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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
ee00f8dc5e42189716c2b2bb334d200658a810d7 | 38bf3fd2bb651ab70511408fcf70e2029e2ba310 | /src/algebra/geom_sum.lean | 4ce9555372f01466d18920c15803edcfebcc1154 | [
"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 | 5,405 | lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Neil Strickland
Sums of finite geometric series
-/
import algebra.big_operators algebra.commute
universe u
variable {α : Type u}
open finset
/-- Sum of the finite geometric serie... |
46b6ffb874fb0e92e6f52cd8f1c72ffc907f8b27 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/ring_theory/polynomial/basic.lean | 0108ac8987e6e2460ada45b75992be85dea208b0 | [
"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 | 50,304 | lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import algebra.char_p.basic
import data.mv_polynomial.comm_ring
import data.mv_polynomial.equiv
import ring_theory.polynomial.content
import ring_theory.unique_factorization_d... |
f9e4d592b21fe1ad7f60589e225137cf8b759591 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/ring_theory/nakayama.lean | e1ee04629f7c5e66163675ff70c28c87ace912fd | [
"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 | 4,429 | lean | /-
Copyright (c) 2021 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import ring_theory.jacobson_ideal
/-!
# Nakayama's lemma
This file contains some alternative statements of Nakayama's Lemma as found in
[Stacks: Nakayama's Lemma](https... |
c20cea9170a19977d9a7a3d258bcabf4dee8474a | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/combinatorics/simple_graph/regularity/bound.lean | 4771c319aacf19a5b3e311bbf0ca20615c418bbd | [
"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 | 6,473 | lean | /-
Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import analysis.special_functions.pow
import order.partition.equipartition
/-!
# Numerical bounds for Szemerédi Regularity Lemma
This file g... |
65db0a1d31935aa0fdfe0b2a5254215227c120dc | c777c32c8e484e195053731103c5e52af26a25d1 | /src/analysis/calculus/cont_diff.lean | 2a8cced40e013911ce789b41a681cfc3a6fd2c68 | [
"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 | 142,248 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Floris van Doorn
-/
import analysis.calculus.cont_diff_def
import analysis.calculus.mean_value
import analysis.normed_space.finite_dimension
import data.nat.choos... |
eccfe6435721a81c3d0ab6c1216740a701d28a89 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/order/bounds.lean | 1c2c10c2a4fb58f17ff6e903ca185d4580318671 | [] | 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 | 36,756 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.set.intervals.basic
import Mathlib.algebra.ordered_group
import Mathl... |
fcc695485f3edfcbf496182c3e5e8e42db2ddabc | 02005f45e00c7ecf2c8ca5db60251bd1e9c860b5 | /src/data/polynomial/algebra_map.lean | 22dfaa3576377cd5d0b9b446e87aed9f99373770 | [
"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 | 9,649 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
-/
import data.polynomial.eval
import algebra.algebra.tower
/-!
# Theory of univariate polynomials
We show that `polynomia... |
4398c4afbce12cb29f5fcd9044a57bb521588890 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/data/rbtree/insert.lean | f2ec9570eab081ce36d2362baa038da3faaad1ca | [
"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 | 33,912 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import data.rbtree.find
universes u v
local attribute [simp] rbnode.lift
namespace rbnode
variables {α : Type u}
open color
@[simp] lemma balance1_eq₁ (... |
71d99cc9df5a6b4ad7ff360967caed3c8d0d70a6 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/computability/primrec.lean | d0ca8d9e0a5f1e9bb23c3579de42ae786add7f9e | [
"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 | 51,929 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.equiv.list
import logic.function.iterate
/-!
# The primitive recursive functions
The primitive recursive functions are the least collection of functions... |
436904fef1cb6e9a9978c14a32d84e7cf8665390 | 1a61aba1b67cddccce19532a9596efe44be4285f | /library/logic/quantifiers.lean | edf1c6ef226051a27741b182cafcc21cdf529470 | [
"Apache-2.0"
] | permissive | eigengrau/lean | 07986a0f2548688c13ba36231f6cdbee82abf4c6 | f8a773be1112015e2d232661ce616d23f12874d0 | refs/heads/master | 1,610,939,198,566 | 1,441,352,386,000 | 1,441,352,494,000 | 41,903,576 | 0 | 0 | null | 1,441,352,210,000 | 1,441,352,210,000 | null | UTF-8 | Lean | false | false | 3,640 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad
Universal and existential quantifiers. See also init.logic.
-/
import .connectives
open inhabited nonempty
theorem exists_imp_distrib {A : Typ... |
2e66abc0a1c90862ef42f65c1505eda21b895b28 | ce6917c5bacabee346655160b74a307b4a5ab620 | /src/ch3/ex0304.lean | b5d7e18a055ce742cb90c39097de7f22038b4444 | [] | no_license | Ailrun/Theorem_Proving_in_Lean | ae6a23f3c54d62d401314d6a771e8ff8b4132db2 | 2eb1b5caf93c6a5a555c79e9097cf2ba5a66cf68 | refs/heads/master | 1,609,838,270,467 | 1,586,846,743,000 | 1,586,846,743,000 | 240,967,761 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 104 | lean | variables p q : Prop
example (h : p ∧ q) : q ∧ p := and.intro (and.elim_right h) (and.elim_left h)
|
756897d3c294e93a4c6c7499fb8bbe1abd043ea0 | 5c7fe6c4a9d4079b5457ffa5f061797d42a1cd65 | /src/exercises/src_06_rewriting_implicit.lean | 1986bded2505063d67fd9cfd033bc9fad771a4b3 | [] | no_license | gihanmarasingha/mth1001_tutorial | 8e0817feeb96e7c1bb3bac49b63e3c9a3a329061 | bb277eebd5013766e1418365b91416b406275130 | refs/heads/master | 1,675,008,746,310 | 1,607,993,443,000 | 1,607,993,443,000 | 321,511,270 | 3 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,305 | lean | import tactic.linarith
import .src_05_if_and_only_if
variables p q r : Prop
namespace mth1001
section rewriting
/-
Statements of the form `p ↔ q` play a cruicial role in logic. Given `h : p ↔ q`, we can
replace `p`, wherever it appears, with `q`. This is called rewriting.
-/
/-
Here, the `rewrite` tactic (abbrev... |
77e7fd2008434f475c688347637f3b0419ebfeaf | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/data/set/basic.lean | 78d0b5da8393e8a9dd1c63f17bd4d2a9dad31e17 | [
"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 | 55,390 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad, Leonardo de Moura
-/
import tactic.basic tactic.finish data.subtype logic.unique
open function
/- set coercion to a type -/
namespace set
instance {α : Type*} : has_coe_... |
23090104e590b3820bceab6716c3b9581530f9c7 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/data/two_pointing.lean | 91a1b94219ef48bff27e798f0cc09716a5b3d36f | [
"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 | 3,401 | lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import data.sum.basic
import logic.nontrivial
/-!
# Two-pointings
This file defines `two_pointing α`, the type of two pointings of `α`. A two-pointing is the data of
tw... |
5f16b8985afbf38d30711c379a497e79472456b2 | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /tests/lean/run/coe4.lean | 08c4e4097e8b7e5880c0ab6543e244d34ce9afa9 | [
"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 | 825 | lean | import logic
namespace setoid
inductive setoid : Type :=
mk_setoid: Π (A : Type'), (A → A → Prop) → setoid
set_option pp.universes true
check setoid
definition test : Type.{2} := setoid.{0}
definition carrier (s : setoid)
:= setoid.rec (λ a eq, a) s
definition eqv {s : setoid} : carrier s → carrier... |
0a1421ce50175584d667b648c9455742544262c9 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/topology/uniform_space/uniform_embedding.lean | 1622af04bdd3cd1e8db343e03aad60fca6494f63 | [
"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 | 20,235 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Sébastien Gouëzel, Patrick Massot
Uniform embeddings of uniform spaces. Extension of uniform continuous functions.
