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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
9a9157e3b16c3bb6127b9448bbb4d89aaba4e9ea | 36938939954e91f23dec66a02728db08a7acfcf9 | /lean/deps/galois_stdlib/src/galois/data/rbtree.lean | ebcb3c7ad614e082a172f35983002f835e51129e | [
"Apache-2.0"
] | permissive | pnwamk/reopt-vcg | f8b56dd0279392a5e1c6aee721be8138e6b558d3 | c9f9f185fbefc25c36c4b506bbc85fd1a03c3b6d | refs/heads/master | 1,631,145,017,772 | 1,593,549,019,000 | 1,593,549,143,000 | 254,191,418 | 0 | 0 | null | 1,586,377,077,000 | 1,586,377,077,000 | null | UTF-8 | Lean | false | false | 738 | lean | /-
This defines functionality that could be in data.rbmap
-/
namespace rbnode
universes u
variables {α : Type u}
variable (lt : α → α → Prop)
instance mem.decidable [h : decidable_rel lt] (a : α) (m:rbnode α) : decidable (rbnode.mem lt a m) :=
begin
induction m,
{ simp [mem], apply_instance },
{ let p := h a m_... |
7f3efc08abbaa33cc620517e7417730e25b8bdfe | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/field_theory/laurent.lean | d504346dd9d9f5dd516663551821b01a439791e2 | [
"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 | 3,665 | lean | /-
Copyright (c) 2022 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
import data.polynomial.taylor
import field_theory.ratfunc
/-!
# Laurent expansions of rational functions
## Main declarations
* `ratfunc.laurent`: the Laurent e... |
22b1d2c70ce651a832f52a1341cd16d7cd09afa2 | 618003631150032a5676f229d13a079ac875ff77 | /src/category_theory/limits/lattice.lean | 4989a35e79a7c0680cf139cbc7d19b737106c80c | [
"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 | 2,545 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.limits.limits
import category_theory.limits.shapes.finite_products
import order.complete_lattice
universes u
open category_theory
namespace ... |
e1fa3262b2de5fc47f4e0cb8255236d92a27e614 | f3a5af2927397cf346ec0e24312bfff077f00425 | /src/game/world7/level2.lean | 7f18fa980791343645f3aab336b315c22959323c | [
"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 | 2,524 | lean | /-
# Advanced proposition world.
## Level 2: the `cases` tactic.
If `P ∧ Q` is in the goal, then we can make progress with `split`.
But what if `P ∧ Q` is a hypothesis? In this case, the `cases` tactic will enable
us to extract proofs of `P` and `Q` from this hypothesis.
The lemma below asks us to prove `P ∧ Q → ... |
6413f09119fe550da320fd265437c6478b3eef11 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/ring_theory/tensor_product.lean | 95948ab5228f1f7ab750bd464a4c32b919d7ca17 | [
"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 | 29,134 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Johan Commelin
-/
import linear_algebra.tensor_product_basis
import ring_theory.adjoin.basic
/-!
# The tensor product of R-algebras
Let `R` be a (semi)ring and `A` a... |
f70b1b12a01c12be5c1f58c584ca30e34559d067 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/analysis/inner_product_space/basic.lean | 251be997c4c7c806451c4558fc7da78d3fefd9d6 | [
"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 | 109,331 | lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Sébastien Gouëzel, Frédéric Dupuis
-/
import algebra.direct_sum.module
import analysis.complex.basic
import analysis.convex.uniform
import analysis.normed_space.completio... |
556398eb7ccc313ff82a3d408d0ecb515455d49b | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /tests/lean/run/indimp.lean | 3e124076cd4a8966fb6748b467246ec2babe1e2a | [
"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 | 492 | lean | definition Prop := Type.{0}
inductive nat :=
zero : nat,
succ : nat → nat
inductive list (A : Type) :=
nil {} : list A,
cons : A → list A → list A
inductive list2 (A : Type) : Type :=
nil2 {} : list2 A,
cons2 : A → list2 A → list2 A
inductive and (A B : Prop) : Prop :=
and_intro : A → B → and A B
inductive cls... |
24a61ca21cf293240165972a58c1e053884685f3 | 495c02489c2d6a1db94dfdba71dd800d3cc67df2 | /group_theory/finsubg.lean | 3cd189e8e92fe32dab9c54c615f58011fff41e50 | [
"Apache-2.0"
] | permissive | leodemoura/leanproved | e0fcbe4f4d72bf0dad9a962ed111b5975cf90712 | de56e0af159dd0c0421733289c76aa79c78a0191 | refs/heads/master | 1,606,822,676,898 | 1,435,711,541,000 | 1,435,711,541,000 | 36,675,856 | 0 | 0 | null | 1,433,178,724,000 | 1,433,178,724,000 | null | UTF-8 | Lean | false | false | 4,553 | lean | /-
Copyright (c) 2015 Haitao Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author : Haitao Zhang
-/
-- develop the concept of finite subgroups based on finsets so that the properties
-- can be used directly without translating from the set based theory first
import d... |
3452499127d603a0234d7ec60f13ce8b44323ca0 | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /tests/lean/run/concatElim.lean | 73b93c171fa2d0e2be68f140d8977dad1c45a298 | [
"Apache-2.0"
] | permissive | williamdemeo/lean4 | 72161c58fe65c3ad955d6a3050bb7d37c04c0d54 | 6d00fcf1d6d873e195f9220c668ef9c58e9c4a35 | refs/heads/master | 1,678,305,356,877 | 1,614,708,995,000 | 1,614,708,995,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,700 | lean | universes u
def concat {α} : List α → α → List α
| [], a => [a]
| x::xs, a => x :: concat xs a
def last {α} : (xs : List α) → xs ≠ [] → α
| [], h => absurd rfl h
| [a], h => a
| _::a::as, h => last (a::as) (fun h => by injection h)
def dropLast {α} : List α → List α
| [] => []
| [a] ... |
8e6c87a2f3be5aa3792981cdabf2def5c3867b44 | 626e312b5c1cb2d88fca108f5933076012633192 | /src/field_theory/galois.lean | 1ad1668274b6dbbef62050888934583958f772c9 | [
"Apache-2.0"
] | permissive | Bioye97/mathlib | 9db2f9ee54418d29dd06996279ba9dc874fd6beb | 782a20a27ee83b523f801ff34efb1a9557085019 | refs/heads/master | 1,690,305,956,488 | 1,631,067,774,000 | 1,631,067,774,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 18,088 | lean | /-
Copyright (c) 2020 Thomas Browning, Patrick Lutz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning, Patrick Lutz
-/
import field_theory.normal
import field_theory.primitive_element
import field_theory.fixed
import ring_theory.power_basis
/-!
# Galois... |
2cec5fec96e4662bba82934235b0b51013d61b93 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/convPatternAtLetIssue.lean | 2ced3e81eaed919050bef979b6bf7e7f4a2eaa9e | [
"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 | 224 | lean | def f (x : Nat) := x
def test : (λ x => f x)
=
(λ x : Nat =>
let foo := λ y => id (id y)
foo x) := by
conv =>
pattern (id _)
trace_state
simp
trace_state
|
0f140ac8147c4c041b2fb967a3b233f69c9437d5 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/analysis/normed/field/unit_ball.lean | 9de3087c3a72d083ea3ddac325d40e60e475af9e | [
"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 | 7,409 | lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Heather Macbeth
-/
import analysis.normed.field.basic
import analysis.normed.group.ball_sphere
/-!
