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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
891f3ccf313b4f79a67fc82efec7437f045f2539 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/char_p/basic.lean | 096e1bac263fc676d1243832b72e6475e7b137df | [
"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 | 17,505 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Joey van Langen, Casper Putz
-/
import algebra.hom.iterate
import data.int.modeq
import data.nat.choose.dvd
import data.nat.choose.sum
import group_theory.order_of_element
impor... |
99a3d3ff0defc963c321188a853ee6d7bbfa1091 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/limits/types.lean | 1bb2b8ebd2db9f5b729787f36af84a6aefd9e2b4 | [] | 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 | 15,197 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Reid Barton
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.limits.shapes.images
import Mathlib.category_theory.filtered
i... |
96e249e0227c9cfd98b19b2ee03d5a0c40b84309 | ba4794a0deca1d2aaa68914cd285d77880907b5c | /src/game/world3/level4.lean | bd1db8ae1c4a7f4c6d0f9cad35e9343f0077d60f | [
"Apache-2.0"
] | permissive | ChrisHughes24/natural_number_game | c7c00aa1f6a95004286fd456ed13cf6e113159ce | 9d09925424da9f6275e6cfe427c8bcf12bb0944f | refs/heads/master | 1,600,715,773,528 | 1,573,910,462,000 | 1,573,910,462,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,387 | lean | import game.world3.level3 -- hide
namespace mynat -- hide
/-
# Multiplication World
## Level 4: `mul_add`
Where are we going? Well we want to prove `mul_comm`
and `mul_assoc`, i.e. that `a * b = b * a` and
`(a * b) * c = a * (b * c)`. But we *also* want to
establish the way multiplication interacts with addition,
i.... |
9f705b615e0fd15cd5b3434e8d5a7c7ab27bfbb5 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/nat/enat.lean | e278d5b7108a3aa8488dd6967381dbfbb95f0d05 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 16,378 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.pfun
import Mathlib.tactic.norm_num
import Mathlib.data.equiv.mul_add
import Mathlib.PostP... |
ebccbe3c6a37427dd7f662b09852f01842a16298 | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /src/Lean/Meta/Match/CaseValues.lean | d2e05fe82ac95287e6478965717bf6956bb138df | [
"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 | 4,508 | 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.Subst
import Lean.Meta.Tactic.Clear
namespace Lean.Meta
structure CaseValueSubgoal where
mvarId : MVarId
newH : FVarId
sub... |
54a67e0ba5c95fb2d9e55a8d4326384af5669c70 | 0a354201ce5d10ac9334623ab4426a02ba66d8d2 | /src/somemaths-comparisons.lean | f32902fe399e7cf7d3946020db91fd457a165212 | [] | no_license | khoek/leancache-example | e09c85d88013968ccab9f01855aa2b7805031f96 | 5c55bb5a792c6a711ab12e6e6d2c7118d99a936c | refs/heads/master | 1,587,379,301,297 | 1,549,096,088,000 | 1,549,096,088,000 | 168,796,024 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,950 | 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 .obviously
-- **** Begin caching stuff ****
-- **** Enable tactic block caching (just include) ****
import tactic.tcache.enable
-- Tr... |
8749cf6d454fb8175bb12e977faf0f3fa518fc7f | 618003631150032a5676f229d13a079ac875ff77 | /src/analysis/analytic/composition.lean | 770c82976534a4d6923366a75aba3700505f778e | [
"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 | 56,788 | lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Johan Commelin
-/
import analysis.analytic.basic
import combinatorics.composition
/-!
# Composition of analytic functions
in this file we prove that the composi... |
b8d121302f7d6f9e45a79f628343fc9aca23099a | bb31430994044506fa42fd667e2d556327e18dfe | /src/data/fin/tuple/sort.lean | 38430667b8f63d398f942ce13f36087190c117d7 | [
"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 | 6,217 | lean | /-
Copyright (c) 2021 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import data.finset.sort
import data.list.fin_range
import data.prod.lex
import group_theory.perm.basic
/-!
# Sorting tuples by their values
Given an `n`-tuple `f : fin n... |
6544e043b932402bc7bef5eb0b0d97b23f298d42 | 8e381650eb2c1c5361be64ff97e47d956bf2ab9f | /src/sheaves/sheaf_of_rings.lean | 6ad6cea21569ef2217cfc9515e8956209248d923 | [] | 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 | 965 | lean | /-
Sheaf of rings.
https://stacks.math.columbia.edu/tag/0071
-/
import sheaves.sheaf
import sheaves.presheaf_of_rings
universes u
-- A sheaf of rings is essentially a sheaf of types because we assume that the
-- category of commutative rings has limits (proved later). This is tag 0073.
structure sheaf_of_ri... |
a047defb50a81e3090e7c8b9e53b756c6223a802 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/linear_algebra/affine_space/ordered.lean | bf24d3cc4a36ddde30eaab924f2f67b12e9bcc63 | [
"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 | 15,410 | lean | /-
Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Yury G. Kudryashov
-/
import linear_algebra.affine_space.midpoint
import algebra.module.ordered
/-!
# Ordered modules as affine spaces
In this file we define the slope of a functi... |
0e8f4f70d897a5d11fd9fea97290d5cca31132e0 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/restate_axiom_auto.lean | 86a8e4319e8c32a8782738e8b96ab439aa9c236a | [] | 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 | 1,392 | lean | /-
Copyright (c) 2017 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.Lean3Lib.data.buffer.parser
import Mathlib.tactic.doc_commands
import Mathlib.PostPort
nam... |
a4de2ce8e679db35dcba2acc1f120576deedfe68 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /archive/imo/imo2005_q3.lean | 9d4ef279453ea77f5357c1397ea3b8649f526915 | [
"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 | 2,972 | lean | /-
Copyright (c) 2021 Manuel Candales. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Manuel Candales
-/
import data.real.basic
import tactic.positivity
/-!
# IMO 2005 Q3
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR... |
97617dc1eacf423d8cbb7abe74d6e08a4cfa85cd | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/int/char_zero.lean | f8209451f13cb4a41acaea3907380c7608046ae8 | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 1,546 | 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.cast
import algebra.char_zero
/-!
# Injectivity of `int.cast` into characteristic zero rings.
-/
variables {α : Type*}
open nat
namespace int
@[... |
2e3b2ed5d599e98d769e38a19b09696ada6f63e5 | 3b15c7b0b62d8ada1399c112ad88a529e6bfa115 | /stage0/src/Lean/Server/FileWorker.lean | 2a34bb15e7e7578f35da831d9f1401407f20e1db | [
"Apache-2.0"
] | permissive | stephenbrady/lean4 | 74bf5cae8a433e9c815708ce96c9e54a5caf2115 | b1bd3fc304d0f7bc6810ec78bfa4c51476d263f9 | refs/heads/master | 1,692,621,473,161 | 1,634,308,743,000 | 1,634,310,749,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 20,794 | lean | /-
Copyright (c) 2020 Marc Huisinga. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Marc Huisinga, Wojciech Nawrocki
-/
import Init.System.IO
import Std.Data.RBMap
import Lean.Environment
import Lean.Data.Lsp
import Lean.Data.Json.FromToJson
import Lean.Util.Paths
... |
4e8fcf8bc4bb95469cf48cb77fc126230d1e6743 | 3dc4623269159d02a444fe898d33e8c7e7e9461b | /.github/workflows/project_1_a_decrire/lean-scheme-submission/src/to_mathlib/topologcal_space.lean | caa9c6f1b66be2cb24093a18f2d006ec8d6d9369 | [] | no_license | Or7ando/lean | cc003e6c41048eae7c34aa6bada51c9e9add9e66 | d41169cf4e416a0d42092fb6bdc14131cee9dd15 | refs/heads/master | 1,650,600,589,722 | 1,587,262,906,000 | 1,587,262,906,000 | 255,387,160 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 599 | lean | /-
Defining a topological space by giving the closeds instead of the opens.
-/
import topology.basic
universe u
def topological_space.of_closed {α : Type u} (T : set (set α))
(H1 : ∅ ∈ T)
(H2 : ∀ A ⊆ T, ⋂₀ A ∈ T)
(H3 : ∀ A B ∈ T, A ∪ B ∈ T) :
topological_space α :=
{ is_open := λ X, -X ∈ T,
is_open_univ ... |
42500a13e3814f379195b6a87ea5443a9e7269af | 4da0c8e61fcd6ec3f3be47ee14a038850c03d0c3 | /src/s5/semantics/basic.lean | 9cd20712a2a9830988d7167973e013b6195e18e1 | [
"Apache-2.0"
] | permissive | bbentzen/mpl | fcbea60204bc8fd64667e0f76a5cebf4b67fb6ca | bb5066ec51fa11a4b66f440c4f6c9a3d8fb2e0de | refs/heads/master | 1,625,175,849,308 | 1,624,207,634,000 | 1,624,207,634,000 | 142,774,375 | 9 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,603 | lean | /-
Copyright (c) 2018 Bruno Bentzen. All rights reserved.
