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617068c16b3e6f2a7292f8bd43fda79d620a9688 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /archive/imo/imo2019_q4.lean | 700aa1be727aec97629bb368896abb3e899f7fbf | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 4,181 | lean | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import tactic.interval_cases
import algebra.big_operators.order
import algebra.big_operators.part_enat
import data.nat.multiplicity
/-!
# IMO 2019 Q4
Find all p... |
37e03586e13845ab63137ea25c67fc48a0da847a | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /stage0/src/Init/Notation.lean | 8d06cf45d359a90e8e10e0c3f34b60e262465312 | [
"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 | 11,466 | 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
Notation for operators defined at Prelude.lean
-/
prelude
import Init.Prelude
-- DSL for specifying parser precedences and priorities
namespace Lean.Parser.... |
c8469953f82bf2fa30ddd84af97e6e47d94cca39 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/category_theory/limits/lattice.lean | 1f331094c6e5e623557b315b8a404a8ec792b50d | [
"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 | 1,532 | 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 order.complete_lattice
universes u
open category_theory
namespace category_theory.limits
variables {α : Type u}
-- It... |
f39ea5024d685bcb3f9b7763f312006ea0ded231 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/ring_theory/polynomial/homogeneous.lean | 785f5758e678d5ae454263233450dc347f93dc07 | [
"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 | 10,360 | 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.fintype.card
import data.mv_polynomial.variables
/-!
# Homogeneous polynomi... |
6c139d7d3b212f2de466e9c4a438dec50698cae5 | f3a5af2927397cf346ec0e24312bfff077f00425 | /src/game/world7/level6.lean | d8b5cff205466825a67c26859f76b6f73186a425 | [
"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 | 1,196 | lean | import game.world7.level5 -- hide
/-
# Advanced proposition world.
## Level 6: Or, and the `left` and `right` tactics.
`P ∨ Q` means "$P$ or $Q$". So to prove it, you
need to choose one of `P` or `Q`, and prove that one.
If `⊢ P ∨ Q` is your goal, then `left` changes this
goal to `⊢ P`, and `right` changes it to `⊢... |
5d1785374a8ee5129808ac99adff4f2468d4b7e2 | 59a4b050600ed7b3d5826a8478db0a9bdc190252 | /src/category_theory/equivalence/default.lean | a866ebe342e852783e71b7bbb7c4e5125c06b888 | [] | no_license | rwbarton/lean-category-theory | f720268d800b62a25d69842ca7b5d27822f00652 | 00df814d463406b7a13a56f5dcda67758ba1b419 | refs/heads/master | 1,585,366,296,767 | 1,536,151,349,000 | 1,536,151,349,000 | 147,652,096 | 0 | 0 | null | 1,536,226,960,000 | 1,536,226,960,000 | null | UTF-8 | Lean | false | false | 2,285 | lean | -- Copyright (c) 2017 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Tim Baumann, Stephen Morgan, Scott Morrison
import category_theory.embedding
import category_theory.tactics.obviously
namespace category_theory
universes u₁ v₁ u₂ v₂
structur... |
292a85f688e8e24355770c6dd455e09753f5695c | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /src/Lean/Meta/Transform.lean | dc9c7ca8c391a9046b9ab5f40deaa7ead2add5da | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | EdAyers/lean4 | 57ac632d6b0789cb91fab2170e8c9e40441221bd | 37ba0df5841bde51dbc2329da81ac23d4f6a4de4 | refs/heads/master | 1,676,463,245,298 | 1,660,619,433,000 | 1,660,619,433,000 | 183,433,437 | 1 | 0 | Apache-2.0 | 1,657,612,672,000 | 1,556,196,574,000 | Lean | UTF-8 | Lean | false | false | 7,424 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.Basic
namespace Lean
inductive TransformStep where
| done (e : Expr)
| visit (e : Expr)
namespace Core
/--
Tranform the expressi... |
e0c63adf7cc4077e5eb911e69de53cdc95119721 | 5c4b17dae42fab1d4f493f3b52977bffa54fefea | /5.8.2.lean | 5a2925f5158abc2625dd8f6882316c39683beb2d | [] | no_license | hyponymous/theorem-proving-in-lean-solutions | 9214cb45cc87347862fd17dfdea79fdf24b9df92 | a95320ae81c90c1b15da04574602cd378794400d | refs/heads/master | 1,585,777,733,214 | 1,541,039,359,000 | 1,541,039,359,000 | 153,676,525 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 602 | lean | -- there are several ways of doing this, and probably more compact and/or
-- idiomatic ways than what I have here
example (p q r : Prop) (hp : p) :
(p ∨ q ∨ r) ∧ (q ∨ p ∨ r) ∧ (q ∨ r ∨ p) :=
by simp *
example (p q r : Prop) (hp : p) :
(p ∨ q ∨ r) ∧ (q ∨ p ∨ r) ∧ (q ∨ r ∨ p) :=
by { constructor, left, assumpti... |
080866301271daef841ca57b8f435fb22cdb14c4 | fe84e287c662151bb313504482b218a503b972f3 | /src/exercises/mathcomp_book/odd.lean | b3ed8a6b493e77acf831c5213be2c25ddeea6b46 | [] | no_license | NeilStrickland/lean_lib | 91e163f514b829c42fe75636407138b5c75cba83 | 6a9563de93748ace509d9db4302db6cd77d8f92c | refs/heads/master | 1,653,408,198,261 | 1,652,996,419,000 | 1,652,996,419,000 | 181,006,067 | 4 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 3,125 | lean | import tactic.interactive tactic.squeeze data.nat.modeq
variables n m : nat
@[simp]
def is_odd_a : ℕ → bool
| 0 := ff
| (nat.succ n) := bnot (is_odd_a n)
#reduce is_odd_a (n + 2)
lemma odd_ss_a : is_odd_a (n + 2) = is_odd_a n :=
begin
dsimp[is_odd_a],
cases is_odd_a n; refl,
end
lemma odd_add_a : ∀ n m : ℕ ,
... |
7d6463dda91bd2da2e3788ab948dcb1b57c4eac4 | d5ecf6c46a2f605470a4a7724909dc4b9e7350e0 | /data/int/basic.lean | 80304a71a2944b33ded2f006938df251a4a53939 | [
"Apache-2.0"
] | permissive | MonoidMusician/mathlib | 41f79df478987a636b735c338396813d2e8e44c4 | 72234ef1a050eea3a2197c23aeb345fc13c08ff3 | refs/heads/master | 1,583,672,205,771 | 1,522,892,143,000 | 1,522,892,143,000 | 128,144,032 | 0 | 0 | Apache-2.0 | 1,522,892,144,000 | 1,522,890,892,000 | Lean | UTF-8 | Lean | false | false | 42,194 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
The integers, with addition, multiplication, and subtraction.
-/
import data.nat.basic algebra.char_zero algebra.order_functions
open nat
namespace int
instance : inhab... |
8ff2e73711f0f160d58c5d3b3d4aaf560be665cb | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/data/zmod/polynomial.lean | 8b50ceedbc88d8c9f8ee0c4d2b76b81758580744 | [
"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 | 627 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import data.mv_polynomial.basic
import data.zmod.basic
/-!