# Algebraic structures on unit balls and spheres
In this file we ... |
bc433978fba80f154cb37d1cfd2c9ffd0c7ee82e | c055f4b7c29cf1aac2223bd8c1ac8d181a7c6447 | /src/categories/opposites.lean | f955e33cb03a06261fc0bf93050f22fa9518c668 | [
"Apache-2.0"
] | permissive | rwbarton/lean-category-theory-pr | 77207b6674eeec1e258ec85dea58f3bff8d27065 | 591847d70c6a11c4d5561cd0eaf69b1fe85a70ab | refs/heads/master | 1,584,595,111,303 | 1,528,029,041,000 | 1,528,029,041,000 | 135,919,126 | 0 | 0 | null | 1,528,041,805,000 | 1,528,041,805,000 | null | UTF-8 | Lean | false | false | 3,692 | 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 .functor
import .products
import .types
open categories
open categories.functor
open categories.products
open categories.types
namespace ... |
7c3ad127b209e26f64814991f1cced751216c94c | 947b78d97130d56365ae2ec264df196ce769371a | /tests/lean/run/macroid.lean | 6c7301035098a77d9c5c4d8450155b73f1f8c2a7 | [
"Apache-2.0"
] | permissive | shyamalschandra/lean4 | 27044812be8698f0c79147615b1d5090b9f4b037 | 6e7a883b21eaf62831e8111b251dc9b18f40e604 | refs/heads/master | 1,671,417,126,371 | 1,601,859,995,000 | 1,601,860,020,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 622 | lean | new_frontend
syntax "[" ident "↦" term "]" : term
macro_rules `([$x ↦ $v]) => `(fun $x => $v)
#check [x ↦ x + 1]
syntax "case!" ident ":" term "with" term "," term : term
macro_rules `(case! $h : $c with $t, $e) => `((fun $h => cond $h $t $e) $c)
#check case! h : 0 == 0 with h, not h
syntax "case2!" ident ":" term... |
8d202edd782ebb79d9d06e218c1e663bd09f47af | a6f55abce20abcd06e718cb3e5fba7bf8a230fa1 | /topic/fruit.lean | 0bde883c4e2f59b4e8e24c15173831f695993953 | [] | no_license | sonna0909/abc | b8a53e906d4d000d1f2347173a1cd4221757fabf | ff7b4c621cdf6d53937f2d1b6def28de2085a2aa | refs/heads/master | 1,599,114,664,248 | 1,573,634,309,000 | 1,573,634,309,000 | 219,406,484 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 20,305 | lean | [
{
"key": "apple",
"title": "Apple",
"spelling": "/’æpl/",
"subs": [
{
"key": "apple",
"title": "An apple",
"spelling": ""
},
{
"key": "apples",
"title": "Apples",
"spelling": ""
},
{
"key": "apple",
"title"... |
5110912a1412243e2eeef34974db31a19eab4700 | 4fa161becb8ce7378a709f5992a594764699e268 | /src/number_theory/lucas_lehmer.lean | afe1eacbbafedbc39d31e665f32937378a639d3e | [
"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 | 17,085 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro, Scott Morrison, Ainsley Pahljina
-/
import data.nat.parity
import data.zmod.basic
import group_theory.order_of_element
import ring_theory.fintype
/-!
# The Lucas-Lehme... |
4f48bf5646c2a18820e9a9a351e0e5da9fe1d92b | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/category_theory/category/basic.lean | 60477f4fe162f823340a8d9971e13d5079fba727 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 10,961 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stephen Morgan, Scott Morrison, Johannes Hölzl, Reid Barton
-/
import combinatorics.quiver.basic
import tactic.basic
/-!
# Categories
Defines a category, as a type class parametrised... |
5a60d1c1952a9e651eb781b00eb861ccbe5223fc | 8f67b34bba98f894155dedf263bc8d61c31e89cd | /2ltt/limit.lean | 03c7575db4b14fdab01663a7800a1b7c8f039827 | [] | no_license | 5HT/two-level | 3b1523db242cba819681b862fbc8f490d9571a66 | 370f5a91311db3b463b10a31891370721e2476e2 | refs/heads/master | 1,648,254,367,420 | 1,576,269,550,000 | 1,576,269,550,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,307 | lean | import data.equiv algebra.category .facts
open natural_transformation sigma.ops
open category function equiv
notation X `≃ₛ` Y := equiv X Y
-- Given categories J and C, we have a canonical functor [const_funct] from the category C to the functor category C^J.
-- Here, we do not define this functor in full, but we de... |
3533b0dce84db43679f67cf7009098dcff902489 | 8c9f90127b78cbeb5bb17fd6b5db1db2ffa3cbc4 | /induction_base_k.lean | d98c99d679f27f3077bd8c24a3f272a54e6e3908 | [] | no_license | picrin/lean | 420f4d08bb3796b911d56d0938e4410e1da0e072 | 3d10c509c79704aa3a88ebfb24d08b30ce1137cc | refs/heads/master | 1,611,166,610,726 | 1,536,671,438,000 | 1,536,671,438,000 | 60,029,899 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,926 | lean | lemma same_lt {a : nat} (P : a < a) : false :=
have H : a = a, from eq.refl a,
ne_of_lt P H
lemma nat.lte_zero (n : nat) : 0 ≤ n :=
@nat.rec_on (λ k', 0 ≤ k') n (le_refl 0) (λ k (p : 0 ≤ k),
have q : 0 ≤ 1, from nat.le_add_left 0 1,
show (0 ≤ k + 1), from le_add_of_le_of_nonneg p q
)
l... |
8fe2f7bdac8388b8a9a1f5986a392ed6d6a6dc04 | ff5230333a701471f46c57e8c115a073ebaaa448 | /library/init/data/repr.lean | 3f0c1b3426d1d46cf1e38853d2b501faf415b07a | [
"Apache-2.0"
] | permissive | stanford-cs242/lean | f81721d2b5d00bc175f2e58c57b710d465e6c858 | 7bd861261f4a37326dcf8d7a17f1f1f330e4548c | refs/heads/master | 1,600,957,431,849 | 1,576,465,093,000 | 1,576,465,093,000 | 225,779,423 | 0 | 3 | Apache-2.0 | 1,575,433,936,000 | 1,575,433,935,000 | null | UTF-8 | Lean | false | false | 4,437 | 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.string.basic init.data.bool.basic init.data.subtype.basic
import init.data.unsigned.basic init.data.prod init.data.sum.basic init.da... |
dabc03c7282d1ad08bf9c143f4604b838a03d7c2 | b3fced0f3ff82d577384fe81653e47df68bb2fa1 | /src/category/monad/basic.lean | 738738929ca1861c0dff2bc54436cc611279fa05 | [
"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 | 1,319 | lean | /-
Copyright (c) 2019 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author(s): Simon Hudon
-/
import tactic.basic
/-!
# Monad
## Attributes
* extensionality
* functor_norm
* monad_norm
## Implementation Details
Set of rewrite rules and automation for mona... |
285e9d4e00f37eb9812cdcf54bddabc310349a6a | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/quote_error_pos.lean | e1ef36df03b04444bc16cc3adf994cfe2b7b5e40 | [
"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 | 562 | lean | open tactic
class add_monoid (α : Type) extends has_zero α, has_add α :=
(zero_add : ∀ a : α, 0 + a = a)
lemma zero_add {α : Type} [add_monoid α] (a : α) : (0 : α) + a = a :=
add_monoid.zero_add a
meta def apply_zero_add (a : pexpr) : tactic unit :=
to_expr ``(zero_add %%a) >>= exact
example (a : nat) : 0 + a = a :... |
7065e82841542ffe0a6519aff99f327b0ce964ff | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/ring_theory/mv_polynomial/homogeneous.lean | e3b3e6e53cbd8ef63c6447c40d6e583660780ef9 | [
"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 | 10,970 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Eric Wieser
-/
import algebra.direct_sum.internal
import algebra.graded_monoid
import data.mv_polynomial.variables
/-!
# Homogeneous polynomials
> THIS FILE IS SYNCHR... |
56918d2f5a5d0fca4b16ff0f7118070977d69cec | 5df84495ec6c281df6d26411cc20aac5c941e745 | /src/formal_ml/vcd_examples.lean | 74f421816f55e1cd9f9e44f0c171b3377a25317f | [
"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 | 13,971 | lean | import formal_ml.vcd
namespace list
variable {α:Type*}
lemma nth_lt_of_sorted_of_lt [L:linear_order α] {a b:ℕ} {l:list α} (ha:a < l.length)
(hb:b < l.length):list.sorted (<) l → (a < b) → (l.nth_le a ha) < (l.nth_le b hb) :=
begin
intros A1 A2,
simp [list.sorted] at A1,
rw list.pairwise_iff_nth_le at A1,
a... |
d005c24d64f3f937c93520cc03ef002866465157 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/direct_limit.lean | 9c55402b38d1b1f0f7deb8a6cc6a0d9e6d855828 | [
"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 | 25,563 | 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
-/
import data.finset.order
import algebra.direct_sum.module
import ring_theory.free_comm_ring
import ring_theory.ideal.operations
/-!