Released under the Apache License 2.0 (see "License");
Author: Bruno Bentzen
-/
import ..default
open form classical
@[reducible] def wrld (σ : nat) := ctx σ
variable {σ : nat}
/- Kripke models -/
structure model := (wrlds : set (wrld σ)) (... |
2db1ca3418081119897752e9fd1a1972a9761c12 | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/algebra/group_with_zero_power.lean | c581986b4eae0436c065fa7b8dcf70e7c6728a4c | [
"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 | 9,414 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import algebra.group_power
/-!
# Powers of elements of groups with an adjoined zero element
In this file we define integer power functions for groups with an adjoin... |
14fdb19fc0cc55ba24c35a544e8e0dcfd1ce25e7 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/sizeof5.lean | e857b8695c6e731fc2d659b19fef646abb9b4e20 | [
"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 | 294 | lean | inductive Vec (α : Type u) : Nat → Type u where
| nil : Vec α 0
| cons : α → {n : Nat} → Vec α n → Vec α (n+1)
inductive Expr where
| app2 (f : String) (args : Vec Expr 2)
| app3 (f : String) (args : Vec Expr 3)
#print Expr.app2.sizeOf_spec
#print Expr.app3.sizeOf_spec
|
6d420ae87476632f53183253f83b2ade2a0823eb | 4fa161becb8ce7378a709f5992a594764699e268 | /src/category_theory/opposites.lean | 1d7d209a2b06664dbf1f006479c5de24ce929dab | [
"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 | 9,654 | 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 category_theory.types
import category_theory.equivalence
import data.opposite
universes v₁ v₂ u₁ u₂ -- declare the `v`'s first; see `category_... |
004aa79136b459b0bb601f2a793c52f1508e42e3 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/measure_theory/measure/haar.lean | 7f81eef302559165b540c0f6eba504d6c57e33e1 | [
"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 | 37,045 | lean | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import measure_theory.measure.content
import measure_theory.group.prod
/-!
# Haar measure
In this file we prove the existence and uniqueness (up to scalar multi... |
06f6628efa6ad9d1c2aceeea6c840404a2abcd67 | 26ac254ecb57ffcb886ff709cf018390161a9225 | /src/data/equiv/encodable/lattice.lean | 606f209daed25df5d0ab1a9256ffc5b28f5f954b | [
"Apache-2.0"
] | permissive | eric-wieser/mathlib | 42842584f584359bbe1fc8b88b3ff937c8acd72d | d0df6b81cd0920ad569158c06a3fd5abb9e63301 | refs/heads/master | 1,669,546,404,255 | 1,595,254,668,000 | 1,595,254,668,000 | 281,173,504 | 0 | 0 | Apache-2.0 | 1,595,263,582,000 | 1,595,263,581,000 | null | UTF-8 | Lean | false | false | 1,936 | lean | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Floris van Doorn
-/
import data.equiv.encodable.basic
import data.finset
import data.set.disjointed
/-!
# Lattice operations on encodable types
Lemmas about lattice and set operation... |
7861203b9bf12c091c667263d1ce5a5f3801f421 | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/testing/slim_check/sampleable.lean | 1006e490e5f8dbcf014d76d6bd1a6d78a70a3b1d | [
"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 | 31,318 | 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 data.lazy_list.basic
import data.tree
import data.int.basic
import control.bifunctor
import tactic.linarith
import testing.slim_check.gen
/-!
# `sampleable` Class... |
695583d707925804ff804b0bbd40ffd61690b1fb | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/algebra/quandle.lean | 716d33f621cb4b1536e304ad8b8ad6b6e64756f3 | [
"Apache-2.0"
] | permissive | waynemunro/mathlib | e3fd4ff49f4cb43d4a8ded59d17be407bc5ee552 | 065a70810b5480d584033f7bbf8e0409480c2118 | refs/heads/master | 1,693,417,182,397 | 1,634,644,781,000 | 1,634,644,781,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 24,809 | lean | /-
Copyright (c) 2020 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import data.zmod.basic
import data.equiv.mul_add
import tactic.group
/-!
# Racks and Quandles
This file defines racks and quandles, algebraic structures for sets
that bij... |
ec1ed3fb76e6482527d644db0a3dc4a80ab3c668 | 367134ba5a65885e863bdc4507601606690974c1 | /src/category_theory/limits/cofinal.lean | 75e5b54bf5ec9d8622a512fbcfdf9b4be9aca377 | [
"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 | 16,622 | 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.punit
import category_theory.comma
import category_theory.is_connected
import category_theory.limits.yoneda
import category_theory.limits.types... |
783eda563957abd2d6596fe52122e00dab08adda | ff5230333a701471f46c57e8c115a073ebaaa448 | /library/data/rbtree/find.lean | c4b9ec6dfde4f239bbb3945f7a9b460ff58c2c20 | [
"Apache-2.0"
] | permissive | stanford-cs242/lean | f81721d2b5d00bc175f2e58c57b710d465e6c858 | 7bd861261f4a37326dcf8d7a17f1f1f330e4548c | refs/heads/master | 1,600,957,431,849 | 1,576,465,093,000 | 1,576,465,093,000 | 225,779,423 | 0 | 3 | Apache-2.0 | 1,575,433,936,000 | 1,575,433,935,000 | null | UTF-8 | Lean | false | false | 6,024 | 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
-/
import data.rbtree.basic
universe u
namespace rbnode
variables {α : Type u}
@[elab_simple]
lemma find.induction {p : rbnode α → Prop} (lt) [decidable_rel ... |
ab3ca586bf18b0358406e3bc69786eded2d12986 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/lake/Lake/Config/Module.lean | f0cbc9518421c6d7ce4cd6380ae7536917d07137 | [
"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 | 4,314 | lean | /-
Copyright (c) 2022 Mac Malone. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mac Malone
-/
import Lake.Build.Trace
import Lake.Config.LeanLib
import Lake.Util.OrdHashSet
namespace Lake
open Lean System
/-- A buildable Lean module of a `LeanLib`. -/
structure Modu... |
bb81ec0dc0415291553026a6196126da2bdc5314 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/algebra/group/to_additive.lean | 9280c2e2929d3f46719f1822ca0d6310d40c8d66 | [
"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 | 21,442 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Yury Kudryashov, Floris van Doorn
-/
import tactic.transform_decl
import tactic.algebra
/-!
# Transport multiplicative to additive
This file defines an attribute `to_... |
8a6da8aeba8a716ad140a96957df8698c16d58bd | ea11767c9c6a467c4b7710ec6f371c95cfc023fd | /src/monoidal_categories/examples/groups/monoidal_category_of_groups.lean | e4e3d475e974482bf38603608835796820c4dea9 | [] | no_license | RitaAhmadi/lean-monoidal-categories | 68a23f513e902038e44681336b87f659bbc281e0 | 81f43e1e0d623a96695aa8938951d7422d6d7ba6 | refs/heads/master | 1,651,458,686,519 | 1,529,824,613,000 | 1,529,824,613,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 850 | 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 ...braided_monoidal_category
import categories.universal.instances
import ...monoidal_structure_from_products
import categories.examples.gr... |
1f139e3725ca71a4989ad4169cbd25b47d09b253 | 86f6f4f8d827a196a32bfc646234b73328aeb306 | /examples/basics/unnamed_235.lean | 824feff6e74c161d2eae0bac3faace758da4485a | [] | no_license | jamescheuk91/mathematics_in_lean | 09f1f87d2b0dce53464ff0cbe592c568ff59cf5e | 4452499264e2975bca2f42565c0925506ba5dda3 | refs/heads/master | 1,679,716,410,967 | 1,613,957,947,000 | 1,613,957,947,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 183 | lean | import data.real.basic
-- BEGIN
variables a b c d e f g : ℝ
example (h : a * b = c * d) (h' : e = f) :
a * (b * e) = c * (d * f) :=
by rw [h', ←mul_assoc, h, mul_assoc]
-- END |
75c25ac98cf5fa1c00eb033b2285df3c45a81920 | 75db7e3219bba2fbf41bf5b905f34fcb3c6ca3f2 | /tests/lean/run/eassumption.lean | 833d687456ec6ee51f9da130db607ddeab20a0c2 | [
"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 | 190 | lean | variable p : nat → Prop
variable q : nat → Prop
variables a b c : nat
example : p c → p b → q b → p a → ∃ x, p x ∧ q x :=
by intros; repeat (constructor | eassumption); now
|
a1293902fc6b152eed7a431efa3d0a276eb42fae | e791a827712b9cda7e14eb9861a152725a60f884 | /complex.lean | 4f5988362babcd136b6b221de54c4ff3345f6f63 | [] | no_license | Shamrock-Frost/FormalComplexAnalysis | 29bf1d45f59b22d6553b24fe5b630464f9c2d9fa | 3cac79d9b603b1edf7df1bc7e948c74eb86a2cc0 | refs/heads/master | 1,588,634,495,874 | 1,554,397,551,000 | 1,554,397,551,000 | 179,541,347 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 21,459 | lean | import .reals
open classical
structure complex :=
(Re : real) (Im : real)
def pure_real (z : complex) := z.Im = 0
def pure_imaginary (z : complex) := z.Re = 0
notation `ℂ` := complex
open complex
@[reducible] noncomputable
def complex.zero : complex := ⟨0,0⟩
@[reducible] noncomputable
def complex.one : complex := ... |
61fcdb6deaaad46569594043535a516e48e96f4a | 94e33a31faa76775069b071adea97e86e218a8ee | /src/topology/algebra/order/basic.lean | 9d43af5ec7b81c22abe297f4f339ff07b3e47b10 | [
"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 | 135,658 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
-/
import algebra.group_with_zero.power
import data.set.intervals.pi
import order.filter.interval
import topology.algebra.field
import t... |
e74515e6110bd1add57ad1f5ba29687c42e67476 | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/field_theory/abel_ruffini.lean | c5613fee129e40194d3e72b434737af4c2998666 | [
"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 | 16,485 | lean | /-
Copyright (c) 2020 Thomas Browning and Patrick Lutz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning, Patrick Lutz
-/
import group_theory.solvable
import field_theory.polynomial_galois_group
import ring_theory.roots_of_unity
/-!