## Facts concerning polynomials over `zmod n`
-/
namespace mv_polynomial
/-- A polynomial over the inte... |
fb33494bcebb25fdf34bd3c56795ea1df4488800 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/noncomp.lean | 162d670aa1ab5886567b75b8b5f12c2186b17d63 | [
"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 | 137 | lean | open nat
axiom n : nat
definition f (x : nat) := -- Error this is not computable
x + n
noncomputable definition g (x : nat) := x + n
|
ad10162425653b7a593ed88cbda94c4bd9f193d0 | a7eef317ddec01b9fc6cfbb876fe7ac00f205ac7 | /src/category_theory/monoidal/of_has_finite_products.lean | b339970530563af6d33593c43209c301967b0aed | [
"Apache-2.0"
] | permissive | kmill/mathlib | ea5a007b67ae4e9e18dd50d31d8aa60f650425ee | 1a419a9fea7b959317eddd556e1bb9639f4dcc05 | refs/heads/master | 1,668,578,197,719 | 1,593,629,163,000 | 1,593,629,163,000 | 276,482,939 | 0 | 0 | null | 1,593,637,960,000 | 1,593,637,959,000 | null | UTF-8 | Lean | false | false | 4,802 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Simon Hudon
-/
import category_theory.monoidal.category
import category_theory.limits.shapes.binary_products
import category_theory.limits.types
/-!
# The natural mono... |
8dc86b325a3f3c81bcaab448a7dc6723be030454 | 618003631150032a5676f229d13a079ac875ff77 | /src/data/set/finite.lean | bb843129581adb79ec1c9fa7fa9bffe23f82d23e | [
"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 | 23,131 | 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 data.fintype.basic
import algebra.big_operators
/-!
# Finite sets
This file defines predicates `finite : set α → Prop` and `infinite : set α ... |
7c74369915c16f6b28a61b173635edc693e3a848 | 022547453607c6244552158ff25ab3bf17361760 | /src/algebra/pointwise.lean | 246b77dd56d5caf136ca9d796e78f380e0069108 | [
"Apache-2.0"
] | permissive | 1293045656/mathlib | 5f81741a7c1ff1873440ec680b3680bfb6b7b048 | 4709e61525a60189733e72a50e564c58d534bed8 | refs/heads/master | 1,687,010,200,553 | 1,626,245,646,000 | 1,626,245,646,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 25,624 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Floris van Doorn
-/
import algebra.module.basic
import data.set.finite
import group_theory.submonoid.basic
/-!
# Pointwise addition, multiplication, and scalar multipl... |
1bccfd3295061a578b661a20200d3a517599052b | 9d2e3d5a2e2342a283affd97eead310c3b528a24 | /src/hints/thursday/afternoon/category_theory/exercise4/hint4.lean | 9fd7fe7ef1c8f09190dbd33dc67550addb99808c | [] | permissive | Vtec234/lftcm2020 | ad2610ab614beefe44acc5622bb4a7fff9a5ea46 | bbbd4c8162f8c2ef602300ab8fdeca231886375d | refs/heads/master | 1,668,808,098,623 | 1,594,989,081,000 | 1,594,990,079,000 | 280,423,039 | 0 | 0 | MIT | 1,594,990,209,000 | 1,594,990,209,000 | null | UTF-8 | Lean | false | false | 1,662 | lean | import algebra.category.CommRing
import category_theory.yoneda
noncomputable theory
open category_theory
open opposite
open polynomial
/-!
It would be nice to use `polynomial.aeval`, which produces an algebra homomorphism,
and then convert that use `.to_ring_hom`.
However we get a mysterious error message:
-/
def C... |
d400fba3e2957a4a4eb7f21730558cf9fddfa38f | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/data/sum/default.lean | 8e1ff90018e1cc15af6b42839e8ecb0e74465ea7 | [] | 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 | 253 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.data.sum.basic
namespace Mathlib
|
2aef9f1a1fd85aff92fef67890e4892d7a439722 | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /src/Lean/Elab/Structure.lean | 6cf47c33aaa6e757caa07f155eec3329da966d5b | [
"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 | 27,852 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Parser.Command
import Lean.Meta.Closure
import Lean.Meta.SizeOf
import Lean.Elab.Command
import Lean.Elab.DeclModifiers
import Lean.Elab.DeclUti... |
924bbf115786383a3e4d846a1275f9a86ef9405b | dd4e652c749fea9ac77e404005cb3470e5f75469 | /src/is_norm.lean | 22d581a836bf11787696fff73da7e0c151640098 | [] | no_license | skbaek/cvx | e32822ad5943541539966a37dee162b0a5495f55 | c50c790c9116f9fac8dfe742903a62bdd7292c15 | refs/heads/master | 1,623,803,010,339 | 1,618,058,958,000 | 1,618,058,958,000 | 176,293,135 | 3 | 2 | null | null | null | null | UTF-8 | Lean | false | false | 5,987 | lean |
-- TODO: move
class is_norm (α : Type*) {β : Type*} (N : β → ℝ) [normed_field α] [add_comm_group β] [vector_space α β] :=
(norm_eq_zero_iff: ∀ x : β, N x = 0 ↔ x = 0)
(norm_smul : ∀ c : α, ∀ x : β, N (c • x) = @has_norm.norm α (normed_field.to_has_norm α) c * N x)
(triangle : ∀ x y : β, N (x + y) ≤ N x + N y)
-... |
ef260eca166acffc20184cf548b0c6bc9c689c03 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/algebra/order_bigops.lean | 45794111029acba160b6daad65795f4915f323a5 | [
"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 | 19,034 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
Min and max over finite sets.
To support constructive theories, we start with the class
decidable_linear_ordered_cancel_comm_monoid, because:
(1) We need a decidable lin... |
917a7ae210bb9a67d97159d9ba258d332bc2176e | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/data/string/default.lean | bdd6c61ab2c31c9101abcbabe104abc5bedee7a6 | [] | 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 | 301 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.data.string.basic
import Mathlib.Lean3Lib.init.data.string.ops
namespace Mathlib
|
eb77dacdb6a6c9cdacaa59b49457e1d256357e5a | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /stage0/src/Lean/Elab/Tactic/Conv/Delta.lean | 433ff2b40ff2d14c550262ebf353592bc8d4cee3 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | EdAyers/lean4 | 57ac632d6b0789cb91fab2170e8c9e40441221bd | 37ba0df5841bde51dbc2329da81ac23d4f6a4de4 | refs/heads/master | 1,676,463,245,298 | 1,660,619,433,000 | 1,660,619,433,000 | 183,433,437 | 1 | 0 | Apache-2.0 | 1,657,612,672,000 | 1,556,196,574,000 | Lean | UTF-8 | Lean | false | false | 567 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Elab.Tactic.Delta
import Lean.Elab.Tactic.Conv.Basic
namespace Lean.Elab.Tactic.Conv
open Meta
@[builtinTactic Lean.Parser.Tactic.Conv.delta] ... |
7fe043fb2155314ba8a91c6349e56d16ca07ab7b | 29cc89d6158dd3b90acbdbcab4d2c7eb9a7dbf0f | /Exercises week 5/22_exercise_sheet.lean | 5efb051878fe1b9fe8b54a4379b575030b7c5637 | [] | 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 | 3,798 | lean | /- Exercise 2.2: Functional Programming — Trees -/
/- Question 1: Even and odd -/
/- 1.1. Define an inductive predicate `even` on `ℕ` that is true for even numbers and false for odd
numbers.
Hint: Your predicate should have two introduction rules, one for the 0 case and one for the `n + 2`
case. -/
inductive even :... |
efe84c8f9d9d1588a3436e5896506d65556d1ff1 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/unicode_lit.lean | 69438d5c5501e50615a542dc47138968289cfc7d | [
"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 | 86 | lean | #eval "≠∀Π∃⁻ʰℵ⬝"
#eval "≠∀Π∃⁻ʰℵ⬝".to_list.map char.to_nat
|
d6308b1b6eb4774aa56ff78299dc68f6ee665e12 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/field_theory/normal.lean | 527e38883137cd1c730fb7b2ca6558e8e1097786 | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 16,830 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Thomas Browning, Patrick Lutz
-/
import field_theory.adjoin
import field_theory.tower
import group_theory.solvable
import ring_theory.power_basis
/-!