-/
import topology.uniform_space.cauchy topology.uni... |
4557d24fc16723d748e82663f883ebed34ca0fa0 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/algebra/support.lean | 2f46a6e282cdf2f7c021ae29fe08bd0fae68bd09 | [
"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 | 11,165 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import order.conditionally_complete_lattice
import algebra.big_operators.basic
import algebra.group.prod
import algebra.group.pi
import algebra.module.pi
/-!
# Sup... |
8101776cb0a0d34e1c9064bac32c6c6c9a03f091 | f3a5af2927397cf346ec0e24312bfff077f00425 | /src/game/world3/level5.lean | 7661ca00d898f7aaaa6a1b04f05ccedcc3a623bc | [
"Apache-2.0"
] | permissive | ImperialCollegeLondon/natural_number_game | 05c39e1586408cfb563d1a12e1085a90726ab655 | f29b6c2884299fc63fdfc81ae5d7daaa3219f9fd | refs/heads/master | 1,688,570,964,990 | 1,636,908,242,000 | 1,636,908,242,000 | 195,403,790 | 277 | 84 | Apache-2.0 | 1,694,547,955,000 | 1,562,328,792,000 | Lean | UTF-8 | Lean | false | false | 1,168 | lean | import game.world3.level4 -- hide
import mynat.mul -- hide
namespace mynat -- hide
/-
# Multiplication World
## Level 5: `mul_assoc`
We now have enough to prove that multiplication is associative.
## Random tactic hints
1) Did you know you can do `repeat {rw mul_succ}`?
2) Did you know you can do `rwa [hd, mul_a... |
510e7c80c33d2aba4c7b54826c07bb591fa3221b | 76ce87faa6bc3c2aa9af5962009e01e04f2a074a | /Exam2-Review.lean | 01eaab310102ed3f49918e5c4de77ad12c4ca8b7 | [] | no_license | Mnormansell/Discrete-Notes | db423dd9206bbe7080aecb84b4c2d275b758af97 | 61f13b98be590269fc4822be7b47924a6ddc1261 | refs/heads/master | 1,585,412,435,424 | 1,540,919,483,000 | 1,540,919,483,000 | 148,684,638 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,055 | lean | /-
You need to understand the following
elements of automated predicate logic
for Exam 2
Suppose P and Q are arbitrary propositions
(i.e., P Q : Prop) and T and V are arbitrary
types (i.e., T V : Type).
Know the following forms, how to prove them,
how to use proofs of them, and how to do these
things in Lean.
... |
dba06286c4bad232f5d1d70f434e309ab0fa1b2f | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /src/Init/Data/List/BasicAux.lean | af6f411116073f08fe1834f5dd7e4ab9db0406d6 | [
"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 | 1,825 | lean | /-
Copyright (c) 2019 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.List.Basic
import Init.Util
universes u
namespace List
/- The following functions can't be defined at `init.data.list.basic`, beca... |
c2d7e3cb3e554c49357c5c582bfb2b172c5c9f72 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/group/semiconj.lean | f3d9217d9a060e0767bb35f48d8243c69057e321 | [
"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 | 7,861 | lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
Some proofs and docs came from `algebra/commute` (c) Neil Strickland
-/
import algebra.group.units
/-!
# Semiconjugate elements of a semigroup
> THIS FILE IS SYNCHR... |
b0b26e87eb0700138fdfa17c093314af07e361dc | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/unsafeInit.lean | 56e8afa9753a4a3099080e5a50f9b167d2caea14 | [
"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 | 50 | lean | unsafe initialize no : Nat ← pure lcUnreachable
|
49a9aa05209e54a676f92154b2a4855d5e745896 | 96b8fa8ff5edc088c62b8e0d92e4599e8edbf1e2 | /Cli/Extensions.lean | f8af3e6640f4c4308ea97be356d50d6d1389155e | [
"MIT"
] | permissive | pnwamk/lean4-cli | 4429db4cebfca510573150ade5e8ed3087014051 | 0a66055885086864114c8b281830a47f2b601ff4 | refs/heads/main | 1,678,627,315,712 | 1,614,105,437,000 | 1,614,105,437,000 | 342,072,945 | 0 | 0 | null | 1,614,212,319,000 | 1,614,212,318,000 | null | UTF-8 | Lean | false | false | 4,541 | lean | import Cli.Basic
section Utils
namespace Array
/--
Appends those elements of `right` to `left` whose `key` is not already
contained in `left`.
-/
def leftUnionBy [HasLess α] [DecidableRel ((· < ·) : α → α → Prop)]
(key : β → α) (left : Array β) (right : Array β)
: Array β := do
... |
848342d7c4778725a028a7754976e2d1777dbc34 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/order/lexicographic.lean | 83bb4acc9b6982406ef50bf1366e1b79eeda58f7 | [
"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 | 8,718 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Minchao Wu
-/
import tactic.basic
/-!
# Lexicographic order
This file defines the lexicographic relation for pairs and dependent pairs of orders, partial orders
and l... |
b6fde5911f254f936a64b6903be62553378603da | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/ring_theory/localization.lean | 436f2a4d53a58c959eb966b5b58a4e86fb838a18 | [
"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 | 27,189 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Mario Carneiro, Johan Commelin
-/
import tactic.ring data.quot data.equiv.ring ring_theory.ideal_operations group_theory.submonoid
universes u v
local attribute [instance, prio... |
818fd40271096f8cd2218aa4e089f987d382ed8a | 4f065978c49388d188224610d9984673079f7d91 | /canonically_isomorphic.lean | aac568210b79a9f2ef151c72f64d9f5376f91e19 | [] | no_license | kckennylau/Lean | b323103f52706304907adcfaee6f5cb8095d4a33 | 907d0a4d2bd8f23785abd6142ad53d308c54fdcb | refs/heads/master | 1,624,623,720,653 | 1,563,901,820,000 | 1,563,901,820,000 | 109,506,702 | 3 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 1,390 | lean | universe zfc_u
structure equiv' (α : Type zfc_u) (β : Type zfc_u) :=
(i : α → β)
(j : β → α)
(ij : ∀ x, j (i x) = x)
(ji : ∀ y, i (j y) = y)
namespace equiv'
variables {α β γ : Type zfc_u}
@[refl] protected def refl (α : Type zfc_u) : equiv' α α := ⟨id, id, λ x, rfl, λ x, rfl⟩
@[symm] protected def symm (e : equ... |
0bb972852c0995a131c04cf34a17af0e00ab4d27 | 3dd1b66af77106badae6edb1c4dea91a146ead30 | /tests/lean/run/class3.lean | 9c81dd297dbc3cd81e6222a0f2f0534a9b7ab26e | [
"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 | 428 | lean | import standard
using num pair
section
parameter {A : Type}
parameter {B : Type}
parameter Ha : inhabited A
parameter Hb : inhabited B
-- The section mechanism only includes parameters that are explicitly cited.
