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75d4bbd1f0c9513e1e4fd9f47e80af74b86d1a65 | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /stage0/src/Init/Data/FloatArray/Basic.lean | 2c56cee764f5368a1c6b74c145ca2387e96b52e1 | [
"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 | 2,001 | lean | /-
Copyright (c) 2020 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.Array.Basic
import Init.Data.Float
import Init.Data.Option.Basic
universe u
structure FloatArray where
data : Array Float
attrib... |
691680b3114f98965e1dbbfc1a357b0a5865ebff | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/qpf/multivariate/constructions/const_auto.lean | 0c0d975b0e141431398365625b5fb70ea8582ab6 | [] | 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 | 2,463 | lean | /-
Copyright (c) 2020 Simon Hudon All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Simon Hudon
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.control.functor.multivariate
import Mathlib.data.qpf.multivariate.basic
import Mathlib.PostPort
un... |
9503c14d022da34d008ce814e66648b256ce91c7 | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /stage0/src/Lean/Meta/Tactic/ElimInfo.lean | 921485bdeaaefea242413f2b8a00eab2cd3a29c2 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | tobiasgrosser/lean4 | ce0fd9cca0feba1100656679bf41f0bffdbabb71 | ebdbdc10436a4d9d6b66acf78aae7a23f5bd073f | refs/heads/master | 1,673,103,412,948 | 1,664,930,501,000 | 1,664,930,501,000 | 186,870,185 | 0 | 0 | Apache-2.0 | 1,665,129,237,000 | 1,557,939,901,000 | Lean | UTF-8 | Lean | false | false | 6,847 | 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.Basic
import Lean.Meta.Check
import Lean.ScopedEnvExtension
namespace Lean.Meta
structure ElimAltInfo where
name : Name
declName... |
ef76eaae730e2c6abbc1ff37a3c1465cb54bf5f0 | 54d7e71c3616d331b2ec3845d31deb08f3ff1dea | /tests/lean/run/listex3.lean | bd66f785c5ee1af069df79ac3c2c2a449ab9fee2 | [
"Apache-2.0"
] | permissive | pachugupta/lean | 6f3305c4292288311cc4ab4550060b17d49ffb1d | 0d02136a09ac4cf27b5c88361750e38e1f485a1a | refs/heads/master | 1,611,110,653,606 | 1,493,130,117,000 | 1,493,167,649,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,362 | lean | universe variable u
constant in_tail {α : Type u} {a : α} (b : α) {l : list α} : a ∈ l → a ∈ b::l
constant in_head {α : Type u} (a : α) (l : list α) : a ∈ a::l
constant in_left {α : Type u} {a : α} {l : list α} (r : list α) : a ∈ l → a ∈ l ++ r
constant in_right {α : Type u} {a : α} (l : l... |
35217562dea344fdff2e94d7000fb24f8e2ffc0d | b147e1312077cdcfea8e6756207b3fa538982e12 | /order/galois_connection.lean | dd523dc94ebe70245fe72846a6a593876929a149 | [
"Apache-2.0"
] | permissive | SzJS/mathlib | 07836ee708ca27cd18347e1e11ce7dd5afb3e926 | 23a5591fca0d43ee5d49d89f6f0ee07a24a6ca29 | refs/heads/master | 1,584,980,332,064 | 1,532,063,841,000 | 1,532,063,841,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,799 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
Galois connections - order theoretic adjoints.
-/
import order.bounds
open function set lattice
universes u v w x
variables {α : Type u} {β : Type v} {γ : Type w} {ι : ... |
2228c674c1ceecf94c2c5b10f29afb7cad8168e9 | fe25de614feb5587799621c41487aaee0d083b08 | /stage0/src/Lean/Meta/SynthInstance.lean | c983ab7ec84a0798a34d15439137b0bd1f9e0bac | [
"Apache-2.0"
] | permissive | pollend/lean4 | e8469c2f5fb8779b773618c3267883cf21fb9fac | c913886938c4b3b83238a3f99673c6c5a9cec270 | refs/heads/master | 1,687,973,251,481 | 1,628,039,739,000 | 1,628,039,739,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 27,576 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Selsam, Leonardo de Moura
Type class instance synthesizer using tabled resolution.
-/
import Lean.Meta.Basic
import Lean.Meta.Instances
import Lean.Meta.LevelDefEq
impor... |
447457e5426dcdbb653fcdd2d2c77213a50e9ea0 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/linear_algebra/matrix/nonsingular_inverse.lean | 66b7ddd6cdcaabef3a28cebfe446eb9317087d93 | [
"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 | 26,157 | lean | /-
Copyright (c) 2019 Tim Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tim Baanen, Lu-Ming Zhang
-/
import linear_algebra.matrix.adjugate
/-!
# Nonsingular inverses
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a correspondin... |
8bd509b1febbf9094130cda7013cee76384a9da7 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/abstract_zeta.lean | e019ccf0359a80d0c8c73c2be9605706f0473f0e | [
"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 | 482 | lean | -- The type of h depends on the zeta-expansion of n. When we abstract the
-- subterm proving `n < 5`, we need to zeta-expand n not just in the subterm,
-- but also in the local context.
noncomputable
lemma bug₁ : fin 5 :=
let n : ℕ := 3 in
have h : n < 5, from dec_trivial,
⟨n, by abstract { exact h }⟩
def bug₂ : fin... |
16f78abba276137e66ad2f0bac39f99d2d5ba3ba | b2fe74b11b57d362c13326bc5651244f111fa6f4 | /src/algebra/category/Group/Z_Module_equivalence.lean | ee61e41d4e542c2a449552c62b3b1472044c4ede | [
"Apache-2.0"
] | permissive | midfield/mathlib | c4db5fa898b5ac8f2f80ae0d00c95eb6f745f4c7 | 775edc615ecec631d65b6180dbcc7bc26c3abc26 | refs/heads/master | 1,675,330,551,921 | 1,608,304,514,000 | 1,608,304,514,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,337 | 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 algebra.category.Module.basic
/-!
The forgetful functor from ℤ-modules to additive commutative groups is
an equivalence of categories.
TODO:
either use this ... |
74324eaa9e0a4fc76f52fe5f19a7457cab32c6fe | 6b10c15e653d49d146378acda9f3692e9b5b1950 | /examples/logic/unnamed_427.lean | 53be96229b58236ba613aca13929efc7c1cb3b15 | [] | no_license | gebner/mathematics_in_lean | 3cf7f18767208ea6c3307ec3a67c7ac266d8514d | 6d1462bba46d66a9b948fc1aef2714fd265cde0b | refs/heads/master | 1,655,301,945,565 | 1,588,697,505,000 | 1,588,697,505,000 | 261,523,603 | 0 | 0 | null | 1,588,695,611,000 | 1,588,695,610,000 | null | UTF-8 | Lean | false | false | 349 | lean | variables A B C : Prop
-- BEGIN
theorem impl_compose : (A → B) → (B → C) → A → C :=
λ h₁ h₂ h₃, h₂ (h₁ h₃)
example : (A → B) → ¬ B → ¬ A :=
by apply impl_compose
example : (A → B) → ¬ B → ¬ A :=
impl_compose A B false
example (h₁ : A → B) (h₂ : ¬ B) : ¬ A :=
impl_compose A B false h₁ h₂
-- END |
7aa5aa04839c563b2dff1806682d48d01a56a248 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/data/set/pointwise.lean | a10504bc3d005a1c4ff90bd837174a10f3d13cfe | [
"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 | 73,080 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Floris van Doorn
-/
import algebra.module.basic
import data.fin.tuple.basic
import group_theory.submonoid.basic
import order.well_founded_set
/-!
# Pointwise operation... |
76d0c483d782e70d5ea8259808e7a5c0a4b38a5e | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/continued_fractions/convergents_equiv.lean | 1018b2c393850f017b723906a86e27e993d488b5 | [
"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 | 19,493 | lean | /-
Copyright (c) 2020 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import algebra.continued_fractions.continuants_recurrence
import algebra.continued_fractions.terminated_stable
import tactic.field_simp
import tactic.ring
/-!