# Direct limit o... |
f38844b8f5edff783e249412d3118b475f67d61c | b00eb947a9c4141624aa8919e94ce6dcd249ed70 | /src/Std/Data/RBTree.lean | 292bdae34f4683362812ebcb4a784ba87ddb5d90 | [
"Apache-2.0"
] | permissive | gebner/lean4-old | a4129a041af2d4d12afb3a8d4deedabde727719b | ee51cdfaf63ee313c914d83264f91f414a0e3b6e | refs/heads/master | 1,683,628,606,745 | 1,622,651,300,000 | 1,622,654,405,000 | 142,608,821 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,356 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Std.Data.RBMap
namespace Std
universes u v w
def RBTree (α : Type u) (cmp : α → α → Ordering) : Type u :=
RBMap α Unit cmp
instance : Inhabited (... |
24473f6f672794d12738503547e63417b9a44a2a | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/hom/aut.lean | d0e2bfe47879ff0a2729a6cea4401f20288624a3 | [
"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 | 7,430 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Callum Sutton, Yury Kudryashov
-/
import group_theory.perm.basic
/-!
# Multiplicative and additive group automorphisms
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> An... |
949008c20d9d9b9a3a16a1d80de4107b342f1723 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /stage0/src/Init/Data/Hashable.lean | 3f81ec033e83277d76ff79182551fdd4bf9d37b5 | [
"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 | 1,213 | 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.Data.UInt
import Init.Data.String
universe u
instance : Hashable Nat where
hash n := UInt64.ofNat n
instance [Hashable α] [Hashable ... |
aebdaa8fa02a3c6a3eb28d31c9ea53a9b5193e8a | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/data/nat/unique_factorization.lean | 8a479c274eb2ca52c103eee7c78d7e483451078c | [
"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 | 1,856 | lean | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import data.nat.associated
import ring_theory.unique_factorization_domain
/-#
# Unique factorization in `ℕ`
This file defines the `unique_factorization_monoid` st... |
ec5df4cc7e8f369d4c985161aa1b402a68ad5431 | 137c667471a40116a7afd7261f030b30180468c2 | /src/measure_theory/interval_integral.lean | dd17dfc3f06589e54579d5450b78690063804e3e | [
"Apache-2.0"
] | permissive | bragadeesh153/mathlib | 46bf814cfb1eecb34b5d1549b9117dc60f657792 | b577bb2cd1f96eb47031878256856020b76f73cd | refs/heads/master | 1,687,435,188,334 | 1,626,384,207,000 | 1,626,384,207,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 104,231 | lean | /-
Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov, Patrick Massot
-/
import measure_theory.set_integral
import measure_theory.lebesgue_measure
import analysis.calculus.fderiv_measurable
import analysis.calculus.... |
f25ffb51a36d3b3da5a0a99fcd3cc503c5b5ff9e | 29fc903502a2f31a2009389392484557342601fe | /src/graph.lean | 77d474be4caa81a9ee92b1e041b699f610bdb392 | [] | no_license | NicolasRouquette/digraphs | 9a7ed10ce54ce3d60983db153624d33e47391f8f | c6a88abc2565b0b25a0b3a93665d4b285c79e51b | refs/heads/master | 1,673,439,036,710 | 1,604,799,582,000 | 1,604,799,582,000 | 310,965,050 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 50,137 | lean | -- A basic framework for graph theory on multidigraphs in Lean
-- and a proof that no_watershed_condition is sufficient to
-- establish that a graph has a unique sink for each vertex
--
-- I hope to give some introduction to the syntax of how Lean works here,
-- but I assume some familiarity with functions, pattern mat... |
3a6226bb2230086b2310333b321152246bebbb0f | f3a5af2927397cf346ec0e24312bfff077f00425 | /src/game/world7/level9.lean | 5844c7dbb6c7037abbb202767368fba3b5670d57 | [
"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 | 2,041 | lean | import game.world7.level8 -- hide
import game.world6.level8 -- hide
import tactic.tauto -- useful high-powered tactic
local attribute [instance, priority 10] classical.prop_decidable -- hide
/-
# Advanced proposition world.
You already know enough to embark on advanced addition world. But here are just a couple
more... |
24c984dae0599d71767183fca9a33428fd47ebe4 | a623837965543f72645ad3de4797a693f5c64274 | /test/terminal_goal.lean | 778c8e14f2279ea278f3f4b4011643eaed6ecdd6 | [] | no_license | khoek/lean-tidy | 9e1c8ffebc6a3e4739128e6cf7b7e84cba3a0625 | 995fbf6efa56f6c01cdb3754fc4a84b648a6dd91 | refs/heads/master | 1,619,535,208,982 | 1,549,094,268,000 | 1,549,094,268,000 | 122,460,123 | 0 | 0 | null | 1,534,214,616,000 | 1,519,293,337,000 | Lean | UTF-8 | Lean | false | false | 1,441 | 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 tidy.recover
structure C :=
( w : Type )
( x : list w )
( y : Type )
( z : prod w y )
def test_terminal_goal : C :=
begin
fsplit,
success_if... |
f02ad93930d84ddd249866e5ae09704280c8c479 | 0845ae2ca02071debcfd4ac24be871236c01784f | /tests/playground/zipper.lean | 27a828ec57ec5de38ee0e2491d29ffb0fd78358f | [
"Apache-2.0"
] | permissive | GaloisInc/lean4 | 74c267eb0e900bfaa23df8de86039483ecbd60b7 | 228ddd5fdcd98dd4e9c009f425284e86917938aa | refs/heads/master | 1,643,131,356,301 | 1,562,715,572,000 | 1,562,715,572,000 | 192,390,898 | 0 | 0 | null | 1,560,792,750,000 | 1,560,792,749,000 | null | UTF-8 | Lean | false | false | 1,448 | lean | structure ListZipper (α : Type) :=
(xs : List α) (bs : List α)
-- set_option trace.compiler.ir.rc true
variables {α : Type}
namespace ListZipper
def goForward : ListZipper α → ListZipper α
| ⟨[], bs⟩ := ⟨[], bs⟩
| ⟨x::xs, bs⟩ := ⟨xs, x::bs⟩
def goBackward : ListZipper α → ListZipper α
| ⟨xs, []⟩ := ⟨xs, []⟩
... |
95c516cb45431aa8fe06c061b6f49c72e4869680 | 853df553b1d6ca524e3f0a79aedd32dde5d27ec3 | /src/ring_theory/matrix_algebra.lean | 4b6776fe96fb42479b0abe441379bf9cf77afe93 | [
"Apache-2.0"
] | permissive | DanielFabian/mathlib | efc3a50b5dde303c59eeb6353ef4c35a345d7112 | f520d07eba0c852e96fe26da71d85bf6d40fcc2a | refs/heads/master | 1,668,739,922,971 | 1,595,201,756,000 | 1,595,201,756,000 | 279,469,476 | 0 | 0 | null | 1,594,696,604,000 | 1,594,696,604,000 | null | UTF-8 | Lean | false | false | 6,758 | 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 tactic.tidy
import ring_theory.tensor_product
import data.matrix.basic
/-!
We provide the `R`-algebra structure on `matrix n n A` when `A` is an `R`-algebra,
... |
70ca8aceacc3e767e53d1b88e8098c52186b8db0 | 3f7026ea8bef0825ca0339a275c03b911baef64d | /src/algebra/ordered_field.lean | 5ef266be28932f70c2777fcf8faac22891b4602b | [
"Apache-2.0"
] | permissive | rspencer01/mathlib | b1e3afa5c121362ef0881012cc116513ab09f18c | c7d36292c6b9234dc40143c16288932ae38fdc12 | refs/heads/master | 1,595,010,346,708 | 1,567,511,503,000 | 1,567,511,503,000 | 206,071,681 | 0 | 0 | Apache-2.0 | 1,567,513,643,000 | 1,567,513,643,000 | null | UTF-8 | Lean | false | false | 9,573 | 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.ordered_ring algebra.field
section linear_ordered_field
variables {α : Type*} [linear_ordered_field α] {a b c d : α}
def div_pos := @div_pos_of_pos_o... |
49bfb7149404591f46001f3ffe4e98acd919d176 | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/set_theory/game.lean | 7eee7eadf242df6987a928e55fc622a585ca08fa | [
"Apache-2.0"
] | permissive | vaibhavkarve/mathlib | a574aaf68c0a431a47fa82ce0637f0f769826bfe | 17f8340912468f49bdc30acdb9a9fa02eeb0473a | refs/heads/master | 1,621,263,802,637 | 1,585,399,588,000 | 1,585,399,588,000 | 250,833,447 | 0 | 0 | Apache-2.0 | 1,585,410,341,000 | 1,585,410,341,000 | null | UTF-8 | Lean | false | false | 5,378 | lean | /-
Copyright (c) 2019 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Mario Carneiro, Isabel Longbottom, Scott Morrison
-/
import set_theory.pgame
/-!