-- So, we use the 'including' expression to make explicit we want to use
-- Ha and Hb
theor... |
dbfe442096913ae04acd24d7bbd2d5748da8ef6b | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/measure_theory/decomposition/lebesgue.lean | d42dfab5e70c2c5337c9df2ba1fb0533393b18ed | [
"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 | 63,303 | lean | /-
Copyright (c) 2021 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import measure_theory.measure.complex
import measure_theory.measure.sub
import measure_theory.decomposition.jordan
import measure_theory.measure.with_density_vector_measure... |
c9c77fb18c6f4b234a11ff10ca226ee875ee9225 | 892c0ca8b8ddfe17a2c64fb7b721f9e2d9287539 | /semantics.lean | 85445eb8438b06ed870c7fc2663f04aa8eb3520e | [] | no_license | ssomayyajula/stlc | f7ef96de541f9519b00912337332366317282dce | cf92bf387b4418f9a6261c7ea4876db4e4280dd2 | refs/heads/master | 1,630,729,373,254 | 1,516,045,347,000 | 1,516,045,347,000 | 115,835,353 | 5 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,592 | lean | import .syntax
def fv : term → set var
| (term.var x) := {x}
| (term.app e₁ e₂) := fv e₁ ∪ fv e₂
| (term.abs x _ e) := fv e \ {x}
| term.unit := ∅
-- e' = e{v/x}
inductive is_subst : term → term → term → var → Prop
| unit (x : var) (e : term) : is_subst term.unit term.unit e x
-- e = x{e/x}
| same_var (x... |
c3f0c4afc940c4a6e7e1d7b2f8028fcaf48d0e69 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /03_Propositions_and_Proofs.org.5.lean | aef7ba193b5634694e0e8119567616fab650af80 | [] | 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 | 108 | lean | /- page 35 -/
import standard
constants p q : Prop
theorem t1 : p → q → p := λ Hp : p, λ Hq : q, Hp
|
a70a9f5479b35dbd9547915454a344cba5e06adb | 05b503addd423dd68145d68b8cde5cd595d74365 | /src/computability/turing_machine.lean | 5b8e3856bc6bfdb4f39a248e691b269cfe785ce1 | [
"Apache-2.0"
] | permissive | aestriplex/mathlib | 77513ff2b176d74a3bec114f33b519069788811d | e2fa8b2b1b732d7c25119229e3cdfba8370cb00f | refs/heads/master | 1,621,969,960,692 | 1,586,279,279,000 | 1,586,279,279,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 68,075 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
Define a sequence of simple machine languages, starting with Turing
machines and working up to more complex lanaguages based on
Wang B-machines.
-/
import data.fintype.b... |
843fc2c33bc193e3598170fdec8b33ab7e2c9e13 | 8e31b9e0d8cec76b5aa1e60a240bbd557d01047c | /scratch/simplex_no_bar.lean | bd3e11d3a4a57ddc7b70656f5ac5129cacb6424c | [] | no_license | ChrisHughes24/LP | 7bdd62cb648461c67246457f3ddcb9518226dd49 | e3ed64c2d1f642696104584e74ae7226d8e916de | refs/heads/master | 1,685,642,642,858 | 1,578,070,602,000 | 1,578,070,602,000 | 195,268,102 | 4 | 3 | null | 1,569,229,518,000 | 1,562,255,287,000 | Lean | UTF-8 | Lean | false | false | 33,798 | lean | import data.matrix data.rat.basic
import linear_algebra.determinant .misc order.pilex
import order.lexicographic .list_sup .fin_find tactic.omega tactic.abel
import data.list.min_max algebra.associated .matrix_pequiv
open matrix fintype finset function
variables {m n : ℕ}
variables (A : matrix (fin m) (fin n) ℚ)
loc... |
047a13833bafc63498b88f5814e1b0bc3c3d53bd | 6fca17f8d5025f89be1b2d9d15c9e0c4b4900cbf | /src/game/world3/level8.lean | e9235d69fa682e585b7d71ff57a7ec7834abaeba | [
"Apache-2.0"
] | permissive | arolihas/natural_number_game | 4f0c93feefec93b8824b2b96adff8b702b8b43ce | 8e4f7b4b42888a3b77429f90cce16292bd288138 | refs/heads/master | 1,621,872,426,808 | 1,586,270,467,000 | 1,586,270,467,000 | 253,648,466 | 0 | 0 | null | 1,586,219,694,000 | 1,586,219,694,000 | null | UTF-8 | Lean | false | false | 982 | lean | import game.world3.level7 -- hide
namespace mynat -- hide
/-
# Multiplication World
## Level 8: `mul_comm`
Finally, the boss level of multiplication world. But (assuming you
didn't cheat) you are well-prepared for it -- you have `zero_mul`
and `mul_zero`, as well as `succ_mul` and `mul_succ`. After this
level you ca... |
84fd49cf2cf27d0d5a2e9828d2bef2342c202f52 | 6c56e3fbe5d7711b66a3b46f1810b44cfa109768 | /src/day1.lean | 4e088f15c3c41e31b94622e55ba66d690708233c | [] | no_license | kodyvajjha/lean-mmc2021 | 015e7ba9d2f43397582d42ad282e88c8ce876dc3 | cc774208f9dc041cad4def289357301b4a0a8173 | refs/heads/master | 1,689,416,888,246 | 1,630,161,054,000 | 1,630,161,054,000 | 384,140,257 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,496 | lean | /-
# Propositions as Types.
In this file, we shall be introduced to the paradigm of
*Propositions as Types* and how they are handled in Lean.
We shall also use this oppurtunity to get familiar with
Lean's syntax.
Acknowledgements : Heavily borrowed from Jalex Stark and
Apurva Nakade's tutorial.
Import commands... |
1880249437e0c26f9e196d153ad19ad149c9de14 | 3f1a1d97c03bb24b55a1b9969bb4b3c619491d5a | /library/data/rbtree/find.lean | 1ab55ad83d4e23806f283faab6bd0c1060d51125 | [
"Apache-2.0"
] | permissive | praveenmunagapati/lean | 00c3b4496cef8e758396005013b9776bb82c4f56 | fc760f57d20e0a486d14bc8a08d89147b60f530c | refs/heads/master | 1,630,692,342,183 | 1,515,626,222,000 | 1,515,626,222,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,124 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import data.rbtree.basic
universe u
namespace rbnode
variables {α : Type u}
@[elab_simple]
lemma find.induction {p : rbnode α → Prop} (lt) [decidable_rel ... |
a60633cc616a24d2d1a46db44fe6a165e407ec4f | fecda8e6b848337561d6467a1e30cf23176d6ad0 | /test/tauto.lean | 44a371647910d2cf42a032e4367184a247c8fe92 | [
"Apache-2.0"
] | permissive | spolu/mathlib | bacf18c3d2a561d00ecdc9413187729dd1f705ed | 480c92cdfe1cf3c2d083abded87e82162e8814f4 | refs/heads/master | 1,671,684,094,325 | 1,600,736,045,000 | 1,600,736,045,000 | 297,564,749 | 1 | 0 | null | 1,600,758,368,000 | 1,600,758,367,000 | null | UTF-8 | Lean | false | false | 3,025 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import tactic.tauto
import tactic
section tauto₀
variables p q r : Prop
variables h : p ∧ q ∨ p ∧ r
include h
example : p ∧ p :=
by tauto
end tauto₀
section tauto₁
varia... |
f5ca4299422312c02429a2b8c26888f478bd3dd3 | d0f9af2b0ace5ce352570d61b09019c8ef4a3b96 | /exam_2/predicate_logic/proofs.lean | 5d2acd53c12332d93d635ba4ba610b9f2fc7dedd | [] | no_license | jngo13/Discrete-Mathematics | 8671540ef2da7c75915d32332dd20c02f001474e | bf674a866e61f60e6e6d128df85fa73819091787 | refs/heads/master | 1,675,615,657,924 | 1,609,142,011,000 | 1,609,142,011,000 | 267,190,341 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,130 | lean | /-
Today we will see in that proofs can be understood as formal
objects in their own right.
