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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1ec3dd1ff70ba758e39f75d0976e1f2c817ae6b1 | bae21755a4a03bbe0a5c22e258db8633407711ad | /library/init/category/applicative.lean | 3538f85e0ac2461851ef416467b52d51f977e8a2 | [
"Apache-2.0"
] | permissive | nor-code/lean | f437357a8f85db0f06f186fa50fcb1bc75f6b122 | aa306af3d7c47de3c7937c98d3aa919eb8da6f34 | refs/heads/master | 1,662,613,329,886 | 1,586,696,014,000 | 1,586,696,014,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,114 | 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, Sebastian Ullrich
-/
prelude
import init.category.functor
open function
universes u v
class has_pure (f : Type u → Type v) :=
(pure {α : Type u} : α → f α)
... |
c2ebc00420ff61eed66afd2acf6c01a0bc1c4bba | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/bool/set.lean | b911c3d8711dd4e4268a6d10e8c4bb70de60d94e | [
"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 | 587 | lean | /-
Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import data.bool.basic
import data.set.basic
/-!
# Booleans and set operations
This file contains two trivial lemmas about `bool`, `set.univ`, and `set.rang... |
db2a59a5890de9dc4a12ea3a9f80caf23b338730 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/measure_theory/lebesgue_measure.lean | 12f8e39b18835acd3f0f45e47bf8bc7cb83eb358 | [] | 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 | 9,450 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.measure_theory.pi
import Mathlib.PostPort
universes u_1
namespace Mathl... |
e7659b4093f301302d2826803d57f5f0b20502b6 | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /stage0/src/Lean/Data/Lsp/Extra.lean | 2237e2c71d3e2848b9cff19d654359e536f46788 | [
"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 | 1,990 | lean | /-
Copyright (c) 2020 Marc Huisinga. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Marc Huisinga
-/
import Lean.Data.Json
import Lean.Data.JsonRpc
import Lean.Data.Lsp.Basic
/-!
This file contains Lean-specific extensions to LSP.
The following additional requests an... |
68e862789bef1daf446aa29058d6c8be49fbadd7 | 9028d228ac200bbefe3a711342514dd4e4458bff | /test/nontriviality.lean | 9a0db53c1c8272e79717f4d8a7f04c0f4b22ef9d | [
"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 | 920 | lean | import logic.nontrivial
import algebra.ordered_ring
import data.nat.basic
example {R : Type} [ordered_ring R] {a : R} (h : 0 < a) : 0 < a :=
begin
nontriviality,
guard_hyp _inst : nontrivial R,
assumption,
end
example {R : Type} [comm_ring R] {r s : R} : r * s = s * r :=
begin
nontriviality,
guard_hyp _inst... |
39afaf0d1b8a90fda562e1c5d4cc1330031ce0a3 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/tactic/slice.lean | b97dd0e0eba05dc8c9d862a10d1a7842916d28b4 | [
"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 | 3,509 | 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.category.basic
open category_theory
-- TODO someone might like to generalise this tactic to work with other associative structures.
namespac... |
066367db8fd7b86bc8196007eb4f3156e162dd3c | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/tactic/rcases.lean | cb3dd3208d1c43a96a53a8f18599dbe3fb3196b0 | [
"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 | 39,969 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.dlist
import tactic.core
import tactic.clear
/-!
# Recursive cases (`rcases`) tactic and related tactics
`rcases` is a tactic that will perform `cases`... |
cba802bf15671beb48111beadcf012debb8396f3 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/probability/process/adapted.lean | 3cb162bc3b916647e6051c916484613ec33b304d | [
"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 | 8,921 | lean | /-
Copyright (c) 2021 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying, Rémy Degenne
-/
import probability.process.filtration
import topology.instances.discrete
/-!
# Adapted and progressively measurable processes
This file defines some standar... |
aebef5c95861e4107d9fa99dc0da8014fded30a1 | b29f946a2f0afd23ef86b9219116968babbb9f4f | /src/lean_format_tests/monotone_formatted.lean | 2ece232655870c68062eb18083cf4b124c6f5ed8 | [
"Apache-2.0"
] | permissive | ImperialCollegeLondon/M1P1-lean | 58be7394fded719d95e45e6b10e1ecf2ed3c7c4c | 3723468cc50f8bebd00a9811caf25224a578de17 | refs/heads/master | 1,587,063,867,779 | 1,572,727,164,000 | 1,572,727,164,000 | 165,845,802 | 14 | 4 | Apache-2.0 | 1,549,730,698,000 | 1,547,554,675,000 | Lean | UTF-8 | Lean | false | false | 3,301 | lean | -- begin header
import tactic.linarith
import data.real.basic
noncomputable theory
local attribute [instance, priority 0] classical.prop_decidable
local notation `|` x `|` := abs x
-- end header
/- Section
Sequences, subsequences, and monotonic subsequences.
-/
/- Sub-section
Definitions
-/
/-
We model a sequence ... |
faf2e392f1aa3ec287326aae8d994f8c22e757f9 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/control/basic.lean | ebb5951a0403439966450e7dd5c7c30dbda12e36 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 6,745 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Extends the theory on functors, applicatives and monads.
-/
universes u v w
variables {α β γ : Type u}
notation a ` $< `:1 f:1 := f a
section functor
variables {f : ... |
076b571bd2549725b6b44a757d0ba336f5f24c71 | 4fa161becb8ce7378a709f5992a594764699e268 | /src/algebra/group/basic.lean | b39d507d474d71ccedcfb8653194a7ed7e1cd93a | [
"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 | 12,557 | 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, Simon Hudon, Mario Carneiro
-/
import algebra.group.to_additive
import algebra.group.defs
import tactic.simpa
import logic.function.basic
import tactic... |
add8311dc48984102a6cafa498af3cba6f63581e | 3f48345ac9bbaa421714efc9872a0409379bb4ae | /src/set_category/diagram_lemmas.lean | e4ab594254ce55225b5b4f1fbe04df5501d54a61 | [] | no_license | QaisHamarneh/Coalgebra-in-Lean | b4318ee6d83780e5c734eb78fed98b1fe8016f7e | bd0452df98bc64b608e5dfd7babc42c301bb6a46 | refs/heads/master | 1,663,371,200,241 | 1,661,004,695,000 | 1,661,004,695,000 | 209,798,828 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,947 | lean | import category_theory.category
import category_theory.functor
import category_theory.types
import help_functions
import tactic.tidy
namespace diagram_lemmas
universe u
open classical function set category_theory help_functions
local notation f ` ⊚ ` :80 g:80 := category_struct.comp g f
variables {F : Type u ⥤ ... |
883b9b86dcb90fabfb2f1813f19fef5ada3ae88a | 4727251e0cd73359b15b664c3170e5d754078599 | /src/topology/category/Top/adjunctions.lean | 62a4711da14c769c7452a75f67e8e7a25c3d4f86 | [
"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 | 1,252 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Mario Carneiro
-/
import topology.category.Top.basic
import category_theory.adjunction.basic
/-!