# Normal field extensions
... |
bb768c93fbdf6a2e675a86aac2596487d30d9254 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/coe3.lean | 700f0d2513c19d7c4c4426aaf82bf0e33fa9c211 | [
"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 | 319 | lean | constants A B₁ B₂ C D : Type
constant A_to_B₁ : has_coe A B₁
constant A_to_B₂ : has_coe A B₂
constant B₁_to_C : has_coe B₁ C
constant B₂_to_D : has_coe B₂ D
attribute [instance] A_to_B₁ A_to_B₂ B₁_to_C B₂_to_D
constant a : A
constant f : C → C
constant g : D → D
check f a
check g a
|
927d2739f0562c428b94fe3f1478d5801332b9ef | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /tests/lean/ctor_layout.lean | c2c9250bf6e7995242b2e7f772edf1d3929aab60 | [
"Apache-2.0"
] | permissive | walterhu1015/lean4 | b2c71b688975177402758924eaa513475ed6ce72 | 2214d81e84646a905d0b20b032c89caf89c737ad | refs/heads/master | 1,671,342,096,906 | 1,599,695,985,000 | 1,599,695,985,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 639 | lean | import Lean.Compiler.IR
open Lean
open Lean.IR
unsafe def main : IO Unit :=
withImportModules [{module := `Lean.Compiler.IR.Basic}] 0 fun env => do
ctorLayout ← IO.ofExcept $ getCtorLayout env `Lean.IR.Expr.reuse;
ctorLayout.fieldInfo.forM $ fun finfo => IO.println (format finfo);
IO.println "---";
ctorLay... |
1d135e80c676dfbb501c5456feb3c76da8bf803c | 649957717d58c43b5d8d200da34bf374293fe739 | /src/data/equiv/algebra.lean | cdf5e28c0ce7d1066cfda806691ba7f638ee475f | [
"Apache-2.0"
] | permissive | Vtec234/mathlib | b50c7b21edea438df7497e5ed6a45f61527f0370 | fb1848bbbfce46152f58e219dc0712f3289d2b20 | refs/heads/master | 1,592,463,095,113 | 1,562,737,749,000 | 1,562,737,749,000 | 196,202,858 | 0 | 0 | Apache-2.0 | 1,562,762,338,000 | 1,562,762,337,000 | null | UTF-8 | Lean | false | false | 11,286 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
The role of this file is twofold. In the first part there are theorems of the following
form: if α has a group structure and α ≃ β then β has a group structure, and
sim... |
42c1e0504e957ec29c9954b98ce1e24a003c47fc | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/1841.lean | 94a898f27af243b6df2f69d5f25112b05f43db18 | [
"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 | 846 | lean | variable {α : Type} {r : α → α → Prop} {b : α}
inductive ReflTransGen (r : α → α → Prop) (a : α) : α → Prop
| refl : ReflTransGen r a a
| tail {b c} : ReflTransGen r a b → r b c → ReflTransGen r a c
namespace ReflTransGen
theorem head (hab : r a b) (hbc : ReflTransGen r b c) : ReflTransGen r a c := by
induction hb... |
9328d9df9410640d3ec44fe84de2de687022d55c | 853df553b1d6ca524e3f0a79aedd32dde5d27ec3 | /src/meta/expr.lean | 3bac692e77c8964d195f5da5be2091dcaa227f4d | [
"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 | 33,671 | lean | /-
Copyright (c) 2019 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Simon Hudon, Scott Morrison, Keeley Hoek, Robert Y. Lewis
-/
import data.string.defs
import tactic.derive_inhabited
/-!
# Additional operations on expr and related typ... |
ef886d819076f90f4e8702590b1f8d48558a4409 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/linear_algebra/determinant.lean | 2d4b4870ca51d9aa865f21a76594a73f43b6b3d1 | [
"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 | 23,812 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-/
import linear_algebra.multilinear.basis
import linear_algebra.matrix.reindex
import ring_theory.algebra_tower
import tactic.... |
92653497851c5072e1c21837ce10cf247908f318 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/normed_space/matrix_exponential.lean | 678d4710a310b0dd12ec5653a204d16a8e1473fd | [
"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 | 9,590 | lean | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import analysis.normed_space.exponential
import analysis.matrix
import linear_algebra.matrix.zpow
import linear_algebra.matrix.hermitian
import linear_algebra.matrix.symme... |
43743bfb493e14b581edaa5bd7d376c7f1dda69e | 947b78d97130d56365ae2ec264df196ce769371a | /tests/lean/run/def14.lean | a774be56ce890e79e6ea020ac9021c3faeb7f676 | [
"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 | 395 | lean | new_frontend
inductive Formula
| eqf : Nat → Nat → Formula
| impf : Formula → Formula → Formula
def Formula.denote : Formula → Prop
| eqf n1 n2 => n1 = n2
| impf f1 f2 => denote f1 → denote f2
theorem Formula.denote_eqf (n1 n2 : Nat) : denote (eqf n1 n2) = (n1 = n2) :=
rfl
theorem Formula.denote_impf (f1 f2 : For... |
e29d2624dba350835597d82db8e892911e58b99a | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/set_theory/ordinal/natural_ops.lean | 38f6a566ec06e29394eb84ea0f8c28a2dd8ce9d4 | [
"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 | 26,219 | lean | /-
Copyright (c) 2022 Violeta Hernández Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Violeta Hernández Palacios
-/
import set_theory.ordinal.arithmetic
import tactic.abel
/-!
# Natural operations on ordinals
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> A... |
436c40f93ef3c3cb338be66e3906c4b78e851130 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/data/nat/cast.lean | 65d9a50f747a60474b5abde839fa911147d3d72c | [
"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 | 12,250 | lean | /-
Copyright (c) 2014 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import algebra.order.field
import data.nat.basic
/-!
# Cast of naturals
This file defines the *canonical* homomorphism from the natural numbers into a type `α` with... |
b856fd1c16a06e4edb9b82ec3b24b3168c0ca1bd | 2c096fdfecf64e46ea7bc6ce5521f142b5926864 | /src/Lean/Util.lean | cb67fb422d202f479256ad7a8a3a883c6f1bb7e0 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | Kha/lean4 | 1005785d2c8797ae266a303968848e5f6ce2fe87 | b99e11346948023cd6c29d248cd8f3e3fb3474cf | refs/heads/master | 1,693,355,498,027 | 1,669,080,461,000 | 1,669,113,138,000 | 184,748,176 | 0 | 0 | Apache-2.0 | 1,665,995,520,000 | 1,556,884,930,000 | Lean | UTF-8 | Lean | false | false | 762 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Util.CollectFVars
import Lean.Util.CollectLevelParams
import Lean.Util.CollectMVars
import Lean.Util.FindMVar
import Lean.Util.FindLevelMVar
imp... |
5a23e24ae0480b19882d1dcc3ff5e472ec12f7ff | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/category/Group/equivalence_Group_AddGroup.lean | 036c5d21709929330cc160d890d213a36794662d | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 2,786 | lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
import algebra.category.Group.basic
import algebra.hom.equiv.type_tags
/-!
# Equivalence between `Group` and `AddGroup`
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any... |
3289b64f13ac0731868ad403252f19060a63d303 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/linear_algebra/linear_pmap.lean | a871763ff770f9e64fb339cb06d793f3e4035c26 | [
"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 | 15,693 | 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 linear_algebra.basic
/-!