# The Abel-Ruffini T... |
20872ed9cefd43ecb52f90d4c2a223a655c2ba4f | 02005f45e00c7ecf2c8ca5db60251bd1e9c860b5 | /src/algebra/free_algebra.lean | 0ca3d00a82aeaf7e165df7611f133c82810c834c | [
"Apache-2.0"
] | permissive | anthony2698/mathlib | 03cd69fe5c280b0916f6df2d07c614c8e1efe890 | 407615e05814e98b24b2ff322b14e8e3eb5e5d67 | refs/heads/master | 1,678,792,774,873 | 1,614,371,563,000 | 1,614,371,563,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 16,077 | lean | /-
Copyright (c) 2020 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Scott Morrison, Adam Topaz.
-/
import algebra.algebra.subalgebra
import algebra.monoid_algebra
import linear_algebra
import data.equiv.transfer_instance
/-!
# Free Algebras
Given a commut... |
c290ef5d96d44ce35e61f1897734d6fbdb696bdb | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /05_Interacting_with_Lean.org.22.lean | a7968f5019d474114cd732b86a91028dca4eeeff | [] | no_license | cjmazey/lean-tutorial | ba559a49f82aa6c5848b9bf17b7389bf7f4ba645 | 381f61c9fcac56d01d959ae0fa6e376f2c4e3b34 | refs/heads/master | 1,610,286,098,832 | 1,447,124,923,000 | 1,447,124,923,000 | 43,082,433 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 371 | lean | /- page 75 -/
import standard
import data.nat data.int
open nat int
check 2 + 2
eval 2 + 2
check #nat 2 + 2
eval #nat 2 + 2
check #int 2 + 2
eval #int 2 + 2
check nat.add 2 2
eval nat.add 2 2
check int.add 2 2
eval int.add 2 2
check (2 + 2 : nat)
eval (2 + 2 : nat)
check (2 + 2 : int)
eval (2 + 2 : int)
check ... |
d859f864ec1a3d04519a9e958c654cc357ea71d6 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/algebra/divisibility.lean | aaf3eddfce2192c346aa37e7e01db0b726c209d0 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 10,432 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Amelia Livingston, Yury Kudryashov,
Neil Strickland, Aaron Anderson
-/
import algebra.group_with_zero.basic
/-!
# Divisibility
Thi... |
95d4837848a07ac405d4cc4e8ca930e328346018 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/generalizeTelescope.lean | 86d38404d5849402cbe3bbb4db65a03de9dc5bc1 | [
"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 | 1,388 | lean | import Lean
open Lean
open Lean.Meta
inductive Vec (α : Type) : Nat → Type
| nil : Vec α 0
| cons {n} : α → Vec α n → Vec α (n+1)
set_option trace.Meta.debug true
def nat := mkConst `Nat
def succ := mkConst `Nat.succ
def tst1 : MetaM Unit :=
withLocalDeclD `n nat fun n => do
let n1 := mkApp succ n
let vec... |
792824b7f08615b1d863d4c7a8fc6c14c2ded6aa | 5ee26964f602030578ef0159d46145dd2e357ba5 | /src/for_mathlib/topological_field.lean | 7384c6c636faf6dce21090b51babc5775b42924e | [
"Apache-2.0"
] | permissive | fpvandoorn/lean-perfectoid-spaces | 569b4006fdfe491ca8b58dd817bb56138ada761f | 06cec51438b168837fc6e9268945735037fd1db6 | refs/heads/master | 1,590,154,571,918 | 1,557,685,392,000 | 1,557,685,392,000 | 186,363,547 | 0 | 0 | Apache-2.0 | 1,557,730,933,000 | 1,557,730,933,000 | null | UTF-8 | Lean | false | false | 2,613 | lean | import tactic.converter.interactive
import topology.algebra.ring
open topological_space
namespace topological_space
variables {α : Type*} {β : Type*} {γ : Type*} {δ : Type*}
variables [topological_space β] [topological_space δ]
/-- A product of induced topologies is induced by the product map -/
lemma prod_induced_i... |
2d91c3f02aea183610fc550f732709dc9b773f95 | dc44027cf56929ab978847c471fbb9d769959991 | /IMP.lean | 9a13be46be6a583b29e42e2139dc5ef7f9c042ce | [] | no_license | PrestonTong/LeanIMP | f8862096d5a354aca011673145bf5ad0e0bbbca4 | bc69a2af202fc0cdf97e924935c920236132866a | refs/heads/master | 1,600,843,830,997 | 1,575,836,133,000 | 1,575,836,133,000 | 225,431,451 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,655 | lean | inductive aexp : Type
| ANum (n : nat)
| AId (x : string)
| APlus (a1 a2 : aexp)
| AMinus (a1 a2 : aexp)
| AMult (a1 a2 : aexp)
inductive sinstr : Type
| SPush (n : nat)
| SLoad (x : string)
| SPlus
| SMinus
| SMult
def total_map (A : Type) := string -> A
def st := total_map nat
def aeval : st -> aexp... |
f08b1c602c8ee4251e7f16f4bb0d8becf2c58443 | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/measure_theory/decomposition.lean | 2e48b1a69cc1c49a51f0b14035f635e522fca43b | [
"Apache-2.0"
] | permissive | vaibhavkarve/mathlib | a574aaf68c0a431a47fa82ce0637f0f769826bfe | 17f8340912468f49bdc30acdb9a9fa02eeb0473a | refs/heads/master | 1,621,263,802,637 | 1,585,399,588,000 | 1,585,399,588,000 | 250,833,447 | 0 | 0 | Apache-2.0 | 1,585,410,341,000 | 1,585,410,341,000 | null | UTF-8 | Lean | false | false | 8,677 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Hahn decomposition theorem
TODO:
* introduce finite measures (into nnreal)
* show general for signed measures (into ℝ)
-/
import measure_theory.measure_space
open set... |
d565cb4061d6d0c4a309a7573c109cd050985fa5 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/algebra/module/submodule_lattice.lean | ead9994e7c6aed7e28dd2b58fea0100458182083 | [
"Apache-2.0"
] | permissive | abentkamp/mathlib | d9a75d291ec09f4637b0f30cc3880ffb07549ee5 | 5360e476391508e092b5a1e5210bd0ed22dc0755 | refs/heads/master | 1,682,382,954,948 | 1,622,106,077,000 | 1,622,106,077,000 | 149,285,665 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,939 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov
-/
import algebra.module.submodule
/-!
# The lattice structure on `submodule`s
This file defines the lattice structure ... |
47b846049b045b34c3d7369fb33c2c3a837e19a2 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /counterexamples/map_floor.lean | 8c00769a84eaf66fe9e828f07187b5cdaf068ae0 | [
"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 | 4,673 | lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import algebra.order.hom.ring
import data.polynomial.reverse
/-!
