4a3c7dc01e0fb | /src/algebra/smul_with_zero.lean | 435294d90aff414c0d7c394a6d453cc2444a0eea | [
"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 | 2,423 | lean | /-
Copyright (c) 2021 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import group_theory.group_action.defs
/-!
# Introduce `smul_with_zero`
In analogy with the usual monoid action on a Type `M`, we introduce an action of a
`monoid_with_... |
b50dbc46f90f080aa9961d96b65402e8ee2a54b6 | cbcb0199842f03e7606d4e43666573fc15dd07a5 | /src/measure_theory/borel_space.lean | b001835370bce20e1a07a8bc06e1de2566bf51bc | [
"Apache-2.0"
] | permissive | truonghoangle/mathlib | a6a7c14b3767ec71156239d8ea97f6921fe79627 | 673bae584febcd830c2c9256eb7e7a81e27ed303 | refs/heads/master | 1,590,347,998,944 | 1,559,728,860,000 | 1,559,728,860,000 | 187,431,971 | 0 | 0 | null | 1,558,238,525,000 | 1,558,238,525,000 | null | UTF-8 | Lean | false | false | 18,619 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Borel (measurable) space -- the smallest σ-algebra generated by open sets
It would be nice to encode this in the topological space type class, i.e. each topological sp... |
c0fd5a5d310930cdd4a83a3713269149f8f71336 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/list/palindrome.lean | 7e741c4ea071e9e9d46ef3b173f9bcf54458d912 | [] | 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 | 1,869 | lean | /-
Copyright (c) 2020 Google LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Wong
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.list.basic
import Mathlib.PostPort
universes u_1
namespace Mathlib
/-!
# Palindromes
This... |
aa0061fb0f3ef90f07dc3c3772d2cc226e13292a | bb31430994044506fa42fd667e2d556327e18dfe | /src/order/hom/complete_lattice.lean | e37431e776b624337cfb6d5afe573f8d25503c26 | [
"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 | 26,672 | 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 order.complete_lattice
import order.hom.lattice
/-!
# Complete lattice homomorphisms
This file defines frame homorphisms and complete lattice homomorphisms.
We ... |
6cd1eed1d7bd3a917bdb97b0c3883236abfb4ace | a4673261e60b025e2c8c825dfa4ab9108246c32e | /stage0/src/Init/Data/Array/Subarray.lean | f1af76e1d47c06a3463064a7aa510783c81afef1 | [
"Apache-2.0"
] | permissive | jcommelin/lean4 | c02dec0cc32c4bccab009285475f265f17d73228 | 2909313475588cc20ac0436e55548a4502050d0a | refs/heads/master | 1,674,129,550,893 | 1,606,415,348,000 | 1,606,415,348,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,018 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import Init.Data.Array.Basic
universes u v w
structure Subarray (α : Type u) :=
(as : Array α)
(start : Nat)
(stop : Nat)
(h₁ : start ≤ s... |
e64d243017faa25eda1e7d6dc4488a5ac9e6558d | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/sites/compatible_plus.lean | dc0f90947a65848ccb9fdcdd62dd7d04eb72cc38 | [
"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 | 8,728 | lean | /-
Copyright (c) 2021 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import category_theory.sites.whiskering
import category_theory.sites.plus
/-!
In this file, we prove that the plus functor is compatible with functors which
preserve the co... |
8d143854e8eb856e43cb55fcb3222f85936e4f37 | 36c7a18fd72e5b57229bd8ba36493daf536a19ce | /library/data/int/power.lean | f461849c0dc151e1f95141b8301c0f544da1bdeb | [
"Apache-2.0"
] | permissive | YHVHvx/lean | 732bf0fb7a298cd7fe0f15d82f8e248c11db49e9 | 038369533e0136dd395dc252084d3c1853accbf2 | refs/heads/master | 1,610,701,080,210 | 1,449,128,595,000 | 1,449,128,595,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 787 | lean | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
The power function on the integers.
-/
import data.int.basic data.int.order data.int.div algebra.group_power data.nat.power
namespace int
open algebra
definition int_has... |
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