# ... |
f9a0a2ec275ebee464dba8eb1eb10f4b463cc706 | 367134ba5a65885e863bdc4507601606690974c1 | /src/category_theory/limits/creates.lean | 84c20ec4e0789ed7b8d94e731785373578b684d0 | [
"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 | 21,574 | 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.preserves.basic
open category_theory category_theory.limits
noncomputable theory
namespace category_theory
universes v u₁ u₂ u₃
variabl... |
7272a0347d90654ab8252cd61ecb97fbb9945069 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/data/rel.lean | 8204025ede594182275ead2e7b1e52712073f5c5 | [
"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 | 7,467 | lean | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
import data.set.lattice
/-!
# Relations
This file defines bundled relations. A relation between `α` and `β` is a function `α → β → Prop`.
Relations are also known as ... |
dea83c5e767a7ba59609ea92ba28bebd6235c881 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/geometry/manifold/charted_space.lean | 9e7705a5ed866999ab86eab9e6eae6bed1d431f0 | [
"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 | 49,389 | 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 topology.local_homeomorph
/-!
# Charted spaces
A smooth manifold is a topological space `M` locally modelled on a euclidean space (or a euclidean
half-... |
8b0a989f9706ef0d2d20163da5156522d251a17a | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/magical.lean | 81f707fec18ebc9aeae1ec51e05d391d887b6510 | [
"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 | 258 | lean | -- Projection to the witness should be rejected.
def witness : Nat := (⟨1, Nat.le_refl _⟩ : ∃ x, x ≥ 1).1
-- Projection to the property as well (it could contain the witness projection).
theorem witness_eq (h : ∃ x : Nat, True) : h.2 = h.2 := rfl
|
211a158d43779903431cd03b0ec4d06081dca568 | f3849be5d845a1cb97680f0bbbe03b85518312f0 | /tests/lean/run/wfrec1.lean | e0f8daa7fdc8478c55fc9623aba084e203c9e184 | [
"Apache-2.0"
] | permissive | bjoeris/lean | 0ed95125d762b17bfcb54dad1f9721f953f92eeb | 4e496b78d5e73545fa4f9a807155113d8e6b0561 | refs/heads/master | 1,611,251,218,281 | 1,495,337,658,000 | 1,495,337,658,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 605 | lean | private def S := Σ a : nat, nat
private def R : S → S → Prop := sigma.skip_left nat (<)
private def Rwf : well_founded R :=
sigma.skip_left_wf nat nat.lt_wf
private def f_aux : ∀ (p₁ : S), (∀ p₂ : S, R p₂ p₁ → nat) → nat
| ⟨n, m+1⟩ F := F ⟨n+10, m - n⟩ (sigma.mk_skip_left _ _ (nat.sub_lt_succ _ _))
| ⟨n, 0⟩ F := n... |
1f2d7bf99ac32233b10693641c36e67298c21cef | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/declare_axiom.lean | f34574e6cba4f356e6e60de248b09d215199cc7c | [
"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 | 105 | lean | open tactic
run_cmd (do
e ← to_expr ``(false),
add_decl $ declaration.ax `useful_assumption [] e)
|
af6771423ca01778bc39682181307269654e0a73 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /test/library_search/filter.lean | 903c8f5d05b33e5d11fd4473718877bbf50da326 | [
"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 | 1,096 | lean | import order.filter.basic
open filter
/- Turn off trace messages so they don't pollute the test build: -/
set_option trace.silence_library_search true
example {α β γ : Type*} {A : filter α} {B : filter β} {C : filter γ} {f : α → β} {g : β → γ}
(hf : tendsto f A B) (hg : tendsto g B C) : map (g ∘ f) A = map g (map ... |
89ba4c9319209c70cd74d673c72ae18d6e8d7873 | cc060cf567f81c404a13ee79bf21f2e720fa6db0 | /lean/20170325-eq.rec.lean | 4ad3e211a3a734ac2b27f1a5b5c66b2022c0da16 | [
"Apache-2.0"
] | permissive | semorrison/proof | cf0a8c6957153bdb206fd5d5a762a75958a82bca | 5ee398aa239a379a431190edbb6022b1a0aa2c70 | refs/heads/master | 1,610,414,502,842 | 1,518,696,851,000 | 1,518,696,851,000 | 78,375,937 | 2 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 1,018 | lean | lemma foo { α : Type } ( a b : α ) ( h : a = b ): (eq.rec (eq.refl a) h) = eq.refl b := begin
end
-- set_option pp.all true
#check eq.rec
#check prod.rec
-- eq.rec (thing : type) (p : type = type')
-- (eq.rec (C^.identity (tensor^.onObjects (tensor^.onObjects (Y^.fst), Y^.snd)))
-- (id_locked
-- (... |
107beb2f6d4f8a275ad0f9182917f1591f1c6340 | da3a76c514d38801bae19e8a9e496dc31f8e5866 | /library/init/meta/environment.lean | 733812ab51548cb1826fa6b42f1a129decb46b71 | [
"Apache-2.0"
] | permissive | cipher1024/lean | 270c1ac5781e6aee12f5c8d720d267563a164beb | f5cbdff8932dd30c6dd8eec68f3059393b4f8b3a | refs/heads/master | 1,611,223,459,029 | 1,487,566,573,000 | 1,487,566,573,000 | 83,356,543 | 0 | 0 | null | 1,488,229,336,000 | 1,488,229,336,000 | null | UTF-8 | Lean | false | false | 5,452 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.meta.declaration init.meta.exceptional init.data.option.basic
meta constant environment : Type
namespace environment
/--
Information f... |
5e290e434d32b274787a5c177b591a9b47254a8d | f5f7e6fae601a5fe3cac7cc3ed353ed781d62419 | /src/category_theory/core.lean | 46f815537e143808cc3aeb2c023efbef819fab36 | [
"Apache-2.0"
] | permissive | EdAyers/mathlib | 9ecfb2f14bd6caad748b64c9c131befbff0fb4e0 | ca5d4c1f16f9c451cf7170b10105d0051db79e1b | refs/heads/master | 1,626,189,395,845 | 1,555,284,396,000 | 1,555,284,396,000 | 144,004,030 | 0 | 0 | Apache-2.0 | 1,533,727,664,000 | 1,533,727,663,000 | null | UTF-8 | Lean | false | false | 1,581 | lean | /-
Copyright (c) 2019 Scott Morrison All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
The core of a category C is the groupoid whose morphisms are all the
isomorphisms of C.
-/
import category_theory.groupoid
import category_theory.equivalence
import cat... |
49706a69322a189e611046ba291b57b86841152b | 80746c6dba6a866de5431094bf9f8f841b043d77 | /src/data/equiv/basic.lean | c8eed852bd74498981d49b0a0897efb912d6a2ff | [
"Apache-2.0"
] | permissive | leanprover-fork/mathlib-backup | 8b5c95c535b148fca858f7e8db75a76252e32987 | 0eb9db6a1a8a605f0cf9e33873d0450f9f0ae9b0 | refs/heads/master | 1,585,156,056,139 | 1,548,864,430,000 | 1,548,864,438,000 | 143,964,213 | 0 | 0 | Apache-2.0 | 1,550,795,966,000 | 1,533,705,322,000 | Lean | UTF-8 | Lean | false | false | 31,584 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Mario Carneiro
In the standard library we cannot assume the univalence axiom.
We say two types are equivalent if they are isomorphic.
Two equivalent types h... |
e6a3762220251b992f7153e5a723709938d51e42 | a721fe7446524f18ba361625fc01033d9c8b7a78 | /src/principia/mylist/map.lean | 06c4aa189f285350baf5b5136612f7efa2ed99c4 | [] | no_license | Sterrs/leaning | 8fd80d1f0a6117a220bb2e57ece639b9a63deadc | 3901cc953694b33adda86cb88ca30ba99594db31 | refs/heads/master | 1,627,023,822,744 | 1,616,515,221,000 | 1,616,515,221,000 | 245,512,190 | 2 | 0 | null | 1,616,429,050,000 | 1,583,527,118,000 | Lean | UTF-8 | Lean | false | false | 18,584 | lean | import .mylist
import .sorting
namespace hidden
namespace mylist
open mynat
universes u v
variables {T: Sort v} {T2: Sort u}
variables {T3: Type u} {T4: Type v}
variables {m n k: mynat}
variables {lst lst1 lst2: mylist T}
variables {lst' lst1' lst2': mylist T2}
-- classic map function
def map (f: T → T2): mylist T ... |
835371a8b8e87ac097584122a3270561bcb8b12f | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/algebra/opposites.lean | b9d39acbea52363fbfea4a825583263ede997775 | [
"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 | 8,447 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import algebra.group.defs
import data.equiv.basic
import logic.nontrivial
/-!