# Adjunctions regarding the category of topological spaces
This file ... |
fe48e3c07f4ebceed94aaa13008c42acbef273af | ba4794a0deca1d2aaa68914cd285d77880907b5c | /src/tactic/modded.lean | a3f7a6abc8c765edeb9b10325ccf68ca8c04213a | [
"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 | 3,445 | lean | -- modded induction', cases', rw'
-- *TODO* -- waiting for simon PR for symmetry'
import tactic.interactive
run_cmd mk_simp_attr `leakage
open lean
open lean.parser
local postfix `?`:9001 := optional
local postfix *:9001 := many
namespace tactic
namespace interactive
open interactive interactive.types expr
privat... |
ab28c51a54cdaec2e711f2e5ac31ba9dc747338c | d642a6b1261b2cbe691e53561ac777b924751b63 | /src/topology/uniform_space/pi.lean | caf122a244dc041182e327d771130f58328e3899 | [
"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 | 1,964 | lean | /-
Copyright (c) 2019 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
Indexed product of uniform spaces
-/
import topology.uniform_space.cauchy
import topology.uniform_space.separation
noncomputable theory
open_locale uniformity
sectio... |
97f30675030fa1fc92692de42580834f8c931d95 | ca1ad81c8733787aba30f7a8d63f418508e12812 | /clfrags/src/hilbert/wr/proofs/or.lean | d1cf3a4431a3cbe3abc845180ad2b45515b0102c | [] | no_license | greati/hilbert-classical-fragments | 5cdbe07851e979c8a03c621a5efd4d24bbfa333a | 18a21ac6b2e890060eb4ae65752fc0245394d226 | refs/heads/master | 1,591,973,117,184 | 1,573,822,710,000 | 1,573,822,710,000 | 194,334,439 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,011 | lean | import hilbert.wr.or
namespace clfrags
namespace hilbert
namespace wr
namespace or
theorem d₁' {a b : Prop} (h₁ : b) : or a b :=
have h₂ : or b a, from or.d₁ h₁,
show or a b, from or.d₃ h₂
theorem d₄' {a b c : Prop} (h₁ :... |
b5dcbd47c8d397131552c140fef311557a581f58 | 3618c6e11aa822fd542440674dfb9a7b9921dba0 | /src/multirelation/approach2/free_group2.lean | 0093029c2828ce55125820b8246cdc0e91bd3c9f | [] | no_license | ChrisHughes24/single_relation | 99ceedcc02d236ce46d6c65d72caa669857533c5 | 057e157a59de6d0e43b50fcb537d66792ec20450 | refs/heads/master | 1,683,652,062,698 | 1,683,360,089,000 | 1,683,360,089,000 | 279,346,432 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,845 | lean | import algebra.group
import data.list.basic
namespace group_rel
namespace free_group
open native
@[reducible] def free_group := list (ℕ × bool)
def ap : free_group → free_group → free_group := (++)
def cons (i : ℕ) (b : bool) (a : free_group) : free_group :=
⟨i, b⟩ :: a
instance : has_one (free_group) := ⟨[]⟩
lemm... |
c77c0ae404ce1480d2544d880ce19edaf3a01c13 | 1dd482be3f611941db7801003235dc84147ec60a | /src/analysis/normed_space/basic.lean | d6432b6d650e82f9e11eb04e1d70a5650c32eacd | [
"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 | 17,060 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Normed spaces.
Authors: Patrick Massot, Johannes Hölzl
-/
import algebra.pi_instances
import linear_algebra.basic
import topology.instances.nnreal
variables {α : Type*} {β : Type*} {γ : Type*... |
c3e1057200d5a60b1cb8c501d450531e03a26b1b | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /src/Lean/Meta/Eqns.lean | 238f3074a1cfc3fb3601d2da52ca4fd14f991b65 | [
"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 | 5,248 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.Basic
import Lean.Meta.AppBuilder
namespace Lean.Meta
def GetEqnsFn := Name → MetaM (Option (Array Name))
private builtin_initialize get... |
476defb6122f4c48aeabb8a39752d578ad94352f | 2c096fdfecf64e46ea7bc6ce5521f142b5926864 | /tests/lean/interactive/hover.lean | d7e10d5929b7d512d20e6c54a66d7cfee5e895ca | [
"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 | Kha/lean4 | 1005785d2c8797ae266a303968848e5f6ce2fe87 | b99e11346948023cd6c29d248cd8f3e3fb3474cf | refs/heads/master | 1,693,355,498,027 | 1,669,080,461,000 | 1,669,113,138,000 | 184,748,176 | 0 | 0 | Apache-2.0 | 1,665,995,520,000 | 1,556,884,930,000 | Lean | UTF-8 | Lean | false | false | 5,770 | lean | import Lean
example : True := by
apply True.intro
--^ textDocument/hover
example : True := by
simp [True.intro]
--^ textDocument/hover
example (n : Nat) : True := by
match n with
| Nat.zero => _
--^ textDocument/hover
| n + 1 => _
/-- My tactic -/
macro "mytac" o:"only"? e:term : tactic => ... |
7ac55ec6fe03a3ef9801a13cfccd9ed1c768b417 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/playground/simp_binders.lean | bf77039b2e22093808889047223d2ed7c1b9f054 | [
"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 | 767 | lean | axiom let_in {A B} (x : A) (f : A -> B) : B
axiom add (x y : Nat) : Nat
@[simp] axiom addZero (x : Nat) : add x 0 = x
syntax "bigAdd0Seq! " num term:max : term
syntax "bigAddSeq! " num term:max : term
macro_rules
| `(bigAdd0Seq! $n $acc) =>
let n := n.toNat
if n == 0 then
`(add $acc (add $acc 0))
... |
91c0d583c6be56352d307d4495d5677ff9476cc8 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Parser/Level.lean | 3f05122c4647bcce54771dd04ea17faa9d656bc3 | [
"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 | 1,094 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
import Lean.Parser.Extra
namespace Lean
namespace Parser
builtin_initialize
registerBuiltinParserAttribute `builtin_level_parser ``Ca... |
affbf38750b122c1368fd5370e6329a185127df2 | 75db7e3219bba2fbf41bf5b905f34fcb3c6ca3f2 | /hott/types/equiv.hlean | 60d48e3ae7a71dd4bb919b05e8130c8e4de52902 | [
"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 | 8,387 | hlean | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Floris van Doorn
Ported from Coq HoTT
Theorems about the types equiv and is_equiv
-/
import .fiber .arrow arity ..hprop_trunc
open eq is_trunc sigma sigma.ops pi fiber function equ... |
e1be557f6d97c78b2c75a6c211af25defad9c74a | 827a8a5c2041b1d7f55e128581f583dfbd65ecf6 | /moebius.hlean | f0c771eb59e7a4837b5318933b3a0d6db3152417 | [
"Apache-2.0"
] | permissive | fpvandoorn/leansnippets | 6af0499f6f3fd2c07e4b580734d77b67574e7c27 | 601bafbe07e9534af76f60994d6bdf741996ef93 | refs/heads/master | 1,590,063,910,882 | 1,545,093,878,000 | 1,545,093,878,000 | 36,044,957 | 2 | 2 | null | 1,442,619,708,000 | 1,432,256,875,000 | Lean | UTF-8 | Lean | false | false | 4,346 | hlean | import homotopy.circle
open eq bool equiv circle sigma pi
namespace bool
-- definition elim2_type_seg1_pathover (Pb1 Pb2 : Type) (Ps1 Ps2 : Pb1 ≃ Pb2) (x : Pb1) :
-- pathover (elim2_type Pb1 Pb2 Ps1 Ps2) x seg1 (Ps1 x) :=
-- pathover_of_tr_eq (apd10 (elim2_type_seg1 Pb1 Pb2 Ps1 Ps2) x)
-- definition elim2... |
e1c0d825147858dcb8df8808f84eda154864aaef | d1a52c3f208fa42c41df8278c3d280f075eb020c | /stage0/src/Lean/Elab/Tactic/Conv/Congr.lean | 67268ba377c616864d7da06f9884db74c2466d22 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | cipher1024/lean4 | 6e1f98bb58e7a92b28f5364eb38a14c8d0aae393 | 69114d3b50806264ef35b57394391c3e738a9822 | refs/heads/master | 1,642,227,983,603 | 1,642,011,696,000 | 1,642,011,696,000 | 228,607,691 | 0 | 0 | Apache-2.0 | 1,576,584,269,000 | 1,576,584,268,000 | null | UTF-8 | Lean | false | false | 4,859 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.Tactic.Simp.Main
import Lean.Elab.Tactic.Conv.Basic
namespace Lean.Elab.Tactic.Conv
open Meta
private def congrApp (mvarId : MVarId) (lhs... |
1450c8aef0445a7e43edd63dfbc282b6283f504a | d6124c8dbe5661dcc5b8c9da0a56fbf1f0480ad6 | /Papyrus/IR/ArgumentRef.lean | acaa91bc2af6247562d5b000d11dc396685d9d87 | [
"Apache-2.0"
] | permissive | xubaiw/lean4-papyrus | c3fbbf8ba162eb5f210155ae4e20feb2d32c8182 | 02e82973a5badda26fc0f9fd15b3d37e2eb309e0 | refs/heads/master | 1,691,425,756,824 | 1,632,122,825,000 | 1,632,123,075,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 566 | lean | import Papyrus.Context
import Papyrus.IR.ValueRef
namespace Papyrus
/--
A reference to an external LLVM
[Argument](https://llvm.org/doxygen/classllvm_1_1Argument.html).
-/
structure ArgumentRef extends ValueRef where
is_argument : toValueRef.valueKind = ValueKind.argument
instance : Coe ArgumentRef ValueRef :=... |
b1db347845e3eb5979b793c32b7de3f8fdbcf6c7 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/list/alist.lean | ba275f2017909b01723e6ca6c4ad65fb143ab2c2 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 11,223 | lean | /-
Copyright (c) 2018 Sean Leather. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sean Leather, Mario Carneiro
-/
import data.list.sigma
/-!