# Combinatorial games.
In this file we define the quotient of pre-games by the equivalen... |
d106221f2ec5647d2c5b54a69cfadb5b0a12e4e3 | 1136b4d61007050cc632ede270de45a662f8dba4 | /library/init/data/nat/basic.lean | 2bc927a867c37973127355369860c5cbfdff12a0 | [
"Apache-2.0"
] | permissive | zk744750315/lean | 7fe895f16cc0ef1869238a01cae903bbd623b4a9 | c17e5b913b2db687ab38f53285326b9dbb2b1b6e | refs/heads/master | 1,618,208,425,413 | 1,521,520,544,000 | 1,521,520,936,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,039 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura
-/
prelude
import init.logic
notation `ℕ` := nat
namespace nat
inductive less_than_or_equal (a : ℕ) : ℕ → Prop
| refl : less_than_or_equal... |
30e3ecb96f81510811a1a0430987066979cc5e86 | f10d66a159ce037d07005bd6021cee6bbd6d5ff0 | /to_semiring.lean | 4f14ea46f3a112a4163092f5565831e2167be64e | [] | no_license | johoelzl/mason-stother | 0c78bca183eb729d7f0f93e87ce073bc8cd8808d | 573ecfaada288176462c03c87b80ad05bdab4644 | refs/heads/master | 1,631,751,973,492 | 1,528,923,934,000 | 1,528,923,934,000 | 109,133,224 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 1,380 | lean | import data.finsupp
import algebra.ring
import .to_finset
import .to_multiset
local infix ^ := monoid.pow
universe u
variable {α : Type u}
variable [semiring α]
def associated (x y : α) : Prop:=
∃u : units α, x = u * y
local notation a `~ᵤ` b : 50 := associated a b
def is_unit (a : α) : Prop := ∃b : units α, a =... |
9fec1420315b4928b6bd88f381f2b455d64834f4 | 4e3bf8e2b29061457a887ac8889e88fa5aa0e34c | /lean/love05_inductive_predicates_exercise_sheet.lean | adfdf1aadd72bc1bdd720d502625e54bd83d13dd | [] | no_license | mukeshtiwari/logical_verification_2019 | 9f964c067a71f65eb8884743273fbeef99e6503d | 16f62717f55ed5b7b87e03ae0134791a9bef9b9a | refs/heads/master | 1,619,158,844,208 | 1,585,139,500,000 | 1,585,139,500,000 | 249,906,380 | 0 | 0 | null | 1,585,118,728,000 | 1,585,118,727,000 | null | UTF-8 | Lean | false | false | 1,804 | lean | /- LoVe Exercise 5: Inductive Predicates -/
import .love05_inductive_predicates_demo
namespace LoVe
/- Question 1: Even and Odd -/
/- The `even` predicate is true for even numbers and false for odd numbers. -/
#check even
/- 1.1. Prove that 0, 2, 4, and 6 are even. -/
-- enter your answer here
/- We define `od... |
b0248fc434b502c2bee51fa10dbe5c1d1e29e818 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/algebra/continued_fractions/computation/correctness_terminating.lean | b6ee4ce5c915225bbbfbd3078ca9fc50e187d089 | [
"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 | 12,389 | 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.computation.translations
import algebra.continued_fractions.terminated_stable
import algebra.continued_fractions.continuants_re... |
fbf6f2baed68a9de913e85b6da201c70e2a247f4 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/analysis/convex/combination.lean | 8aac405b7832b7b9716eb388f78bbc01a0181976 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 22,181 | lean | /-
Copyright (c) 2019 Yury Kudriashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudriashov
-/
import algebra.big_operators.order
import analysis.convex.hull
import linear_algebra.affine_space.basis
/-!
# Convex combinations
This file defines convex combina... |
ec2eb824364f42bff5823f28ea8b03450eb4d6f5 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebraic_topology/dold_kan/degeneracies.lean | 3a831d4e85ee4834262a30dc91d08ccfd4a49ff6 | [
"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 | 5,992 | 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 algebraic_topology.dold_kan.decomposition
/-!
# Behaviour of P_infty with respect to degeneracies
For any `X : simplicial_object C` where `C` is an abelian category,... |
a723921622eb697888508b8c9324ab123e1d0be4 | a537b538f2bea3181e24409d8a52590603d1ddd9 | /test/rewrite_search_discovery.lean | e1a62664af81ae67de262c7a5a24c3f755245f66 | [] | no_license | rwbarton/lean-tidy | 6134813ded72b275d19d4d32514dba80c21708e3 | fe1125d32adb60decda7a77d0f679614ba9f6fbb | refs/heads/master | 1,585,549,718,705 | 1,538,120,619,000 | 1,538,120,624,000 | 150,864,330 | 0 | 0 | null | 1,538,225,790,000 | 1,538,225,790,000 | null | UTF-8 | Lean | false | false | 4,606 | lean | import tidy.rewrite_search
open tidy.rewrite_search.metric
open tidy.rewrite_search.strategy
open tidy.rewrite_search.tracer
open tidy.rewrite_search.discovery
namespace tidy.rewrite_search.testing
@[bundle] meta def algebraic_geometry : bundle := {}
private axiom foo : [0] = [1]
private axiom bar1 : [1] = [2]
priv... |
2aa4b3df2c9c3cf1cbd8e66a56915f4a63a9ef63 | 33340b3a23ca62ef3c8a7f6a2d4e14c07c6d3354 | /lia/asubst.lean | 10ebbb797107eba1f02780adfc215f6a4a85821f | [] | no_license | lclem/cooper | 79554e72ced343c64fed24b2d892d24bf9447dfe | 812afc6b158821f2e7dac9c91d3b6123c7a19faf | refs/heads/master | 1,607,554,257,488 | 1,578,694,133,000 | 1,578,694,133,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,677 | lean | import .atom
open list znum
def asubst (i') (ks') : atom → atom
| (atom.le i (k::ks)) := atom.le (i - (k * i')) (comp_add (map_mul k ks') ks)
| (atom.dvd d i (k::ks)) := atom.dvd d (i + (k * i')) (comp_add (map_mul k ks') ks)
| (atom.ndvd d i (k::ks)) := atom.ndvd d (i + (k * i')) (comp_add (map_mul k ks') ks)
... |
d61d82671e0aa544410201d69d24c58e3b545d09 | 952248371e69ccae722eb20bfe6815d8641554a8 | /src/datatypes/basic.lean | 5305895514703f5b2b5d9cc3bc7e5e17e06342bb | [] | no_license | robertylewis/lean_polya | 5fd079031bf7114449d58d68ccd8c3bed9bcbc97 | 1da14d60a55ad6cd8af8017b1b64990fccb66ab7 | refs/heads/master | 1,647,212,226,179 | 1,558,108,354,000 | 1,558,108,354,000 | 89,933,264 | 1 | 2 | null | 1,560,964,118,000 | 1,493,650,551,000 | Lean | UTF-8 | Lean | false | false | 250 | lean | import data.hash_map data.complex.basic rat_additions
def {u v} hash_map.ifind {α : Type u} {β : α → Type v} [decidable_eq α] (m : hash_map α β) (a : α) [inhabited (β a)] : β a :=
match m.find a with
| none := default _
| some b := b
end
|
950c269f75f24140418dc7747591880b3c6f83d1 | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /stage0/src/Init/Data/Float.lean | ac99122aa68dbb3ef076fc1764ce957f95fcc855 | [
"Apache-2.0"
] | permissive | dupuisf/lean4 | d082d13b01243e1de29ae680eefb476961221eef | 6a39c65bd28eb0e28c3870188f348c8914502718 | refs/heads/master | 1,676,948,755,391 | 1,610,665,114,000 | 1,610,665,114,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,409 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import Init.Core
import Init.Data.ToString.Basic
structure FloatSpec where
float : Type
val : float
lt : float → float → Prop
le : ... |
372d32597107eb2338117e6ab9a1a755b3d4d9e8 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/fin/vec_notation.lean | cd64938c565d71ae6180cfa208ef2590ec7919fc | [
"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 | 12,809 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import data.fin.basic
import data.list.range
import algebra.module.pi
/-!