# Multiplicative opposite and algebraic operations on it
In this file we define `mul_opposite α ... |
7cafb28f69b5faf27be82deb1a5d45570dc99b77 | 1f6fe2f89976b14a4567ab298c35792b21f2e50b | /algebra/arrow_group.hlean | 3db123c6c89a81ca3d78774d5d3c104775c04825 | [
"Apache-2.0"
] | permissive | jonas-frey/Spectral | e5c1c2f7bcac26aa55f7b1e041a81272a146198d | 72d521091525a4bc9a31cac859840efe9461cf66 | refs/heads/master | 1,610,235,743,345 | 1,505,417,795,000 | 1,505,417,795,000 | 102,653,342 | 0 | 0 | null | 1,504,728,483,000 | 1,504,728,483,000 | null | UTF-8 | Lean | false | false | 12,204 | hlean | /-
Copyright (c) 2016-2017 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Ulrik Buchholtz
Various groups of maps. Most importantly we define a group structure
on trunc 0 (A →* Ω B) and the dependent version trunc 0 (ppi _ _),
which ... |
799c8aabbbc7b2e8545d36c86f7295d6b9acea32 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebraic_geometry/presheafed_space/has_colimits_auto.lean | d9ec371dbb1629be8a0f632bac75b7fc0d221549 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,077 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebraic_geometry.presheafed_space
import Mathlib.topology.category.Top.limits
import Math... |
5b11a32db1c77738779d2d60ed7194fed6e8b027 | c8b4b578b2fe61d500fbca7480e506f6603ea698 | /src/norm/norm_prime.lean | da2a1b1a56884708ca572a1b2d05a9d089e54718 | [] | no_license | leanprover-community/flt-regular | aa7e564f2679dfd2e86015a5a9674a6e1197f7cc | 67fb3e176584bbc03616c221a7be6fa28c5ccd32 | refs/heads/master | 1,692,188,905,751 | 1,691,766,312,000 | 1,691,766,312,000 | 421,021,216 | 19 | 4 | null | 1,694,532,115,000 | 1,635,166,136,000 | Lean | UTF-8 | Lean | false | false | 4,221 | lean | import linear_algebra.smodeq
import number_theory.number_field.norm
open_locale number_field
open ring_of_integers ideal finset nat finite_dimensional
variables {K : Type*} [field K] (pb : power_basis ℤ (𝓞 K))
local notation `R` := 𝓞 K
lemma exists_int_smodeq (x : R) : ∃ (n : ℤ), smodeq (span ({pb.gen} : set R))... |
2b925b86a4942c40df1f4040921d3c195ed46a0f | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/category_theory/limits/functor_category.lean | 506d907900d46092a49a07895d9e5227c5b273f0 | [
"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 | 10,548 | 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.limits.preserves.limits
open category_theory category_theory.category
namespace category_theory.limits
universes v v₂ u -- morphism levels b... |
84e6b268571c0b284224d61b5c0dcc4e76efa668 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/monoid_algebra/basic.lean | f66f0c170473e2abbf825daf1751e64492d50892 | [
"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 | 66,626 | 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 G. Kudryashov, Scott Morrison
-/
import algebra.big_operators.finsupp
import algebra.hom.non_unital_alg
import linear_algebra.finsupp
/-!
# Monoid algebras
When ... |
1f628f45aeccd49d9f2bfb8ef4d4a9654f723b32 | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/category_theory/instances/Top/opens.lean | ef59a5590fbc2b3f78ef15b0c5930de8e6675279 | [
"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 | 3,504 | lean | import category_theory.instances.Top.basic
import category_theory.natural_isomorphism
import category_theory.opposites
import category_theory.eq_to_hom
import topology.opens
open category_theory
open category_theory.instances
open topological_space
universe u
open category_theory.instances
namespace topological_spa... |
4cffdf16b881dc3dfe08481c68dbc115cc48def9 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /tests/lean/local_notation_bug2.lean | 7ce70798a72ca163bbdc1a518facc6002a68dcbb | [
"Apache-2.0"
] | permissive | davidmueller13/lean | 65a3ed141b4088cd0a268e4de80eb6778b21a0e9 | c626e2e3c6f3771e07c32e82ee5b9e030de5b050 | refs/heads/master | 1,611,278,313,401 | 1,444,021,177,000 | 1,444,021,177,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 144 | lean | open nat
section
parameters (b : ℕ)
definition add_b (n : ℕ) := n + b
local postfix `%`:max := add_b
end
eval 5% -- Error, unexpected token
|
9329930b9819d543295040af86edbcda27f9cdff | ee8cdbabf07f77e7be63a449b8483ce308d37218 | /lean/src/test/algebra-others-exirrpowirrrat.lean | 6727520627057448de323c813c3751959a8fff68 | [
"MIT",
"Apache-2.0"
] | permissive | zeta1999/miniF2F | 6d66c75d1c18152e224d07d5eed57624f731d4b7 | c1ba9629559c5273c92ec226894baa0c1ce27861 | refs/heads/main | 1,681,897,460,642 | 1,620,646,361,000 | 1,620,646,361,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 330 | lean | /-
Copyright (c) 2021 OpenAI. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kunhao Zheng
-/
import data.real.irrational
import data.real.basic
import analysis.special_functions.pow
example : ∃ a b, irrational a ∧ irrational b ∧ ¬ irrational (a ^ b) :=
begin
sorry
e... |
5b579b7eeb56b310191b0edc33cf0087584ec796 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/order/prime_ideal.lean | 847b5b305ae68497302fa5851eb03fc2779a61eb | [
"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 | 6,213 | lean | /-
Copyright (c) 2021 Noam Atar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Noam Atar
-/
import order.ideal
import order.pfilter
/-!
# Prime ideals
## Main definitions
Throughout this file, `P` is at least a preorder, but some sections require more
structure, su... |
e0b42910a31b521ccde4c05bb467b5a97fdf0d82 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/ring_theory/unique_factorization_domain.lean | 95d23ef4a22df05d978c19ade8f4aabcd8362dae | [
"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 | 69,920 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker, Aaron Anderson
-/
import algebra.big_operators.associated
import algebra.gcd_monoid.basic
import data.finsupp.multiset
import ring_theory.noetherian
im... |
3ab173a8dc30b7030c89a31ce5c7c387e69166d8 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/limits/shapes/binary_products.lean | 016568840f3e6f39f04350fcb29c381b6361d879 | [] | 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 | 42,845 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Bhavik Mehta
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.limits.limits
import Mathlib.category_theory.limits.shapes.te... |
7f8bc1c2fd930b23ba3454fc37791496f436a0a6 | 271e26e338b0c14544a889c31c30b39c989f2e0f | /stage0/src/Init/Lean/Parser/Command.lean | 772561efc05aa9bded10cadedabb4c9b66974255 | [
"Apache-2.0"
] | permissive | dgorokho/lean4 | 805f99b0b60c545b64ac34ab8237a8504f89d7d4 | e949a052bad59b1c7b54a82d24d516a656487d8a | refs/heads/master | 1,607,061,363,851 | 1,578,006,086,000 | 1,578,006,086,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,184 | 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.Term
namespace Lean
namespace Parser
@[init mkBuiltinParsingTablesRef]
constant builtinCommandParsingTa... |
b26894d4277e284d14dfdc45fb70f5c8b07b3cb0 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebraic_topology/dold_kan/compatibility.lean | 516e38ecaf374ea8b66ce3d74c90142a8c004838 | [
"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 | 12,180 | lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import category_theory.equivalence
/-!
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
Tools for compatibilitie... |
c5fbf82757ce9b1a1cdbd46805abd6f5a8ce2e73 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/analysis/convex/body.lean | 7fa9402b26c89129878edeba68f1411a8d00f534 | [
"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 | 3,793 | lean | /-
Copyright (c) 2022 Paul A. Reichert. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul A. Reichert
-/
import analysis.convex.basic
import analysis.normed_space.basic
import data.real.nnreal
import data.set.pointwise.basic
import topology.subset_properties
/-!