# Association lists
-/
universes u v w
open list
variables {α : Type u} {β : α → Type v}
/-- `alist β` is a key-value map st... |
e0dea87192986c26328daacf39460484e4652775 | 94637389e03c919023691dcd05bd4411b1034aa5 | /src/inClassNotes/equallity/equality.lean | 60ed31ae7a7e5841d69615c949c479aefda58fe8 | [] | no_license | kevinsullivan/complogic-s21 | 7c4eef2105abad899e46502270d9829d913e8afc | 99039501b770248c8ceb39890be5dfe129dc1082 | refs/heads/master | 1,682,985,669,944 | 1,621,126,241,000 | 1,621,126,241,000 | 335,706,272 | 0 | 38 | null | 1,618,325,669,000 | 1,612,374,118,000 | Lean | UTF-8 | Lean | false | false | 2,994 | lean | /-
Properties and Relations: Type Families
-/
#check @eq
-- Π {α : Sort u_1}, α → α → Prop
#check eq 1 0 -- 1 = 0
#check eq 1 1 -- 1 = 1
#check 1 = 1
/-
Introduction: construct a term
-/
#check @eq.refl
-- ∀ {α : Sort u_1} (a : α), a = a
example : eq 1 0 := _
example : eq 1 1 := eq.refl 1
/-
Elimination: use ... |
cead756a1a95b156549e37fcb31ee80319487645 | 274748215b6d042f0d9c9a505f9551fa8e0c5f38 | /src/for_mathlib/algebraically_closed.lean | ebb7d0b7723552694a831340e70c761ca4afb09e | [
"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 | 872 | lean | import data.polynomial
import analysis.complex.polynomial -- just a sanity check, probably shouldn't be imported
open polynomial
class algebraically_closed_field (k : Type*) extends discrete_field k :=
(exists_root' : ∀ (f : polynomial k) (hf : 0 < degree f),
∃ z : k, is_root f z)
namespace algebraically_closed_f... |
272504b25e5b282a78777b877b2750e1bbbc05a9 | dc253be9829b840f15d96d986e0c13520b085033 | /algebra/spectral_sequence.hlean | d8cf03537e234898068f08a14528fe01dbb7874e | [
"Apache-2.0"
] | permissive | cmu-phil/Spectral | 4ce68e5c1ef2a812ffda5260e9f09f41b85ae0ea | 3b078f5f1de251637decf04bd3fc8aa01930a6b3 | refs/heads/master | 1,685,119,195,535 | 1,684,169,772,000 | 1,684,169,772,000 | 46,450,197 | 42 | 13 | null | 1,505,516,767,000 | 1,447,883,921,000 | Lean | UTF-8 | Lean | false | false | 8,677 | hlean | /- Spectral sequences
- basic properties of spectral sequences
- currently, we only construct an spectral sequence from an exact couple
-/
-- Author: Floris van Doorn
import .exact_couple
open algebra is_trunc left_module is_equiv equiv eq function nat sigma set_quotient group
left_module group int prod pr... |
f677de7bd7075e9f1e56015fce9f7a75bdcc5a4f | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /stage0/src/Lean/Elab.lean | 5e8a751bec2be2332f6c095d9b3389f898566cab | [
"Apache-2.0"
] | permissive | collares/lean4 | 861a9269c4592bce49b71059e232ff0bfe4594cc | 52a4f535d853a2c7c7eea5fee8a4fa04c682c1ee | refs/heads/master | 1,691,419,031,324 | 1,618,678,138,000 | 1,618,678,138,000 | 358,989,750 | 0 | 0 | Apache-2.0 | 1,618,696,333,000 | 1,618,696,333,000 | null | UTF-8 | Lean | false | false | 895 | 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.Elab.Import
import Lean.Elab.Exception
import Lean.Elab.Command
import Lean.Elab.Term
import Lean.Elab.App
import Lean.Elab.Binders
import Lean.... |
93578d8e4d82619fc8b826b0e89c6a6417ec7cf0 | c09f5945267fd905e23a77be83d9a78580e04a4a | /src/topology/subset_properties.lean | c6cc5a3dab05a667fef8a20ee8ff4cb924694de2 | [
"Apache-2.0"
] | permissive | OHIHIYA20/mathlib | 023a6df35355b5b6eb931c404f7dd7535dccfa89 | 1ec0a1f49db97d45e8666a3bf33217ff79ca1d87 | refs/heads/master | 1,587,964,529,965 | 1,551,819,319,000 | 1,551,819,319,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 24,165 | 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
Properties of subsets of topological spaces: compact, clopen, irreducible,
connected, totally disconnected, totally separated.
-/
import topology.basic... |
72027aa79d0b180ed72af45090a0fcac5dfcef2a | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/data/quot.lean | fc2cf383adedfa4988f94a0142db5e97b4b4b1ff | [
"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 | 22,325 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import logic.relator
/-!
# Quotient types
This module extends the core library's treatment of quotient types (`init.data.quot`).
## Tags
quotient
-/
variables {α... |
df672dd0d2d2a7edd53b8e4f0300ec7d62bc45ff | 88fb7558b0636ec6b181f2a548ac11ad3919f8a5 | /library/init/data/fin/basic.lean | 0809bd1a8cf5ae45f5a34584939401520e07421f | [
"Apache-2.0"
] | permissive | moritayasuaki/lean | 9f666c323cb6fa1f31ac597d777914aed41e3b7a | ae96ebf6ee953088c235ff7ae0e8c95066ba8001 | refs/heads/master | 1,611,135,440,814 | 1,493,852,869,000 | 1,493,852,869,000 | 90,269,903 | 0 | 0 | null | 1,493,906,291,000 | 1,493,906,291,000 | null | UTF-8 | Lean | false | false | 1,053 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import init.data.nat.basic
open nat
structure fin (n : nat) := (val : nat) (is_lt : val < n)
namespace fin
def {u} elim0 {α : Type u} : fin 0 → α
|... |
7ea4166f872e340458847bb5daf6e92d26daf54f | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/logic/unique.lean | 4f10a67a3ed6f4473306f691b857eaccc8ba7bf5 | [
"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 | 8,185 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import tactic.basic
import logic.is_empty
/-!
# Types with a unique term
In this file we define a typeclass `unique`,
which expresses that a type has a unique term.... |
a275caf6cacdf9b07c0d4416ceab637075f43662 | c3f2fcd060adfa2ca29f924839d2d925e8f2c685 | /tests/lean/run/def_tac.lean | 2f4f7ec824aec83911012abf891b99bc0f1954b0 | [
"Apache-2.0"
] | permissive | respu/lean | 6582d19a2f2838a28ecd2b3c6f81c32d07b5341d | 8c76419c60b63d0d9f7bc04ebb0b99812d0ec654 | refs/heads/master | 1,610,882,451,231 | 1,427,747,084,000 | 1,427,747,429,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 887 | lean | context
open tactic
definition cases_refl (e : expr) : tactic :=
cases e expr_list.nil; apply rfl
definition cases_lst_refl : expr_list → tactic
| cases_lst_refl expr_list.nil := apply rfl
| cases_lst_refl (expr_list.cons a l) := cases a expr_list.nil; cases_lst_refl l
-- Similar to cases_refl, b... |
c7051085e769e39091d5b973f3c3cdddb26d546d | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/logic/function/iterate.lean | 2466aac5716621855e699dffc6ad3764013bab11 | [
"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 | 5,968 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import logic.function.conjugate
/-!
# Iterations of a function
In this file we prove simple properties of `nat.iterate f n` a.k.a. `f^[n]`:
* `iterate_zero`, `it... |
6f3086f1ccd6fed57407a20bcde9362c05e731d9 | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/number_theory/sum_two_squares.lean | 3db8a51133c2ce8ae0325ef116ae41536fd51a4d | [
"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 | 3,154 | lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Chris Hughes
Proof of Fermat's theorem on the sum of two squares. Every prime congruent to 1 mod 4 is the sum
of two squares
-/
import data.zsqrtd.gaussian_int data.zmod.quadratic_recip... |
7500f6ec98429695efe36c6e6f42e2fe4e0d8057 | 36c7a18fd72e5b57229bd8ba36493daf536a19ce | /library/data/real/complete.lean | ccf9fefbfe3c89881c6a18ec19d8da00fb7e4c74 | [
"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 | 30,710 | lean | /-
Copyright (c) 2015 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Robert Y. Lewis
The real numbers, constructed as equivalence classes of Cauchy sequences of rationals.
This construction follows Bishop and Bridges (1985).
At this point, we no longer... |
4437abc9bbfbaa03146a64e04109671ba6cd75e0 | ba4794a0deca1d2aaa68914cd285d77880907b5c | /src/solutions/world1_addition.lean | 250180a1e4e3f93690f49cb21659210d2b874969 | [
"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 | 6,403 | lean | import mynat.definition -- Imports the natural numbers.