# Partially defined linear maps
A `linear_pmap R E F` is a linear map from a submodule of `E` to `F`. We define
a `semilattice_inf_... |
2bad5d40bb3257b2e69813a4bfd754d82f950bea | 94e33a31faa76775069b071adea97e86e218a8ee | /src/data/finset/fold.lean | 4c76ff85c76e232db02f7eac045c86b5d3aea175 | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 8,675 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.finset.basic
import data.multiset.fold
/-!
# The fold operation for a commutative associative operation over a finset.
-/
namespace finset
open multiset... |
fec457dcb2995948b78daba81818f75f21c3f3ef | b561a44b48979a98df50ade0789a21c79ee31288 | /src/Lean/Meta/Tactic/Util.lean | 006b9c5f62f22a59e61595d2a2f1f78309967c37 | [
"Apache-2.0"
] | permissive | 3401ijk/lean4 | 97659c475ebd33a034fed515cb83a85f75ccfb06 | a5b1b8de4f4b038ff752b9e607b721f15a9a4351 | refs/heads/master | 1,693,933,007,651 | 1,636,424,845,000 | 1,636,424,845,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,120 | 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.Util.ForEachExpr
import Lean.Meta.Basic
import Lean.Meta.AppBuilder
import Lean.Meta.LevelDefEq
import Lean.Meta.PPGoal
namespace Lean.Meta
/-... |
5b5957a3ab5151ae32404debd4ac1bf6531c5106 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/measure_theory/measure/stieltjes.lean | d8e43bc743a1cb54550e6c8e2741710182c33dc7 | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 16,630 | lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov, Sébastien Gouëzel
-/
import measure_theory.constructions.borel_space
/-!
# Stieltjes measures on the real line
Consider a function `f : ℝ → ℝ` whi... |
cc29924c6a46e82835402ea9d7d88b4e6609e460 | 670b1582ba4780d3b4a49063d5afea44a337bc24 | /src/problem_translation.lean | 3752bbb10921b762edfa5c941671ae9309899f0b | [] | no_license | robertylewis/Lean_hammer | 9bd8a75cb6fc76b3387c84f0678ccfd69fa10c88 | 7c8b6235c064fac164cbd389c8d459bd106e09b1 | refs/heads/master | 1,587,608,490,192 | 1,550,228,670,000 | 1,550,228,670,000 | 170,843,813 | 0 | 0 | null | 1,550,225,214,000 | 1,550,225,213,000 | null | UTF-8 | Lean | false | false | 5,570 | lean | import .tptp.tptp
import .tptp.translation_tptp
import .tptp.simplification_tptp
--##################################
--## 5.3 Translating declarations ##
--##################################
meta def translate_axiom_expression: expr → hammer_tactic unit
-- | `()
| `(%%l = %%r) := -- c = t : τ
do (τ, _) ← using_h... |
f568ff861c0faf55ec414f484f0b6524972f370b | a4673261e60b025e2c8c825dfa4ab9108246c32e | /stage0/src/Lean/Compiler/IR/CtorLayout.lean | f36921e78b98a430f0702527a5c45d23659a0d5b | [
"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 | 960 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Environment
import Lean.Compiler.IR.Format
namespace Lean
namespace IR
inductive CtorFieldInfo :=
| irrelevant
| object (i : Nat)
| usiz... |
48dae2d654d5218126481f1114c0b7ae80bc1497 | 8e31b9e0d8cec76b5aa1e60a240bbd557d01047c | /scratch/assoc_simp.lean | f0d5b7d6742c23754f9c873b5620a1cd0c0e1ed9 | [] | 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 | 2,315 | lean | import data.matrix tactic.ring
open tactic declaration expr binder_info
#print binder_fin
local infix ` ⬝ `:70 := matrix.mul
local postfix `ᵀ` : 1500 := matrix.transpose
#print matrix.mul
--set_option trace.class_instances true
set_option eqn_compiler.max_steps 100000
set_option trace.app_builder true
meta def mk_new... |
4b3a7c15e0cfd2e9fa91c0d363aeaeb781a6f132 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/ring_theory/class_group.lean | 5906c8ca465f754baf3f091b6833465b3370c68a | [
"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 | 10,459 | lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import group_theory.quotient_group
import ring_theory.dedekind_domain
/-!
# The ideal class group
This file defines the ideal class group `class_group R K` of fractional... |
c9bfe63ba1cb1481d20c50dff1a503697ac0369e | bb31430994044506fa42fd667e2d556327e18dfe | /src/measure_theory/function/strongly_measurable/basic.lean | be7925460e9af9410f6caa3ebe4ee9bd074d7838 | [
"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 | 87,458 | 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 analysis.normed_space.bounded_linear_maps
import topology.metric_space.metrizable
import measure_theory.function.simple_func_dense
/-!
# Strong... |
3472e6d110bcd4ab464701e6806c65d1e507e716 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/tactic4.lean | 4a333dc407434cd3871d0afdbb5cf473cf404bdf | [
"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 | 138 | lean | import logic
open tactic (renaming id->id_tac)
theorem tst {A B : Prop} (H1 : A) (H2 : B) : id A
:= by unfold id; assumption
check tst
|
c135d403a961fb24ad931966502fe77ffb2811d4 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/order/euclidean_absolute_value.lean | cef698d857b7855f75b11f4a8c5b9bd875375945 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 2,234 | lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import algebra.order.absolute_value
import algebra.euclidean_domain.instances
/-!
# Euclidean absolute values
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to ... |
7deeb175a2406769c688d1c41172b8e2d469e8db | 556aeb81a103e9e0ac4e1fe0ce1bc6e6161c3c5e | /src/starkware/cairo/lean/semantics/soundness/assembly.lean | 060f4c0aec3c7a131d6ae0cb8ff0b7524d7cc516 | [
"Apache-2.0"
] | permissive | starkware-libs/formal-proofs | d6b731604461bf99e6ba820e68acca62a21709e8 | f5fa4ba6a471357fd171175183203d0b437f6527 | refs/heads/master | 1,691,085,444,753 | 1,690,507,386,000 | 1,690,507,386,000 | 410,476,629 | 32 | 9 | Apache-2.0 | 1,690,506,773,000 | 1,632,639,790,000 | Lean | UTF-8 | Lean | false | false | 21,970 | lean | /-
This file does the following:
o defines the Cairo assembly language in terms of the raw machine language instructions
o defines Lean notation for the assembly language instructions
o proves theorems characterizing the next state for each instruction
-/
import starkware.cairo.lean.semantics.cpu
/-
Functions for cli... |
244cb0c16e8d730edb515ea56fae4a670bf1669e | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/blast_tuple2.lean | cbcba8d9aeaf575f5495bee1d767adaa2beac1b4 | [
"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 | 3,340 | lean | import data.fin
open function
constant tuple.{l} : Type.{l} → nat → Type.{l}
constant nil {A : Type} : tuple A 0
constant cons {A : Type} {n : nat} : A → tuple A n → tuple A (nat.succ n)
constant append {A : Type} {n m : nat} : tuple A n → tuple A m → tuple A (n + m)
constant reverse {A : Type} {n : nat} : tuple A n →... |
942addefaf03d2c1f0914fc60505db68e9b59ef6 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/linear_algebra/eigenspace.lean | adcae415e2635c64918aabc9a219c9214dd63cf9 | [
"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 | 24,980 | lean | /-
Copyright (c) 2020 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp
-/
import field_theory.algebraic_closure
import linear_algebra.finsupp
import linear_algebra.matrix.to_lin
import order.preorder_hom
/-!