We will start to make our way through the valid rules of
inference from our unit on propositional logic. We will
emphasize that they are rules for combining and deriving
Boolean truth values. In predicate logic, by contrast, w... |
bfacce3274a6cea6c957700e95061288c87f8faf | 17d3c61bf162bf88be633867ed4cb201378a8769 | /library/init/meta/congr_lemma.lean | d2445a316d24a41d2e0120cdea7f5bb6b7ad7278 | [
"Apache-2.0"
] | permissive | u20024804/lean | 11def01468fb4796fb0da76015855adceac7e311 | d315e424ff17faf6fe096a0a1407b70193009726 | refs/heads/master | 1,611,388,567,561 | 1,485,836,506,000 | 1,485,836,625,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,722 | 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.format init.function
inductive congr_arg_kind
/- It is a parameter for the congruence lemma, the parameter occurs... |
9a4b599bc1dc209a7c3932bb68ca3ec4ac614847 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/category_theory/concrete_category/basic.lean | 2511901ec5badefc09f0b604b7ee20dd808ced61 | [
"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 | 10,279 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Johannes Hölzl, Reid Barton, Sean Leather, Yury Kudryashov
-/
import category_theory.types
import category_theory.functor.epi_mono
import category_theory.limits.constru... |
fd889603c5cb1d1ccd99dbbab715a89dd21c2b8f | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/prec_max.lean | 30f6942ed07d516822679d663af1738eaec7d5a8 | [
"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 | 354 | lean | open nat
reserve postfix ⁻¹:(max + 1)
postfix ⁻¹ := eq.symm
constant foo (a b : nat) : a + b = 0
theorem tst1 (a b : nat) : 0 = a + b :=
!foo⁻¹
constant f {a b : nat} (h1 : 0 = a + b) (h2 : a = b) : a = 0 ∧ b = 0
example (a b : nat) : a = 0 ∧ b = 0 :=
f !foo⁻¹ sorry
example (a b : nat) : a = 0 ∧ b = 0 :=
f !foo⁻... |
abb45e39105b720d743068faf05be8dc75328c5a | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/blast_by_contradiction.lean | 4eff2381f845ba1e2efe168282b29d1eb0950514 | [
"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 | 419 | lean | constants P Q : Prop
namespace with_classical
open classical
example : Q → (Q → ¬ P → false) → P := by blast
example : Q → (Q → P → false) → ¬ P := by blast
end with_classical
namespace with_decidable
constant P_dec : decidable P
attribute P_dec [instance]
definition foo : Q → (Q → ¬ P → false) → P := by blast
exam... |
54547feb42edc79105e0ced822b8ecc03a12baf2 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/data/mv_polynomial/equiv.lean | 9e6f07645586b40fd88a2958ccd5211228bb36b7 | [
"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 | 12,140 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
-/
import data.mv_polynomial.rename
import data.equiv.fin
import data.polynomial.algebra_map
/-!
# Equivalences between polynomial ring... |
ab4f6ced516e8ee6ec8ae285301f1782e3561110 | 7b66d83f3b69dae0a3dfb684d7ebe5e9e3f3c913 | /src/solutions/thursday/afternoon/category_theory/exercise7.lean | 38523506dafc5b59cee1f40619dec8102d36b181 | [] | permissive | dpochekutov/lftcm2020 | 58a09e10f0e638075b97884d3c2612eb90296adb | cdfbf1ac089f21058e523db73f2476c9c98ed16a | refs/heads/master | 1,669,226,265,076 | 1,594,629,725,000 | 1,594,629,725,000 | 279,213,346 | 1 | 0 | MIT | 1,594,622,757,000 | 1,594,615,843,000 | null | UTF-8 | Lean | false | false | 1,875 | lean | import algebra.category.CommRing.basic
import data.polynomial
/-!
Let show that taking polynomials over a ring is functor `Ring ⥤ Ring`.
-/
noncomputable theory -- the default implementation of polynomials is noncomputable
/-!
mathlib is undergoing a transition at the moment from using "unbundled" homomorphisms
(e.g... |
280eb247c0fe554d0e28a54d0e2010cd98a99e79 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/cases_failure.hlean | 348b7a95e4bbdf543196a5fc0501cc54fcd53062 | [
"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 | 388 | hlean | -- .hlean file
open eq
inductive square {A : Type} {a₀₀ : A}
: Π{a₀₁ a₁₀ a₁₁ : A}, a₀₀ = a₀₁ → a₁₀ = a₁₁ → a₀₀ = a₁₀ → a₀₁ = a₁₁ → Type :=
ids : square idp idp idp idp
definition foo {A : Type} {x y z : A} {t : x = y} {b : z = y} {l : x = z} {r : y = y}
(s : square t b l r) : unit :=
begin
cases s,
exact uni... |
a8bbfa98477ea8d0159b659b1a4d7764020fbf57 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/topology/vector_bundle/hom.lean | 20c00d4d1189445ce1bda656dbe5158450d6bbad | [
"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 | 17,052 | lean | /-
Copyright © 2022 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth, Floris van Doorn
-/
import topology.vector_bundle.basic
import analysis.normed_space.operator_norm
/-!
# The vector bundle of continuous (semi)linear maps
We define ... |
255c4575a70c47366edc92aed64d303670539329 | 4fa161becb8ce7378a709f5992a594764699e268 | /src/ring_theory/subring.lean | 3a1ea1c95a5163c2617dce9849ea63e5107f66bf | [
"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 | 8,253 | 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 deprecated.subgroup
universes u v
open group
variables {R : Type u} [ring R]
section prio
set_option default_priority 100 -- see Note [default priority]
/-... |
68735f9cb9063da710aaedcd45bcb1fbd55db941 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /test/norm_cast_lemma_order.lean | 243f39b1e91c2bbbbb5102cd0e93e9d51d2758a5 | [
"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 | 640 | lean | import data.nat.cast
import tactic.norm_cast
constant ℝ : Type
@[instance] constant real.add_monoid_with_one : add_monoid_with_one ℝ
-- set_option trace.simplify.rewrite true
set_option pp.notation false
set_option pp.numerals false
-- should work
run_cmd norm_cast.numeral_to_coe `(0 : ℝ)
run_cmd norm_cast.numeral_t... |
1a0100a724f90a007508a65d2628ffea8ce8d931 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/run/io_state.lean | a126a41ca413f38938b0f4920f60ad5fda45ae6c | [
"Apache-2.0"
] | permissive | GaloisInc/lean | aa1e64d604051e602fcf4610061314b9a37ab8cd | f1ec117a24459b59c6ff9e56a1d09d9e9e60a6c0 | refs/heads/master | 1,592,202,909,807 | 1,504,624,387,000 | 1,504,624,387,000 | 75,319,626 | 2 | 1 | Apache-2.0 | 1,539,290,164,000 | 1,480,616,104,000 | C++ | UTF-8 | Lean | false | false | 315 | lean | import system.io
open io state_t
variable [io.interface]
@[reducible] def my_io := state_t nat io
instance lift_io {α} : has_coe (io α) (my_io α) :=
⟨state_t.lift⟩
def tst : my_io unit :=
do x ← read,
print_ln x,
write (x+10),
y ← read,
print_ln y,
put_str "end of program"
#eval tst 5
|
1ae0a36aade223d1706c1e5f960b479f2a207548 | 4fa161becb8ce7378a709f5992a594764699e268 | /src/group_theory/semidirect_product.lean | d080f42f6f8f88032d5ef65e4f2c9944988b41fb | [
"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 | 6,765 | lean | /-
Copyright (c) 2020 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import data.equiv.mul_add logic.function.basic group_theory.subgroup
/-!