/- Here's what you get from the import:
1) The following data:
* a type called `mynat`
* a term `0 : mynat`, interpreted as the number zero.
* a function `succ : mynat → mynat`, with `succ n` interpreted as "the number after n".
* Usual numerical notatio... |
5b9981ff7d1bb7299e7fca84e1872dfa47fdbda0 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/tactic/linarith/datatypes.lean | e6be83348097804ce6db4f4dec852598978650bd | [
"Apache-2.0"
] | permissive | dupuisf/mathlib | 62de4ec6544bf3b79086afd27b6529acfaf2c1bb | 8582b06b0a5d06c33ee07d0bdf7c646cae22cf36 | refs/heads/master | 1,669,494,854,016 | 1,595,692,409,000 | 1,595,692,409,000 | 272,046,630 | 0 | 0 | Apache-2.0 | 1,592,066,143,000 | 1,592,066,142,000 | null | UTF-8 | Lean | false | false | 11,114 | lean | /-
Copyright (c) 2020 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
-/
import meta.rb_map
import tactic.ring
import tactic.linarith.lemmas
/-!
# Datatypes for `linarith`
Some of the data structures here are used in multiple parts of... |
3db053b7b5307eecfa557701eac12ddcfaf2f54e | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/rat/order.lean | 46004118b583a26c2f9e30c3cb3378e9b9619fbb | [
"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 | 8,736 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import algebra.order.field.defs
import data.rat.basic
import data.int.cast.lemmas
import tactic.assert_exists
/-!
# Order for Rational Numbers
## Su... |
0b6a499bd29cba0a1d217409af1512d62a51285c | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/data/nat/digits.lean | 6f3a88fd8cb7cc92fa9d6c9e7a896868aa473824 | [
"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 | 20,662 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Shing Tak Lam, Mario Carneiro
-/
import data.int.modeq
import tactic.interval_cases
import tactic.linarith
/-!
# Digits of a natural number
This provides a basic API ... |
e02427e98af7fcc2c3b771f055f9679c0d9c9b70 | f22a91842f18b5e855075b9becd55d2233756c6a | /src/ch02.lean | 4dd588928b00374205f869264e9f5440afee97d5 | [] | no_license | kckennylau/tao-analysis-one | 48cef1ee896d6703fcaf47ce5548e44f88901a0e | 2bd2d14c3c722bb36526c5a4e6b87618b2c081b1 | refs/heads/master | 1,621,002,517,963 | 1,514,151,057,000 | 1,514,151,057,000 | 115,971,702 | 0 | 0 | null | 1,514,864,495,000 | 1,514,864,495,000 | null | UTF-8 | Lean | false | false | 9,177 | lean | --------------------------------------------------------------------------------
-- Chapter 2 - Starting at the beginning: the natural numbers
-- Analysis 1, Third Edition, Tao
--------------------------------------------------------------------------------... |
0283133d7f9e0c7d713ca64f3628308207467764 | 856e2e1615a12f95b551ed48fa5b03b245abba44 | /src/topology/compact_open.lean | a265c0a976b0a2a8640ba9da0ef962ede6aaa196 | [
"Apache-2.0"
] | permissive | pimsp/mathlib | 8b77e1ccfab21703ba8fbe65988c7de7765aa0e5 | 913318ca9d6979686996e8d9b5ebf7e74aae1c63 | refs/heads/master | 1,669,812,465,182 | 1,597,133,610,000 | 1,597,133,610,000 | 281,890,685 | 1 | 0 | null | 1,595,491,577,000 | 1,595,491,576,000 | null | UTF-8 | Lean | false | false | 3,809 | lean | /-
Copyright (c) 2018 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton
Type of continuous maps and the compact-open topology on them.
-/
import topology.subset_properties
import topology.continuous_map
import tactic.tidy
open set
open_locale to... |
257bc40f23b53c960d067f2d38d5543c4e4cb398 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/analysis/special_functions/trigonometric/basic.lean | 5f261359e7d787af98d78af9f47e6aad316fc745 | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 41,831 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-/
import analysis.special_functions.exp
import data.set.intervals.infinite
/-!
# Trigonometric functions... |
52f4fac0ff40ff229d16f16044d0a0fb8bcd1cd0 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/sizeof.lean | c82a953cd7c828022c57c8424640f2f7013c71fd | [
"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 | 464 | lean | -- Recall that we do not generate code for `sizeOf` instances since they are only used for proving termination
#reduce sizeOf 10
#reduce sizeOf [1, 2]
#reduce sizeOf #[1, 2]
#reduce sizeOf (10 : UInt8)
#reduce sizeOf 'a'
#reduce sizeOf ['h', 'e', 'l', 'l', 'o']
#reduce sizeOf "abc"
#reduce sizeOf `abc
inductive InfTr... |
2c5f3ba3e3e8c6d59bd5bfd20c36a48126aef0e2 | 0c1546a496eccfb56620165cad015f88d56190c5 | /library/init/meta/smt/default.lean | 8fd097dad7410ee3f1f61ab90392d64770ee358a | [
"Apache-2.0"
] | permissive | Solertis/lean | 491e0939957486f664498fbfb02546e042699958 | 84188c5aa1673fdf37a082b2de8562dddf53df3f | refs/heads/master | 1,610,174,257,606 | 1,486,263,620,000 | 1,486,263,620,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 313 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.meta.smt.congruence_closure init.cc_lemmas
import init.meta.smt.ematch
import init.meta.smt.smt_tactic init.meta.smt.interactive
|
93f386530f9e6b292f2e226744716e6bdba84d78 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/dynamics/fixed_points/basic.lean | 2bc976b3213f10382df793781cf018b69f1e11c0 | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 5,565 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import data.set.function
import logic.function.iterate
/-!
# Fixed points of a self-map
In this file we define
* the predicate `is_fixed_pt f x := f x = x`;
* th... |
9c238b94879884b8a160ab4b1dc19a2c3e82e4aa | f3a5af2927397cf346ec0e24312bfff077f00425 | /src/game/world7/level8.lean | 5c23fd6051c467ff8c08a5f31f28d3da6bc0cf21 | [
"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 | 1,294 | lean | import tactic.finish game.world7.level7 -- hide
namespace mynat -- hide
/-
# Advanced proposition world.
## Level 8: `and_or_distrib_left`
We know that `x(y+z)=xy+xz` for numbers, and this
is called distributivity of multiplication over addition.
The same is true for `∧` and `∨` -- in fact `∧` distributes
over `∨` ... |
3b109f1e0417ac3cb940947221ca2982026e4462 | e953c38599905267210b87fb5d82dcc3e52a4214 | /hott/init/path.hlean | 385f376823665383156b0bd3eeecf840592e0654 | [
"Apache-2.0"
] | permissive | c-cube/lean | 563c1020bff98441c4f8ba60111fef6f6b46e31b | 0fb52a9a139f720be418dafac35104468e293b66 | refs/heads/master | 1,610,753,294,113 | 1,440,451,356,000 | 1,440,499,588,000 | 41,748,334 | 0 | 0 | null | 1,441,122,656,000 | 1,441,122,656,000 | null | UTF-8 | Lean | false | false | 25,378 | hlean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Jakob von Raumer, Floris van Doorn
Ported from Coq HoTT
-/
prelude
import .function .tactic
open function eq
/- Path equality -/
namespace eq
variables {A ... |
5c578fa80613a090085c42c6a3ba2bf70f3ac43c | 1d265c7dd8cb3d0e1d645a19fd6157a2084c3921 | /src/other/int_vector3d_cross.lean | 50d7544c1bebd976f3839a3d9996489aac049da5 | [
"MIT"
] | permissive | hanzhi713/lean-proofs | de432372f220d302be09b5ca4227f8986567e4fd | 4d8356a878645b9ba7cb036f87737f3f1e68ede5 | refs/heads/master | 1,585,580,245,658 | 1,553,646,623,000 | 1,553,646,623,000 | 151,342,188 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 1,950 | lean | -- this is a proof that ∀ vectors a, b ∈ ℤ³,
-- (a × b) ⬝ a = 0 ∧ (a × b) ⬝ b = 0
def dot: ℤ × ℤ × ℤ → ℤ × ℤ × ℤ → ℤ := λ ⟨a, b, c⟩ ⟨d, e, f⟩, a*d + b*e + c*f
def cross: ℤ × ℤ × ℤ → ℤ × ℤ × ℤ → ℤ × ℤ × ℤ := λ ⟨a, b, c⟩ ⟨d, e, f⟩, ⟨b*f - c*e, c*d - a*f, a*e - b*d⟩
variables m n p j k l : ℤ
#eval cross (124, 1294, 123... |
c16293a1bae8e0be0ed9e05ba9cf42ebfdde63db | 4950bf76e5ae40ba9f8491647d0b6f228ddce173 | /src/category_theory/monad/coequalizer.lean | 1cf2dfc4637ccbb0fc52c58d16b252ae3bd484d1 | [
"Apache-2.0"
] | permissive | ntzwq/mathlib | ca50b21079b0a7c6781c34b62199a396dd00cee2 | 36eec1a98f22df82eaccd354a758ef8576af2a7f | refs/heads/master | 1,675,193,391,478 | 1,607,822,996,000 | 1,607,822,996,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,905 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import category_theory.limits.shapes.reflexive
import category_theory.limits.preserves.shapes.equalizers
import category_theory.limits.shapes.split_coequalizer
import ca... |
64964118152a8106d55ce1989f741bac86b58114 | 46125763b4dbf50619e8846a1371029346f4c3db | /src/topology/opens.lean | 95d61c66b4d79dd47ba928f60053e970e8f54fd7 | [
"Apache-2.0"
] | permissive | thjread/mathlib | a9d97612cedc2c3101060737233df15abcdb9eb1 | 7cffe2520a5518bba19227a107078d83fa725ddc | refs/heads/master | 1,615,637,696,376 | 1,583,953,063,000 | 1,583,953,063,000 | 246,680,271 | 0 | 0 | Apache-2.0 | 1,583,960,875,000 | 1,583,960,875,000 | null | UTF-8 | Lean | false | false | 6,350 | 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
Subtype of open subsets in a topological space.