# Matrix and vector notation
This file defines notation for vectors and matrices. Given `a b c d... |
30020905816e0d7f2cbf9247dfe25b7c9c24f488 | 5749d8999a76f3a8fddceca1f6941981e33aaa96 | /src/order/filter/basic.lean | 8317a58f0a608b87c99ab288b90d25b75e18ca5d | [
"Apache-2.0"
] | permissive | jdsalchow/mathlib | 13ab43ef0d0515a17e550b16d09bd14b76125276 | 497e692b946d93906900bb33a51fd243e7649406 | refs/heads/master | 1,585,819,143,348 | 1,580,072,892,000 | 1,580,072,892,000 | 154,287,128 | 0 | 0 | Apache-2.0 | 1,540,281,610,000 | 1,540,281,609,000 | null | UTF-8 | Lean | false | false | 94,998 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jeremy Avigad
-/
import order.galois_connection order.zorn
import data.set.finite
/-! # Theory of filters on sets
## Main definitions
* `filter` : filter on a set;
*... |
51622704c21588ce3bb76bdad3a561992be1ea2d | dc253be9829b840f15d96d986e0c13520b085033 | /algebra/ses.hlean | f4379878f65a1063912b211d83592ee5c6a6dc96 | [
"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 | 10,412 | hlean | /-
Copyright (c) 2017 Egbert Rijke. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Egbert Rijke
Basic facts about short exact sequences.
At the moment, it only covers short exact sequences of abelian groups, but this should be extended to short exact sequences in any... |
960e89eac14aec27f9e44823433ce80bd262c2a2 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/tactic/core.lean | 0d169db89fc70886d66832bfecfbf7eb417d5e4d | [
"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 | 97,054 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Simon Hudon, Scott Morrison, Keeley Hoek
-/
import control.basic
import data.dlist.basic
import meta.expr
import system.io
import tactic.binder_matching
import tactic.i... |
d8f7dd13b89b8e25de7f5f88828c7a78d97bc83c | b074a51e20fdb737b2d4c635dd292fc54685e010 | /src/ring_theory/noetherian.lean | 7e2808abeb46cc7faa78774630c3a347c32ac300 | [
"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 | 21,285 | lean | /-
Copyright (c) 2018 Mario Carneiro and Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kevin Buzzard
-/
import data.equiv.algebra
import linear_algebra.finsupp
import ring_theory.ideal_operations
import ring_theory.subring
import linear... |
895566d5eeb171306496e974ad463a5a137f40df | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/algebra/restrict_scalars.lean | ea90c084b2611f88b420dcb5aac2fd803cc4d5dc | [
"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 | 8,463 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov
-/
import algebra.algebra.tower
/-!
# The `restrict_scalars` type alias
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresp... |
35e76266f6900e0b7be1afe69f8a5057225b844c | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/specialize2.lean | 55b62870ebf3d33a30af673b6faadcf9baaa9125 | [
"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 | 328 | lean | example : (p → q → False) ↔ (¬ p ∨ ¬ q) := by
apply Iff.intro
· intro h
by_cases hp:p <;> by_cases hq:q
· specialize h hp hq; contradiction
· exact Or.inr hq
· exact Or.inl hp
· exact Or.inr hq
· intro
| Or.inl hnp => intros; contradiction
| Or.inr hnq => intros; contradiction
|
25ceae7e27b93329aade464838d6e105082f486e | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/ring_theory/laurent_series.lean | 4b18c5ab9bbc1a43c1cd4ea89b86ae8c6bc878d1 | [
"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 | 6,230 | lean | /-
Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import ring_theory.hahn_series
import ring_theory.localization
/-!
# Laurent Series
## Main Definitions
* Defines `laurent_series` as an abbreviation for `hahn_seri... |
f0cc9ab6332f206876d2d1b1bafea4cc8fd9e04b | fd3506535396cef3d1bdcf4ae5b87c8ed9ff2c2e | /migrated/nat.lean | a81b65fd2c284bd9b01a54e66a5755a6ae32f066 | [] | no_license | williamdemeo/leanproved | 77933dbcb8bfbae61a753ae31fa669b3ed8cda9d | d8c2e2ca0002b252fce049c4ff9be0e9e83a6374 | refs/heads/master | 1,598,674,802,432 | 1,437,528,488,000 | 1,437,528,488,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 685 | lean |
import theories.number_theory.primes data.nat
open nat eq.ops
namespace shadow
section order
lemma lt_succ_of_lt {i j : nat} : i < j → i < succ j :=
assume Plt, lt.trans Plt (self_lt_succ j)
end order
section power
lemma pow_dvd_of_pow_succ_dvd {p i n : nat} : p^(succ i) ∣ n → p^i ∣ n :=
assume Psuccdvd,
assert Pd... |
b1e838c127f981301f80fa228a4b390d10524e2d | 94637389e03c919023691dcd05bd4411b1034aa5 | /src/inClassNotes/01_polymorphicFunctions.lean | 4b38191d4d3b7e1ae031fde4fe511955fe71c817 | [] | 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 | 936 | lean |
def id_nat : nat → nat :=
λ n, n
def id_string : string → string :=
λ n, n
def id_bool : bool → bool :=
λ n, n
-- parametric polymorphism
namespace hidden
#check 1
#check "Hello"
#check tt
-- Types are terms
#check nat
#check string
#check bool
def id' : Π (α : Type), α → α :=
λ α,
λ n,
... |
ed920d07a943f6def503c6d98c2858e2fb4d2723 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /docs/tutorial/category_theory/calculating_colimits_in_Top.lean | b74ebc59c3d0e3f1c15cb82a030a92fd99b1f8f7 | [
"Apache-2.0"
] | permissive | agjftucker/mathlib | d634cd0d5256b6325e3c55bb7fb2403548371707 | 87fe50de17b00af533f72a102d0adefe4a2285e8 | refs/heads/master | 1,625,378,131,941 | 1,599,166,526,000 | 1,599,166,526,000 | 160,748,509 | 0 | 0 | Apache-2.0 | 1,544,141,789,000 | 1,544,141,789,000 | null | UTF-8 | Lean | false | false | 3,567 | lean | import topology.category.Top.limits
import category_theory.limits.shapes
import topology.instances.real
import topology.tactic
/-! This file contains some demos of using the (co)limits API to do topology. -/
noncomputable theory
open category_theory
open category_theory.limits
def R : Top := Top.of ℝ
def I : Top :=... |
a6a78454d958d5ae01fbfe71a3272797dd4ba460 | f09e92753b1d3d2eb3ce2cfb5288a7f5d1d4bd89 | /src/for_mathlib/is_cover.lean | d0de1575c65768790fc50e290f1202fa6ef59e53 | [
"Apache-2.0"
] | permissive | PatrickMassot/lean-perfectoid-spaces | 7f63c581db26461b5a92d968e7563247e96a5597 | 5f70b2020b3c6d508431192b18457fa988afa50d | refs/heads/master | 1,625,797,721,782 | 1,547,308,357,000 | 1,547,309,364,000 | 136,658,414 | 0 | 1 | Apache-2.0 | 1,528,486,100,000 | 1,528,486,100,000 | null | UTF-8 | Lean | false | false | 274 | lean | import analysis.topology.topological_space
definition is_cover {X γ : Type} (U : γ → set X) := ∀ x, ∃ i, x ∈ U i
structure is_open_cover {X γ : Type} [H : topological_space X] (U : γ → set X) :=
(is_open : ∀ i, H.is_open (U i))
(is_cover : is_cover U)
|
c5c0c6487a6a1cf645de78920a1e4c17f698661f | f4e8ebc2be0df6ce96aeff2aea4781e55522cb21 | /src/solutions/02_iff_if_and.lean | 896fced5baf5a544c1937f1cccd5cdd44747837f | [
"Apache-2.0"
] | permissive | robertylewis/tutorials | fb8a78d1352405077d4c82c6a04deabb32c1e37b | d3e1ac9ce73b9ed93a20036ce2a354ee923c783e | refs/heads/master | 1,666,261,949,784 | 1,591,464,085,000 | 1,591,464,607,000 | 270,056,466 | 0 | 0 | Apache-2.0 | 1,591,465,315,000 | 1,591,465,314,000 | null | UTF-8 | Lean | false | false | 15,330 | lean | import data.real.basic
/-
In the previous file, we saw how to rewrite using equalities.
The analogue operation with mathematical statements is rewriting using
equivalences. This is also done using the `rw` tactic.
Lean uses ↔ to denote equivalence instead of ⇔.
