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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
5f466182fb283d211713bdfa62f984c2f99afc5d | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/data/equiv/denumerable.lean | 0cf55c33ae1c8cc81f68013a323247a474c777bd | [
"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 | 8,831 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
Denumerable (countably infinite) types, as a typeclass extending
encodable. This is used to provide explicit encode/decode functions
from nat, where the functions are kn... |
bfbafa88cbd114fbcfd9e4da2c83cb7aaf0e6679 | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /src/Lean/Meta/Tactic/FVarSubst.lean | ebc51dac71467fff4a488edf2072c565f8779659 | [
"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 | 2,309 | 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.Data.AssocList
import Lean.Expr
import Lean.LocalContext
import Lean.Util.ReplaceExpr
namespace Lean.Meta
/--
Some tactics substitute hypothe... |
ee52c75208c14f8f6be352572dcf81c3daeb46d6 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/meta/tactic.lean | 720cd26bcecb1d3b3d06e574008f54743347c53a | [] | 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 | 20,155 | 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.function
import Mathlib.Lean3Lib.init.data.option.basic
import Mathlib.Lean3Lib.init.util
import Mathlib... |
269d3d0a12f6aa2af6d9ca2d3299d9bfaed067c9 | 6fbf10071e62af7238f2de8f9aa83d55d8763907 | /hw/hw5-exam1-practice.lean | 2ba87d4edab6ef81efc0e591c5b42c0c2eca4bb5 | [] | no_license | HasanMukati/uva-cs-dm-s19 | ee5aad4568a3ca330c2738ed579c30e1308b03b0 | 3e7177682acdb56a2d16914e0344c10335583dcf | refs/heads/master | 1,596,946,213,130 | 1,568,221,949,000 | 1,568,221,949,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,100 | lean | /-
Here is the practice exam. It provides you
with a set of problems illustrative of the
material to be tested. This is a homework
assignment due this coming Thursday. We will
review the questions in class.
Copy this file your "work" directory. Work
on it there. Upload to Collab when done.
Note: An incorrect answer a... |
c97155f4e0ace6a365223d526d7a16ff3b855ddd | 1a61aba1b67cddccce19532a9596efe44be4285f | /hott/hit/cylinder.hlean | 917e8be638a72ab37e11f35828e3d9b8132b3204 | [
"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 | 3,187 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
Declaration of mapping cylinders
-/
import .quotient
open quotient eq sum equiv equiv.ops
namespace cylinder
section
universe u
parameters {A B : Type.{u}} (f :... |
22aa0bad23ef52caff86d253275d63eedcab1543 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/interactive/term_goal_info.lean | 21cff6d73f1d334e2937c5f565b3d764e3cabf7e | [
"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 | 1,049 | lean | example (p q r : Prop) : p → (p ∧ q → r) → q → r :=
λ hp hpqr hq, hpqr (and.intro (id hp) hq)
--^ "command":"info"
example (p q r : Prop) : p → (p ∧ q → r) → q → r :=
λ hp hpqr, by intro hq; exact hpqr (and.intro hp hq)
--^ "command":"info"
example (p q r : Prop) : p → (p ∧ q → r) → q → r :=
λ... |
99fdafe1bba7362cae28ea273e22d78b869c1f61 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/ring_theory/int/basic.lean | d3cae070796eeee9598659ce5f8bfdc1c6f59e5e | [
"Apache-2.0"
] | permissive | abentkamp/mathlib | d9a75d291ec09f4637b0f30cc3880ffb07549ee5 | 5360e476391508e092b5a1e5210bd0ed22dc0755 | refs/heads/master | 1,682,382,954,948 | 1,622,106,077,000 | 1,622,106,077,000 | 149,285,665 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,403 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker, Aaron Anderson
-/
import data.int.basic
import data.int.gcd
import ring_theory.multiplicity
import ring_theory.principal_ideal_domain
/-!
# Divisibili... |
381d7cfd350dc50febe3fd42ccd508ace28b1ea3 | bb31430994044506fa42fd667e2d556327e18dfe | /src/number_theory/zsqrtd/basic.lean | 4e29530bb4f3799e2547d35cd0dd55d4ce1dd604 | [
"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 | 33,365 | 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 algebra.associated
import ring_theory.int.basic
import tactic.ring
/-! # ℤ[√d]
The ring of integers adjoined with a square root of `d : ℤ`.
After defining t... |
572c7c3b8c14370ea9baead35ab9b520af63a576 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/field_theory/minimal_polynomial.lean | 1ff4d258ddc29df25e7184e6990bd3a92649e0e8 | [
"Apache-2.0"
] | permissive | rmitta/mathlib | 8d90aee30b4db2b013e01f62c33f297d7e64a43d | 883d974b608845bad30ae19e27e33c285200bf84 | refs/heads/master | 1,585,776,832,544 | 1,576,874,096,000 | 1,576,874,096,000 | 153,663,165 | 0 | 2 | Apache-2.0 | 1,544,806,490,000 | 1,539,884,365,000 | Lean | UTF-8 | Lean | false | false | 8,597 | lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johan Commelin
-/
import ring_theory.integral_closure
/-!