# Semidirect product
This file defines semidirect products of groups, and the canonical maps in ... |
1c7ee3ce6da3dc5fde0f6d3540a6d240a0b8a920 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /library/init/subtype.lean | a6304f5120d6c85cfee1632c1bb4f248f6655bab | [
"Apache-2.0"
] | permissive | soonhokong/lean | cb8aa01055ffe2af0fb99a16b4cda8463b882cd1 | 38607e3eb57f57f77c0ac114ad169e9e4262e24f | refs/heads/master | 1,611,187,284,081 | 1,450,766,737,000 | 1,476,122,547,000 | 11,513,992 | 2 | 0 | null | 1,401,763,102,000 | 1,374,182,235,000 | C++ | UTF-8 | Lean | false | false | 1,363 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura, Jeremy Avigad
-/
prelude
import init.datatypes init.logic
open decidable
set_option structure.proj_mk_thm true
structure subtype {A : Type} (P : A → Prop) :=... |
3003cc7631f7650086786db49006cfced94a7334 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/category/Ring/filtered_colimits.lean | 342960aea4128a621ad197264ddbbc57e76bfd19 | [
"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 | 13,210 | lean | /-
Copyright (c) 2021 Justus Springer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Justus Springer
-/
import algebra.category.Ring.basic
import algebra.category.Group.filtered_colimits
/-!
# The forgetful functor from (commutative) (semi-) rings preserves filtered ... |
dbd41d36761ec92c24cbf9e9277cbd26bf169686 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/run/div_wf.lean | 1fc1c8970527f88140b5c1c6ca37d462454b6698 | [
"Apache-2.0"
] | permissive | GaloisInc/lean | aa1e64d604051e602fcf4610061314b9a37ab8cd | f1ec117a24459b59c6ff9e56a1d09d9e9e60a6c0 | refs/heads/master | 1,592,202,909,807 | 1,504,624,387,000 | 1,504,624,387,000 | 75,319,626 | 2 | 1 | Apache-2.0 | 1,539,290,164,000 | 1,480,616,104,000 | C++ | UTF-8 | Lean | false | false | 1,741 | lean | open nat well_founded decidable prod
set_option pp.all true
-- Auxiliary lemma used to justify recursive call
private definition lt_aux {x y : nat} (H : 0 < y ∧ y ≤ x) : x - y < x :=
and.rec_on H (λ ypos ylex,
sub_lt (nat.lt_of_lt_of_le ypos ylex) ypos)
definition wdiv.F (x : nat) (f : Π x₁, x₁ < x → nat → nat) (y... |
d7e726b2dabe72312fb8e7917bac8ad403318f64 | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /library/init/datatypes.lean | 882f0b3488eb5890e4110734a253dc0874e38f76 | [
"Apache-2.0"
] | permissive | tjiaqi/lean | 4634d729795c164664d10d093f3545287c76628f | d0ce4cf62f4246b0600c07e074d86e51f2195e30 | refs/heads/master | 1,622,323,796,480 | 1,422,643,069,000 | 1,422,643,069,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,716 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
Basic datatypes
-/
prelude
notation `Prop` := Type.{0}
notation [parsing-only] `Type'` := Type.{_+1}
notation [parsing-only] `Type₊` := Type.{_+1}
notation ... |
ff994692312fae771631a5528dab06e043dc8a89 | 5df84495ec6c281df6d26411cc20aac5c941e745 | /src/formal_ml/alt_pac_bounds.lean | 9f3fdf692bac7e7485223e185203ea0b51b08f08 | [
"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 | 32,249 | 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... |
1b658f8774079aea7f94d1d3828c85ef308795e0 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/homology/exact.lean | 4f29c327700894a8e667b6a3b6d92925deffeee5 | [
"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 | 12,916 | lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import algebra.homology.image_to_kernel
/-!
# Exact sequences
In a category with zero morphisms, images, and equalizers we say that `f : A ⟶ B` and `g : B ⟶ C`
are ex... |
0fd10570408548e9de9df09a9542f7cbdc982b8e | e0f9ba56b7fedc16ef8697f6caeef5898b435143 | /src/group_theory/sylow.lean | ca7af552e9cc63c1ae87726130bab901d7098d8f | [
"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 | 11,923 | 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 group_theory.group_action
import group_theory.quotient_group
import group_theory.order_of_element
import data.zmod.basic
import data.fintype.card
import data.list.... |
53bd8dbbadc276757feba81b7d97877d576d44d3 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/typevec.lean | 778f801331ba41cf1022c5e1fa6890a4cb60ec8f | [
"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 | 24,486 | lean | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Mario Carneiro, Simon Hudon
-/
import data.fin.fin2
import logic.function.basic
import tactic.basic
/-!
# Tuples of types, and their categorical structure.
## Features... |
9e31fb5b62d84a475dafaa700c9978871fa378ad | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/int/conditionally_complete_order.lean | 63efc9885b7e29a60e91a827d4a1728a9202e454 | [
"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 | 3,079 | lean | /-
Copyright (c) 2021 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import order.conditionally_complete_lattice.basic
import data.int.least_greatest
/-!
## `ℤ` forms a conditionally complete linear order
> THIS FILE IS SYNCHRONI... |
257b1c8f9d6739ea7ce008e2f8cafecb539e16e3 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/dynamics/ergodic/conservative.lean | 254d7ea25256ea20abcdec17b6a2fd5f2323801f | [
"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 | 10,063 | lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import measure_theory.constructions.borel_space
import dynamics.ergodic.measure_preserving
import combinatorics.pigeonhole
/-!
# Conservative systems
In this file... |
4e76a60985cc6adbac7a49a69528abbc76bf11da | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/limits/preserves/finite.lean | 2512c091e6de69d8f2b51876f0dcd49452f227be | [
"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 | 7,361 | lean | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import category_theory.limits.preserves.basic
import category_theory.fin_category
/-!
# Preservation of finite (co)limits.
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> An... |
ea8dc1acf1815ce2bf4be70f22e81e3e95e8465e | 29cc89d6158dd3b90acbdbcab4d2c7eb9a7dbf0f | /1.1/Homework week1.lean | 78d0c840f89370ab1c486d4480ad8e8faa7f7574 | [] | no_license | KjellZijlemaker/Logical_Verification_VU | ced0ba95316a30e3c94ba8eebd58ea004fa6f53b | 4578b93bf1615466996157bb333c84122b201d99 | refs/heads/master | 1,585,966,086,108 | 1,549,187,704,000 | 1,549,187,704,000 | 155,690,284 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,284 | lean | /- Homework 1.1: Basics — Specifications -/
/- Question 1: Snoc -/
/- 1.1. Define the function `snoc` that appends a single element to the end of
a list. -/
def snoc {α : Type} : list α → α → list α
| [] l := [] ++ [l]
| (a::b) l := a :: b ++ [l]
-- ZZZ: Jasmins solution using append.
def snoc' {α : Type} : list... |
cf4f8cd2b6a1b4c910d8f3bcf6809e1536e117b1 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/measure_theory/function/strongly_measurable.lean | aa58802f339e843e03394c99a582929853666e26 | [
"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 | 79,788 | lean | /-
Copyright (c) 2021 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Sébastien Gouëzel
-/
import measure_theory.function.ess_sup
import measure_theory.integral.mean_inequalities
import topology.continuous_function.compact
import topology.met... |
6fa8cd8c4c27955b903cd258d5a961e080d97b3c | 02005f45e00c7ecf2c8ca5db60251bd1e9c860b5 | /src/algebra/algebra/basic.lean | b9349b54ff3c5d743759a64d4f83a8c9c20aeaf2 | [
"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 | 52,178 | 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 tactic.nth_rewrite
import data.matrix.basic
import data.equiv.ring_aut
import linear_algebra.tensor_product
import ring_theory.subring
import deprecated... |
ec0a27a89735a858ef3325898c8fb29459a236ef | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/data/int/gcd.lean | ac2514652ce40d964b3839410942e8706b8d180e | [
"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 | 5,391 | lean | /-
Copyright (c) 2018 Guy Leroy. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sangwoo Jo (aka Jason), Guy Leroy, Johannes Hölzl, Mario Carneiro
-/
import data.nat.prime
/-!