In the following exercises we will use the lemma:
su... |
15b1e8df87ebd002bedde4cca7b706c1187e9dff | 9995dfaf2c112e67489d4a6be1858e7b3c67ded6 | /proofs.lean | ff6fe9ab60ab2aa1ed51faab9157092a6ded5ee9 | [] | no_license | PJ41/proof-checking | dfe291be8e6a8872ec81e01c8326dc51ff06a17a | e7ce9c7905434f84e02e5707cec4f6a07749c4dd | refs/heads/master | 1,596,760,214,588 | 1,570,386,047,000 | 1,570,386,047,000 | 213,219,595 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,722 | lean | /- ****************** -/
/- *** PREDICATES *** -/
/- ****************** -/
/-
Define a function called isOdd that
takes an argument, n : ℕ, and returns a
proposition that asserts that n is odd.
The function will thus be a predicate on
values of type ℕ. Hint: a number is odd
if it's one more than an even number.
-/
... |
d5fb8a9b8df63a17400a515b9c2ed3f60864c12b | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /tests/lean/run/def13.lean | a41c43be30bc48f478aa5f85a62be9950b3ab454 | [
"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 | 586 | lean | variable {α} (p : α → Prop) [DecidablePred p]
def filter : List α → List α
| [] => []
| a::as => if p a then a :: filter as else filter as
theorem filter_nil : filter p [] = [] :=
rfl
theorem filter_cons (a : α) (as : List α) : filter p (a :: as) = if p a then a :: filter p as else filter p as :=
rfl
theorem fil... |
2f26986901398895adce064102889fe069d73e89 | 5d166a16ae129621cb54ca9dde86c275d7d2b483 | /library/init/meta/well_founded_tactics.lean | 92ad74b9af83e8ab3e45640b8546e0a25fc20c25 | [
"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 | 6,223 | 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 init.data.sigma.lex init.data.nat.lemmas init.data.list.instances
import init.data.list.qsort
/- TODO(Leo): move this lemma, or de... |
7fd0e40b6363fb56ef1a075dc181ac952e387e5e | 8d65764a9e5f0923a67fc435eb1a5a1d02fd80e3 | /src/ring_theory/ideal/basic.lean | be50543493ad8e3bcbbfba3e518853169be1331c | [
"Apache-2.0"
] | permissive | troyjlee/mathlib | e18d4b8026e32062ab9e89bc3b003a5d1cfec3f5 | 45e7eb8447555247246e3fe91c87066506c14875 | refs/heads/master | 1,689,248,035,046 | 1,629,470,528,000 | 1,629,470,528,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 36,658 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Chris Hughes, Mario Carneiro
-/
import algebra.associated
import linear_algebra.basic
import order.zorn
import order.atoms
import order.compactly_generated
/-!
# Ideals over a r... |
94d0bae095da320889114fc1e7970d988e5c8972 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /hott/cubical/squareover.hlean | 2f833ef141be8a8e22f635b53d2e2bcabcee1e86 | [
"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 | 17,129 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Floris van Doorn
Squareovers
-/
import .square
open eq equiv is_equiv sigma
namespace eq
-- we give the argument B explicitly, because Lean would find (λa, B a) by itself, whic... |
fc56090e838da95f6f3454e61baa22772b69b191 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /04_Quantifiers_and_Equality.org.28.lean | 7a92e70e0080bcf6b7d807fc421b7fc862cbc4ba | [] | no_license | cjmazey/lean-tutorial | ba559a49f82aa6c5848b9bf17b7389bf7f4ba645 | 381f61c9fcac56d01d959ae0fa6e376f2c4e3b34 | refs/heads/master | 1,610,286,098,832 | 1,447,124,923,000 | 1,447,124,923,000 | 43,082,433 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 300 | lean | /- page 59 -/
import standard
import data.nat
open nat
variable f : ℕ → ℕ
premise H : ∀ x : ℕ, f x ≤ f (x + 1)
-- BEGIN
example : f 0 ≤ f 3 :=
have f 0 ≤ f 1, from H 0,
have f 0 ≤ f 2, from le.trans `f 0 ≤ f 1` (H 1),
show f 0 ≤ f 3, from le.trans `f 0 ≤ f 2` (H 2)
-- END
|
415f0b807c6338bae64b8c64a4a259c9dbac9026 | 2a70b774d16dbdf5a533432ee0ebab6838df0948 | /_target/deps/mathlib/src/data/padics/padic_norm.lean | 50d5e71656b944b29b638bd0e84aef9039afbcc4 | [
"Apache-2.0"
] | permissive | hjvromen/lewis | 40b035973df7c77ebf927afab7878c76d05ff758 | 105b675f73630f028ad5d890897a51b3c1146fb0 | refs/heads/master | 1,677,944,636,343 | 1,676,555,301,000 | 1,676,555,301,000 | 327,553,599 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 26,096 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
-/
import ring_theory.int.basic
import algebra.field_power
import ring_theory.multiplicity
import data.real.cau_seq
import tactic.ring_exp
import tactic.basic
/-!
# p... |
716f21a12745609d2fabcaa4bb57f90ff6bef7ed | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/analysis/special_functions/pow.lean | 11c1967daf2281053f5b822f49e09d338ee33435 | [
"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 | 64,858 | 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, Sébastien Gouëzel,
Rémy Degenne
-/
import analysis.special_functions.trigonometric
import analysis.calculus.extend_deriv
... |
a4a5aa3373619543a85c724abd91aad58cdccb50 | 9b9a16fa2cb737daee6b2785474678b6fa91d6d4 | /src/category_theory/category.lean | df14d9953cbc34f2277e6441b06597744bd1e50f | [
"Apache-2.0"
] | permissive | johoelzl/mathlib | 253f46daa30b644d011e8e119025b01ad69735c4 | 592e3c7a2dfbd5826919b4605559d35d4d75938f | refs/heads/master | 1,625,657,216,488 | 1,551,374,946,000 | 1,551,374,946,000 | 98,915,829 | 0 | 0 | Apache-2.0 | 1,522,917,267,000 | 1,501,524,499,000 | Lean | UTF-8 | Lean | false | false | 5,258 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stephen Morgan, Scott Morrison, Johannes Hölzl, Reid Barton
Defines a category, as a typeclass parametrised by the type of objects.
Introduces notations
`X ⟶ Y` for the morphism spa... |
01ff050a22a8d0dd1c293c04418aa3b6076c15bd | 7565ffb53cc64430691ce89265da0f944ee43051 | /hott/algebra/inf_group.hlean | 5a8009b43721468d2f390da7785f8d96f520f248 | [
"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 | 26,768 | hlean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
-/
import algebra.binary algebra.priority
open eq eq.ops -- note: ⁻¹ will be overloaded
open binary algebra is_trunc
set_option class.force_new tru... |
7e6d99cc4374ef29457d875a64c16e8730701f21 | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/geometry/euclidean/circumcenter.lean | 4af9103976beb0770ef4e0b1e2024109362ef84b | [
"Apache-2.0"
] | permissive | jumpy4/mathlib | d3829e75173012833e9f15ac16e481e17596de0f | af36f1a35f279f0e5b3c2a77647c6bf2cfd51a13 | refs/heads/master | 1,693,508,842,818 | 1,636,203,271,000 | 1,636,203,271,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 38,254 | lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import geometry.euclidean.basic
import linear_algebra.affine_space.finite_dimensional
import tactic.derive_fintype
/-!
# Circumcenter and circumradius
This file proves ... |
028c04ba1e056696ae4a606b657d774b282f250e | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/group_theory/perm/cycle/type.lean | afc73b7b01826245528753580efcbea0b78caf59 | [
"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 | 28,045 | lean | /-
Copyright (c) 2020 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import algebra.gcd_monoid.multiset
import combinatorics.partition
import group_theory.perm.cycle.basic
import ring_theory.int.basic
import tactic.linarith
/-!
# C... |
99c626400f586229e068578d13508e7193792386 | 02005f45e00c7ecf2c8ca5db60251bd1e9c860b5 | /src/algebra/big_operators/basic.lean | f9530ed6c022a2133d15885e348aecd63951f239 | [
"Apache-2.0"
] | permissive | anthony2698/mathlib | 03cd69fe5c280b0916f6df2d07c614c8e1efe890 | 407615e05814e98b24b2ff322b14e8e3eb5e5d67 | refs/heads/master | 1,678,792,774,873 | 1,614,371,563,000 | 1,614,371,563,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 51,283 | 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 data.finset.fold
import data.equiv.mul_add
import tactic.abel
/-!