-/
import topology.bases topology.separation
import order.copy
open filter lattice
variables {α : Type... |
aec68d18ce4709aa0a46e8f1e178248a6d283ee1 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/group_theory/is_free_group.lean | 528ee7e69965da1c538f0da68fb585e4d0f812cb | [
"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 | 5,404 | lean | /-
Copyright (c) 2021 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn, Eric Wieser, Joachim Breitner
-/
import group_theory.free_group
/-!
# Free groups structures on arbitrary types
This file defines a type class for type that are free groups, t... |
d833aaceb6ee0ed8f97f6d00880a64345d7c5bb2 | e0f9ba56b7fedc16ef8697f6caeef5898b435143 | /src/ring_theory/free_comm_ring.lean | 181f524e8983e3293bef4fdb98f3fc827f040d8a | [
"Apache-2.0"
] | permissive | anrddh/mathlib | 6a374da53c7e3a35cb0298b0cd67824efef362b4 | a4266a01d2dcb10de19369307c986d038c7bb6a6 | refs/heads/master | 1,656,710,827,909 | 1,589,560,456,000 | 1,589,560,456,000 | 264,271,800 | 0 | 0 | Apache-2.0 | 1,589,568,062,000 | 1,589,568,061,000 | null | UTF-8 | Lean | false | false | 16,022 | lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Johan Commelin
-/
import data.equiv.functor
import data.mv_polynomial
import ring_theory.ideal_operations
import ring_theory.free_ring
noncomputable theory
local attribute [inst... |
cc07b66b1620463fa38666a9c22ae7082dbd688a | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /tmp/new-frontend/parser/notation.lean | bce3240f6ddd53bd1851b93ae784744e45c46ce4 | [
"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 | 5,694 | lean | /-
Copyright (c) 2018 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Sebastian Ullrich
Notation parsers
-/
prelude
import init.lean.parser.token
namespace Lean
namespace Parser
open Combinators MonadParsec
open Parser.HasTokens Parser.HasView
... |
38612783a7bb07433aaa58de50839ee01dcec066 | f7315930643edc12e76c229a742d5446dad77097 | /tests/lean/run/univ2.lean | fbaf29e83f8711bcf8e057485a0343552eaa867c | [
"Apache-2.0"
] | permissive | bmalehorn/lean | 8f77b762a76c59afff7b7403f9eb5fc2c3ce70c1 | 53653c352643751c4b62ff63ec5e555f11dae8eb | refs/heads/master | 1,610,945,684,489 | 1,429,681,220,000 | 1,429,681,449,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 228 | lean | import logic
axiom I : Type
definition F (X : Type) : Type := (X → Prop) → Prop
axiom unfold : I → F I
axiom foldd : F I → I
axiom iso1 : ∀x, foldd (unfold x) = x
theorem iso2 : ∀x, foldd (unfold x) = x
:= sorry
|
58a00814d36b8338f403266199c69b070f0e39c6 | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/topology/algebra/group_completion.lean | 465a7cd7823aa8fe06ba643cc748539ba770c234 | [
"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 | 5,554 | 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... |
7da122c441c50843473da23ea6c8f55085e16266 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/preadditive/left_exact.lean | d98a6fa81a43f1ffbbf94ad570a5bbb88729ce2f | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 10,378 | lean | /-
Copyright (c) 2022 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Jakob von Raumer
-/
import category_theory.limits.constructions.finite_products_of_binary_products
import category_theory.limits.preserves.shapes.kernels
import catego... |
d948a0ae071d299975479a20afe2b771602bf015 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/rflProofsCongrCastsIssue.lean | 8499da213d5f0130ace9ba83e29a4ed944a303a2 | [
"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 | 117 | lean | example (h₁: m < n) (h₂: m.succ.pred < n) :
(Fin.mk m h₁).succ = (Fin.mk m.succ.pred h₂).succ := by
simp
|
ffa00523c8f663cc554e007e61231c0ab430dd82 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/struct_inst_exprs2.lean | 15d123f48f9560884548c584ba2fdc704d716e03 | [
"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 | 573 | lean | #exit
-- import data.nat.basic
open nat
structure s1 (A : Type) :=
(x : A) (y : A) (h : x = y)
structure s2 (A : Type) :=
(mul : A → A → A) (one : A)
structure s3 (A : Type) extends s1 A, s2 A :=
(mul_one : ∀ a : A, mul a one = a)
definition v1 : s1 nat := {| s1, x := 10, y := 10, h := rfl |}
definition v2 : s2 nat... |
2f679004950e473ca50686f0cd96b7f4e9c87883 | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/topology/uniform_space/pi.lean | 130fbe9a4bf829ea32e2bee4c9d3343b7f098148 | [
"Apache-2.0"
] | permissive | ChrisHughes24/mathlib | 98322577c460bc6b1fe5c21f42ce33ad1c3e5558 | a2a867e827c2a6702beb9efc2b9282bd801d5f9a | refs/heads/master | 1,583,848,251,477 | 1,565,164,247,000 | 1,565,164,247,000 | 129,409,993 | 0 | 1 | Apache-2.0 | 1,565,164,817,000 | 1,523,628,059,000 | Lean | UTF-8 | Lean | false | false | 1,977 | lean | /-
Copyright (c) 2019 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
Indexed product of uniform spaces
-/
import topology.uniform_space.cauchy
import topology.uniform_space.separation
noncomputable theory
local notation `𝓤` := uniform... |
b38fa7e0fb4d81251248115b04bc6fc934aac68d | 367134ba5a65885e863bdc4507601606690974c1 | /src/category_theory/monad/kleisli.lean | 2561841e945f3886055a63f8ce9c747dece8c6cf | [
"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 | 3,093 | lean | /-
Copyright (c) 2020 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Wojciech Nawrocki, Bhavik Mehta
-/
import category_theory.adjunction
import category_theory.monad.adjunction
import category_theory.monad.basic
/-! # Kleisli category on a monad
T... |
d96d17dbd46d66b0da0ad7da8207b347047c57fe | df561f413cfe0a88b1056655515399c546ff32a5 | /3-multiplication-world/l2.lean | 534d2d7630ae007d29beda2ec06e9fbd583ab11b | [] | no_license | nicholaspun/natural-number-game-solutions | 31d5158415c6f582694680044c5c6469032c2a06 | 1e2aed86d2e76a3f4a275c6d99e795ad30cf6df0 | refs/heads/main | 1,675,123,625,012 | 1,607,633,548,000 | 1,607,633,548,000 | 318,933,860 | 3 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 116 | lean | lemma mul_one (m : mynat) : m * 1 = m :=
begin
rw one_eq_succ_zero,
rw mul_succ,
rw mul_zero,
rw zero_add,
refl,
end |
8a19dc373d7f90063012ef42fe39eeffa99437af | d4df7c538bbc0b06771d7b7a6f46fbadebb8c5eb | /src/parser.lean | ac66bc56bb9b0e011162fae53dd7c7bd6ae78b0b | [] | no_license | breakerzirconia/LeanTransformers | 11bb924b59ac589d0c6b39586d27cccc8f9e939c | 3c52441b8990bab7d8cf1817df6e04f657a14e1c | refs/heads/main | 1,682,610,526,027 | 1,620,477,129,000 | 1,620,477,129,000 | 365,507,838 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,859 | lean | ----------------------------
-- Definition + instances --
----------------------------
structure Parser (s a : Type) : Type := (run : list s → option (a × list s))
open Parser
instance Parser_functor {s : Type} : functor (Parser s) := {
map := λ α β f p,
mk (λ l,
match p.run l with
... |
8416ea325e63d6978979674334e0d2786adce193 | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /tests/lean/run/trans.lean | 8c6a02cd7ae0c0e271065e28283cd29b66a3fc92 | [