# Eigenvectors and eig... |
1bae05b64927e01d91f16d44314cd9757462ecfe | abd85493667895c57a7507870867b28124b3998f | /src/data/fintype/card.lean | 0cb2ad4e844e12009ec6a214eca34bf555d8753b | [
"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 | 15,077 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
-/
import data.fintype.basic
import data.nat.choose
import tactic.ring
/-!
Results about "big operations" over a `fintype`, and consequent
results about cardinalities of... |
6f979aceaeb635adccb0872bbede68ca57e06741 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/tactic/monotonicity/basic_auto.lean | 5cd2bb8edda8030ce30290d34b4a785f6cfc58cf | [] | 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 | 651 | lean | /-
Copyright (c) 2019 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Simon Hudon
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.ordered_ring
import Mathlib.order.bounded_lattice
import Mathlib.PostPort
universes l u_1... |
2ed2326336525fb888521b87596424ebdabe9176 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/ring_theory/valuation/integral.lean | d8244b4c9b1dee528e93b0bce470f7364b1137df | [
"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 | 2,097 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import ring_theory.integrally_closed
import ring_theory.valuation.integers
/-!
# Integral elements over the ring of integers of a valution
The ring of integers is integrally... |
916109b444aeb649d194ae54b85befef0cce9a37 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/types.lean | ad97ce8539f579bc321386921954147f33c672eb | [
"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 | 11,259 | 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
-/
import category_theory.epi_mono
import category_theory.functor.fully_faithful
import logic.equiv.basic
/-!
# The category `Type`.
> ... |
6420748266fb9de8dc0e13fe9b9b4a122df48951 | 205f0fc16279a69ea36e9fd158e3a97b06834ce2 | /src/12_Sets/quiz.lean | 8bc927109da628c93e3bff7d68396f63d09326ad | [] | no_license | kevinsullivan/cs-dm-lean | b21d3ca1a9b2a0751ba13fcb4e7b258010a5d124 | a06a94e98be77170ca1df486c8189338b16cf6c6 | refs/heads/master | 1,585,948,743,595 | 1,544,339,346,000 | 1,544,339,346,000 | 155,570,767 | 1 | 3 | null | 1,541,540,372,000 | 1,540,995,993,000 | Lean | UTF-8 | Lean | false | false | 360 | lean | #reduce { 2, 4 } ⊆ { n : ℕ | ∃ m, n = 2 * m }
example : { 2, 4 } ⊆ { n : ℕ | ∃ m, n = 2 * m } :=
begin
change ∀ ⦃a : ℕ⦄, a = 4 ∨ a = 2 ∨ false → (∃ (m : ℕ), a = nat.mul 2 m),
intro,
assume h,
cases h with four rest,
apply exists.intro 2,
assumption,
cases rest with two f,
apply exists.intro 1,
assumption,
contradic... |
6a4383a00a32a1584f649d5d9dd21d728b03e88e | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/measure_theory/probability_mass_function.lean | 627b563a5076e4471cb1fbe3cee61581c70e3a8c | [
"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 | 16,349 | 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 topology.instances.ennreal
/-!
# Probability mass functions
This file is about probability mass functions or discrete probability measures:
a function `α → ℝ... |
ae9d59217dbf26c47971832b5dd38f15c34f74e8 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/measure_theory/pi_system.lean | 0af61def42504b9fbe5111d9d985a031ca16e896 | [
"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 | 28,573 | lean | /-
Copyright (c) 2021 Martin Zinkevich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Martin Zinkevich, Rémy Degenne
-/
import logic.encodable.lattice
import measure_theory.measurable_space_def
/-!
# Induction principles for measurable sets, related t... |
fcda1711f81f7386529835e9ccd0adef29fb7963 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/mutwf1.lean | cc140cdd6c79e14a7f04f69d33cc38158691aa3c | [
"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 | 587 | lean | mutual
def f : Nat → Bool → Nat
| n, true => 2 * f n false
| 0, false => 1
| n, false => n + g n
def g (n : Nat) : Nat :=
if h : n ≠ 0 then
f (n-1) true
else
n
end
termination_by
invImage
(fun
| Sum.inl ⟨n, true⟩ => (n, 2)
| Sum.inl ⟨n, false⟩ => (n, 1)
| Sum.i... |
869c81b36db361e9e633a0827ac5c2e23c79f28b | 05b503addd423dd68145d68b8cde5cd595d74365 | /src/analysis/normed_space/basic.lean | de2442d40c07d65a4a01a821eb9483254b16c6e9 | [
"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 | 40,269 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
-/
import algebra.pi_instances
import linear_algebra.basic
import topology.instances.nnreal topology.instances.complex
import topology.algebra.module
im... |
3fd43b7a13134cf7a03d68ffc711f988303a373f | a7eef317ddec01b9fc6cfbb876fe7ac00f205ac7 | /src/algebra/associated.lean | 5484fe1d002be1a519b92ca630b817f61314f98e | [
"Apache-2.0"
] | permissive | kmill/mathlib | ea5a007b67ae4e9e18dd50d31d8aa60f650425ee | 1a419a9fea7b959317eddd556e1bb9639f4dcc05 | refs/heads/master | 1,668,578,197,719 | 1,593,629,163,000 | 1,593,629,163,000 | 276,482,939 | 0 | 0 | null | 1,593,637,960,000 | 1,593,637,959,000 | null | UTF-8 | Lean | false | false | 24,801 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker
-/
import data.multiset.basic
/-!
# Associated, prime, and irreducible elements.
-/
variables {α : Type*} {β : Type*} {γ : Type*} {δ : Type*}
@[simp] ... |
752ce7ef7f078974452faeae300315ee62adb280 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/group_theory/noncomm_pi_coprod.lean | 5dd7f2871e239878117e72f6c87545545be38b96 | [
"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 | 9,645 | lean | /-
Copyright (c) 2022 Joachim Breitner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joachim Breitner
-/
import group_theory.order_of_element
import data.finset.noncomm_prod
import data.fintype.card
/-!
# Canonical homomorphism from a finite family of monoids
This ... |
db7fcc563c478f36d002314d4c4ebb04923c3969 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/monoid_algebra/support.lean | 9d94e76b6fb2a61d017ec59e6721a618f2be70a7 | [
"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 | 6,080 | lean | /-
Copyright (c) 2022 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import algebra.monoid_algebra.basic
/-!
# Lemmas about the support of a finitely supported function
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this ... |
2cd375e8fb1d62ff86d466678d667379c28dd026 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/analysis/locally_convex/polar.lean | fbabe99e3fd6ae44ba4b6692c88e22f46093b6fe | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 4,694 | lean | /-
Copyright (c) 2022 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll, Kalle Kytölä
-/
import analysis.normed.field.basic
import analysis.convex.basic
import linear_algebra.sesquilinear_form
import topology.algebra.module.weak_dual
/-!
# Polar... |
964f32d388523fd0769288b96ee9994899d085c9 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/category_theory/pi/basic.lean | 6e4591392d83e93d60fd36d347449f205768a285 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 5,070 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Scott Morrison
-/
import category_theory.natural_isomorphism
import category_theory.eq_to_hom
/-!
# Categories of indexed families of objects.
We define the pointwise ca... |
a608731aa49ea11050324c52a92aa11798261942 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/sum.lean | 7953f2e8694916cb9a3622e456350f2b25443e5e | [
"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 | 9,463 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Yury G. Kudryashov
-/
import logic.function.basic
/-!
# More theorems about the sum type
-/
universes u v w x
variables {α : Type u} {α' : Type w} {β : Type v} {β' : ... |
1befbf3b0ec0846cbebb1d46a52a857b91f2bddf | bb31430994044506fa42fd667e2d556327e18dfe | /src/algebra/ring/divisibility.lean | 21dcb248c7b1cc7ec1a019fbc94d7d56cac2408f | [
"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 | 4,204 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Yury Kudryashov, Neil Strickland
-/
import algebra.divisibility.basic
import algebra.ring.defs
/-!