# Big operators
In this file we define products and sums indexed by finite sets (specifica... |
1d3a7f5f817b485c91b515d8e6d68cfba8faa3c4 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/tactic/nontriviality.lean | a039590b5a7248bf604f18a163966761f7ffd19c | [
"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 | 4,031 | 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 logic.nontrivial
/-!
# The `nontriviality` tactic.
-/
namespace tactic
/--
Tries to generate a `nontrivial α` instance by performing case analysis on
`sub... |
09be59e32f8ee8bf6014cee42a9a4760db056255 | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/induction2.lean | b8f4136e6f0857d4e0910b795a20ea7bba4ca1ac | [
"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 | 727 | lean | import macros -- loads the λ, λ, obtain macros
using Nat -- using the Nat namespace (it allows us to suppress the Nat:: prefix)
axiom Induction : ∀ P : Nat → Bool, P 0 → (∀ n, P n → P (n + 1)) → ∀ n, P n.
-- induction on n
theorem Comm1 : ∀ n m, n + m = m + n
:= Induction
_ -- I use a placeholder ... |
4a058e90f7f031a3196e4ac46038f1a925d330a4 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/logic/function/basic.lean | 69a318a5d230c5406c1225293b8d4801baa4f945 | [
"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 | 28,068 | lean | /-
Copyright (c) 2016 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import logic.basic
import data.option.defs
/-!
# Miscellaneous function constructions and lemmas
-/
universes u v w
namespace function
section
var... |
2264a5da0efc236ec915fb289a30c82028ee61f8 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/bicategory/functor.lean | 753c00ca9eb49e9ee7b330c10e5171346c067b41 | [
"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 | 19,514 | lean | /-
Copyright (c) 2022 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
import category_theory.bicategory.basic
/-!
# Oplax functors and pseudofunctors
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a correspond... |
1f71027b7c8c2eb4369710eb36cb13d1e506499e | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/set_theory/cardinal/basic.lean | e7b7eefa30b7c762bf5ec6bbbe1d1566b83c804c | [
"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 | 67,498 | 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, Floris van Doorn
-/
import data.fintype.card
import data.finsupp.defs
import data.nat.part_enat
import data.set.countable
import logic.small
import orde... |
93921dd43a90463d4daa2b810e0644accd639844 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/category_theory/limits/shapes/finite_products.lean | 4ae891118b8fb94bd69ba9714353ca76332e198c | [
"Apache-2.0"
] | permissive | rmitta/mathlib | 8d90aee30b4db2b013e01f62c33f297d7e64a43d | 883d974b608845bad30ae19e27e33c285200bf84 | refs/heads/master | 1,585,776,832,544 | 1,576,874,096,000 | 1,576,874,096,000 | 153,663,165 | 0 | 2 | Apache-2.0 | 1,544,806,490,000 | 1,539,884,365,000 | Lean | UTF-8 | Lean | false | false | 1,746 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.limits.shapes.products
import category_theory.limits.shapes.finite_limits
import category_theory.discrete_category
import data.fintype
univers... |
ffb06042464c2a401d0fd320b2a4e2ef0d8b6c77 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /09_Type_Classes.org.14.lean | 66543bf25b5bd69b999a3163d39d6a609e85ffcc | [] | no_license | cjmazey/lean-tutorial | ba559a49f82aa6c5848b9bf17b7389bf7f4ba645 | 381f61c9fcac56d01d959ae0fa6e376f2c4e3b34 | refs/heads/master | 1,610,286,098,832 | 1,447,124,923,000 | 1,447,124,923,000 | 43,082,433 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 211 | lean | import standard
namespace hide
-- BEGIN
definition dite (c : Prop) [H : decidable c] {A : Type} (t : c → A) (e : ¬ c → A) : A :=
decidable.rec_on H (λ Hc : c, t Hc) (λ Hnc : ¬ c, e Hnc)
-- END
end hide
|
58c8f06aa033c58ef4de9bdd912ea1421e1e1ec1 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/topology/instances/nnreal.lean | 27f38c343a2be9e5b55da1257328f6739ae6bd47 | [
"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 | 7,790 | lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import topology.algebra.infinite_sum
import topology.algebra.group_with_zero
/-!
# Topology on `ℝ≥0`
The natural topology on `ℝ≥0` (the one induced from `ℝ`), and a... |
8ba6acd870f09455f32fcb367f5bd003cb293ec0 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/category_theory/monoidal/functor.lean | 0024b6322bfc9110e2dd7d063677c767206a11a0 | [
"Apache-2.0"
] | permissive | gebner/mathlib | eab0150cc4f79ec45d2016a8c21750244a2e7ff0 | cc6a6edc397c55118df62831e23bfbd6e6c6b4ab | refs/heads/master | 1,625,574,853,976 | 1,586,712,827,000 | 1,586,712,827,000 | 99,101,412 | 1 | 0 | Apache-2.0 | 1,586,716,389,000 | 1,501,667,958,000 | Lean | UTF-8 | Lean | false | false | 6,463 | lean | /-
Copyright (c) 2018 Michael Jendrusch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Jendrusch, Scott Morrison
-/
import category_theory.monoidal.category
open category_theory
universes v₁ v₂ v₃ u₁ u₂ u₃
open category_theory.category
open category_theory.... |
8bf06a583fec6a88f833b048ddaf1460ec0ce416 | 1dd482be3f611941db7801003235dc84147ec60a | /src/data/fintype.lean | 843784753f0827437829aad683119d7fcaf8a3af | [
"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 | 29,375 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
Finite types.
-/
import data.finset algebra.big_operators data.array.lemmas data.vector2 data.equiv.encodable
universes u v
variables {α : Type*} {β : Type*} {γ : Type*... |
571f30c44c96150aae70228dabc23f402a37dd41 | 3c9dc4ea6cc92e02634ef557110bde9eae393338 | /src/Init/Meta.lean | d07970a6ca969be0c2400b38749e69d9dbd2695b | [
"Apache-2.0"
] | permissive | shingtaklam1324/lean4 | 3d7efe0c8743a4e33d3c6f4adbe1300df2e71492 | 351285a2e8ad0cef37af05851cfabf31edfb5970 | refs/heads/master | 1,676,827,679,740 | 1,610,462,623,000 | 1,610,552,340,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 28,467 | 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 and Sebastian Ullrich
Additional goodies for writing macros
-/
prelude
import Init.Data.Array.Basic
namespace Lean
@[extern c inline "lean_box(LEAN_VERSION_... |
8d06eac6a628bd3d3d6cfb44e60c46472a45d634 | 4fa118f6209450d4e8d058790e2967337811b2b5 | /src/valuation/localization.lean | f4172c8d2277a7e24ebdf0ea319f8ba8d4b99a5d | [
"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 | 13,435 | lean | import ring_theory.localization
import valuation.basic
/-!
# Extending valuations to localizations
In this file we extend valuations on a ring R to localizations of R.
We use this to define the valuation field, the valuation ring,
and the residue field of a valued ring.
If v is a valuation on an integral domain R a... |
db00c36bdfa33d02d512dd6124e95db7c3ec5b36 | c61b91f85121053c627318ad8fcde30dfb8637d2 | /Chapter2/2-5.lean | ff5a4c63a2f660dfde6bf71b23e9b26f35bfec2b | [] | no_license | robkorn/theorem-proving-in-lean-exercises | 9e2256360eaf6f8df6cdd8fd656e63dfb04c8cdb | 9c51da587105ee047a9db55d52709d881a39be7a | refs/heads/master | 1,585,403,341,988 | 1,540,142,619,000 | 1,540,142,619,000 | 148,431,678 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 203 | lean |
#check let y:= 20 in y * y
def e (a : ℕ) : ℕ :=
let y := a + a in y * y
#reduce e 2
def foo := let a := nat in λ x : a, x + 2
#print foo
-- def bar := (λ a, λ x : a, x + 2) nat |
99a4e2e2b6044abca33c95eb2586782173a140c5 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/ring_theory/mv_polynomial/symmetric.lean | 9eb7b27d26b8f1981cd9da45e1b9897ee380cb7e | [
"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 | 7,944 | lean | /-
Copyright (c) 2020 Hanting Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Hanting Zhang, Johan Commelin
-/
import data.mv_polynomial.rename
import data.mv_polynomial.comm_ring
import algebra.algebra.subalgebra.basic
/-!