"Apache-2.0"
] | permissive | codyroux/lean | 7f8dff750722c5382bdd0a9a9275dc4bb2c58dd3 | 0cca265db19f7296531e339192e9b9bae4a31f8b | refs/heads/master | 1,610,909,964,159 | 1,407,084,399,000 | 1,416,857,075,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,561 | 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
import logic
open eq
definition refl := @eq.refl
definition transport {A : Type} {a b : A} {P : A → Type} (p : a = b) (H : P a) : P b
:= eq.rec H p
theo... |
8fbbeb1b1a050ef68b1129515c5be62371cadc3d | 57fdc8de88f5ea3bfde4325e6ecd13f93a274ab5 | /data/option.lean | daedb3345beebe3299966cdacb7852da35a2e66b | [
"Apache-2.0"
] | permissive | louisanu/mathlib | 11f56f2d40dc792bc05ee2f78ea37d73e98ecbfe | 2bd5e2159d20a8f20d04fc4d382e65eea775ed39 | refs/heads/master | 1,617,706,993,439 | 1,523,163,654,000 | 1,523,163,654,000 | 124,519,997 | 0 | 0 | Apache-2.0 | 1,520,588,283,000 | 1,520,588,283,000 | null | UTF-8 | Lean | false | false | 2,298 | 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 logic.basic data.bool init.data.option.instances
namespace option
universe u
variables {α β : Type u}
instance has_mem : has_mem α (option α) := ⟨λ a b, b = ... |
42f2e02b299911cf6362e17e3a0d3b03f75287e0 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/group_theory/index.lean | c83b097b10af77afe1bd4fddef84ca3038a98741 | [
"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 | 11,593 | lean | /-
Copyright (c) 2021 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import group_theory.quotient_group
import set_theory.cardinal.finite
/-!
# Index of a Subgroup
In this file we define the index of a subgroup, and prove several ... |
cd7ca43d393d1a35eb03f92a903167b6a4d9ca05 | cf39355caa609c0f33405126beee2739aa3cb77e | /library/init/control/default.lean | cde32ca680bad2a26825ef406ccba0ca76169f68 | [
"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 | 423 | 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.control.applicative init.control.functor init.control.alternative
import init.control.monad init.control.lift init.control.lawful
import... |
e85738b8dd714c2eaf0e90cecf5e1b4293c27ffb | c5b07d17b3c9fb19e4b302465d237fd1d988c14f | /src/category/adjoint.lean | 6d7ec4e08024e0f395f8d1dec25dd1831d5ac0c3 | [
"MIT"
] | permissive | skaslev/papers | acaec61602b28c33d6115e53913b2002136aa29b | f15b379f3c43bbd0a37ac7bb75f4278f7e901389 | refs/heads/master | 1,665,505,770,318 | 1,660,378,602,000 | 1,660,378,602,000 | 14,101,547 | 0 | 1 | MIT | 1,595,414,522,000 | 1,383,542,702,000 | Lean | UTF-8 | Lean | false | false | 507 | lean | import data.iso
-- Adjoint functors
-- bᶠ⁽ᵃ⁾ = g(b)ᵃ
def adj (f g : Type → Type) := Π A B, (f A → B) ≃ (A → g B)
notation f ` ⊣ ` g := adj f g
-- "Every monad arises from some adjunction — in fact, typically from many adjunctions"
-- The slogan is "Adjoint functors arise everywhere".
-- — Saunders Mac Lane, Cat... |
78a561e2d2fd233cc52824ab52e0d746cd7ed638 | 75db7e3219bba2fbf41bf5b905f34fcb3c6ca3f2 | /hott/algebra/category/functor/attributes.hlean | 1534c5e9c659c1b6d821e4e9a4e9c4df8497c7f0 | [
"Apache-2.0"
] | permissive | jroesch/lean | 30ef0860fa905d35b9ad6f76de1a4f65c9af6871 | 3de4ec1a6ce9a960feb2a48eeea8b53246fa34f2 | refs/heads/master | 1,586,090,835,348 | 1,455,142,203,000 | 1,455,142,277,000 | 51,536,958 | 1 | 0 | null | 1,455,215,811,000 | 1,455,215,811,000 | null | UTF-8 | Lean | false | false | 6,532 | 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
Attributes of functors (full, faithful, split essentially surjective, ...)
Adjoint functors, isomorphisms and equivalences have their own file
-/
import ..constru... |
a59c428845c35ed199785b52c1d111b3e57795e3 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/logic/nonempty.lean | 1e2df5304b30b00d641476bd4667ef26ee5686f0 | [
"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 | 5,691 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import logic.basic
/-!
# Nonempty types
This file proves a few extra facts about `nonempty`, which is defined in core Lean.
## Main declarations
* `nonempty.some`... |
c4c8557742e5caaabe01875c61013f2b4394e9a1 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/preadditive/eilenberg_moore.lean | fdb3f3332c17099b2fafbf0f10dc0a5461ecfb61 | [
"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 | 4,734 | lean | /-
Copyright (c) 2022 Julian Kuelshammer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Kuelshammer
-/
import category_theory.preadditive.basic
import category_theory.monad.algebra
import category_theory.preadditive.additive_functor
/-!
# Preadditive structur... |
ef6665a1555ff146f88de6ca69b35c254b0b08e2 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/order/lexicographic.lean | ea40cd5e0b166a5ffe11ba3ae3161eedcc8969ca | [
"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 | 8,623 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Minchao Wu
-/
import tactic.basic
/-!
# Lexicographic order
This file defines the lexicographic relation for pairs and dependent pairs of orders, partial orders
and l... |
4b8baae87952fc985d30e6decb29a86643e43ee0 | d5ecf6c46a2f605470a4a7724909dc4b9e7350e0 | /set_theory/cardinal.lean | d219f9a5248a0ecd7521dd1d4b5533db4260a8c5 | [
"Apache-2.0"
] | permissive | MonoidMusician/mathlib | 41f79df478987a636b735c338396813d2e8e44c4 | 72234ef1a050eea3a2197c23aeb345fc13c08ff3 | refs/heads/master | 1,583,672,205,771 | 1,522,892,143,000 | 1,522,892,143,000 | 128,144,032 | 0 | 0 | Apache-2.0 | 1,522,892,144,000 | 1,522,890,892,000 | Lean | UTF-8 | Lean | false | false | 27,369 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl, Mario Carneiro
Cardinal arithmetic.
Cardinals are represented as quotient over equinumerous types.
-/
import data.set.finite data.quot logic.schroeder_bernstein logic... |
49d5c6e2705d645641463a5390c1acf58cd1d07b | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /test/lint_coe_t.lean | 9177ae4222fcd1fb5aa832c985463ac9b6035c83 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 1,088 | lean | import tactic.lint
open tactic
-- bad, because every iteration of tc search will loop, generating nested quotients
section
local attribute [instance]
def a_to_quot {α} (R : setoid α) : has_coe α (quotient R) := ⟨quotient.mk⟩
run_cmd do
d ← get_decl ``a_to_quot,
some _ ← linter.has_coe_variable.test d,
d ← get_d... |
8e0a9d2c057bd425c1f556774539e0d44cb9029c | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/ring_theory/fractional_ideal.lean | eff5b0d9314e9155ead0920ccedd898ff8d18062 | [
"Apache-2.0"
] | permissive | AntoineChambert-Loir/mathlib | 64aabb896129885f12296a799818061bc90da1ff | 07be904260ab6e36a5769680b6012f03a4727134 | refs/heads/master | 1,693,187,631,771 | 1,636,719,886,000 | 1,636,719,886,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 50,282 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Filippo A. E. Nuccio
-/
import ring_theory.localization
import ring_theory.noetherian
import ring_theory.principal_ideal_domain
import tactic.field_simp
/-!