# Lemmas about divisibility in ri... |
da3dc6ea17a28df955a9b446d67fa42661bb6815 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/algebra/module/projective.lean | 0114317b3d8976c24b06cf2db650781c8c25b5a2 | [
"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 | 6,893 | lean | /-
Copyright (c) 2021 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard
-/
import algebra.module.basic
import linear_algebra.finsupp
import linear_algebra.free_module
/-!
# Projective modules
This file contains a definition of a projective... |
aabaafc50c7a36ae32115d2b1433f7b971e225c8 | 359199d7253811b032ab92108191da7336eba86e | /src/instructor/lectures/lecture_4.lean | b7681ef1afea1c51466cd7bb466a81a0ac59ed5b | [] | no_license | arte-et-marte/my_cs2120f21 | 0bc6215cb5018a3b7c90d9d399a173233f587064 | 91609c3609ad81fda895bee8b97cc76813241e17 | refs/heads/main | 1,693,298,928,348 | 1,634,931,202,000 | 1,634,931,202,000 | 399,946,705 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,995 | lean | /-
We've seen that logics start with axioms that
can then be combined (with other information)
using *inference rules* to derive theorems. In
this file we review what we've covered so far
and then we introduce:
(1) The concept of introduction and elimination
rules for a given logical construct.
(2) We distinguish the ... |
36956ffe490c6ea85f759cc884753d7b01c1f31d | bb31430994044506fa42fd667e2d556327e18dfe | /src/combinatorics/simple_graph/basic.lean | 2434050c024213d1cb056322000d0bd52709dc42 | [
"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 | 55,303 | lean | /-
Copyright (c) 2020 Aaron Anderson, Jalex Stark, Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson, Jalex Stark, Kyle Miller, Alena Gusakov, Hunter Monroe
-/
import data.rel
import data.set.finite
import data.sym.sym2
/-!
# Simple graphs
Th... |
e59a40642ef6d76182455c609daad9d1120bb669 | 8e2026ac8a0660b5a490dfb895599fb445bb77a0 | /library/init/algebra/ac.lean | 5da51c6f4560676c38d923a1ababd96c22c80a7f | [
"Apache-2.0"
] | permissive | pcmoritz/lean | 6a8575115a724af933678d829b4f791a0cb55beb | 35eba0107e4cc8a52778259bb5392300267bfc29 | refs/heads/master | 1,607,896,326,092 | 1,490,752,175,000 | 1,490,752,175,000 | 86,612,290 | 0 | 0 | null | 1,490,809,641,000 | 1,490,809,641,000 | null | UTF-8 | Lean | false | false | 412 | 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.logic
universe u
class is_associative (α : Type u) (op : α → α → α) :=
(assoc : ∀ a b c, op (op a b) c = op a (op b c))
class is_commu... |
f1744a63c34dc8e486130583df20c31f05671486 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/category/Ring/colimits.lean | f786d20f28eb3e2e7add23764a22273b1f549cd5 | [
"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 | 12,904 | 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.Ring.basic
import category_theory.limits.has_limits
import category_theory.limits.concrete_category
/-!
# The category of commutative rings h... |
c91cd06dc542e509ab8f2f766ea6427c59227816 | e22cb3c96cab3b1635ab1f31bcc6f998a4cab507 | /src/advice/default.lean | a4d93a401c38590b34c27460d1eef0a4703a2fb4 | [
"Apache-2.0"
] | permissive | jroesch/advice | 455909b7fed462b70f60e6f2d8a8809d97baa311 | f8b12ee428a128b191f02c4435462ecdd6479812 | refs/heads/master | 1,610,346,401,725 | 1,497,946,648,000 | 1,497,946,716,000 | 94,866,826 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 297 | lean | meta def advice_action : list pexpr → tactic (list (string × string)) := fun ps, tactic.trace_state >> pure []
@[hole_command]
meta def advice_type_cmd : hole_command :=
{ name := "Advice",
descr := "Provide advice about how to procede with the current goal",
action := advice_action
}
|
c90dfb0b895fa6a7423b472e7d5121c40c515753 | 592ee40978ac7604005a4e0d35bbc4b467389241 | /Library/generated/mathscheme-lean/DoubleMonoid.lean | 7d46138dc976ef92ebe5ee8a6c094dd444c2f59c | [] | no_license | ysharoda/Deriving-Definitions | 3e149e6641fae440badd35ac110a0bd705a49ad2 | dfecb27572022de3d4aa702cae8db19957523a59 | refs/heads/master | 1,679,127,857,700 | 1,615,939,007,000 | 1,615,939,007,000 | 229,785,731 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,978 | lean | import init.data.nat.basic
import init.data.fin.basic
import data.vector
import .Prelude
open Staged
open nat
open fin
open vector
section DoubleMonoid
structure DoubleMonoid (A : Type) : Type :=
(zero : A)
(plus : (A → (A → A)))
(lunit_zero : (∀ {x : A} , (plus zero x) = x))
(runit_z... |
9dc20994de045d62105c923d38aa68df42d1c0ff | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /stage0/src/Lean/Elab/Tactic/Conv/Unfold.lean | fd2c60c8e4904878c23f255420aa2b4068c611f9 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | tobiasgrosser/lean4 | ce0fd9cca0feba1100656679bf41f0bffdbabb71 | ebdbdc10436a4d9d6b66acf78aae7a23f5bd073f | refs/heads/master | 1,673,103,412,948 | 1,664,930,501,000 | 1,664,930,501,000 | 186,870,185 | 0 | 0 | Apache-2.0 | 1,665,129,237,000 | 1,557,939,901,000 | Lean | UTF-8 | Lean | false | false | 567 | lean | /-
Copyright (c) 2022 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Elab.Tactic.Unfold
import Lean.Elab.Tactic.Conv.Simp
namespace Lean.Elab.Tactic.Conv
open Meta
@[builtinTactic Lean.Parser.Tactic.Conv.unfold]... |
57c05cae600be1f3bde7c7666ca3ca538267b029 | 4950bf76e5ae40ba9f8491647d0b6f228ddce173 | /src/measure_theory/bochner_integration.lean | ae6cd4cbe8ffaed5cec95fb810e230ab041d381d | [
"Apache-2.0"
] | permissive | ntzwq/mathlib | ca50b21079b0a7c6781c34b62199a396dd00cee2 | 36eec1a98f22df82eaccd354a758ef8576af2a7f | refs/heads/master | 1,675,193,391,478 | 1,607,822,996,000 | 1,607,822,996,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 64,861 | lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Yury Kudryashov
-/
import measure_theory.simple_func_dense
import analysis.normed_space.bounded_linear_maps
import topology.sequences
/-!
# Bochner integral
The Bochner... |
7ff96ff7d663d3af0de397d5c5eae9139852974b | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/category_theory/subobject/basic.lean | 10c301af39121dcd92ed50a103274ba70d7e7c9c | [
"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 | 24,142 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Scott Morrison
-/
import category_theory.subobject.mono_over
import category_theory.skeletal
import tactic.elementwise
import tactic.apply_fun
/-!
# Subobjects
We define ... |
76d226b00a2d60ad3b887875b17f7fb4e6d9a040 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/data/finset/basic.lean | 625cf405e624eb8ba7133c15473043aa33522c78 | [
"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 | 28,642 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura, Jeremy Avigad
Finite sets.