# c... |
4995f8e9b087c95824b9027edfd6eadb7f5f38e6 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/char_p/two.lean | 639cc2e8cbc8787969c913992174556f7c8c3e78 | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 3,226 | 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.char_p.basic
/-!
# Lemmas about rings of characteristic two
This file contains results about `char_p R 2`, in the `char_two` namespace.
The lemmas in this... |
1339a1dac3b90c12fa4f9ca49611711ac5b7bc49 | 4950bf76e5ae40ba9f8491647d0b6f228ddce173 | /src/field_theory/minimal_polynomial.lean | c4de39d9629263b7197701207b882a5d00b07f45 | [
"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 | 14,236 | lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johan Commelin
-/
import ring_theory.integral_closure
import data.polynomial.field_division
import ring_theory.polynomial.gauss_lemma
/-!
# Minimal polynomials
This file ... |
cdfc191778c1d6009dad74eac3ee03cf2c6007e4 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /hott/homotopy/circle.hlean | bf2f6825d3323c5822e4675bb1529e7dc459cbc8 | [
"Apache-2.0"
] | permissive | davidmueller13/lean | 65a3ed141b4088cd0a268e4de80eb6778b21a0e9 | c626e2e3c6f3771e07c32e82ee5b9e030de5b050 | refs/heads/master | 1,611,278,313,401 | 1,444,021,177,000 | 1,444,021,177,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,947 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
Declaration of the circle
-/
import .sphere
import types.bool types.int.hott types.equiv
import algebra.fundamental_group algebra.hott
open eq susp bool sphere_in... |
6357ffeaad5d43ed43f8c6941d52f5af4c8a6e77 | 8c02fed42525b65813b55c064afe2484758d6d09 | /src/spec/lemmas.lean | 3d8beece77821a392cbb522eff20b3401114b1b4 | [
"LicenseRef-scancode-generic-cla",
"MIT"
] | permissive | microsoft/AliveInLean | 3eac351a34154efedd3ffc4fe2fa4ec01b219e0d | 4b739dd6e4266b26a045613849df221374119871 | refs/heads/master | 1,691,419,737,939 | 1,689,365,567,000 | 1,689,365,568,000 | 131,156,103 | 23 | 18 | NOASSERTION | 1,660,342,040,000 | 1,524,747,538,000 | Lean | UTF-8 | Lean | false | false | 19,954 | lean | -- Copyright (c) Microsoft Corporation. All rights reserved.
-- Licensed under the MIT license.
import ..smtexpr
import ..smtcompile
import ..bitvector
import .spec
import .lemmas_basic
import tactic.interactive
namespace spec
open smt
open irsem
open spec
-- unfold
meta def unfold_ops: tactic unit :=
`[ try { u... |
1eff14ee491ba2fa869616b21171842b90bf62c4 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/try_for1.lean | d78f076f8fac98c1b2d4c778416860968798bf37 | [
"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 | 390 | lean | meta def f : nat → nat
| n := f (n + 1)
#eval try_for 100 (f 10)
#eval try_for 1000 (f 10)
meta def mk : nat → list nat
| 0 := []
| (n+1) := n :: mk n
example : true :=
begin
tactic.fail_if_success (guard(to_bool (try_for 1 ((mk 1000)^.length) = some 1000))),
constructor
end
example : true :=
begin
guard... |
69eb6da5d720eeb4ac77a1af2c8b67c844fc52c7 | cc060cf567f81c404a13ee79bf21f2e720fa6db0 | /lean/weird-class-typesignature.lean | 45697fc24e0b4350a7f5185a262a6fb833a787d5 | [
"Apache-2.0"
] | permissive | semorrison/proof | cf0a8c6957153bdb206fd5d5a762a75958a82bca | 5ee398aa239a379a431190edbb6022b1a0aa2c70 | refs/heads/master | 1,610,414,502,842 | 1,518,696,851,000 | 1,518,696,851,000 | 78,375,937 | 2 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 643 | lean | set_option pp.implicit true
class foo {A : Type} :=
(bar : A)
(baz : A → A)
print foo
-- attribute [class]
-- structure foo : Π {A : Type}, Type
-- fields:
-- foo.bar : (A : Type) [c : @foo A], A
-- foo.baz : {A : Type} [c : @foo A], A → A
-- I guess the issue here is that since the field baz is a function
-- A ... |
36203dcc65ee3a472308ed95e1eb2feb87a879a6 | 88fb7558b0636ec6b181f2a548ac11ad3919f8a5 | /tests/lean/run/unfold_issue.lean | dcd86ef6e19f929618437ea9832abed1c685691e | [
"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 | 303 | lean | def f : nat → nat → nat
| 0 := λ x, x
| (n+1) := λ x, x + 1
meta def check_expr (p : pexpr) (t : expr) : tactic unit :=
do e ← tactic.to_expr p, guard (t = e)
example (n : nat): f (n+1) n = n + 1 :=
begin
unfold f,
(tactic.target >>= check_expr `((n + 1 = n + 1))),
reflexivity,
end
|
28947d36725ffb5d026f8168d71665d70eedb903 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /counterexamples/canonically_ordered_comm_semiring_two_mul.lean | b170384f1731ab1868d796e8f20acaecf4135129 | [
"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 | 9,499 | lean | /-
Copyright (c) 2021 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import data.zmod.basic
import ring_theory.subsemiring.basic
import algebra.order.monoid
/-!
A `canonically_ordered_comm_semiring` with two different elements `a` and `... |
0e617973ed80173a22b301414bd0c0c2e4306b7c | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/order/omega_complete_partial_order.lean | b69173f783ef566b186f24654d936c9b5ba2deb4 | [
"Apache-2.0"
] | permissive | lacker/mathlib | f2439c743c4f8eb413ec589430c82d0f73b2d539 | ddf7563ac69d42cfa4a1bfe41db1fed521bd795f | refs/heads/master | 1,671,948,326,773 | 1,601,479,268,000 | 1,601,479,268,000 | 298,686,743 | 0 | 0 | Apache-2.0 | 1,601,070,794,000 | 1,601,070,794,000 | null | UTF-8 | Lean | false | false | 29,984 | lean | /-
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Simon Hudon
-/
import data.pfun
import order.preorder_hom
import tactic.wlog
import tactic.monotonicity
/-!
# Omega Complete Partial Orders
An omega-complete partial order is a partial o... |
97355dd1e77eff89fc2b6510e8490d50f0a19a45 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/algebraic_geometry/prime_spectrum/basic.lean | ad98e61dcd8fd2a1d64615dbc0a0fb24e6712e12 | [
"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 | 36,410 | 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.punit_instances
import linear_algebra.finsupp
import ring_theory.ideal.over
import ring_theory.ideal.prod
import ring_theory.localization.away
import r... |
ef465072a9b05b123106c929ad635a2b13ea84c4 | 77c5b91fae1b966ddd1db969ba37b6f0e4901e88 | /src/order/complete_lattice.lean | 8454623943d8094b3313b308cfbd4d7458ac5f07 | [
"Apache-2.0"
] | permissive | dexmagic/mathlib | ff48eefc56e2412429b31d4fddd41a976eb287ce | 7a5d15a955a92a90e1d398b2281916b9c41270b2 | refs/heads/master | 1,693,481,322,046 | 1,633,360,193,000 | 1,633,360,193,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 53,216 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import order.bounds
import data.set.bool
/-!
# Theory of complete lattices
## Main definitions
* `Sup` and `Inf` are the supremum and the infimum of a set;
* `supr... |
f8dd015b87d8e253e581f978c2dbc769f4c77b7c | aa2345b30d710f7e75f13157a35845ee6d48c017 | /data/complex/exponential.lean | ee4488f1fb334291869829bd08ae40ae19951236 | [
"Apache-2.0"
] | permissive | CohenCyril/mathlib | 5241b20a3fd0ac0133e48e618a5fb7761ca7dcbe | a12d5a192f5923016752f638d19fc1a51610f163 | refs/heads/master | 1,586,031,957,957 | 1,541,432,824,000 | 1,541,432,824,000 | 156,246,337 | 0 | 0 | Apache-2.0 | 1,541,434,514,000 | 1,541,434,513,000 | null | UTF-8 | Lean | false | false | 46,510 | 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 algebra.archimedean
import data.nat.choose data.complex.basic
import tactic.linarith
local attribute [instance, priority 0] classical.prop_decidable
loc... |
4fd51e9b28e1b72791d9fa2a42f16832f469c86f | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/real/cau_seq.lean | 3df09cc742b4e9216f75adaf0769c76c56c4219c | [
"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 | 23,619 | 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 algebra.order.absolute_value
import algebra.big_operators.order
/-!