# Floors and ceils aren't preserved under ordered ring homomorphisms
Intuitively, if `f : α → β` is an ... |
0cb8200510aa51c891c43b9e625c0bce33b3e35b | 43390109ab88557e6090f3245c47479c123ee500 | /src/inner_product_spaces/subrings_subfields.lean | c410e9c35086a4490abdc657f2d1bee7cc7a5c09 | [
"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 | 4,390 | lean | import algebra.field data.set
universe u
class is_subring {R : Type u} [ring R] (s : set R) : Prop :=
(one_mem : (1 : R) ∈ s)
(sub_mem : ∀ {x y : R}, x ∈ s → y ∈ s → x - y ∈ s)
(mul_mem : ∀ {x y : R}, x ∈ s → y ∈ s → x * y ∈ s)
open is_subring set
namespace is_subring
lemma zero_mem {R : Type u} [ring R] {s : set... |
ff9d0970b3c50affb9abfa3ebbdb3f1efbab82b6 | 9dd3f3912f7321eb58ee9aa8f21778ad6221f87c | /tests/lean/run/rw_set4.lean | 52a4f6604010a5b5855c5837c00c44cd8249c959 | [
"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 | 422 | lean | open tactic
attribute [congr, priority std.priority.default+1]
theorem forall_congr_prop_eq {P₁ P₂ Q₁ Q₂ : Prop} :
P₁ = P₂ → (P₂ → Q₁ = Q₂) → (P₁ → Q₁) = (P₂ → Q₂) :=
sorry
print [congr] default
example (A : Type) (a b c : A) : (a = b) → (a = c) → a = b := by simp {contextual := tt}
example (A : Type) (a b c : A) ... |
504025736e14ae6dff00f106b76fc9e20e43834b | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/data/pi.lean | ca8f1c5b227ade6e70691602da4fcb98ac708206 | [
"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 | 2,464 | lean | /-
Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot, Eric Wieser
-/
import tactic.split_ifs
import tactic.simpa
import algebra.group.to_additive
/-!
# Instances and theorems on pi types
This file provides basic... |
3fcaae651e0584ffc7cac36b2a3a4ed1509c5b7c | 6329dd15b8fd567a4737f2dacd02bd0e8c4b3ae4 | /src/game/world1/level12.lean | ffecbec6b25152104a157552844e32e25065f7e9 | [
"Apache-2.0"
] | permissive | agusakov/mathematics_in_lean_game | 76e455a688a8826b05160c16c0490b9e3d39f071 | ad45fd42148f2203b973537adec7e8a48677ba2a | refs/heads/master | 1,666,147,402,274 | 1,592,119,137,000 | 1,592,119,137,000 | 272,111,226 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,159 | lean | import data.real.basic --imports the real numbers
import tactic.maths_in_lean_game -- hide
namespace calculating -- hide
/-
#Calculating
## Level 11: `section` and `#check`
We can delimit the scope of the declaration by putting it
in a `section ... end` block.
Finally, Lean provides us with a command
to determine t... |
e02e908c3777272ee76ff5ee38dfe149c5317a9d | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /src/Lean/Data/OpenDecl.lean | fad2a525648ffecd8cace0af90b519b03d13a6a1 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | EdAyers/lean4 | 57ac632d6b0789cb91fab2170e8c9e40441221bd | 37ba0df5841bde51dbc2329da81ac23d4f6a4de4 | refs/heads/master | 1,676,463,245,298 | 1,660,619,433,000 | 1,660,619,433,000 | 183,433,437 | 1 | 0 | Apache-2.0 | 1,657,612,672,000 | 1,556,196,574,000 | Lean | UTF-8 | Lean | false | false | 809 | 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.Data.Name
namespace Lean
/-- Data for representing `open` commands -/
inductive OpenDecl where
| simple (ns : Name) (except : List Name)
... |
9a09be5f682b48257176ed85340e5700205a9da4 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/graded_monoid.lean | 454603c0a8341f56a5ca8a9226b4261599f4c1de | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 22,113 | lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import algebra.group.inj_surj
import data.list.big_operators.basic
import data.list.fin_range
import group_theory.group_action.defs
import group_theory.submonoid.basic
impo... |
3bd847537dd65b154aed0d94d59a7d4a990071f1 | 0845ae2ca02071debcfd4ac24be871236c01784f | /library/init/lean/parser/term.lean | 0eed4057c38ec9923d441003369b5b06c71aa8f7 | [
"Apache-2.0"
] | permissive | GaloisInc/lean4 | 74c267eb0e900bfaa23df8de86039483ecbd60b7 | 228ddd5fdcd98dd4e9c009f425284e86917938aa | refs/heads/master | 1,643,131,356,301 | 1,562,715,572,000 | 1,562,715,572,000 | 192,390,898 | 0 | 0 | null | 1,560,792,750,000 | 1,560,792,749,000 | null | UTF-8 | Lean | false | false | 6,447 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
prelude
import init.lean.parser.parser
import init.lean.parser.level
namespace Lean
namespace Parser
@[init mkBuiltinParsingTablesRef]
... |
82acee879cbf969f603a3f5a72e5dbd07cf2d4a9 | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /tests/lean/interactive/missing.lean | 1136a21b1b20c2f342d081196c00ff211c8d4187 | [
"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 | 314 | lean | import logic
inductive tree (A : Type) :=
leaf : A → tree A,
node : tree A → tree A → tree A
namespace tree
definition below_rec {A : Type} (t : tree A) {P : tree A → Type} (iH : Π (t : tree A), P t) : P t :=
have general : ∀ (t : tree A),
P t, from
-- take t, iH t,
sorry,
general t
end tree
|
50591989bf6dd8dd60e1e258461fc629d46d6dc8 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /src/Init/Lean/Compiler/IR/RC.lean | 51ae1cb0ac3b24deee188f078d2940dd9e19cd36 | [
"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 | 12,634 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import Init.Lean.Runtime
import Init.Lean.Compiler.IR.CompilerM
import Init.Lean.Compiler.IR.LiveVars
namespace Lean
namespace IR
namespace Explici... |
fd5b08129b702eb5d0d1c5135fdc9aa3c5d44fcc | ec5e5a9dbe7f60fa5784d15211d8bf24ada0825c | /src/Memory.lean | ed1af7815acdf7ebeb0b640ce79759713c0465c3 | [] | no_license | pnwamk/lean-llvm | fcd9a828e52e80eb197f7d9032b3846f2e09ef74 | ebc3bca9a57a6aef29529d46394f560398fb5c9c | refs/heads/master | 1,668,418,078,706 | 1,593,548,643,000 | 1,593,548,643,000 | 258,617,753 | 0 | 0 | null | 1,587,760,298,000 | 1,587,760,298,000 | null | UTF-8 | Lean | false | false | 5,183 | lean | import Init.Data.Array
import Init.Data.Int
import Init.Data.RBMap
import Galois.Data.Bitvec
import LeanLLVM.AST
import LeanLLVM.PP
import LeanLLVM.TypeContext
import LeanLLVM.SimMonad
import LeanLLVM.Value
namespace LLVM
open Sim
namespace Mem
partial def decomposeIntLE : Nat → Nat → List (bitvec 8)
| w, v =>
i... |
a7dc31875ebbfd3b9e5d29e4bed0b8136580d240 | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/simp13.lean | a890abea1d71b7b110ee5726c3b88adcedf7bade | [
"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 | 307 | lean | rewrite_set simple
add_rewrite and_truer and_truel and_falser and_falsel : simple
(*
add_congr_theorem("simple", "and_congr")
*)
variables a b c : Nat
(*
local t = parse_lean([[a = 1 ∧ b = 0 ∧ b > a]])
local s, pr = simplify(t, "simple")
print(s)
print(pr)
print(get_environment():type_check(pr))
*) |
0a37610987b4f8b37e2a8a13148f2060042f3946 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /src/Lean/Compiler/IR/CompilerM.lean | 7af84f6b6ea7760a4e6e40b3d7c4f64d51b5fa7f | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | EdAyers/lean4 | 57ac632d6b0789cb91fab2170e8c9e40441221bd | 37ba0df5841bde51dbc2329da81ac23d4f6a4de4 | refs/heads/master | 1,676,463,245,298 | 1,660,619,433,000 | 1,660,619,433,000 | 183,433,437 | 1 | 0 | Apache-2.0 | 1,657,612,672,000 | 1,556,196,574,000 | Lean | UTF-8 | Lean | false | false | 5,023 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Environment
import Lean.Compiler.IR.Basic
import Lean.Compiler.IR.Format
namespace Lean.IR
inductive LogEntry where
| step (cls : Name) (dec... |
186848b1d321676a625bc0541a9238d9c156da7b | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/linear_algebra/matrix/block.lean | 02c9018bbdaeb1bb409488479aa3a699d8e92117 | [
"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 | 9,842 | 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 linear_algebra.matrix.determinant
/-!