# Minimal polynomials
This file defines the minimal polynomial of an element x of an A-algebra B,
under the ass... |
028cc73aa547648b58bfe91adcc84d7e8ee96795 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/tactic/monotonicity/basic.lean | 1662abb704955b2d0bba92e8e9e49014399c172f | [
"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 | 5,734 | 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 algebra.order_functions
namespace tactic.interactive
open tactic list
open lean lean.parser interactive
open interactive.types
@[derive inhabited]
structure mono_cf... |
dc2bd45141e18271d46a6988d9cd0408ac836189 | fe84e287c662151bb313504482b218a503b972f3 | /src/algebra/cdga.lean | 2f4ef7e4e265284b5b954fe0cb8837177a8e7ce8 | [] | 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 | 2,117 | lean | import algebra.ring group_theory.subgroup.basic tactic.ring data.finsupp
variables (A : ℤ → Type*) [∀ n, add_comm_group (A n)]
def tp {n m : ℤ} (h : n = m) : A n →+ A m := {
to_fun := (congr_arg A h).mp,
map_zero' := by { cases h, refl },
map_add' := by { cases h, intros, refl }
}
class dga :=
(one : A 0)
(mu... |
b4b0e9e8e4504ce27743db55a6362d1656bb92fb | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/group_theory/congruence.lean | 07ee5f7f3bdeace7ab86b3f7067157a92f79724f | [
"Apache-2.0"
] | permissive | rmitta/mathlib | 8d90aee30b4db2b013e01f62c33f297d7e64a43d | 883d974b608845bad30ae19e27e33c285200bf84 | refs/heads/master | 1,585,776,832,544 | 1,576,874,096,000 | 1,576,874,096,000 | 153,663,165 | 0 | 2 | Apache-2.0 | 1,544,806,490,000 | 1,539,884,365,000 | Lean | UTF-8 | Lean | false | false | 43,364 | 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 group_theory.submonoid
import data.setoid
import algebra.pi_instances
/-!
# Congruence relations
This file defines congruence relations: equivalence r... |
7fa410175153f85c670b42ae52cc4f9b381fcd31 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/measure_theory/measure/ae_measurable.lean | 99b01758f417e082b525db9ca592df49e89c8d6d | [
"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 | 15,104 | lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import measure_theory.measure.measure_space
/-!
# Almost everywhere measurable functions
A function is almost everywhere measurable if it coincides almost eve... |
84060621d55b1f2d82381e70ae897a391ad8a6a7 | e030b0259b777fedcdf73dd966f3f1556d392178 | /library/init/logic.lean | 334aee2423eae41a6834a39121aca58b88fb4bd0 | [
"Apache-2.0"
] | permissive | fgdorais/lean | 17b46a095b70b21fa0790ce74876658dc5faca06 | c3b7c54d7cca7aaa25328f0a5660b6b75fe26055 | refs/heads/master | 1,611,523,590,686 | 1,484,412,902,000 | 1,484,412,902,000 | 38,489,734 | 0 | 0 | null | 1,435,923,380,000 | 1,435,923,379,000 | null | UTF-8 | Lean | false | false | 36,811 | 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, Floris van Doorn
-/
prelude
import init.core
universe variables u v w
@[reducible] def id {α : Type u} (a : α) : α := a
def flip {α : Type u... |
306e72ac0ebb4a710c27ab1b5794fed4e19f1a95 | 432d948a4d3d242fdfb44b81c9e1b1baacd58617 | /src/data/fintype/basic.lean | 29319a29fe413b63dd239cea698f04c41266bcdb | [
"Apache-2.0"
] | permissive | JLimperg/aesop3 | 306cc6570c556568897ed2e508c8869667252e8a | a4a116f650cc7403428e72bd2e2c4cda300fe03f | refs/heads/master | 1,682,884,916,368 | 1,620,320,033,000 | 1,620,320,033,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 63,919 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
Finite types.