# Cauchy sequences
A basic theory of Cauchy sequences, used in the construction of the re... |
0df690831f43e4dee7c9761f3aea3e58e67da410 | 649957717d58c43b5d8d200da34bf374293fe739 | /src/category_theory/sparse.lean | 2e3fc0ba931d7b48db016073951bc3c22cc3bc99 | [
"Apache-2.0"
] | permissive | Vtec234/mathlib | b50c7b21edea438df7497e5ed6a45f61527f0370 | fb1848bbbfce46152f58e219dc0712f3289d2b20 | refs/heads/master | 1,592,463,095,113 | 1,562,737,749,000 | 1,562,737,749,000 | 196,202,858 | 0 | 0 | Apache-2.0 | 1,562,762,338,000 | 1,562,762,337,000 | null | UTF-8 | Lean | false | false | 304 | lean | import category_theory.category
universes u v
namespace category_theory
variables {C : Type u} [category_struct.{v} C]
-- This doesn't work well as an instance; use it to construct specific cases.
def sparse_category [∀ X Y : C, subsingleton (X ⟶ Y)] : category.{v} C := { }
end category_theory
|
0508350cd06ec099a90a28710c628db30a502301 | efce24474b28579aba3272fdb77177dc2b11d7aa | /src/category_theory/base.lean | edfd580e479f638fde0fbf40be0a6e552bbd6348 | [
"Apache-2.0"
] | permissive | rwbarton/lean-homotopy-theory | cff499f24268d60e1c546e7c86c33f58c62888ed | 39e1b4ea1ed1b0eca2f68bc64162dde6a6396dee | refs/heads/lean-3.4.2 | 1,622,711,883,224 | 1,598,550,958,000 | 1,598,550,958,000 | 136,023,667 | 12 | 6 | Apache-2.0 | 1,573,187,573,000 | 1,528,116,262,000 | Lean | UTF-8 | Lean | false | false | 418 | lean | --- Project-wide declarations related to category theory.
import category_theory.functor
import tactic.tidy
-- Set up `tidy` as the tactic to be invoked by `obviously`.
@[obviously] meta def tidy_1 := tactic.tidy -- TODO: can we just delete this?
-- TODO: Notation for composition of functors, etc.?
-- TODO: Transit... |
bb0649d15d148eeb5f1de6ada027da3ac40e8749 | 969dbdfed67fda40a6f5a2b4f8c4a3c7dc01e0fb | /src/data/nat/basic.lean | 7d717a72c0601fd490bdc73f8b3be12f5cc6baac | [
"Apache-2.0"
] | permissive | SAAluthwela/mathlib | 62044349d72dd63983a8500214736aa7779634d3 | 83a4b8b990907291421de54a78988c024dc8a552 | refs/heads/master | 1,679,433,873,417 | 1,615,998,031,000 | 1,615,998,031,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 65,882 | lean | /-
Copyright (c) 2014 Floris van Doorn (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
import algebra.group_power.basic
import algebra.order_functions
import algebra.or... |
0d737c9bd0c9f43321d43b976a39ad08ee00e513 | 38bf3fd2bb651ab70511408fcf70e2029e2ba310 | /src/topology/continuous_on.lean | 9404712e29fc320854278d694493b5afdffb5b8f | [
"Apache-2.0"
] | permissive | JaredCorduan/mathlib | 130392594844f15dad65a9308c242551bae6cd2e | d5de80376088954d592a59326c14404f538050a1 | refs/heads/master | 1,595,862,206,333 | 1,570,816,457,000 | 1,570,816,457,000 | 209,134,499 | 0 | 0 | Apache-2.0 | 1,568,746,811,000 | 1,568,746,811,000 | null | UTF-8 | Lean | false | false | 18,656 | lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import topology.constructions
/-!
# Neighborhoods and continuity relative to a subset
This file defines relative versions
`nhds_within` of `nhds`
`contin... |
b4334d7080a9a5c00721bc9047991aace5897bba | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/generalizes.lean | 0bd726ac600228694a790249224f2fb7ebe34a73 | [
"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 | 159 | lean | import logic
theorem tst (A B : Type) (a : A) (b : B) : a == b → b == a :=
begin
generalizes [a, b, B],
intros [B', b, a, H],
apply (heq.symm H),
end
|
96ff902d3837e04df91ab491ff14f48f070bcca2 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/analysis/inner_product_space/conformal_linear_map.lean | e252ae03ccca70b5aabbc37c5127bb63111f39c8 | [
"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 | 1,829 | lean | /-
Copyright (c) 2021 Yourong Zang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yourong Zang
-/
import analysis.normed_space.conformal_linear_map
import analysis.inner_product_space.basic
/-!
# Conformal maps between inner product spaces
In an inner product space,... |
bce4c50561057d15ef7f5344ed1fa8de1d7b545a | ea11767c9c6a467c4b7710ec6f371c95cfc023fd | /src/monoidal_categories/monoidal_category.lean | bf6be5f5bc352818055737837bbc751aa85c0f5e | [] | 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 | 4,023 | 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 .tensor_product
open categories
open categories.functor
open categories.products
open categories.natural_transformation
namespace categori... |
c717bea5727da414ed65500f56f3b859bad9252d | 46125763b4dbf50619e8846a1371029346f4c3db | /src/linear_algebra/finsupp_vector_space.lean | b04cadbf0e792d5a720a7322be99b765ceb9080a | [
"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 | 6,508 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
Linear structures on function with finite support `ι →₀ β`.
-/
import data.finsupp data.mv_polynomial linear_algebra.dimension
noncomputable theory
local attribute [inst... |
c050ca51a0a1124f6561012e967cbc657a7ce66b | 94e33a31faa76775069b071adea97e86e218a8ee | /src/ring_theory/graded_algebra/radical.lean | f8935fb7c04cca3b791c945c23e41180ca12f945 | [
"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 | 8,841 | lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Eric Wieser
-/
import ring_theory.graded_algebra.homogeneous_ideal
/-!
This file contains a proof that the radical of any homogeneous ideal is a homogeneous ideal
## Ma... |
1e5fb03793c235b7ef57ae6a5fbfebedf49191b8 | 13133fade54057ee588bc056e4eaa14a24773d23 | /report/summation.lean | c9ab25b60adee459158ed4e57e5719bf486b8242 | [] | no_license | lkloh/lean-project-15815 | 444cbdca1d1a2dfa258c76c41a6ff846392e13d1 | 2cb657c0e41baa318193f7dce85974ff37d80883 | refs/heads/master | 1,611,402,038,933 | 1,432,020,760,000 | 1,432,020,760,000 | 33,372,120 | 0 | 0 | null | 1,431,932,928,000 | 1,428,078,840,000 | Lean | UTF-8 | Lean | false | false | 836 | lean |
import data.nat
open nat
-- ****************************************************************** --
definition summ : nat → nat
| summ 0 := 0
| summ(n+1) := summ(n) + (n+1)
eval summ 3
-- ****************************************************************** --
theorem two : 1+1 = 2 := rfl
theorem summ_form : ∀ n,... |
570f3a02929298f6ef344cb490255622a335c075 | 82b86ba2ae0d5aed0f01f49c46db5afec0eb2bd7 | /tests/lean/repr_issue.lean | 842373f442f52ac60c1679a0b24da8c8b31be67a | [
"Apache-2.0"
] | permissive | banksonian/lean4 | 3a2e6b0f1eb63aa56ff95b8d07b2f851072d54dc | 78da6b3aa2840693eea354a41e89fc5b212a5011 | refs/heads/master | 1,673,703,624,165 | 1,605,123,551,000 | 1,605,123,551,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 636 | lean |
def foo {m} [Monad m] [MonadExcept String m] [MonadState (Array Nat) m] : m Nat :=
tryCatch
(do modify $ fun (a : Array Nat) => a.set! 0 33;
throw "error")
(fun _ => do let a ← get; pure $ a.get! 0)
def ex₁ : StateT (Array Nat) (ExceptT String Id) Nat :=
foo
def ex₂ : ExceptT String (StateT (Array Nat) Id)... |
5ff87bb6a59c0cc20b472e8f961c475fb8fa7127 | b074a51e20fdb737b2d4c635dd292fc54685e010 | /src/algebra/direct_limit.lean | 2d223ef0dd1913269e003390fac8e30fbef8d0cc | [
"Apache-2.0"
] | permissive | minchaowu/mathlib | 2daf6ffdb5a56eeca403e894af88bcaaf65aec5e | 879da1cf04c2baa9eaa7bd2472100bc0335e5c73 | refs/heads/master | 1,609,628,676,768 | 1,564,310,105,000 | 1,564,310,105,000 | 99,461,307 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 25,098 | lean | /-
Copyright (c) 2019 Kenny Lau, Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Chris Hughes
Direct limit of modules, abelian groups, rings, and fields.