# Block matrices and their determinant
This file defines a predicate `matrix.... |
ab925dd16025fd6dc65badced27583335d5044d0 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/geometry/manifold/algebra/monoid.lean | 7caed1ba9899bb811996d0270cd1c1a66e6fbea9 | [
"Apache-2.0"
] | permissive | stjordanis/mathlib | 51e286d19140e3788ef2c470bc7b953e4991f0c9 | 2568d41bca08f5d6bf39d915434c8447e21f42ee | refs/heads/master | 1,631,748,053,501 | 1,627,938,886,000 | 1,627,938,886,000 | 228,728,358 | 0 | 0 | Apache-2.0 | 1,576,630,588,000 | 1,576,630,587,000 | null | UTF-8 | Lean | false | false | 11,326 | lean | /-
Copyright © 2020 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri
-/
import geometry.manifold.times_cont_mdiff_map
/-!
# Smooth monoid
A smooth monoid is a monoid that is also a smooth manifold, in which multiplication is a smooth ... |
5274c31361afcd3343c00d69e00d8d999e86cfd7 | 367134ba5a65885e863bdc4507601606690974c1 | /src/topology/sheaves/local_predicate.lean | 5f32edc40bbf659a759781a9800220e2d6b90600 | [
"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 | 16,355 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Scott Morrison, Adam Topaz
-/
import topology.sheaves.sheaf_of_functions
import topology.sheaves.stalks
/-!
# Functions satisfying a local predicate form a sheaf.
At ... |
17889c576d4da426c6591011dc1674365e27b014 | 947b78d97130d56365ae2ec264df196ce769371a | /tests/lean/run/newfrontend5.lean | 7489bcbfa0e007a07837677be47d92c9f3b191ae | [
"Apache-2.0"
] | permissive | shyamalschandra/lean4 | 27044812be8698f0c79147615b1d5090b9f4b037 | 6e7a883b21eaf62831e8111b251dc9b18f40e604 | refs/heads/master | 1,671,417,126,371 | 1,601,859,995,000 | 1,601,860,020,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,981 | lean | new_frontend
def foo {α} (f : {β : Type _} → β → β) (a : α) : α :=
f a
#check_failure let g := id; foo g true -- fails
/-
Expands to
```
let g : ?γ → ?γ := @id ?γ;
@foo ?α (fun (β : Sort ?u) => g) true
```
Unification constraint
```
?γ → ?γ =?= β → β
```
fails because `β` is not in the scope of `?γ`
Error message... |
741bebf3aadb1fe5420ce19f816ff90f680648a8 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /tests/elabissues/issues3.lean | 76e0af51667ea04ce310534416c81303e55f85da | [
"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 | 1,002 | lean | inductive Syntax
| atom : String → Syntax
| node : String → Array Syntax → Syntax
instance coe1 : HasCoe String Syntax := ⟨Syntax.atom⟩
instance coe2 {α} : HasCoe (List α) (Array α) := ⟨List.toArray⟩
def ex10 (s : Syntax) : Syntax :=
Syntax.node "foo" (List.toArray ["boo", s]) -- Works
def ex11 (s : Syntax) :=
[s, "... |
ff84fd08e7686f733435700ff76217c0ec630bbe | ea5678cc400c34ff95b661fa26d15024e27ea8cd | /lagrange_four_square2.lean | c139960c3353c61a946571bc5c2e68aee802b059 | [] | no_license | ChrisHughes24/leanstuff | dca0b5349c3ed893e8792ffbd98cbcadaff20411 | 9efa85f72efaccd1d540385952a6acc18fce8687 | refs/heads/master | 1,654,883,241,759 | 1,652,873,885,000 | 1,652,873,885,000 | 134,599,537 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 16,258 | lean | import data.zmod.basic tactic.ring data.polynomial group_theory.perm.sign
open finset polynomial
lemma add_even_of_add_square_even {m x y : ℤ} (h : 2 * m = x^2 + y^2) : (x + y) % 2 = 0 :=
have hzmod : ∀ x y : zmod 2, x ^ 2 + y ^ 2 = 0 → x + y = 0, from dec_trivial,
have (x : zmod 2)^2 + (y : zmod 2)^2 = 0,
by simpa... |
5874baa7652eb7a5c7d2d56de3694973ba8b637a | 92b50235facfbc08dfe7f334827d47281471333b | /library/init/measurable.lean | 97dab5094746186bcc8ce2f8184812fb7dfb87d8 | [
"Apache-2.0"
] | permissive | htzh/lean | 24f6ed7510ab637379ec31af406d12584d31792c | d70c79f4e30aafecdfc4a60b5d3512199200ab6e | refs/heads/master | 1,607,677,731,270 | 1,437,089,952,000 | 1,437,089,952,000 | 37,078,816 | 0 | 0 | null | 1,433,780,956,000 | 1,433,780,955,000 | null | UTF-8 | Lean | false | false | 1,418 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
Types with a nat-valued complexity measure.
-/
prelude
import init.nat
open nat
inductive measurable [class] (A : Type) :=
mk : (A → nat) → measurable A
def... |
56d39563228d2a19b3d0fc659533354c0bff9c28 | d436468d80b739ba7e06843c4d0d2070e43448e5 | /src/algebra/category/Group.lean | 895bb0c94362516233a5fada990303ddec75e6f2 | [
"Apache-2.0"
] | permissive | roro47/mathlib | 761fdc002aef92f77818f3fef06bf6ec6fc1a28e | 80aa7d52537571a2ca62a3fdf71c9533a09422cf | refs/heads/master | 1,599,656,410,625 | 1,573,649,488,000 | 1,573,649,488,000 | 221,452,951 | 0 | 0 | Apache-2.0 | 1,573,647,693,000 | 1,573,647,692,000 | null | UTF-8 | Lean | false | false | 5,814 | lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import algebra.punit_instances
import algebra.category.Mon.basic
import category_theory.endomorphism
/-!
# Category instances for group, add_group, comm_group, and ... |
93a435555c27fe22d0ed512dff4c77baf6cb4457 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/topology/algebra/group_completion.lean | cb7fd10a32b1bdecb759987992e5a31b69ab1e94 | [
"Apache-2.0"
] | permissive | rmitta/mathlib | 8d90aee30b4db2b013e01f62c33f297d7e64a43d | 883d974b608845bad30ae19e27e33c285200bf84 | refs/heads/master | 1,585,776,832,544 | 1,576,874,096,000 | 1,576,874,096,000 | 153,663,165 | 0 | 2 | Apache-2.0 | 1,544,806,490,000 | 1,539,884,365,000 | Lean | UTF-8 | Lean | false | false | 4,101 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
Completion of topological groups:
-/
import topology.uniform_space.completion topology.algebra.uniform_group
noncomputable theory
section group
open un... |
1f65117b765b72998e740f03ce338a4a4313acea | d29d82a0af640c937e499f6be79fc552eae0aa13 | /src/algebra/lie/subalgebra.lean | 8c8ef8c9120a2b0ef93c89aee6d8e0d8feafc958 | [
"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 | 21,162 | lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import algebra.lie.basic
import ring_theory.noetherian
/-!