# Symmetric Polynomials and Elementary... |
37ad3d1b1ff65130bab8ea90fef4bca387004867 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/casesOnCases.lean | 68b737f6894be72329864a27187d9e695cc8da19 | [
"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 | 326 | lean | import Lean
@[inline] def pred? (x : Nat) : Option Nat :=
match x with
| 0 => none
| x+1 => some x
def isZero (x : Nat) :=
match pred? x with
| some _ => false
| none => true
#eval Lean.Compiler.compile #[``isZero]
-- set_option trace.Compiler.simp true -- TODO: uncomment
#eval Lean.Compiler.compile #[``is... |
f7245bf02bbf1defca079df5c3bd584759dbcc20 | 1fbca480c1574e809ae95a3eda58188ff42a5e41 | /src/util/predicate/lemmas.lean | 59f8548c4b479d1d11b8f0df9619ccfd5bb8871b | [] | no_license | unitb/lean-lib | 560eea0acf02b1fd4bcaac9986d3d7f1a4290e7e | 439b80e606b4ebe4909a08b1d77f4f5c0ee3dee9 | refs/heads/master | 1,610,706,025,400 | 1,570,144,245,000 | 1,570,144,245,000 | 99,579,229 | 5 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 35,359 | lean |
import util.data.fin
import util.predicate.basic
import tactic.tauto
namespace predicate
universe variables u u' u₀ u₁ u₂
variables {α : Sort u₀}
variables {β : Sort u₁}
variables {γ : Sort u₂}
variables {σ : Sort u'}
@[simp, predicate]
lemma value_proj (p : var β γ) (f : var α β) (x : α)
: (p ! f).apply x = p.app... |
b2f82bd9ae7255543e9f670aaaaddded3aeec9b1 | 315b4184091c669ce8e5e07f9b24473c4bcfbaaf | /library/init/meta/interactive.lean | 8e6f9a987ed56f231c3e921fe8e82161ffeef2e4 | [
"Apache-2.0"
] | permissive | haraldschilly/lean | 78404910ad4c258cdf84e0509e4348c1525e57a9 | d01e2d7ae8250e8f69139d8cb37950079e76ca9d | refs/heads/master | 1,619,977,395,095 | 1,517,501,044,000 | 1,517,940,670,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 67,965 | 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.tactic init.meta.rewrite_tactic init.meta.simp_tactic
import init.meta.smt.congruence_closure init.category.combinators
import init... |
81a813b6102458effbf12214598c6d28843b5da9 | f1a12d4db0f46eee317d703e3336d33950a2fe7e | /common/algebra.lean | 9eb1d18eb543259fb98815f2dd417fe8baa74bee | [
"Apache-2.0"
] | permissive | avigad/qelim | bce89b79c717b7649860d41a41a37e37c982624f | b7d22864f1f0a2d21adad0f4fb3fc7ba665f8e60 | refs/heads/master | 1,584,548,938,232 | 1,526,773,708,000 | 1,526,773,708,000 | 134,967,693 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 664 | lean | lemma add_assoc' {α : Type} [add_semigroup α] :
∀ (a b c : α), a + (b + c) = a + b + c :=
begin
intros a b c, rewrite add_assoc
end
lemma mul_assoc' {α : Type} [comm_semigroup α] :
∀ (a b c : α), a * (b * c) = a * b * c :=
begin
intros a b c, rewrite mul_assoc
end
#check add_right_comm
lemma mul_comm_assoc ... |
fb4918502698743f37fdab7717ed3802a3528a1d | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/nat_coe.lean | bb9c5280d7ce543ae45f89e682d9a36133f741e3 | [
"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 | 447 | lean | import logic
namespace experiment
constant nat : Type.{1}
constant int : Type.{1}
constant nat_add : nat → nat → nat
infixl `+` := nat_add
constant int_add : int → int → int
infixl `+` := int_add
constant of_nat : nat → int
attribute of_nat [coercion]
constants a b : nat
constants i j : int
definition c1 := a + b
... |
562d2c940942d0b5a9138ca3b19329025202a499 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/meta_tac3.lean | b3bfd667444f0ea1c6b1b8261c63e1e4bd2158e7 | [
"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 | 483 | lean | open tactic name list
set_option pp.goal.compact true
set_option pp.binder_types true
example : ∀ (A B : Prop), A → A ∧ B → A → A :=
by do
intro_lst [`_, `_, `H1, `H2, `H3],
trace_state,
h2 ← get_local `H2,
infer_type h2 >>= trace,
h1 ← get_local `H1,
h3 ← get_local `H3,
unify h1 h3,
(... |
bec6205c1da03ac1c7e8ed7fefe3f33855d88538 | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /tests/lean/run/concatElim.lean | ead40d45bd4e03a1d095bd0bb47012067a66d762 | [
"Apache-2.0"
] | permissive | dupuisf/lean4 | d082d13b01243e1de29ae680eefb476961221eef | 6a39c65bd28eb0e28c3870188f348c8914502718 | refs/heads/master | 1,676,948,755,391 | 1,610,665,114,000 | 1,610,665,114,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,993 | lean | universes u
def concat {α} : List α → α → List α
| [], a => [a]
| x::xs, a => x :: concat xs a
def last {α} : (xs : List α) → xs ≠ [] → α
| [], h => absurd rfl h
| [a], h => a
| _::a::as, h => last (a::as) (fun h => by injection h)
def dropLast {α} : List α → List α
| [] => []
| [a] ... |
b705c43b4f7f0b2e1315271b26464c91ac942878 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/algebra/monoid.lean | 305780ebd37023e3b35d9a450ec190b0574e025e | [
"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 | 30,841 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import algebra.big_operators.finprod
import order.filter.pointwise
import topology.algebra.mul_action
import algebra.big_operators.pi
import topology.... |
2f3321f3f786a3f78885f609f95ecd6910ece5c8 | e0f9ba56b7fedc16ef8697f6caeef5898b435143 | /src/category_theory/limits/shapes/biproducts.lean | 7bad27816c065dac5d4d0a7c0ddad1ed4369905b | [
"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 | 11,699 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.epi_mono
import category_theory.limits.shapes.binary_products
/-!
# Biproducts and binary biproducts
We introduce the notion of biproducts an... |
ca326e8c5b0e38969e997a852ecea575e437aef8 | 6e9cd8d58e550c481a3b45806bd34a3514c6b3e0 | /src/linear_algebra/affine_space.lean | 699d9f18a2004cf255544334777f3ab1201eeb3a | [
"Apache-2.0"
] | permissive | sflicht/mathlib | 220fd16e463928110e7b0a50bbed7b731979407f | 1b2048d7195314a7e34e06770948ee00f0ac3545 | refs/heads/master | 1,665,934,056,043 | 1,591,373,803,000 | 1,591,373,803,000 | 269,815,267 | 0 | 0 | Apache-2.0 | 1,591,402,068,000 | 1,591,402,067,000 | null | UTF-8 | Lean | false | false | 10,402 | 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 algebra.add_torsor
import linear_algebra.basis
noncomputable theory
/-!
# Affine spaces
This file defines affine spaces (over modules) and subspaces, affine
map... |
59c488b572849b149094f9ff7bb8e388081e3a7b | 0c1546a496eccfb56620165cad015f88d56190c5 | /tests/lean/run/defaul_param3.lean | 1db7967f9a6e89d1924973ec476d5b30698e2f9b | [
"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 | 261 | lean | meta constant f (a : nat) (b : nat := 10) : tactic unit
meta example : tactic unit :=
f 10
constant g (a : nat) (b : nat := 10) (c : nat) : nat
example : g 0 = g 0 10 :=
rfl
noncomputable example : nat :=
g 0 1 2
noncomputable example : nat → nat :=
g 0
|
aa8831ae8d1a36b70fb52d424fc5d3738385a93a | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/theories/analysis/real_limit.lean | b97c1969dcb7f2ae950d3febddf4f63ca6c4dbf3 | [
"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 | 22,416 | lean | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis
Instantiates the reals as a Banach space.
-/
import .metric_space data.real.complete data.set .normed_space
open real classical analysis nat
noncomputabl... |
8ce56ac57ab610dd64acd9660aacbdabbb4a8fc8 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/measure_theory/integral/riesz_markov_kakutani.lean | aeff61a56f4f42b412eaaa937c41595579b5a661 | [
"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 | 5,014 | lean | /-
Copyright (c) 2022 Jesse Reimann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Reimann, Kalle Kytölä
-/
import topology.continuous_function.bounded
import topology.sets.compacts
/-!
# Riesz–Markov–Kakutani representation theorem
This file will prove diffe... |
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