See Atiyah-Macdonald PP.32-33, Matsumura PP.269-270
Generalizes the notion of "union", o... |
4b9596ab94e275afb53e2ee59ab981c4e1f78cd6 | bf532e3e865883a676110e756f800e0ddeb465be | /order/fixed_points.lean | 27cf3087cca5f6e8c4f5fc751d71580fbe5e3725 | [
"Apache-2.0"
] | permissive | aqjune/mathlib | da42a97d9e6670d2efaa7d2aa53ed3585dafc289 | f7977ff5a6bcf7e5c54eec908364ceb40dafc795 | refs/heads/master | 1,631,213,225,595 | 1,521,089,840,000 | 1,521,089,840,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,583 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Fixed point construction on complete lattices.
-/
import order.complete_lattice
universes u v w
variables {α : Type u} {β : Type v} {γ : Type w}
theorem ge_of_eq [pr... |
8cf5a599ce63a9910898a8f963708e971e7f8fce | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/apply2.lean | 13c891827afbb4eeb78f80b3b1568e661aaf1aea | [
"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 | 184 | lean | open tactic
example (p q : Prop) : p → q → p ∧ q ∧ p :=
by do
intros,
c₁ ← return (expr.const `and.intro []),
iterate_at_most 10 (apply c₁ >> skip <|> assumption)
|
ddb89e1819a7bf57949f34db35a9b55e29e32dcb | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/model_theory/graph.lean | f95115deb3c5f622919a77b0b7045f1e3555171f | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 3,811 | lean | /-
Copyright (c) 2022 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import model_theory.satisfiability
import combinatorics.simple_graph.basic
/-!
# First-Ordered Structures in Graph Theory
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.... |
cc57829af7a6d565c325523ab7f09a5e617f320a | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /tests/lean/run/patbug.lean | d5cf82d734f1925ec8d01e07ec47b90bdb0af6da | [
"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 | 201 | lean | open Lean
def f : Name → Name
| n@(`foo.bla) => n
| _ => Name.anonymous
def tst : IO Unit := do
when (hash `foo.bla != hash (f `foo.bla)) $
throw $ IO.userError "bug";
IO.println "ok"
#eval tst
|
eeb790b7064b38cfb3879c48dd86dcc470414a95 | 618003631150032a5676f229d13a079ac875ff77 | /src/data/int/parity.lean | a9e046cb74674f6939b6002851af4ca996dd5a50 | [
"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 | 3,188 | lean | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
The `even` predicate on the integers.
-/
import data.int.modeq
import data.nat.parity
namespace int
@[simp] theorem mod_two_ne_one {n : int} : ¬ n % 2 = 1 ↔ n % 2 = 0 :... |
796418067981d6f6c9ee0d6bd114639ed47f6128 | 8eeb99d0fdf8125f5d39a0ce8631653f588ee817 | /src/geometry/euclidean/basic.lean | 93a938100c22263f1e8e69e456407092ad648c49 | [
"Apache-2.0"
] | permissive | jesse-michael-han/mathlib | a15c58378846011b003669354cbab7062b893cfe | fa6312e4dc971985e6b7708d99a5bc3062485c89 | refs/heads/master | 1,625,200,760,912 | 1,602,081,753,000 | 1,602,081,753,000 | 181,787,230 | 0 | 0 | null | 1,555,460,682,000 | 1,555,460,682,000 | null | UTF-8 | Lean | false | false | 48,486 | 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... |
4a5136c17b85496302525d06cc6eeea35e4bf4e8 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/data/matrix/block.lean | c5df48206bb56ebd81b5f6c83be9f0f21fcd41ad | [
"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 | 26,076 | lean | /-
Copyright (c) 2018 Ellen Arlt. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ellen Arlt, Blair Shi, Sean Leather, Mario Carneiro, Johan Commelin
-/
import data.matrix.basic
/-!
# Block Matrices
## Main definitions
* `matrix.from_blocks`: build a block matrix out... |
bad8aad12756461308b4dd639ea05f868a7fc172 | 88fb7558b0636ec6b181f2a548ac11ad3919f8a5 | /leanpkg/leanpkg/main.lean | 5b45b8d0146f6dbe87fb6d128cf9388ad3a863cd | [
"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 | 5,139 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Gabriel Ebner
-/
import leanpkg.resolve
variable [io.interface]
namespace leanpkg
def write_file (fn : string) (cnts : string) (mode := io.mode.write) : io unit := do
h ← io.mk... |
afd557e5c2e1a94377dacf8554f86758911d3bc6 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/adjunction/default_auto.lean | 98b8567b7f76b25d44aad483e8dc4c15ba68b1b8 | [] | 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 | 269 | lean | import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.adjunction.limits
import Mathlib.category_theory.adjunction.opposites
import Mathlib.category_theory.adjunction.reflective
import Mathlib.PostPort
namespace Mathlib
end Mathlib |
bc14152be21d40037707a76fc927d4750110b681 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/category_theory/limits/shapes/kernel_pair.lean | 67c9e2e2a88ef0b9bb32643b343f69af509b45ac | [
"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 | 8,226 | 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.equalizers
import category_theory.limits.shapes.pullbacks
import category_theory.limits.shapes.regular_mono
/-!
# Kernel pairs
This... |
c3d4718cb9edbf2009a345b3c9bc2d1eafecc38e | 3dd1b66af77106badae6edb1c4dea91a146ead30 | /tests/lean/run/fun.lean | b5e7b8db98f7126178fdcc7f24c620db343d9017 | [
"Apache-2.0"
] | permissive | silky/lean | 79c20c15c93feef47bb659a2cc139b26f3614642 | df8b88dca2f8da1a422cb618cd476ef5be730546 | refs/heads/master | 1,610,737,587,697 | 1,406,574,534,000 | 1,406,574,534,000 | 22,362,176 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 389 | lean | import function logic num bool
using function num bool
variable f : num → bool
variable g : num → num
check f ∘ g ∘ g
check typeof id : num → num
check num → num ⟨is_typeof⟩ id
variable h : num → bool → num
check flip h
check flip h '0 zero
check typeof flip h '0 zero : num
variable f1 : num → num → bool
variab... |
427d2e979f0fc68b5b19e2138194f3e6d9262e35 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/tactic/transport.lean | fd8e531e7843abbb2f625028137566178e2977f7 | [
"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 | 5,585 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner, Simon Hudon, Scott Morrison
-/
import tactic.equiv_rw
/-!
## The `transport` tactic
`transport` attempts to move an `s : S α` expression across an equivalence `e : α ≃... |
68ce34b8439c739e551d4a1d6bf5e9129d8d5082 | 798dd332c1ad790518589a09bc82459fb12e5156 | /algebra/ring.lean | 650cf38c626dfeed6dc1e1863309152062c728f3 | [
"Apache-2.0"
] | permissive | tobiasgrosser/mathlib | b040b7eb42d5942206149371cf92c61404de3c31 | 120635628368ec261e031cefc6d30e0304088b03 | refs/heads/master | 1,644,803,442,937 | 1,536,663,752,000 | 1,536,663,907,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,720 | 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
-/
import algebra.group data.set.basic
universes u v
variable {α : Type u}
section
variable [semiring α]
theorem mul_two (n : α) : ... |
cd699867f5306fe075ea9c310863b362adea977f | 690889011852559ee5ac4dfea77092de8c832e7e | /src/linear_algebra/basic.lean | 1cdcab201ffe60778c0d67102143e9469418e964 | [
"Apache-2.0"
] | permissive | williamdemeo/mathlib | f6df180148f8acc91de9ba5e558976ab40a872c7 | 1fa03c29f9f273203bbffb79d10d31f696b3d317 | refs/heads/master | 1,584,785,260,929 | 1,572,195,914,000 | 1,572,195,913,000 | 138,435,193 | 0 | 0 | Apache-2.0 | 1,529,789,739,000 | 1,529,789,739,000 | null | UTF-8 | Lean | false | false | 70,242 | 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
-/
import algebra.pi_instances data.finsupp data.equiv.algebra order.order_iso
/-!