# Extended GCD and divisibility over ℤ
## Main definitions
* Given `x y : ℕ`, `xgcd x y` com... |
7eab59fe7ac0fd4383f1c51d8c0828b666e0a382 | e38d5e91d30731bef617cc9b6de7f79c34cdce9a | /src/path/function.lean | 6d80ff1581abb2bd0c5aec8e88bd05d39dcf78ac | [
"Apache-2.0"
] | permissive | bbentzen/cubicalean | 55e979c303fbf55a81ac46b1000c944b2498be7a | 3b94cd2aefdfc2163c263bd3fc6f2086fef814b5 | refs/heads/master | 1,588,314,875,258 | 1,554,412,699,000 | 1,554,412,699,000 | 177,333,390 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 786 | lean | /-
Copyright (c) 2019 Bruno Bentzen. All rights reserved.
Released under the Apache License 2.0 (see "License");
Author: Bruno Bentzen
-/
import ..core.path
open pathd interval
namespace path
lemma ap {A B : Type} (f : A → B) {a b : A} :
path A a b → path B (f a) (f b) :=
λ p, path.abs (λ i, f (p @@... |
12aff147f76390dc940b503f4c5fa22faf79412f | c777c32c8e484e195053731103c5e52af26a25d1 | /src/data/finset/basic.lean | 30687beee91e0c5058fb770dbdf22a1435120cae | [
"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 | 113,790 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Minchao Wu, Mario Carneiro
-/
import data.multiset.finset_ops
import tactic.apply
import tactic.nth_rewrite
import tactic.monotonicity
/-!
# F... |
5ec2f204071e19ecf3ad740847bdd2d86e526a13 | 2fbe653e4bc441efde5e5d250566e65538709888 | /src/group_theory/subgroup.lean | d54cd8eba1960bcb533bd12ea7f165d8acea109a | [
"Apache-2.0"
] | permissive | aceg00/mathlib | 5e15e79a8af87ff7eb8c17e2629c442ef24e746b | 8786ea6d6d46d6969ac9a869eb818bf100802882 | refs/heads/master | 1,649,202,698,930 | 1,580,924,783,000 | 1,580,924,783,000 | 149,197,272 | 0 | 0 | Apache-2.0 | 1,537,224,208,000 | 1,537,224,207,000 | null | UTF-8 | Lean | false | false | 28,410 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mitchell Rowett, Scott Morrison, Johan Commelin, Mario Carneiro,
Michael Howes
-/
import group_theory.submonoid
open set function
variables {α : Type*} {β : Type*} {... |
a1882dabd19572a680c409dba8c2087de32ee080 | f3a5af2927397cf346ec0e24312bfff077f00425 | /src/game/world5/level6.lean | 52ca460bf141b147f4a14b459ced08a6a7a41bb0 | [
"Apache-2.0"
] | permissive | ImperialCollegeLondon/natural_number_game | 05c39e1586408cfb563d1a12e1085a90726ab655 | f29b6c2884299fc63fdfc81ae5d7daaa3219f9fd | refs/heads/master | 1,688,570,964,990 | 1,636,908,242,000 | 1,636,908,242,000 | 195,403,790 | 277 | 84 | Apache-2.0 | 1,694,547,955,000 | 1,562,328,792,000 | Lean | UTF-8 | Lean | false | false | 1,672 | lean | /-
# Function world.
## Level 6: `(P → (Q → R)) → ((P → Q) → (P → R))`.
You can solve this level completely just using `intro`, `apply` and `exact`,
but if you want to argue forwards instead of backwards then don't forget
that you can do things like
`have j : Q → R := f p,`
if `f : P → (Q → R)` and `p : P`. Rememb... |
9676e7724cf485111e92206ece7ab7304398b377 | 48eee836fdb5c613d9a20741c17db44c8e12e61c | /src/algebra/theories/lattice.lean | 8b7e3f56cff3d44861ca96a0b327e410023e4d92 | [
"Apache-2.0"
] | permissive | fgdorais/lean-universal | 06430443a4abe51e303e602684c2977d1f5c0834 | 9259b0f7fb3aa83a9e0a7a3eaa44c262e42cc9b1 | refs/heads/master | 1,592,479,744,136 | 1,589,473,399,000 | 1,589,473,399,000 | 196,287,552 | 1 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 5,296 | lean | -- Copyright © 2019 François G. Dorais. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
import .basic
import .semilattice
namespace algebra
signature lattice (α : Type*) :=
(join : α → α → α)
(meet : α → α → α)
namespace lattice_sig
variables {α : Type*} (s : lattice_sig ... |
14882edae613d39f5eec6867a5947bd2a0b3c541 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/measure_theory/measure/measure_space_def.lean | 20356a85ad03c4ae14ea41618cc9ce681e360e01 | [
"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 | 22,651 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import measure_theory.measure.outer_measure
import order.filter.countable_Inter
import data.set.accumulate
/-!
# Measure spaces
This file defines me... |
a214ba4fc29c63208a928474a8f4215e6d3d792f | ba4794a0deca1d2aaa68914cd285d77880907b5c | /src/game/world10/level11.lean | 0d45b49cdef1b63c1e3253fdab334906aee5147b | [
"Apache-2.0"
] | permissive | ChrisHughes24/natural_number_game | c7c00aa1f6a95004286fd456ed13cf6e113159ce | 9d09925424da9f6275e6cfe427c8bcf12bb0944f | refs/heads/master | 1,600,715,773,528 | 1,573,910,462,000 | 1,573,910,462,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 569 | lean | import game.world10.level10 -- hide
namespace mynat -- hide
/-
# Inequality world.
## Level 11: `add_le_add_right`
If you're faced with a goal of the form `forall t, ...`, then the next
line is "so let $t$ be arbitrary". The way to do this in Lean is `intro t`.
-/
/- Lemma
For all naturals $a$ and $b$, $a\le b$ i... |
b89a6cc952094b7814065d067412138ab6515ecf | a4673261e60b025e2c8c825dfa4ab9108246c32e | /stage0/src/Lean/Elab/Level.lean | f3413ef504ea78a420edf3a73137d49a70b3cab1 | [
"Apache-2.0"
] | permissive | jcommelin/lean4 | c02dec0cc32c4bccab009285475f265f17d73228 | 2909313475588cc20ac0436e55548a4502050d0a | refs/heads/master | 1,674,129,550,893 | 1,606,415,348,000 | 1,606,415,348,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,424 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.LevelDefEq
import Lean.Elab.Exception
import Lean.Elab.Log
namespace Lean.Elab.Level
structure Context :=
(ref : Syntax)
(leve... |
61810049ab4958b64943ca5e0ca72bc25c5ae5d4 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/lake/Lake/Config/LeanLib.lean | 89f2819602a53e99e3866a7becf5c18528a30a56 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 4,531 | lean | /-
Copyright (c) 2022 Mac Malone. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mac Malone
-/
import Lake.Config.Package
namespace Lake
open Lean System
/-- A Lean library -- its package plus its configuration. -/
structure LeanLib where
/-- The package the librar... |
29e983f31262793968cf519ffafd99b1322e52bc | 4b846d8dabdc64e7ea03552bad8f7fa74763fc67 | /library/tools/mini_crush/default.lean | 995def3a2284161377fa3dc9840b93bca03025fc | [
"Apache-2.0"
] | permissive | pacchiano/lean | 9324b33f3ac3b5c5647285160f9f6ea8d0d767dc | fdadada3a970377a6df8afcd629a6f2eab6e84e8 | refs/heads/master | 1,611,357,380,399 | 1,489,870,101,000 | 1,489,870,101,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,646 | 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
We implement a crush-like strategy using simplifier,
SMT gadgets, and robust simplifier.