# Fractional ide... |
c2f60949ee8beb2c63af4e57ddd0718ffcd1c57b | 1d265c7dd8cb3d0e1d645a19fd6157a2084c3921 | /src/lessons/lesson5.lean | 4e8c4ed431c581d1624a564ab915597cb2584bae | [
"MIT"
] | permissive | hanzhi713/lean-proofs | de432372f220d302be09b5ca4227f8986567e4fd | 4d8356a878645b9ba7cb036f87737f3f1e68ede5 | refs/heads/master | 1,585,580,245,658 | 1,553,646,623,000 | 1,553,646,623,000 | 151,342,188 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 492 | lean | variable g: false
theorem ttt : true → false := false.elim g
theorem zneqo : 0 ≠ 1.
theorem what : "Hello, Lean!" ≠ "Hello Lean!" :=
begin
assume h : "Hello, Lean!" = "Hello Lean!",
show false,
from string.no_confusion,
end
def f : ℕ → ℕ := λ x, x - 1
def v : Prop := 1 = 1
theorem gg : 1 = 1 := rfl
theo... |
4a19aa12e886b7f60df0afdb1a76b47945ca659c | e38d5e91d30731bef617cc9b6de7f79c34cdce9a | /src/path/induction.lean | 82bb27ad297f926b9179e834077c991a21b72115 | [
"Apache-2.0"
] | permissive | bbentzen/cubicalean | 55e979c303fbf55a81ac46b1000c944b2498be7a | 3b94cd2aefdfc2163c263bd3fc6f2086fef814b5 | refs/heads/master | 1,588,314,875,258 | 1,554,412,699,000 | 1,554,412,699,000 | 177,333,390 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,046 | lean | /-
Copyright (c) 2019 Bruno Bentzen. All rights reserved.
Released under the Apache License 2.0 (see "License");
Author: Bruno Bentzen
-/
import ..core.kan.coe ..core.connection.meet .groupoid.ops
open interval path
-- auxiliary definitions and lemmas
section
variable {A : Type}
private def f {a x... |
dcf5b29b724a1c5bce1e97420a78220a2d0ab63f | 4767244035cdd124e1ce3d0c81128f8929df6163 | /meta/rb_map.lean | 5bc9ce0afece16775a112250a98b6e640ba6a810 | [
"Apache-2.0"
] | permissive | 5HT/mathlib | b941fecacd31a9c5dd0abad58770084b8a1e56b1 | 40fa9ade2f5649569639608db5e621e5fad0cc02 | refs/heads/master | 1,586,978,681,358 | 1,546,681,764,000 | 1,546,681,764,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,110 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Robert Y. Lewis
Additional operations on native rb_maps and rb_sets.
-/
import data.option.defs
namespace native
namespace rb_set
meta def filter {key} (s : rb_set key) ... |
e4efc144c5905dc5fa2441514a945218296127a4 | 3d2a7f1582fe5bae4d0bdc2fe86e997521239a65 | /spatial-reasoning/spatial-reasoning-problem-18.lean | 2be461cd8312bbaecef6ec90701ead0f68299a73 | [] | no_license | own-pt/common-sense-lean | e4fa643ae010459de3d1bf673be7cbc7062563c9 | f672210aecb4172f5bae265e43e6867397e13b1c | refs/heads/master | 1,622,065,660,261 | 1,589,487,533,000 | 1,589,487,533,000 | 254,167,782 | 3 | 2 | null | 1,589,487,535,000 | 1,586,370,214,000 | Lean | UTF-8 | Lean | false | false | 227 | lean | /- Spatial Reasoning Problem 18 -/
/- It can be found at: SpatialQs.txt -/
/- (18) John holds one end of a string.
The other end is tied to a cart.
If the string is taut and John pulls on his end, does the cart move? -/
|
89551b748abcd5f637c66ab79b0133237187ee49 | 6065973b1fa7bbacba932011c9e2f32bf7bdd6c1 | /src/geometry/euclidean/basic.lean | abad398a88c5e5fa87fb22d408104d21438ba04a | [
"Apache-2.0"
] | permissive | khmacdonald/mathlib | 90a0fa2222369fa69ed2fbfb841b74d2bdfd66cb | 3669cb35c578441812ad30fd967d21a94b6f387e | refs/heads/master | 1,675,863,801,090 | 1,609,761,876,000 | 1,609,761,876,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 46,601 | lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Joseph Myers.
-/
import analysis.normed_space.inner_product
import algebra.quadratic_discriminant
import analysis.normed_space.add_torsor
import data.matrix.notation
import linear_algebra... |
179b1c1ba428bd34b990b26aea9abae5ba1b6248 | 7565ffb53cc64430691ce89265da0f944ee43051 | /hott/types/unit.hlean | 38d8a9ed5ffa15a39fba8c8c98ef5c9b79f12bd8 | [
"Apache-2.0"
] | permissive | EgbertRijke/lean2 | cacddba3d150f8b38688e044960a208bf851f90e | 519dcee739fbca5a4ab77d66db7652097b4604cd | refs/heads/master | 1,606,936,954,854 | 1,498,836,083,000 | 1,498,910,882,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,389 | 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
Theorems about the unit type
-/
open is_equiv equiv option eq pointed is_trunc function
namespace unit
protected definition eta : Π(u : unit), ⋆ = u
| eta ⋆ ... |
fbfbc34ed86bc7bf3f6197ce88a31e91b39faae9 | 4fa118f6209450d4e8d058790e2967337811b2b5 | /src/sheaves/covering.lean | 3dec6eb697daaa99c750adf4912cf2e452c89427 | [
"Apache-2.0"
] | permissive | leanprover-community/lean-perfectoid-spaces | 16ab697a220ed3669bf76311daa8c466382207f7 | 95a6520ce578b30a80b4c36e36ab2d559a842690 | refs/heads/master | 1,639,557,829,139 | 1,638,797,866,000 | 1,638,797,866,000 | 135,769,296 | 96 | 10 | Apache-2.0 | 1,638,797,866,000 | 1,527,892,754,000 | Lean | UTF-8 | Lean | false | false | 2,316 | lean | /-
Package the definition of an open cover of an open set.
Author: Ramon Fernandez Mir
-/
import topology.basic
import topology.opens
import sheaves.opens
universes u
open topological_space lattice
section covering
variables {α : Type u} [topological_space α]
-- Open cover.
structure covering (U : opens α) ... |
fbbd63e0cfe80c6880ba45bca2ef9b1ec631fa04 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/playground/ir.lean | 8514077524471b6a7e0eedc0134349e72ca0997a | [
"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 | 220 | lean | import init.lean.compiler.ir
open Lean.IR
def tst1 : IO Unit :=
let fbody : FnBody :=
FnBody.vdecl `x IRType.uint32 (Expr.lit (LitVal.num 0)) $
FnBody.ret `x;
IO.println $ format fbody
def main : IO Unit :=
tst1
|
db7f8a0f925cfe022193d63074857d4260054e11 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/meta/backward.lean | f43fe749fe679e378f233a3de7e30f12e8d4bdb7 | [] | 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 | 326 | 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.tactic
import Mathlib.Lean3Lib.init.meta.set_get_option_tactics
namespace Mathlib
namespace tac... |
a520b925d5b62d5a927775356ac8ebd8c9208cda | c5b07d17b3c9fb19e4b302465d237fd1d988c14f | /src/isos/nat.lean | ca1286a09acd14254215432991498185d8f673a8 | [
"MIT"
] | permissive | skaslev/papers | acaec61602b28c33d6115e53913b2002136aa29b | f15b379f3c43bbd0a37ac7bb75f4278f7e901389 | refs/heads/master | 1,665,505,770,318 | 1,660,378,602,000 | 1,660,378,602,000 | 14,101,547 | 0 | 1 | MIT | 1,595,414,522,000 | 1,383,542,702,000 | Lean | UTF-8 | Lean | false | false | 1,015 | lean | import isos.id
namespace nat
-- ℕ = 1 + ℕ
def def_iso : ℕ ≃ 1 ⊕ ℕ :=
⟨λ x, nat.rec (sum.inl ()) (λ y ih, sum.inr y) x,
λ x, sum.rec (λ y, 0) (λ y, y+1) x,
λ x, begin induction x with x ih, repeat { refl } end,
λ x, begin induction x, { induction x, refl }, refl end⟩
-- ℕ = Σ n:ℕ, 1
def ogf_iso : ℕ ≃ ogf (const 1) ... |
d8fb451647e33811332d6129b436628bd8504ac9 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/playground/lowtech_expander.lean | 9fe4551d5c19a1338bf9c65bee3712882aedd61c | [
"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 | 10,554 | lean | import init.lean.name
open Lean (Name NameMap)
def MacroScope := Nat
abbrev MacroScopes := List MacroScope
structure SourceInfo :=
(leading : Substring)
(pos : Nat)
(trailing : Substring)
def mkUniqIdRef : IO (IO.Ref Nat) :=
IO.mkRef 0
@[init mkUniqIdRef]
constant nextUniqId : IO.Ref Nat := default _
struct... |
ca65c604f5793b7d99ae251f31399b355f22309c | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/logic/is_empty.lean | a866aa51e2c1e10f097a82469f90b44a480d49c6 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 3,850 | lean | /-
Copyright (c) 2021 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import logic.basic
import tactic.protected
/-!