-/
import tactic.wlog
import data.finset.powerset
import data.finset.lattice
import data.finset.pi
import data.array.lemmas
import order.well_founded
impo... |
f404315fb7d2c6429afce15f074907bfa867e405 | 1a61aba1b67cddccce19532a9596efe44be4285f | /tests/lean/calc1.lean | 521e440f178587dd0017ccef2b91eefde930bd93 | [
"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 | 1,631 | lean | prelude constant A : Type.{1}
definition bool : Type.{1} := Type.{0}
constant eq : A → A → bool
infixl `=`:50 := eq
axiom subst (P : A → bool) (a b : A) (H1 : a = b) (H2 : P a) : P b
axiom eq_trans (a b c : A) (H1 : a = b) (H2 : b = c) : a = c
axiom eq_refl (a : A) : a = a
constant le : A → A → bool
infixl `≤`:50 := le... |
8f53b7ea735ad3e3187d37190c6b25a930e8502c | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/ring_theory/witt_vector/discrete_valuation_ring.lean | b21fa0fa572e626b4fcba16da04021b8e2ce8809 | [
"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 | 6,094 | lean | /-
Copyright (c) 2022 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Heather Macbeth, Johan Commelin
-/
import ring_theory.witt_vector.domain
import ring_theory.witt_vector.mul_coeff
import ring_theory.discrete_valuation_ring
import t... |
1d2d44b32911aa3ac7df0348cba80455105e9740 | 8b9f17008684d796c8022dab552e42f0cb6fb347 | /hott/init/priority.hlean | 01d5fcffdfbcdfdd3b226c38c410aa55839182a9 | [
"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 | 316 | hlean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.priority
Authors: Leonardo de Moura
-/
prelude
import init.datatypes
definition std.priority.default : num := 1000
definition std.priority.max : num := 4294967295
|
51cd70272fec5e699c055036ee07b24951c18613 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/data/finset/lattice.lean | 389fc9050830af55c707ab75451ca6fb905ba835 | [
"Apache-2.0"
] | permissive | stjordanis/mathlib | 51e286d19140e3788ef2c470bc7b953e4991f0c9 | 2568d41bca08f5d6bf39d915434c8447e21f42ee | refs/heads/master | 1,631,748,053,501 | 1,627,938,886,000 | 1,627,938,886,000 | 228,728,358 | 0 | 0 | Apache-2.0 | 1,576,630,588,000 | 1,576,630,587,000 | null | UTF-8 | Lean | false | false | 41,887 | 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.finset.fold
import data.multiset.lattice
import order.order_dual
import order.complete_lattice
/-!
# Lattice operations on finsets
-/
variables {α β γ :... |
7d9e76e04c00c698e07d418e25f88483c633a534 | 618003631150032a5676f229d13a079ac875ff77 | /src/measure_theory/probability_mass_function.lean | f81b9401472af8cab0094cbfa607d27166afa931 | [
"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 | 4,771 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
Probability mass function -- discrete probability measures
-/
import topology.instances.ennreal
noncomputable theory
variables {α : Type*} {β : Type*} {γ : Type*}
open_l... |
67571c8f979840530bf80a3a41f6b1473ea90471 | cc62cd292c1acc80a10b1c645915b70d2cdee661 | /src/category_theory/enriched.lean | dde16f5f0e5749772640365e7b091276c0343c90 | [] | no_license | RitaAhmadi/lean-category-theory | 4afb881c4b387ee2c8ce706c454fbf9db8897a29 | a27b4ae5eac978e9188d2e867c3d11d9a5b87a9e | refs/heads/master | 1,651,786,183,402 | 1,565,604,314,000 | 1,565,604,314,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,302 | lean | -- import category_theory.limits.limits
-- import category_theory.limits.preserves
-- import category_theory.limits.types
-- import category_theory.fully_faithful
-- open category_theory.limits
-- universes v u
-- namespace category_theory
-- variables {C : Type u} [𝒞 : category.{v} C]
-- variables (V : Type (v+1)... |
3dba108692a5165bb1142cc9167ab7f1e4351524 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/topology/metric_space/kuratowski.lean | 99fd9607cca3707f3e389b170cc6ab99ca20e1de | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 5,216 | lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import analysis.normed_space.lp_space
import topology.sets.compacts
/-!
# The Kuratowski embedding
Any separable metric space can be embedded isometrically in... |
545204123fc12fb0434e43a5c0468c9d9ba1de34 | 626e312b5c1cb2d88fca108f5933076012633192 | /src/topology/continuous_on.lean | b93e3932de15ee49c240cf9bf38612f0ec602419 | [
"Apache-2.0"
] | permissive | Bioye97/mathlib | 9db2f9ee54418d29dd06996279ba9dc874fd6beb | 782a20a27ee83b523f801ff34efb1a9557085019 | refs/heads/master | 1,690,305,956,488 | 1,631,067,774,000 | 1,631,067,774,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 47,388 | lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import topology.constructions
/-!
# Neighborhoods and continuity relative to a subset
This file defines relative versions
* `nhds_within` of `nhds`
* `co... |
8a26abc3789f55de5bf96dcb7d3452508e5a291b | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /hott/hit/trunc.hlean | 68278b7efac462bfb7acbf591185bfbaebec055b | [
"Apache-2.0"
] | permissive | davidmueller13/lean | 65a3ed141b4088cd0a268e4de80eb6778b21a0e9 | c626e2e3c6f3771e07c32e82ee5b9e030de5b050 | refs/heads/master | 1,611,278,313,401 | 1,444,021,177,000 | 1,444,021,177,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,424 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
n-truncation of types.