-/
import data.fintype.basic data.nat data.list.perm algebra.binary
open nat quot list subtype binary function eq.ops
open [decl] p... |
9a14e6f87c187cb7394bb305283ab6e2e0d44209 | 8b9f17008684d796c8022dab552e42f0cb6fb347 | /library/init/wf.lean | c6abc70dac1687476c846c4868c53e068b4f901b | [
"Apache-2.0"
] | permissive | chubbymaggie/lean | 0d06ae25f9dd396306fb02190e89422ea94afd7b | d2c7b5c31928c98f545b16420d37842c43b4ae9a | refs/heads/master | 1,611,313,622,901 | 1,430,266,839,000 | 1,430,267,083,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,934 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.wf
Author: Leonardo de Moura
-/
prelude
import init.relation
inductive acc {A : Type} (R : A → A → Prop) : A → Prop :=
intro : ∀x, (∀ y, R y x → acc R y) → acc R x
namesp... |
7a73f5bfe2c78672e046ab412d95725e4946b9d9 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/order/filter/extr.lean | 6ca0a533ada0731959a82b86f9ddfcc460c6a5a1 | [
"Apache-2.0"
] | permissive | Lix0120/mathlib | 0020745240315ed0e517cbf32e738d8f9811dd80 | e14c37827456fc6707f31b4d1d16f1f3a3205e91 | refs/heads/master | 1,673,102,855,024 | 1,604,151,044,000 | 1,604,151,044,000 | 308,930,245 | 0 | 0 | Apache-2.0 | 1,604,164,710,000 | 1,604,163,547,000 | null | UTF-8 | Lean | false | false | 20,886 | lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import order.filter.basic
/-!
# Minimum and maximum w.r.t. a filter and on a aet
## Main Definitions
This file defines six predicates of the form `is_A_B`, where... |
960fa9aee7373030c0a8e71fbff9bed44ae39d24 | 5ee26964f602030578ef0159d46145dd2e357ba5 | /src/Huber_ring/localization.lean | ba50d637d6505fb2610885fe831f0305d0f7d9a9 | [
"Apache-2.0"
] | permissive | fpvandoorn/lean-perfectoid-spaces | 569b4006fdfe491ca8b58dd817bb56138ada761f | 06cec51438b168837fc6e9268945735037fd1db6 | refs/heads/master | 1,590,154,571,918 | 1,557,685,392,000 | 1,557,685,392,000 | 186,363,547 | 0 | 0 | Apache-2.0 | 1,557,730,933,000 | 1,557,730,933,000 | null | UTF-8 | Lean | false | false | 15,606 | lean | import ring_theory.localization
import tactic.tidy
import tactic.ring
import Huber_ring.basic
import for_mathlib.topological_rings
import for_mathlib.algebra
import for_mathlib.submodule
import for_mathlib.subgroup
import for_mathlib.nonarchimedean.basic
import for_mathlib.group
universes u v
local attribute [insta... |
9617a86bd542846422a8936d72178f03b4b2570b | 88892181780ff536a81e794003fe058062f06758 | /src/logic_and_proof/exercises.lean | 82fd417090f7a4f782c3f9f7e7156af1a6a6bda3 | [] | no_license | AtnNn/lean-sandbox | fe2c44280444e8bb8146ab8ac391c82b480c0a2e | 8c68afbdc09213173aef1be195da7a9a86060a97 | refs/heads/master | 1,623,004,395,876 | 1,579,969,507,000 | 1,579,969,507,000 | 146,666,368 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,200 | lean | -- § 4.7
section
variables A B C D : Prop
example : A ∧ (A → B) → B := λ ⟨a, f⟩, f a
example : A → ¬(¬A ∧ B) := λ a ⟨f, b⟩, f a
example : ¬ (A ∧ B) → (A → ¬B) := λ f a b, f ⟨a, b⟩
example (h₁ : A ∨ B) (h₂ : A → C) (h₃ : B → D) : C ∨ D := h₁.cases_on (or.inl ∘ h₂) (or.inr ∘ h₃)
example (h : ¬A ∧ ¬B) : ¬(A ∨ B) := ... |
9beec09ea939dea6fbdf9b74e5b03b0343d4d276 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/logic/embedding.lean | 8553ca4321720986883de75981ea6f65a2c766c7 | [
"Apache-2.0"
] | permissive | hikari0108/mathlib | b7ea2b7350497ab1a0b87a09d093ecc025a50dfa | a9e7d333b0cfd45f13a20f7b96b7d52e19fa2901 | refs/heads/master | 1,690,483,608,260 | 1,631,541,580,000 | 1,631,541,580,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 15,337 | 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 data.equiv.basic
import data.sigma.basic
/-!
# Injective functions
-/
universes u v w x
namespace function
/-- `α ↪ β` is a bundled injecti... |
d32ebe29aaa3fdb3d125baee0f4b3848b9fa1005 | 54d7e71c3616d331b2ec3845d31deb08f3ff1dea | /library/init/data/list/basic.lean | ec9763bbbdc7b653498176b0dd361d2bac76ccae | [
"Apache-2.0"
] | permissive | pachugupta/lean | 6f3305c4292288311cc4ab4550060b17d49ffb1d | 0d02136a09ac4cf27b5c88361750e38e1f485a1a | refs/heads/master | 1,611,110,653,606 | 1,493,130,117,000 | 1,493,167,649,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,839 | 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.logic init.data.nat.basic
open decidable list
universes u v w
instance (α : Type u) : inhabited (list α) :=
⟨list.nil⟩
variables {α : ... |
c4e50d352c30fbf325fc3748b0d4a60f99c75665 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/group/to_additive.lean | 36036fda647c26a11db452c477dd14af2d37a1bf | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,847 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Yury Kudryashov.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.tactic.transform_decl
import Mathlib.tactic.algebra
import Mathlib.PostPo... |
d77eb45762c8554018c1c7303fc37616a4e351cc | 4727251e0cd73359b15b664c3170e5d754078599 | /src/linear_algebra/quadratic_form/complex.lean | 63190d440fec23bc8d3676379807138e816bc6e6 | [
"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 | 4,157 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Kexing Ying, Eric Wieser
-/
import linear_algebra.quadratic_form.basic
import analysis.special_functions.pow
/-!
# Quadratic forms over the complex numbers
`equivalent_sum_... |
d5a23c9720d1be95d2df8858f9f79d9d73643616 | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /src/Lean/Parser/Basic.lean | 24fd380ecd11e236c7fa3ebda68146b738efeaf9 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | tobiasgrosser/lean4 | ce0fd9cca0feba1100656679bf41f0bffdbabb71 | ebdbdc10436a4d9d6b66acf78aae7a23f5bd073f | refs/heads/master | 1,673,103,412,948 | 1,664,930,501,000 | 1,664,930,501,000 | 186,870,185 | 0 | 0 | Apache-2.0 | 1,665,129,237,000 | 1,557,939,901,000 | Lean | UTF-8 | Lean | false | false | 75,202 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
import Lean.Data.Trie
import Lean.Syntax
import Lean.Message
/-!
# Basic Lean parser infrastructure
The Lean parser was developed with ... |
cc2d399d6250a062013ce423e7c3b231daca4fa0 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/linear_algebra/basis/bilinear.lean | 59232b8c269982a4daa1988f136da2b0b488f61a | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 2,567 | lean | /-
Copyright (c) 2022 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
import linear_algebra.basis
import linear_algebra.bilinear_map
/-!
# Lemmas about bilinear maps with a basis over each argument
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.... |
2b92716b48504d39ba86a2283056e699c466a600 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/order/filter/ultrafilter.lean | f57ad6d34510d6a348e94b0d48b70ee5e3b3037f | [
"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 | 14,855 | 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, Yury Kudryashov
-/
import order.filter.cofinite
import order.zorn
/-!