# Lie subalgebras
This file defines Lie subalgebras of a Lie algebra and provides basic related definitions and... |
fdf82acafadf69bc472fd7544e4ad9fccab01584 | 8e31b9e0d8cec76b5aa1e60a240bbd557d01047c | /scratch/simplex_new_pivot.lean | 9946db89525b71162a2740c51dcfaad4d1d545f9 | [] | no_license | ChrisHughes24/LP | 7bdd62cb648461c67246457f3ddcb9518226dd49 | e3ed64c2d1f642696104584e74ae7226d8e916de | refs/heads/master | 1,685,642,642,858 | 1,578,070,602,000 | 1,578,070,602,000 | 195,268,102 | 4 | 3 | null | 1,569,229,518,000 | 1,562,255,287,000 | Lean | UTF-8 | Lean | false | false | 43,081 | lean | import data.matrix data.rat.basic .misc tactic.fin_cases
import .matrix_pequiv
open matrix fintype finset function
variables {m n : ℕ}
local infix ` ⬝ `:70 := matrix.mul
local postfix `ᵀ` : 1500 := matrix.transpose
local notation `rvec`:2000 n := matrix (fin 1) (fin n) ℚ
local notation `cvec`:2000 m := matrix (fin m... |
0dd3141cf6ff261c4ccefe9a9fdc3b96922e6779 | 2b2a05a7af89c79da194505bf88205a6c4e05d68 | /src/game/world_09_advanced_multiplication.lean | 037e5e3f870d8cbe7a15264e077845f034887a79 | [] | no_license | lacrosse/natural_number_game | 6401a11a8c965da3903ae6695f84586edf6fac85 | 400179cde1d3fcc9744901dabff98813ba2b544f | refs/heads/master | 1,677,566,006,582 | 1,612,576,917,000 | 1,612,576,917,000 | 335,655,947 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,548 | lean | import game.world_08_advanced_addition
namespace mynat
theorem mul_pos (a b : mynat) : a ≠ 0 → b ≠ 0 → a * b ≠ 0 := begin[nat_num_game]
intros anz bnz f,
cases b, {
apply bnz,
refl
}, {
rw mul_succ at f,
apply anz,
induction a,
refl, {
apply add_left_eq_zero,
rwa f,
}
}
... |
b55a6ddf2b67302dba6c580359f8eb7ef8d55567 | abbfc359cee49d3c5258b2bbedc2b4d306ec3bdf | /src/data/serial/basic.lean | e116adc10a8249a9379510d8085248b94cce9628 | [] | no_license | cipher1024/serialean | 565b17241ba7edc4ee564bf0ae175dd15b06a28c | 47881e4a6bc0a62cd68520564610b75f8a4fef2c | refs/heads/master | 1,585,117,575,599 | 1,535,783,976,000 | 1,535,783,976,000 | 143,501,396 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,699 | lean |
import tactic
import tactic.monotonicity
import tactic.norm_num
import category.basic
import category.serial
import data.serial.medium
universes u v w
def serial_inverse {α : Type u} (encode : α → put_m) (decode : get_m α) : Prop :=
∀ w, decode -<< encode w = pure w
class serial (α : Type u) :=
(encode : α → put_... |
068769dab1185699d16c2f0f57c6c9eee732184b | 3dc4623269159d02a444fe898d33e8c7e7e9461b | /.github/workflows/geo/ne_sieves.lean | dc5f1003fa7094a5e0a33ec05f1f695cdcb27b12 | [] | no_license | Or7ando/lean | cc003e6c41048eae7c34aa6bada51c9e9add9e66 | d41169cf4e416a0d42092fb6bdc14131cee9dd15 | refs/heads/master | 1,650,600,589,722 | 1,587,262,906,000 | 1,587,262,906,000 | 255,387,160 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,288 | lean | import category_theory.comma
import algebra.category.CommRing
import .global
import .ideals
import .Omega
import data.opposite
import ring_theory.ideals
import .src.sieve
import .src.grothendieck
import ring_theory.localization
open category_theory
open localization ---362
open opposite
universes u
local notation ... |
ff96be785a898b5485dd8237de811ba072f99493 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/ring_theory/ideal/local_ring.lean | ef24d745670175bc5e7b6c509bd6ac371f230549 | [
"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 | 17,700 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Chris Hughes, Mario Carneiro
-/
import algebra.algebra.basic
import ring_theory.ideal.operations
import ring_theory.jacobson_ideal
import logic.equiv.transfer_instance
/-!
# L... |
5418d50fc73bd63560580a52f8611dd421fb2a8d | 33340b3a23ca62ef3c8a7f6a2d4e14c07c6d3354 | /lia/batch_tests.lean | 1a80ddbbfc43c4ee38c0f11c6d2fd1b504962f15 | [] | no_license | lclem/cooper | 79554e72ced343c64fed24b2d892d24bf9447dfe | 812afc6b158821f2e7dac9c91d3b6123c7a19faf | refs/heads/master | 1,607,554,257,488 | 1,578,694,133,000 | 1,578,694,133,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,733 | lean | import .main
open tactic
#exit
meta def ex01 : expr := `(∀ x : int, x ≤ -x → x ≤ 0)
meta def ex02 : expr := `(∀ x y : int, (x ≤ 5 ∧ y ≤ 3) → x + y ≤ 8)
meta def ex03 : expr := `(∀ x y z : int, x < y → y < z → x < z)
meta def ex04 : expr := `(∀ x y z : int, x - y ≤ x - z → z ≤ y)
meta def ex05 : expr := `(∀ x : int,... |
490465933e0992f583af4167d741c1486f02aef1 | dd4e652c749fea9ac77e404005cb3470e5f75469 | /src/missing_mathlib/linear_algebra/finsupp.lean | bc4687c4cccf410a058904abc09fb35ac12e04f6 | [] | no_license | skbaek/cvx | e32822ad5943541539966a37dee162b0a5495f55 | c50c790c9116f9fac8dfe742903a62bdd7292c15 | refs/heads/master | 1,623,803,010,339 | 1,618,058,958,000 | 1,618,058,958,000 | 176,293,135 | 3 | 2 | null | null | null | null | UTF-8 | Lean | false | false | 700 | lean | import linear_algebra.finsupp
import missing_mathlib.data.finsupp
import missing_mathlib.algebra.big_operators
import missing_mathlib.linear_algebra.basic
import analysis.complex.polynomial
lemma finsupp.total_on_finset {α β γ : Type*}
[decidable_eq α] [decidable_eq β] [decidable_eq γ] [ring β] [add_comm_group γ] ... |
76fe19ecbedf115daa41a9d4eac0048818a4962b | 947b78d97130d56365ae2ec264df196ce769371a | /tests/lean/binsearch.lean | a3a411edc2166a3113f2ebed5570803957b786ee | [
"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 | 460 | lean | new_frontend
partial def mkAssocArray : Nat → Array (Nat × Bool) → Array (Nat × Bool)
| 0, as => as
| i+1, as => mkAssocArray i (as.push (i, i % 2 == 0))
def tst (n : Nat) : IO Unit :=
do
let as := mkAssocArray n Array.empty;
IO.println as;
let as := as.qsort (fun a b => a.1 < b.1);
(2*n).forM $ fun i => do
let e... |
03d25ad97912974b11b54ef7879d1109c948d9c4 | 2a8b9c9fb34993732e24b7934050207f28675948 | /lua/tests/fixtures/example-lean4-project/Test.lean | 0d217330a7a3fd01fcc819130769a5d22f746b38 | [
"MIT"
] | permissive | jcommelin/lean.nvim | 471b8c2c16f47e76dfc36dc85d1e9cf6938b58e6 | b10a525f65cd2fda1c2e629d4b68f241caf67d64 | refs/heads/main | 1,691,387,304,436 | 1,633,447,198,000 | 1,633,447,198,000 | 413,898,327 | 0 | 0 | MIT | 1,633,451,737,000 | 1,633,451,737,000 | null | UTF-8 | Lean | false | false | 242 | lean | import Test.Test1
def test1 : Nat := test
theorem test2 : p ∨ q → q ∨ p := by
intro h
cases h with
| inl h1 =>
apply Or.inr
exact h1
| inr h2 =>
apply Or.inl
assumption
def new_test : Bool := by
exact false
|
5e65e323ceb6a556f26e05dc4c84884892866c69 | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/number_theory/fermat4.lean | 1e17dd17d6a83e623fd0439b58595d48471bced9 | [
"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 | 12,442 | lean | /-
Copyright (c) 2020 Paul van Wamelen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul van Wamelen
-/
import number_theory.pythagorean_triples
import ring_theory.coprime
/-!