# Types that are empty
In this file we define a typeclass `is_empty`, which expresses that a type has no elements.... |
21e95505d5959ef50736da0fc82d25612d240bf6 | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/group_theory/perm/cycles.lean | d08dc2b260e3d158ba36495c232d40e9672b5caa | [
"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 | 58,407 | lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import data.nat.parity
import data.equiv.fintype
import group_theory.perm.sign
import data.finset.noncomm_prod
/-!
# Cyclic permutations
## Main definitions
In the foll... |
afca860bc97b7ba96621877fc8e25ac2c0125e22 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/nat/choose/central.lean | 9cd4bf6c27000ba06927a9df627d5babbd936d8f | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 8,649 | lean | /-
Copyright (c) 2021 Patrick Stevens. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Stevens, Thomas Browning
-/
import data.nat.prime
import data.nat.choose.basic
import data.nat.choose.sum
import data.nat.multiplicity
import number_theory.padics.padic_norm
... |
1b8e2425756dd13401eeea21398a272123924746 | b70031c8e2c5337b91d7e70f1e0c5f528f7b0e77 | /src/analysis/mean_inequalities.lean | 91332c4685da17e7f245e310cf84cdf19825e17f | [
"Apache-2.0"
] | permissive | molodiuc/mathlib | cae2ba3ef1601c1f42ca0b625c79b061b63fef5b | 98ebe5a6739fbe254f9ee9d401882d4388f91035 | refs/heads/master | 1,674,237,127,059 | 1,606,353,533,000 | 1,606,353,533,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 25,316 | lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Sébastien Gouëzel
-/
import analysis.convex.specific_functions
import analysis.special_functions.pow
import data.real.conjugate_exponents
import tactic.nth_rewrite
/... |
387d45d6f967826b397ed177af8176ccc8cb8ae6 | 4c421481689d399e1e27a9266c47904d9200d42e | /fib.lean | 201e046492d6a0eee3e06b678a114cbfaaccf5c2 | [] | no_license | ivanmoreau/fib | f1fffe4fef5ba9beae88be3a740c8bcfc95e1e01 | 5d3440b45bb5822c80ebe73b4cbdb05e9506cee2 | refs/heads/master | 1,690,506,253,577 | 1,631,324,182,000 | 1,631,324,182,000 | 405,255,296 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 979 | lean | import tactic.basic
import tactic.congr
import init.data.nat
/- Nat minus, where 0 - n = 0 -/
def ominus : ℕ → ℕ → ℕ
| 0 m := 0
| n 0 := n
| (n + 1) (m + 1) := ominus n m
infix ` ⊖ `:60 := ominus
def fib_tail : ℕ → ℕ → ℕ → ℕ × ℕ
| 0 i j := (i , j)
| (s + 1) i j := fib_tail s j (i + j)
--def fib : ℕ → ℕ
--... |
e1341be4fe4f2287bbf97802c11987c8aa49294b | 6e36ebd5594a0d512dea8bc6ffe78c71b5b5032d | /src/mywork/Practice/review_9_13_21.lean | 3e4eda94bc025a0a95c4cc7e855f722949d2181c | [] | no_license | wrw2ztk/cs2120f21 | cdc4b1b4043c8ae8f3c8c3c0e91cdacb2cfddb16 | f55df4c723d3ce989908679f5653e4be669334ae | refs/heads/main | 1,691,764,473,342 | 1,633,707,809,000 | 1,633,707,809,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 811 | lean | namespace implies
axioms (P Q : Prop)
/-P and Q are arbitrary propositions, they could have more complex names -/
def if_P_is_true_then_so_is_Q : Prop := P → Q
axiom p : P
--assume P is true
--assume we have a proof of P (p)
axiom pq : P → Q
--assume that we have a proof, pq, of P → Q
-- intro for implies: assume ... |
f0817d07e73990b5cc31f48de0c0d2895893f4db | cfa891621a41d154f396f5f38cbe2eb7e34c3f62 | /06-formalizacija-dokazov/lambda.lean | f2f77d13104d8516ae00a1575f92208d6762bde2 | [] | no_license | anastern881/teorija-programskih-jezikov | 40b247a26b12a3cbb9cc9aa4efaf30a17bb085c7 | dc5cc9c4a0265bd2ea32bb7c44bb62eb1b6802ab | refs/heads/master | 1,599,914,547,365 | 1,574,072,468,000 | 1,574,072,468,000 | 222,429,267 | 0 | 0 | null | 1,574,075,186,000 | 1,574,075,185,000 | null | UTF-8 | Lean | false | false | 6,130 | lean | inductive ty : Type
| unit : ty
| bool : ty
| arrow : ty -> ty -> ty
def nm := string
inductive tm : Type
| var : nm -> tm
| unit : tm
| true : tm
| false : tm
| app : tm -> tm -> tm
| lam : nm -> tm -> tm
| if_then_else : tm -> tm -> tm -> tm
inductive value : tm -> Prop
| unit : value tm.unit
| true : value tm.tru... |
2adf9c0319ca5cfa8ff88e9d23706973cded3a6f | 0d5fb6eeedc300fb6a7e26c860869d68d1aa7761 | /final/proofs.lean | 7bf781f9b712f081a80827948a3d442ae46ee1d4 | [] | no_license | FlyNeopolitan/CS242ProgrammingLanguage | 95e0cf82b9248d7376aa9a838d9cc4b93f223bf2 | 1ab4a24396afbc2207b421f1a601e5056c39fa20 | refs/heads/master | 1,685,591,558,205 | 1,624,171,234,000 | 1,624,171,234,000 | 371,285,585 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,240 | lean | -- Required: chapters 1, 2, 3
section part1
variables p q r s : Prop
theorem and_commutativity : p ∧ q ↔ q ∧ p :=
sorry
theorem demorgans_law : ¬(p ∨ q) ↔ ¬p ∧ ¬q :=
sorry
theorem contraposition : (p → q) → (¬q → ¬p) :=
sorry
end part1
-- Required: chapters 1, 2, 3, 4.1
section part2
variables... |
5e0f951d0cab0007da352bb2aeff51715eb70d65 | 6ae186a0c6ab366b39397ec9250541c9d5aeb023 | /src/category_theory/rel.lean | 7db7c9da29275f7a4dedcdc5569d4ab515a5a1e2 | [] | no_license | ThanhPhamPhuong/lean-category-theory | 0d5c4fe1137866b4fe29ec2753d99aa0d0667881 | 968a29fe7c0b20e10d8a27e120aca8ddc184e1ea | refs/heads/master | 1,587,206,682,489 | 1,544,045,056,000 | 1,544,045,056,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 249 | lean | import category_theory.category
namespace category_theory
universe u
def Rel : large_category (Type u) :=
{ hom := λ X Y, X → Y → Prop,
id := λ X, λ x y, x = y,
comp := λ X Y Z f g x z, ∃ y, f x y ∧ g y z }
end category_theory |
accbf17bea42d615478527e11f31aacb2df3b016 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/nat/prime.lean | b716196530076295754bc7d4466ae6a1aad3785b | [
"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 | 38,039 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
import algebra.group_power
import data.list.sort
import data.nat.gcd
import data.nat.sqrt
import tactic.norm_num
import tacti... |
5ebe6046ca2a8b70ef78482ad154aa03a5515a63 | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/exists3.lean | 438f94f972ff7b48a0dc4bff5a616c49033b14a7 | [
"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 | 1,081 | lean | import Int.
variable P : Int -> Int -> Bool
set_opaque exists false.
theorem T1 (R1 : not (exists x y, P x y)) : forall x y, not (P x y) :=
fun a b,
not_not_elim (not_not_elim R1 a) b
axiom Ax : forall x, exists y, P x y
theorem T2 : exists x y, P x y :=
by_contradiction (fun R : not (exists x y, P x ... |
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