# Linear algebra
This file defines the basics of lin... |
bdaa8cc49ff945ee585728b447b224457bfc4d57 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/fin/fin2.lean | 97382f66c75f23b8c41918e72da86a1c8ca545cf | [
"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 | 4,183 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
/-!
# Inductive type variant of `fin`
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
`fin` is define... |
d4f15c652fdcab8e79a0be322f0a5ca6522707e7 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/ring_theory/adjoin/power_basis.lean | c4f18ea931feca5d118bbcc62ddbe55589f9b1da | [
"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 | 7,959 | lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import ring_theory.adjoin.basic
import ring_theory.power_basis
import linear_algebra.matrix.basis
/-!
# Power basis for `algebra.adjoin R {x}`
This file defines the cano... |
969cf4b0ff3d7b68c6a2bbf78c58e8c3941006f9 | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/topology/metric_space/gromov_hausdorff.lean | 42d851f815b85aab0f27c094abe1d5ed4b8110ff | [
"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 | 56,063 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Sébastien Gouëzel
The Gromov-Hausdorff distance on the space of nonempty compact metric spaces up to isometry.
We introduces the space of all nonempty compact metric spaces, up to ... |
946e951bfae16799131c25f2e5ccacd7cd8a28f2 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/algebra/ne_zero.lean | cb460646b70713b2be537eef61ffb1be0067baf7 | [
"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 | 3,954 | lean | /-
Copyright (c) 2021 Eric Rodriguez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Rodriguez
-/
import data.nat.cast
import data.pnat.basic
import algebra.group_power.ring
/-!
# `ne_zero` typeclass
We create a typeclass `ne_zero n` which carries around the fa... |
504ed823b32b964654d4f6c6cb24074292b556a0 | 3ca6dd8bf23783927a6f1faedd16c92f0c96da9e | /lean/nat.lean | a6ad3d09f6460354e8626aad792ca69005149286 | [
"MIT"
] | permissive | anqurvanillapy/fpl | 139a368655091c27b0ab78fa266ad9f74348ccb8 | 9576d5b76e6a868992dbe52930712ac67697bed2 | refs/heads/master | 1,623,285,455,999 | 1,616,136,159,000 | 1,616,136,159,000 | 128,802,535 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 473 | lean | inductive N : Type
| zero : N
| succ : N -> N
-- The recursor of `N`
#check @N.rec_on
namespace N
def add (m n : N) : N :=
-- If `n` is 0, give out `m`; if not, sending `n` as `succ n'` with `(add m n')`
-- to `(λ n' add_m_n', succ add_m_n')`
N.rec_on n m (λ n' add_m_n', succ add_m_n')
#reduce add (succ zero) (succ... |
c27b39dfa5289a039a870e310929a8c100fdfeaf | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/set/pointwise/iterate.lean | c12696ba46bd45c0050818f04400650a2d66c840 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 1,983 | lean | /-
Copyright (c) 2022 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import data.set.pointwise.smul
import algebra.hom.iterate
import dynamics.fixed_points.basic
/-!
# Results about pointwise operations on sets with iteration.
> THIS FILE ... |
9ab9b157ecf17af29975cf73faabb630e0da6651 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/print_cmd.lean | d59f9c2c43032e5f364aa385cf8fe221b243e81d | [
"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 | 274 | lean | #print Nat
private def foo (x : Nat) : Nat := x + 1
#print "hello"
#print id
#print propext
#print default
#print ReaderT.read
#print Prod
#print Prod.mk
#print Nat
#print Nat.succ
#print Nat.rec
#print Nat.casesOn
#print foo
#print Quot.mk
#print Quot.ind
#print Quot.mk
|
e9f249e4f33733614724d1cf81eccb78b63dfc5e | c3f2fcd060adfa2ca29f924839d2d925e8f2c685 | /tests/lean/hott/443.hlean | 61b0a2895e8eca5bb33ebae63b663c90fc0fda97 | [
"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 | 344 | hlean | import algebra.group algebra.precategory.basic
open eq sigma unit category path_algebra
context
parameters {P₀ : Type} [P : precategory P₀]
structure my_structure := (a : P₀) (b : P₀) (f : @hom P₀ P a b)
include P
structure another_structure (X : my_structure) := (field1 : hom (my_structure.a X) (my_structu... |
1a09906925a4f6307a602b4412b8cf91d1bcfaf7 | 5df84495ec6c281df6d26411cc20aac5c941e745 | /src/formal_ml/discrete_topological_space.lean | 5bdfa0326ff7d6e7ab2b22be114e2e396425a89c | [
"Apache-2.0"
] | permissive | eric-wieser/formal-ml | e278df5a8df78aa3947bc8376650419e1b2b0a14 | 630011d19fdd9539c8d6493a69fe70af5d193590 | refs/heads/master | 1,681,491,589,256 | 1,612,642,743,000 | 1,612,642,743,000 | 360,114,136 | 0 | 0 | Apache-2.0 | 1,618,998,189,000 | 1,618,998,188,000 | null | UTF-8 | Lean | false | false | 4,578 | lean | /-
Copyright 2020 Google LLC
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
di... |
557deac38c021cc0229198777f490a02e9e705f6 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /archive/wiedijk_100_theorems/herons_formula.lean | 0fb04262d0fe8fceb3664f57f90a85a4450f90b4 | [
"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 | 2,966 | lean | /-
Copyright (c) 2021 Matt Kempster. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matt Kempster
-/
import geometry.euclidean.triangle
/-!
# Freek № 57: Heron's Formula
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR ... |
3717fa6652d5c39b1caea1e78634d4320debcb94 | b3fced0f3ff82d577384fe81653e47df68bb2fa1 | /src/analysis/calculus/times_cont_diff.lean | 02c8236b0069f89007e3b9fd4162b4ac40c8a3a6 | [
"Apache-2.0"
] | permissive | ratmice/mathlib | 93b251ef5df08b6fd55074650ff47fdcc41a4c75 | 3a948a6a4cd5968d60e15ed914b1ad2f4423af8d | refs/heads/master | 1,599,240,104,318 | 1,572,981,183,000 | 1,572,981,183,000 | 219,830,178 | 0 | 0 | Apache-2.0 | 1,572,980,897,000 | 1,572,980,896,000 | null | UTF-8 | Lean | false | false | 39,740 | 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 analysis.calculus.deriv
/-!