# Fermat's Last Theorem for the case n = 4
There are no non-zero integers `a`, `b` and `c... |
c77e8c8f1f07a8060aa64bce00fad577c8703b66 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/linear_algebra/alternating_auto.lean | 1a8255dc523a7d5b7a0a2d34edee39136d4533bd | [] | 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 | 24,858 | lean | /-
Copyright (c) 2020 Zhangir Azerbayev. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Eric Wieser, Zhangir Azerbayev
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.linear_algebra.multilinear
import Mathlib.linear_algebra.linear_independe... |
aa61c5c7bb0988e6631dfc9e9c21d45632e1cee3 | 6e41ee3ac9b96e8980a16295cc21f131e731884f | /tests/lean/run/forest_height.lean | 53b7db492dbf696cad6095891752ec4486fd085d | [
"Apache-2.0"
] | permissive | EgbertRijke/lean | 3426cfa0e5b3d35d12fc3fd7318b35574cb67dc3 | 4f2e0c6d7fc9274d953cfa1c37ab2f3e799ab183 | refs/heads/master | 1,610,834,871,476 | 1,422,159,801,000 | 1,422,159,801,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,283 | lean | import data.nat.basic data.sum data.sigma data.bool
open nat sigma
inductive tree (A : Type) : Type :=
node : A → forest A → tree A
with forest : Type :=
nil : forest A,
cons : tree A → forest A → forest A
namespace manual
check tree.rec_on
definition tree.height {A : Type} (t : tree A) : nat :=
tree.rec_on t
(λ ... |
b7c56d8359a40a514d3c10cfacb917fd55628c81 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/playground/seq2.lean | 3288a5b945787321e11abdf702bb9e18acfbe8d6 | [
"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 | 523 | lean | abbrev M := ExceptT String $ StateT Nat Id
def add (n : Nat) : M Unit :=
modify (· + 0)
@[simp] theorem addZero : add (natLit! 0) = pure () :=
rfl
syntax "bigAdd0Seq! " num : term
macro_rules
| `(bigAdd0Seq! $n) =>
let n := n.toNat
if n == 0 then
`(pure ())
else
`(add (natLit! 0) >>= f... |
c476c737b8ab4135bd503a653bc3e9089e9c7641 | 2a70b774d16dbdf5a533432ee0ebab6838df0948 | /_target/deps/mathlib/src/analysis/convex/cone.lean | 9fd5ca1994a63b3ed89e2fb8225eea8140e81429 | [
"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 | 22,959 | lean | /-
Copyright (c) 2020 Yury Kudryashov All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Frédéric Dupuis
-/
import linear_algebra.linear_pmap
import analysis.convex.basic
import order.zorn
/-!
# Convex cones
In a vector space `E` over `ℝ`, we define a co... |
1c614954d6b7e272cba48d9c2609e6355497cdaa | e030b0259b777fedcdf73dd966f3f1556d392178 | /tests/lean/run/pack_unpack2.lean | eef0c57bb10044a2f2c2d9b330ae2815671710aa | [
"Apache-2.0"
] | permissive | fgdorais/lean | 17b46a095b70b21fa0790ce74876658dc5faca06 | c3b7c54d7cca7aaa25328f0a5660b6b75fe26055 | refs/heads/master | 1,611,523,590,686 | 1,484,412,902,000 | 1,484,412,902,000 | 38,489,734 | 0 | 0 | null | 1,435,923,380,000 | 1,435,923,379,000 | null | UTF-8 | Lean | false | false | 971 | lean | --set_option trace.inductive_compiler.nested.define true
inductive tree (A : Type*)
| leaf : A -> tree
| node : list tree -> tree
set_option trace.eqn_compiler true
definition sz {A : Type*} : tree A → nat
| (tree.leaf a) := 1
| (tree.node l) := list.length l + 1
constant P {A : Type*} : tree A → Type 1
constant mk1 ... |
c8a4fffcc470007e42a35acf39e6a9df40617e8d | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/analysis/analytic/radius_liminf.lean | 728362cd9baf56e9958cbd1cc046c89ced7f2944 | [] | 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 | 1,276 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Yury Kudryashov
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.analysis.analytic.basic
import Mathlib.analysis.special_functions.pow
import Mathlib.PostP... |
4b074bcc04a61a13874474e4931e985de4fa32ec | 4727251e0cd73359b15b664c3170e5d754078599 | /src/category_theory/limits/has_limits.lean | 4ffdb7fb33952f8f429fb13ce87530c973eda285 | [
"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 | 43,140 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Mario Carneiro, Scott Morrison, Floris van Doorn
-/
import category_theory.limits.is_limit
import category_theory.category.ulift
/-!
# Existence of limits and colimits
I... |
96b3f56357a45f1735fd468f9c42f0f7dc820e31 | 9631e35ca5dd719ccc7d3a57ec322fd93d6a0776 | /src/maze_with_fire/solutions/definition.lean | 7dbe2ccb009ce4119c6ddebb65451bccebc94984 | [] | no_license | kbuzzard/maze-game | 123fa47e0262edb6d147178d239a345d847ff147 | 362ab394ae5218c43b24232aaeef08efc0067eab | refs/heads/master | 1,670,131,466,823 | 1,598,546,702,000 | 1,598,546,702,000 | 290,744,081 | 5 | 1 | null | 1,598,546,703,000 | 1,598,523,538,000 | Lean | UTF-8 | Lean | false | false | 3,583 | lean | /-
The asterisks are fire.
******
**234*
*01***
****
Can people write computer programs in Lean which solve
levels like this?
Can people write computer programs in Python which design
levels like this?
The below is Lean 3 code.
Can stuff like this be made to work in Lean 4? I have
Lean 4 working on my laptop, i... |
a8bd93c9ff06f521f6aaed5fb84d3832f2ccb88e | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/generalize_proofs_auto.lean | ba320865416b9389c9b4de7510644e8889cd66e9 | [] | 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 | 853 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.tactic.doc_commands
import Mathlib.PostPort
namespace Mathlib
/-!
# `generalize_proofs`
... |
635fa8bd8fa97f0f20edb083c6b41c98df9aeb15 | 1dd482be3f611941db7801003235dc84147ec60a | /src/data/set/finite.lean | c777a28631381afe23a5507be2b5d9090b1c2823 | [
"Apache-2.0"
] | permissive | sanderdahmen/mathlib | 479039302bd66434bb5672c2a4cecf8d69981458 | 8f0eae75cd2d8b7a083cf935666fcce4565df076 | refs/heads/master | 1,587,491,322,775 | 1,549,672,060,000 | 1,549,672,060,000 | 169,748,224 | 0 | 0 | Apache-2.0 | 1,549,636,694,000 | 1,549,636,694,000 | null | UTF-8 | Lean | false | false | 16,861 | 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
Finite sets.
-/
import data.set.lattice data.nat.basic logic.function
data.fintype
open set lattice function
universes u v w
variables {α : Typ... |
a6f3d1cccabf0714395fa500a4fd352af9d697a1 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /tests/lean/run/instuniv.lean | 97e2be6c9eafea183d5d6e1ed17d58e5b52272d7 | [
"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 | 404 | lean | import Init.Lean
open Lean
def tst : IO Unit :=
do env ← importModules [{module := `Init.Data.Array}];
match env.find? `Array.foldl with
| some info => do
IO.println (info.instantiateTypeLevelParams [levelZero, levelZero]);
IO.println (info.instantiateValueLevelParams [levelZero, levelZero]);
pure... |
f3b28d82f002f4f35686b6d3aece240995b4358f | d436468d80b739ba7e06843c4d0d2070e43448e5 | /src/geometry/manifold/real_instances.lean | 75f7e389113a33f6d613ecedb8db87f692095ae1 | [
"Apache-2.0"
] | permissive | roro47/mathlib | 761fdc002aef92f77818f3fef06bf6ec6fc1a28e | 80aa7d52537571a2ca62a3fdf71c9533a09422cf | refs/heads/master | 1,599,656,410,625 | 1,573,649,488,000 | 1,573,649,488,000 | 221,452,951 | 0 | 0 | Apache-2.0 | 1,573,647,693,000 | 1,573,647,692,000 | null | UTF-8 | Lean | false | false | 14,858 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import geometry.manifold.smooth_manifold_with_corners linear_algebra.finite_dimensional
/-!