This is just a demo.
-/
declare_trace mini_crush
namespace mini_cru... |
33649ba3da68084832d0419b24928be5d64d5468 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/algebra/field_power.lean | a9a1681808edbbeea8b6246a6397c6c48e74d8fb | [
"Apache-2.0"
] | permissive | waynemunro/mathlib | e3fd4ff49f4cb43d4a8ded59d17be407bc5ee552 | 065a70810b5480d584033f7bbf8e0409480c2118 | refs/heads/master | 1,693,417,182,397 | 1,634,644,781,000 | 1,634,644,781,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,784 | 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 algebra.group_with_zero.power
import tactic.linarith
import data.equiv.ring
/-!
# Integer power operation on fields and division rings
This file collects b... |
d8fb3151ece4a717d157fdc7ce2a8efe7c2f0ab2 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/analysis/asymptotics/superpolynomial_decay.lean | ef96c64ac92836fe7dd278470f749707f319fb33 | [
"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 | 14,171 | lean | /-
Copyright (c) 2021 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Devon Tuma
-/
import analysis.asymptotics.asymptotics
import analysis.asymptotics.specific_asymptotics
import data.polynomial.eval
/-!
# Super-Polynomial Function Decay
This file defines... |
f662cfb059c67a316942e7c16527c0bb1a437d31 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/instances/rat.lean | 9e5ed81f1cbfd70c2ea7200f16417008c39f6a22 | [
"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 | 4,219 | 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 topology.metric_space.basic
import topology.algebra.order.archimedean
import topology.instances.int
import topology.instances.nat
import topolo... |
ddc12311c773e3e6a261adc7b082b367675af8a1 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/run/replace.lean | eedc78c1d6b52d3f9e326c0fa9176df951ae3a17 | [
"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 | 605 | lean | import Lean
open Lean
partial def mkBig : Nat → Expr
| 0 => mkConst `a
| (n+1) => mkApp2 (mkConst `f []) (mkBig n) (mkBig n)
def replaceTest (e : Expr) : Expr :=
e.replace $ fun e => match e with
| Expr.const c _ _ => if c == `f then mkConst `g else none
| _ => none
#eval replaceTest $ mkBig 4
#eval (replace... |
011bef12705d0849346d2a409e13a313b6c8505f | 07f5f86b00fed90a419ccda4298d8b795a68f657 | /library/init/meta/interactive.lean | b47dd99ca9652c91c8951b8f55870f4555877bc0 | [
"Apache-2.0"
] | permissive | VBaratham/lean | 8ec5c3167b4835cfbcd7f25e2173d61ad9416b3a | 450ca5834c1c35318e4b47d553bb9820c1b3eee7 | refs/heads/master | 1,629,649,471,814 | 1,512,060,373,000 | 1,512,060,469,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 54,200 | 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... |
5acad7cf6733ddcb58289562eccb5819adfeccca | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/algebra/order/complete_field.lean | 3837dee54f36562af68723be174068adba5fd473 | [
"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 | 13,282 | lean | /-
Copyright (c) 2022 Alex J. Best. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex J. Best, Yaël Dillies
-/
import algebra.order.hom.ring
import algebra.order.pointwise
import analysis.special_functions.pow
/-!
# Conditionally complete linear ordered fields
This... |
83a89c0b17cefa37e2fcef7f97c8fe2b26531a50 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/analysis/normed_space/star/basic.lean | f504ce482ba0e89eb1a5a706bafcf90056452317 | [
"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 | 12,365 | lean | /-
Copyright (c) 2021 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import analysis.normed.group.hom
import analysis.normed_space.basic
import analysis.normed_space.linear_isometry
import analysis.normed_space.operator_norm
import ... |
b9b7f112734e37c1879460f8549f6f17ff575a48 | 28be2ab6091504b6ba250b367205fb94d50ab284 | /src/tactic/modded.lean | a7f691e5ecc723d8674e5a4bfab0735cb38b4b0e | [
"Apache-2.0"
] | permissive | postmasters/natural_number_game | 87304ac22e5e1c5ac2382d6e523d6914dd67a92d | 38a7adcdfdb18c49c87b37831736c8f15300d821 | refs/heads/master | 1,649,856,819,031 | 1,586,444,676,000 | 1,586,444,676,000 | 255,006,061 | 0 | 0 | Apache-2.0 | 1,586,664,599,000 | 1,586,664,598,000 | null | UTF-8 | Lean | false | false | 3,522 | lean | -- modded induction', cases', rw'
-- *TODO* -- waiting for simon PR for symmetry'
import tactic.interactive
run_cmd mk_simp_attr `leakage
open lean
open lean.parser
local postfix `?`:9001 := optional
local postfix *:9001 := many
namespace tactic
namespace interactive
open interactive interactive.types expr
privat... |
9e8f505447b7815fab20f73d081737922744cdd7 | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/category_theory/limits/shapes/finite_limits.lean | 956e5f972f4d39e7996383a1911ad65bd7a043f1 | [
"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 | 1,997 | 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.discrete_category
import data.fintype
universes v u
open category_theory
namespace category_the... |
294609e6de6c6ad9ce7474a9bd6081156e46e341 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/ring_theory/eisenstein_criterion.lean | af7543b8a44ef1adbe519e3178f9e38d7a1ea336 | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 5,563 | lean | /-
Copyright (c) 2020 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import ring_theory.prime
import ring_theory.polynomial.content
/-!
# Eisenstein's criterion
A proof of a slight generalisation of Eisenstein's criterion for the irreduci... |
e74e23ee670c295b6c422962d9d038642ab2931c | 77c5b91fae1b966ddd1db969ba37b6f0e4901e88 | /src/number_theory/dioph.lean | 821d7771976e1d9a09050102979d749bafee5733 | [
"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 | 27,944 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import number_theory.pell
import data.pfun
import data.fin2
import data.vector3
/-!
# Diophantine functions and Matiyasevic's theorem
Hilbert's tenth problem asked... |
54e3944efbe4f4510e5b88a80d5757175eaf7650 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/topology/category/TopCommRing.lean | e0149c0f31aff5959cf6b3dcf03613da2b6b3745 | [
"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 | 3,585 | 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 algebra.category.CommRing.basic
import topology.category.Top.basic
import topology.algebra.ring
/-!
# Category of topological commutative rings
We introduce ... |
8310897cffc662dfbf03b28472fa2ed18e595e6f | 0845ae2ca02071debcfd4ac24be871236c01784f | /library/init/lean/util.lean | 38261a0c105fb5caf967c7830709fd609ff36d00 | [
"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 | 589 | lean | /-
Copyright (c) 2019 Sebastian Ullrich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Sebastian Ullrich
-/
prelude
import init.lean.position init.io
namespace Lean
/-- Print and accumulate run time of `act` when Option `profiler` is set to `True`. -/
@[extern 5 "lea... |
4a0c4b5b89930e167c67973b320665a1c0b03e7d | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/combinatorics/hales_jewett.lean | 9f8eed3974e9ab66053c924e98a1d8ea0264a17f | [
"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 | 15,449 | lean | /-
Copyright (c) 2021 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
import data.fintype.basic
import algebra.big_operators.basic
import data.equiv.fin
/-!