# Higher differentiability
A function is `C^1` on a domain if it is differentiable there, and its derivative is continuous... |
41ab1bfe578fd5a321a7b8e7354436e9beb8b277 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /src/Lean/Elab/Tactic/Conv/Change.lean | f7f2b10c3382ceb67c44b5befa0f20f9a00f352a | [
"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 | 881 | 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.Elab.Tactic.ElabTerm
import Lean.Elab.Tactic.Conv.Basic
namespace Lean.Elab.Tactic.Conv
open Meta
@[builtinTactic Lean.Parser.Tactic.Conv.chan... |
245d6e60f7e5d4ce4557f434e34a34df6cc8e102 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/mvar2.lean | 4e4f49545e7d3e0407cb1a3e84bcc3460612edd9 | [
"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 | 1,550 | lean | import Lean.MetavarContext
open Lean
def check (b : Bool) : IO Unit :=
unless b do throw $ IO.userError "error"
def f := mkConst `f []
def g := mkConst `g []
def a := mkConst `a []
def b := mkConst `b []
def c := mkConst `c []
def b0 := mkBVar 0
def b1 := mkBVar 1
def b2 := mkBVar 2
def u := mkLevelParam `u
def t... |
f29da5df828988fb6c604a857dfffad6f4031ba4 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/eq9.lean | cf427791b4a755954db8fc956da42c4f2a18fe6e | [
"Apache-2.0"
] | permissive | soonhokong/lean-osx | 4a954262c780e404c1369d6c06516161d07fcb40 | 3670278342d2f4faa49d95b46d86642d7875b47c | refs/heads/master | 1,611,410,334,552 | 1,474,425,686,000 | 1,474,425,686,000 | 12,043,103 | 5 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 240 | lean | open nat
attribute [pattern] lt.base
attribute [pattern] lt.step
theorem lt_succ {a : nat} : ∀ {b : nat}, a < b → succ a < succ b
| .(succ a) (lt.base .a) := lt.base (succ a)
| .(succ b) (@lt.step .a b h) := lt.step (lt_succ h)
|
2d4a10680cb13db4d1688676f1340a1ae2fdc0bf | 968e2f50b755d3048175f176376eff7139e9df70 | /examples/prop_logic_theory/unnamed_2524.lean | fef43c33b53e4451ddf14b7f9ae850d902f39c67 | [] | no_license | gihanmarasingha/mth1001_sphinx | 190a003269ba5e54717b448302a27ca26e31d491 | 05126586cbf5786e521be1ea2ef5b4ba3c44e74a | refs/heads/master | 1,672,913,933,677 | 1,604,516,583,000 | 1,604,516,583,000 | 309,245,750 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 479 | lean | variables {p q : Prop}
theorem not_or_not_of_not_and : ¬(p ∧ q) → ¬p ∨ ¬q :=
λ hnpq, or.elim (classical.em p) (λ hp, or.inr (λ hq, hnpq ⟨hp, hq⟩)) (λ hnp, or.inl hnp)
theorem not_and_of_not_or_not : ¬p ∨ ¬q → ¬(p ∧ q) :=
λ hnpnq hpq, or.elim hnpnq (λ hnp, hnp hpq.1) (λ hnq, hnq hpq.2)
-- BEGIN
theorem not_and_distrib :... |
a850ed5df958dfb7d80c97ee714e54144d274f9a | 6f510b1ed724f95a55b7d26a8dcd13e1264123dd | /src/test.lean | efdc9c4db10becba74f82cd4377a8019dff22312 | [] | no_license | jcommelin/oberharmersbach2019 | adaf2e54ba4eff7c178c933978055ff4d6b0593b | d2cdf780a10baa8502a9b0cae01c7efa318649a6 | refs/heads/master | 1,587,558,516,731 | 1,550,558,213,000 | 1,550,558,213,000 | 170,372,753 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 351 | lean | import help data.nat.prime
open nat
theorem Euclid (n : ℕ) : ∃ p ≥ n, prime p :=
begin
let N := n.fact + 1,
let p := min_fac N,
use_this p,
have p_is_prime : prime p := min_fac_prime _,
split,
show p ≥ n,
by_contradiction,
have key_fact : p ∣ n.fact := dvd_fact _ _,
have oops : p ∣ 1,
all_... |
efa300c673e3cf6d697b35164fac846029e7276b | 592ee40978ac7604005a4e0d35bbc4b467389241 | /Library/generated/mathscheme-lean/PseudoInvolution.lean | 33a17c72a26466a6adb34ac8ce1045f6b6b9aff3 | [] | no_license | ysharoda/Deriving-Definitions | 3e149e6641fae440badd35ac110a0bd705a49ad2 | dfecb27572022de3d4aa702cae8db19957523a59 | refs/heads/master | 1,679,127,857,700 | 1,615,939,007,000 | 1,615,939,007,000 | 229,785,731 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,166 | lean | import init.data.nat.basic
import init.data.fin.basic
import data.vector
import .Prelude
open Staged
open nat
open fin
open vector
section PseudoInvolution
structure PseudoInvolution (A : Type) : Type :=
(inv : (A → A))
(op : (A → (A → A)))
(quasiRightInverse_inv_op_e : (∀ {x : A} , (op (op ... |
b638f4d95445e916f2e471cbccb335e9215dd4f2 | 958488bc7f3c2044206e0358e56d7690b6ae696c | /lean/divides.lean | 24edcae6f2406ba60640b55088eb7e7123165c0a | [] | no_license | possientis/Prog | a08eec1c1b121c2fd6c70a8ae89e2fbef952adb4 | d4b3debc37610a88e0dac3ac5914903604fd1d1f | refs/heads/master | 1,692,263,717,723 | 1,691,757,179,000 | 1,691,757,179,000 | 40,361,602 | 3 | 0 | null | 1,679,896,438,000 | 1,438,953,859,000 | Coq | UTF-8 | Lean | false | false | 712 | lean | namespace hidden -- avoiding conflict with library
def divides (m n : ℕ) : Prop := ∃ k, m * k = n
instance : has_dvd nat := ⟨divides⟩ -- for '|' notation ?
def even (n : ℕ) : Prop := divides 2 n -- 2 | n fails
def prime (n : ℕ) : Prop := ¬(n = 1) ∧ (∀ (m:ℕ), divides m n → m = 1 ∨ m = n)
def primes_infinite : ... |
39d61dc31d4efc74219d36d7218bafec62b28f44 | 5d166a16ae129621cb54ca9dde86c275d7d2b483 | /tests/lean/format_to_buffer.lean | a13f29309a5a7af3721a84a3981ff509b2b3ff8f | [
"Apache-2.0"
] | permissive | jcarlson23/lean | b00098763291397e0ac76b37a2dd96bc013bd247 | 8de88701247f54d325edd46c0eed57aeacb64baf | refs/heads/master | 1,611,571,813,719 | 1,497,020,963,000 | 1,497,021,515,000 | 93,882,536 | 1 | 0 | null | 1,497,029,896,000 | 1,497,029,896,000 | null | UTF-8 | Lean | false | false | 193 | lean | import system.io
import data.buffer
meta def main : tactic unit := do
opts ← tactic.get_options,
let buf := format.to_buffer (format.of_string "foobar") opts,
tactic.trace buf
run_cmd main
|
3f1147972197f8f52680469c307fd5855c8cec39 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /test/localized/localized.lean | 70c188719f12b6f44ec6fffa99df3f7c88c0ba25 | [
"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 | 1,438 | lean | import tactic.localized
import algebra.group_power
open tactic
local infix ` ⊹ `:59 := nat.mul
local infix ` ↓ `:59 := pow
local infix ` ⊖ `:59 := pow
example : 2 ⊹ 3 = 6 := rfl
example : 2 ↓ 3 = 8 := rfl
example : 2 ⊖ 3 = 8 := rfl
example {n m : ℕ} (h : n < m) : n ≤ m := by { success_if_fail { simp [h] }, exact le_of... |
8769dc1e8c7c435925695ae39bb30379a632666e | fc086f79b20cf002d6f34b023749998408e94fbf | /src/tidy/forwards_reasoning.lean | 3a761acc9c2dd7fbb9ab3c9cad7431a28bf2fe50 | [] | no_license | semorrison/lean-tidy | f039460136b898fb282f75efedd92f2d5c5d90f8 | 6c1d46de6cff05e1c2c4c9692af812bca3e13b6c | refs/heads/master | 1,624,461,332,392 | 1,559,655,744,000 | 1,559,655,744,000 | 96,569,994 | 9 | 4 | null | 1,538,287,895,000 | 1,499,455,306,000 | Lean | UTF-8 | Lean | false | false | 3,316 | 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 lib.tactic
import lib.pretty_print
open tactic
meta def forward_attribute : user_attribute := {
name := `forward,
descr := "A lemma whose conclusion ... |
8244a211e966b82afa76a321608d239f4bd35f51 | b3fced0f3ff82d577384fe81653e47df68bb2fa1 | /src/analysis/normed_space/basic.lean | 7ee5f4914372bdaf77fbd4fc520613a078c04512 | [
"Apache-2.0"
] | permissive | ratmice/mathlib | 93b251ef5df08b6fd55074650ff47fdcc41a4c75 | 3a948a6a4cd5968d60e15ed914b1ad2f4423af8d | refs/heads/master | 1,599,240,104,318 | 1,572,981,183,000 | 1,572,981,183,000 | 219,830,178 | 0 | 0 | Apache-2.0 | 1,572,980,897,000 | 1,572,980,896,000 | null | UTF-8 | Lean | false | false | 24,818 | 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 topology.instances.complex
import topology.a... |
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