# Ultrafilters
An ultrafilter is a minimal (maximal in the set order) proper filt... |
e15ccee1a1b61b8fc7c5c4a3f0f7ec24b8078d07 | 8cb37a089cdb4af3af9d8bf1002b417e407a8e9e | /tests/lean/run/1590.lean | 90a15ff3eb34697482b07666a76c66c5b9c1cd94 | [
"Apache-2.0"
] | permissive | kbuzzard/lean | ae3c3db4bb462d750dbf7419b28bafb3ec983ef7 | ed1788fd674bb8991acffc8fca585ec746711928 | refs/heads/master | 1,620,983,366,617 | 1,618,937,600,000 | 1,618,937,600,000 | 359,886,396 | 1 | 0 | Apache-2.0 | 1,618,936,987,000 | 1,618,936,987,000 | null | UTF-8 | Lean | false | false | 102 | lean | #check `(true.intro)
#check (`(true.intro) : expr)
variables (h : true) [reflected h]
#check `(id h)
|
427977ee29f4b29bc39f13dcc3d2a61601aa2701 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/monoidal/types.lean | a96a3d16be555c7b6b198165a3f95081e30d83fb | [
"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 | 3,691 | 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.of_chosen_finite_products
import category_theory.limits.shapes.types
import logic.equiv.fin
/-!
# The category ... |
6c52d2721f6de0506755491e792717c671612563 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/playground/fix1.lean | 2079545e46735bed068254c878a4837594e71ef8 | [
"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 | 612 | lean | def foo (rec : Nat → Nat → Nat) : Nat → Nat → Nat
| 0 a := a
| (n+1) a := rec n a + a + rec n (a+1)
partial def fix' (f: (Nat → Nat → Nat) → (Nat → Nat → Nat)) : Nat → Nat → Nat
| a b := f fix' a b
def prof {α : Type} (msg : String) (p : IO α) : IO α :=
let msg := "Time for '" ++ msg ++ "':" in
timeit msg p
def ... |
892261f9fb2efce153c795b6389244dde5330a61 | 93b17e1ec33b7fd9fb0d8f958cdc9f2214b131a2 | /src/sep/affineScheme.lean | d0fe462c2f41722ee8b2eb62f9423a563f3979ff | [] | no_license | intoverflow/timesink | 93f8535cd504bc128ba1b57ce1eda4efc74e5136 | c25be4a2edb866ad0a9a87ee79e209afad6ab303 | refs/heads/master | 1,620,033,920,087 | 1,524,995,105,000 | 1,524,995,105,000 | 120,576,102 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,087 | lean | /- Affine separation schemes
-
-/
import .spec
import .localization
import ..top.sheaf
namespace Sep
universes ℓ ℓ₁ ℓ₂
open Top
def rehome_prime {X : OrdAlg.{ℓ}}
{u o : X.Top.OI}
(q : {p // p ∈ X.Top.Open u})
(H : X.Top.Open u ⊆ X.Top.Open o)
: {p // p ∈ X.Top.Open o}
:= { val := q.val
, property... |
d054b23116abcd3dcadb66f2bd4788ddbbe4d952 | f3a5af2927397cf346ec0e24312bfff077f00425 | /src/game/world4/level2.lean | 9e512a7e3eff6093569d97f2d22e3b185cdfbc4c | [
"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 | 314 | lean | import game.world4.level1 -- hide
namespace mynat -- hide
/-
# Power World
## Level 2: `zero_pow_succ`
-/
/- Lemma
For all naturals $m$, $0 ^{succ (m)} = 0$.
-/
lemma zero_pow_succ (m : mynat) : (0 : mynat) ^ (succ m) = 0 :=
begin [nat_num_game]
rw pow_succ,
rw mul_zero,
refl,
end
end mynat -- hide
|
ea24ee530bd8cb136d7a0068567d36f94eca9a1d | e1fb097d56131b99641125824bf370019b30ab6b | /src/mywork/lecture_4.lean | 1d1201c402e9547e200baa1f6c24a2865ee9d4ae | [] | no_license | pcarey627/CS-2120-Base-Repository | fc18fc35b7d40928af7637625077abff6055271c | 434b2391b131e04cbc3be60dc0320639d0e20fb4 | refs/heads/main | 1,690,861,648,224 | 1,632,323,226,000 | 1,632,323,226,000 | 399,946,234 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,921 | lean | /-
In this file, we give formal statements (our version)
of the two axioms of equality. We also present Lean's
versions of these rules, and show how you can use them
without giving all of the arguments explicitly.
-/
/-
AXIOMS
Everything is equal to itself. A bit more formally,
if one is given a type, T, and a value... |
2c0c96bea751c42d26a167db7bf05556260f5442 | 4fa161becb8ce7378a709f5992a594764699e268 | /src/group_theory/congruence.lean | 0a1e561a07e1c76b8236bd7e9e6888160ee1eae1 | [
"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 | 42,764 | lean | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
import data.setoid.basic
import algebra.pi_instances
/-!
# Congruence relations
This file defines congruence relations: equivalence relations that preserve a ... |
968e8d93a1417bdb673b744829a02fd2da047583 | a339bc2ac96174381fb610f4b2e1ba42df2be819 | /hott/types/fin.hlean | c9f2328e0b07ed31af3ec0b04e2b7d0ed2252eb4 | [
"Apache-2.0"
] | permissive | kalfsvag/lean2 | 25b2dccc07a98e5aa20f9a11229831f9d3edf2e7 | 4d4a0c7c53a9922c5f630f6f8ebdccf7ddef2cc7 | refs/heads/master | 1,610,513,122,164 | 1,483,135,198,000 | 1,483,135,198,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 22,732 | hlean | /-
Copyright (c) 2015 Haitao Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Haitao Zhang, Leonardo de Moura, Jakob von Raumer, Floris van Doorn
Finite ordinal types.
-/
import types.list algebra.bundled function logic types.prod types.sum types.nat.div
open eq ... |
69baefa84851eb941c1237be625ac67156f43769 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/meta/rb_map.lean | 27ae900a748d35be2e1910c830cae9d1a6f31e43 | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 8,037 | 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 data.list.defs
/-!
# rb_map
This file defines additional operations on native rb_maps and rb_sets.
These structures are defined in core in `init.meta.rb_ma... |
6963a217cee29b6fbfe0fce37bddd2c85a742d8a | 3863d2564418bccb1859e057bf5a4ef240e75fd7 | /hott/types/int/hott.hlean | c2a7cb8c4dc3a9caa5f6ee6a64a020fedc7bdbc1 | [
"Apache-2.0"
] | permissive | JacobGross/lean | 118bbb067ff4d4af48a266face2c7eb9868fa91c | eb26087df940c54337cb807b4bc6d345d1fc1085 | refs/heads/master | 1,582,735,011,532 | 1,462,557,826,000 | 1,462,557,826,000 | 46,451,196 | 0 | 0 | null | 1,462,557,826,000 | 1,447,885,161,000 | C++ | UTF-8 | Lean | false | false | 5,845 | 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
Theorems about the integers specific to HoTT
-/
import .basic types.eq arity algebra.bundled
open core eq is_equiv equiv algebra is_trunc
open nat (hiding pred)
na... |
0c8f20973a811c71f84ef6afc16a219037c4816e | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/group_theory/sylow.lean | cb6ae0218a3c8412acdbc18e02764e983b70284f | [
"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 | 35,179 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Thomas Browning
-/
import data.nat.factorization.basic
import data.set_like.fintype
import group_theory.group_action.conj_act
import group_theory.p_group
import group_theo... |
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