# The Hales-Jewett theorem
We prove the Hales-Jewett theorem and deduce Van der Waerd... |
0f4b50f31e6805d6f1e3584caf8803b5327a8113 | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /src/Lean/Elab/Deriving/Hashable.lean | f49fa67726ef1a833648bf858b0d5b569e8af7b9 | [
"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 | 3,642 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dany Fabian
-/
import Lean.Meta.Inductive
import Lean.Elab.Deriving.Basic
import Lean.Elab.Deriving.Util
namespace Lean.Elab.Deriving.Hashable
open Command
open Lean.Parser.Ter... |
813d83f30de3f5461743f1f02a47c2af6b0c61ec | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/topology/algebra/group_with_zero.lean | 34df919eafe84ed360bc2d86cd09fdf12657cfd8 | [
"Apache-2.0"
] | permissive | ilitzroth/mathlib | ea647e67f1fdfd19a0f7bdc5504e8acec6180011 | 5254ef14e3465f6504306132fe3ba9cec9ffff16 | refs/heads/master | 1,680,086,661,182 | 1,617,715,647,000 | 1,617,715,647,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,604 | 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
-/
import topology.algebra.monoid
import algebra.group.pi
import algebra.group_with_zero.power
import topology.homeomorph
/-!
# Topological group with zero
In ... |
2c4b499e275404bebf7c7249f93784ffc58c3fb3 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/data/nat/multiplicity.lean | e6eb975f9220136f41326160fee468f0f5fc2efa | [
"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 | 11,064 | lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import algebra.big_operators.intervals
import algebra.geom_sum
import data.nat.bitwise
import data.nat.log
import data.nat.parity
import ring_theory.int.basic
/-!
# Natu... |
15923225ef27a289712b01ad139e5888217ddc20 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/qpf/multivariate/constructions/fix.lean | 2c1c33ceed19ec1b8cd06ce661a08a6f0f4516a8 | [
"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 | 12,997 | lean | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Simon Hudon
-/
import data.pfunctor.multivariate.W
import data.qpf.multivariate.basic
/-!
# The initial algebra of a multivariate qpf is again a qpf.
> THIS FILE IS SYN... |
291961a265034c74332019050a3b8b6e7bf12935 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/data/matrix/dmatrix.lean | a8a085457870886d469078de7167bf3d0b731e09 | [
"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 | 5,418 | lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import data.fintype.basic
/-!
# Matrices
-/
universes u u' v w z
/-- `dmatrix m n` is the type of dependently typed matrices
whose rows are indexed by the fintype `... |
c355031acbf8afb11bada8f689053fdb045aace1 | bb31430994044506fa42fd667e2d556327e18dfe | /src/analysis/special_functions/pow.lean | 4fd66dc7d331453e7c0990092b0e471cfa7b956f | [
"Apache-2.0"
] | permissive | sgouezel/mathlib | 0cb4e5335a2ba189fa7af96d83a377f83270e503 | 00638177efd1b2534fc5269363ebf42a7871df9a | refs/heads/master | 1,674,527,483,042 | 1,673,665,568,000 | 1,673,665,568,000 | 119,598,202 | 0 | 0 | null | 1,517,348,647,000 | 1,517,348,646,000 | null | UTF-8 | Lean | false | false | 92,853 | 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, David Loeffler
-/
import analysis.special_functions.complex.log
/-!
# Power function on ... |
27a2cb2f8635c86eeee0d0d612592d2420fdce2e | c777c32c8e484e195053731103c5e52af26a25d1 | /src/data/polynomial/div.lean | 9abd9e5cf5e15f2a8ff7ac03e7a713b18dc85e08 | [
"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 | 22,447 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
-/
import data.polynomial.algebra_map
import data.polynomial.inductions
import data.polynomial.monic
import ring_theory.multi... |
8fdbc72c19876d4f944a6fc549bfd9d1227823b6 | 0179bcdbf094a112437450a02dc2bdc8b2f921d4 | /fabstract/Bauer_A_InjBaireNat/fabstract.lean | 415bf45fd255ae717881782314339c41152f7f4f | [
"CC-BY-4.0"
] | permissive | haselwarter/formalabstracts | cf0c129fc086526cef1bd65d95c6f95a9a7ec5c8 | eab6d94850308df9f09d23f3a9a2f7b5ac5c6c7a | refs/heads/master | 1,609,515,992,248 | 1,500,418,815,000 | 1,500,418,815,000 | 97,696,544 | 0 | 0 | null | 1,500,455,350,000 | 1,500,455,350,000 | null | UTF-8 | Lean | false | false | 1,652 | lean | import meta_data
.toposes
.realizability
run_cmd tactic.skip -- temporary fix
namespace Bauer_A_InjBaireNat
noncomputable theory
-- we construct a partial combinatory algebra based on
-- infinite-time Turing machines
unfinished J : PCA :=
{ description := "a partial-combinatory algebra constructured f... |
0611e507d6d72593f2d4692241dd639e7ae9e775 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/def7.lean | 7f6da79b51f8442554d62413a304bdfec2ea9a7c | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 1,405 | lean | inductive InfTree.{u} (α : Type u)
| leaf : α → InfTree α
| node : (Nat → InfTree α) → InfTree α
open InfTree
def szn.{u} {α : Type u} (n : Nat) : InfTree α → InfTree α → Nat
| leaf a, t2 => 1
| node c, leaf b => 0
| node c, node d => szn n (c n) (d n)
universe u
theorem ex1 {α : Type u} (n : Nat) (c : Nat → In... |
a9edae2c2c282db2a0451cfc477ffb4ec4a4f8f3 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/ring_theory/adjoin/fg.lean | 1c598c5365d47648dc194525807f7494576eae64 | [
"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 | 7,013 | lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import ring_theory.polynomial.basic
import ring_theory.principal_ideal_domain
import data.mv_polynomial.basic
/-!
# Adjoining elements to form subalgebras
> THIS FILE IS SYNC... |
448f45ec32507c76f510f22fb9ca5d1c5cfb14cb | 6094e25ea0b7699e642463b48e51b2ead6ddc23f | /tests/lean/replace1.lean | 7629fecd73d809b73444006241f3ed72c713eafb | [
"Apache-2.0"
] | permissive | gbaz/lean | a7835c4e3006fbbb079e8f8ffe18aacc45adebfb | a501c308be3acaa50a2c0610ce2e0d71becf8032 | refs/heads/master | 1,611,198,791,433 | 1,451,339,111,000 | 1,451,339,111,000 | 48,713,797 | 0 | 0 | null | 1,451,338,939,000 | 1,451,338,939,000 | null | UTF-8 | Lean | false | false | 1,508 | lean | constant f : Π {A : Type}, A → A → A
variables a b c : nat
variables H : a = b
set_option pp.all true
#replace f a a, [a], [b]
#replace f (f a b) b, [a,b], [b,a]
variables x y : bool
-- [nat] and [bool] are instances of the telescope (A : Type),
-- but the resulting expression is type incorrect.
-- Thus, #replace c... |
1f5f075c7bec7d6bbce56cfc7f19e11ba74fbe06 | abd85493667895c57a7507870867b28124b3998f | /src/group_theory/subgroup.lean | 42086768c33e3ed3f7529ae8dc569eacaf81e1c3 | [
"Apache-2.0"
] | permissive | pechersky/mathlib | d56eef16bddb0bfc8bc552b05b7270aff5944393 | f1df14c2214ee114c9738e733efd5de174deb95d | refs/heads/master | 1,666,714,392,571 | 1,591,747,567,000 | 1,591,747,567,000 | 270,557,274 | 0 | 0 | Apache-2.0 | 1,591,597,975,000 | 1,591,597,974,000 | null | UTF-8 | Lean | false | false | 38,760 | lean | /-
Copyright (c) 2020 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import group_theory.submonoid
/-!
# Subgroups
This file defines multiplicative and additive subgroups as an extension of submonoids, in a bundled
form (unbundled subgroup... |
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