# Constructing examples of manifolds over ℝ
We introduce the nece... |
303eb98eb9675d60c595d9f98031f5fbccda025c | 934eae675a9d997202bb021816325184e7d694aa | /_notes/Languages/lean/myproject/leanlog.lean | f4be7b1a4d10296da7771d32fc55d6328825c0ba | [] | no_license | philzook58/philzook58.github.io | da78841df4ffd9a19c81e0eab833983d95a64b70 | 76000a5847bd6ee41dff25937ae916835bbcf03f | refs/heads/master | 1,692,951,958,916 | 1,692,631,945,000 | 1,692,631,945,000 | 91,513,884 | 9 | 4 | null | 1,677,330,791,000 | 1,494,977,989,000 | Jupyter Notebook | UTF-8 | Lean | false | false | 5,330 | lean | import Lean.Data.PersistentHashSet
import Lean.Data.PersistentHashMap
import Lean.Data.RBMap
import Lean.Data.RBTree
import Mathlib.Data.List.Basic
import Lean
import Qq
import Lean.Meta.Reduce
import Lean.Meta
import Lean.Meta.DiscrTree
open Lean.PersistentHashSet
open Lean (PHashSet)
#check EmptyCollection
def edge... |
958ea51d9b118fb6c0672a65a2ffa786ab8f84f6 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/combinatorics/simple_graph/degree_sum_auto.lean | 182a093f9cf8346bb1cc5c4edb827179ee3d1b83 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,963 | lean | /-
Copyright (c) 2020 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Kyle Miller
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.combinatorics.simple_graph.basic
import Mathlib.algebra.big_operators.basic
import Mathlib.data.na... |
bdd3ea12e591e3045c3b1ee07fbae155682e946b | efa51dd2edbbbbd6c34bd0ce436415eb405832e7 | /20150803_CADE/examples/ex2.lean | 45e5b1cbea339b7d98b40df282723cda57a7484f | [
"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 | 643 | lean | import data.nat
open nat
check ∀ (x : nat), x > 0
premise h : ∀ (x : nat), x > 0
check h 1
check h 0
theorem my_first_thm (a b : Prop) : a → b → a :=
λ (h₁ : a) (h₂ : b), h₁
check my_first_thm
-- reveal my_first_thm
print my_first_thm
definition id {A : Type} (a : A) : A := a
-- set_option pp.implicit true
che... |
04e7d523a3eee220005e90263f4478d633d0e8af | b7f22e51856f4989b970961f794f1c435f9b8f78 | /library/theories/group_theory/quotient.lean | ca11ea196cdfc40a5d98d23c1b2435287e010de9 | [
"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 | 21,234 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Zipperer, Jeremy Avigad
We provide two versions of the quoptient construction. They use the same names and notation:
one lives in the namespace 'quotient_group' and the other li... |
c58054f31b5a8f5fcf90f57ad4b64a352624beec | 222111140d2023e142b07e9cd5119ac2829b36f5 | /src/demonstration.lean | d170664b281ac335e7b2a4c9633a776d943ae47b | [] | no_license | jjcrawford/lean-gaussian-elimination | 740dfdf2de89dc99c088c53e5221d9dfad3c0b92 | c473d33c07fa6f141d17d9dc42ad07956c33dd03 | refs/heads/master | 1,585,793,867,436 | 1,540,443,865,000 | 1,540,443,865,000 | 153,901,939 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,257 | lean | import ring_theory.matrix
import .gaussian_elimination
import .matrix_repr -- Let us print some things
import analysis.real -- So we can use ℚ
universes u
variables {m n : ℕ}
variable {α : Type u}
variable [division_ring α]
variable [decidable_eq α]
def test1 : matrix (fin 2) (fin 3) ℚ := -- Just like ou... |
527b49a6824c73228ecab8824d7a98b859741b47 | 626e312b5c1cb2d88fca108f5933076012633192 | /src/data/set/basic.lean | 69a76cd0a3dd51e95633dfed2344e07c4a124dfe | [
"Apache-2.0"
] | permissive | Bioye97/mathlib | 9db2f9ee54418d29dd06996279ba9dc874fd6beb | 782a20a27ee83b523f801ff34efb1a9557085019 | refs/heads/master | 1,690,305,956,488 | 1,631,067,774,000 | 1,631,067,774,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 114,527 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
-/
import logic.unique
import logic.relation
import order.boolean_algebra
/-!
# Basic properties of sets
Sets in Lean are homogeneous; all their eleme... |
ddfb88cc52cbffaf07b768dea8bfd72785804675 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/data/equiv/list.lean | 0ddcd0e238ffae427dde68f601916c6126cd4819 | [
"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 | 12,900 | 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.equiv.denumerable
import data.finset.sort
/-!
# Equivalences involving `list`-like types
This file defines some additional constructive equivalences usi... |
8b98c9599626c670bf618a8bb34fefed12a01f55 | acc85b4be2c618b11fc7cb3005521ae6858a8d07 | /theories/set_theory.lean | a4f01b767a5a5585d692400bcbd2edc6e97c6788 | [
"Apache-2.0"
] | permissive | linpingchuan/mathlib | d49990b236574df2a45d9919ba43c923f693d341 | 5ad8020f67eb13896a41cc7691d072c9331b1f76 | refs/heads/master | 1,626,019,377,808 | 1,508,048,784,000 | 1,508,048,784,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 27,697 | lean | import data.set.basic
universes u v
def arity (α : Type u) : nat → Type u
| 0 := α
| (n+1) := α → arity n
inductive pSet : Type (u+1)
| mk (α : Type u) (A : α → pSet) : pSet
namespace pSet
def type : pSet → Type u
| ⟨α, A⟩ := α
def func : Π (x : pSet), x.type → pSet
| ⟨α, A⟩ := A
def mk_type_func :... |
15beb2eecce36f1b4c84e539490f6313ecbe9c8b | f3a5af2927397cf346ec0e24312bfff077f00425 | /src/game/world6/level7.lean | add6b7445d95988b060e62956da44d7b49878e5e | [
"Apache-2.0"
] | permissive | ImperialCollegeLondon/natural_number_game | 05c39e1586408cfb563d1a12e1085a90726ab655 | f29b6c2884299fc63fdfc81ae5d7daaa3219f9fd | refs/heads/master | 1,688,570,964,990 | 1,636,908,242,000 | 1,636,908,242,000 | 195,403,790 | 277 | 84 | Apache-2.0 | 1,694,547,955,000 | 1,562,328,792,000 | Lean | UTF-8 | Lean | false | false | 609 | lean | /-
# Function world.
## Level 7: `(P → Q) → ((Q → R) → (P → R))`
If you start with `intro hpq` and then `intro hqr`
the dust will clear a bit and the level will look like this:
```
P Q R : Prop,
hpq : P → Q,
hqr : Q → R
⊢ P → R
```
So this level is really about showing transitivity of $\implies$,
if you like that s... |
147853d0486ebecec6b8617e5ce41f430f8501de | b2e508d02500f1512e1618150413e6be69d9db10 | /src/algebra/group/type_tags.lean | 255c23c43aad6080899c4b7dd25606c7921860c7 | [
"Apache-2.0"
] | permissive | callum-sutton/mathlib | c3788f90216e9cd43eeffcb9f8c9f959b3b01771 | afd623825a3ac6bfbcc675a9b023edad3f069e89 | refs/heads/master | 1,591,371,888,053 | 1,560,990,690,000 | 1,560,990,690,000 | 192,476,045 | 0 | 0 | Apache-2.0 | 1,568,941,843,000 | 1,560,837,965,000 | Lean | UTF-8 | Lean | false | false | 3,184 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
Type tags `multiplicative` and `additive` that turn additive structures into multiplicative, and vice versa
-/
import algebra.group.to_additive algebra.group.hom
unive... |
20d245cbf45eb952b724d2862359c9618a032e19 | 9b9a16fa2cb737daee6b2785474678b6fa91d6d4 | /src/group_theory/submonoid.lean | 242b43d3a7b425021ce4d4489fc0e3f98ec3363c | [
"Apache-2.0"
] | permissive | johoelzl/mathlib | 253f46daa30b644d011e8e119025b01ad69735c4 | 592e3c7a2dfbd5826919b4605559d35d4d75938f | refs/heads/master | 1,625,657,216,488 | 1,551,374,946,000 | 1,551,374,946,000 | 98,915,829 | 0 | 0 | Apache-2.0 | 1,522,917,267,000 | 1,501,524,499,000 | Lean | UTF-8 | Lean | false | false | 8,974 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro
-/
import algebra.big_operators
import data.finset
import tactic.subtype_instance
variables {α : Type*} [monoid α] {s : set α... |
133a659336c1ccbbcc6f93cb7a9a5a1791a96de0 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/meta/environment.lean | ef5ea7af9f85ca2a9efef9a9c07cdb985632d3dd | [] | 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 | 2,593 | 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
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.meta.declaration
import Mathlib.Lean3Lib.init.meta.exceptional
import Mathlib.Lean3Lib.init.data.option.... |
54463ac5809a84b7525e271de2b64763be07118d | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/induct.lean | 240616b300c96c2ccf7210bb533153c87906b0ae | [
"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 | 115 | lean | import macros
import tactic
using Nat
theorem add_comm2 (a b : Nat) : a + b = b + a
:= induction_on b (by skip) _
|
e15c0da335e441f2f4edc19d8346594d83542321 | aa5a655c05e5359a70646b7154e7cac59f0b4132 | /tests/lean/run/unifhint2.lean | 38130749d550b6e1807d86582987399b8339be1e | [
"Apache-2.0"
] | permissive | lambdaxymox/lean4 | ae943c960a42247e06eff25c35338268d07454cb | 278d47c77270664ef29715faab467feac8a0f446 | refs/heads/master | 1,677,891,867,340 | 1,612,500,005,000 | 1,612,500,005,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 640 | lean | /- The following hints are too expensive, but good enough for small natural numbers -/
unif_hint natAddBase (x y : Nat) where
y =?= 0
|-
Nat.add (Nat.succ x) y =?= Nat.succ x
unif_hint natAddStep (x y z w : Nat) where
y =?= Nat.succ w
z =?= Nat.add (Nat.succ x) w
|-
Nat.add (Nat.succ x) y =?= Nat.succ z
... |
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