Ported from Coq HoTT
-/
/- The hit n-truncation is primitive, declared in init.hit. -/
import types.sigma types.pointed
open is_trunc eq ... |
1d77ad517bb5a646c7707172b7d2b904c7440b70 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/linear_algebra/lagrange.lean | 1e8ebf42f34e34a17958b008b9f422cf57a02218 | [
"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 | 7,260 | 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.polynomial
import algebra.big_operators.basic
/-!
# Lagrange interpolation
## Main definitions
* `lagrange.basis s x` where `s : finset F` and `x : F`: t... |
c79a1238b1cb4db0bb183491c933c732687bb178 | b9d8165d695e844c92d9d4cdcac7b5ab9efe09f7 | /src/order/filter/basic.lean | d53b5d7c955a7089f8b025d807686c6f13d2c684 | [
"Apache-2.0"
] | permissive | spapinistarkware/mathlib | e917d9c44bf85ef51db18e7a11615959f714efc5 | 0a9a1ff463a1f26e27d7c391eb7f6334f0d90383 | refs/heads/master | 1,606,808,129,547 | 1,577,478,369,000 | 1,577,478,369,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 89,578 | 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
Theory of filters on sets.
-/
import order.galois_connection order.zorn
import data.set.finite
open lattice set
universes u v w x y
open_locale classic... |
4c3832189e12b6570146f3ae5103523d361938dc | ea5678cc400c34ff95b661fa26d15024e27ea8cd | /HoTT-play-area.lean | 93c5c72c78073e77ff3f7a85dca9dc32f0b14a7e | [] | no_license | ChrisHughes24/leanstuff | dca0b5349c3ed893e8792ffbd98cbcadaff20411 | 9efa85f72efaccd1d540385952a6acc18fce8687 | refs/heads/master | 1,654,883,241,759 | 1,652,873,885,000 | 1,652,873,885,000 | 134,599,537 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,433 | lean | import hott.init hott.types.sigma hott.types.nat
set_option pp.notation false
#print hott.univalence
namespace hott
local infix ` = `:50 := hott.eq
@[hott] lemma X : bool = bool := eq.refl _
@[hott] def Y (a b : unit) : ∀ (x y : a = b), x = y :=
punit.rec_on a (λ x, @eq.rec_on _ _ (λ b h, ∀ y, eq h y) _ _ $
λ y,... |
81d4d8c034e73ae1cc31a02c1b0e8cbfaadc7633 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/measure_theory/function/lp_order.lean | 8f027a5b464039092d2ee146d67662847b8dd779 | [
"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 | 1,979 | lean | /-
Copyright (c) 2021 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import measure_theory.function.lp_space
import analysis.normed_space.lattice_ordered_group
/-!
# Order related properties of Lp spaces
### Results
- `Lp E p μ` is an `... |
e10f8122341e97b73ed73bd216af50d7b307ef3a | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/tactic/algebra.lean | 6c9c057ae8f415bffe1347cbb9f9bce954d1cb55 | [
"Apache-2.0"
] | permissive | rmitta/mathlib | 8d90aee30b4db2b013e01f62c33f297d7e64a43d | 883d974b608845bad30ae19e27e33c285200bf84 | refs/heads/master | 1,585,776,832,544 | 1,576,874,096,000 | 1,576,874,096,000 | 153,663,165 | 0 | 2 | Apache-2.0 | 1,544,806,490,000 | 1,539,884,365,000 | Lean | UTF-8 | Lean | false | false | 2,313 | 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.core
open lean.parser
namespace tactic
@[user_attribute]
meta def ancestor_attr : user_attribute unit (list name) :=
{ name := `ancestor,
descr := "ance... |
f240f20804f1cc931cc5e0790866cbcb8cdf0fde | 26ac254ecb57ffcb886ff709cf018390161a9225 | /src/linear_algebra/dimension.lean | 58d12231e714044dd4763d16cdb599952c057046 | [
"Apache-2.0"
] | permissive | eric-wieser/mathlib | 42842584f584359bbe1fc8b88b3ff937c8acd72d | d0df6b81cd0920ad569158c06a3fd5abb9e63301 | refs/heads/master | 1,669,546,404,255 | 1,595,254,668,000 | 1,595,254,668,000 | 281,173,504 | 0 | 0 | Apache-2.0 | 1,595,263,582,000 | 1,595,263,581,000 | null | UTF-8 | Lean | false | false | 18,353 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro, Johannes Hölzl, Sander Dahmen
-/
import linear_algebra.basis
import set_theory.ordinal
/-!
# Dimension of modules and vector spaces
## Main definitions
* The dimensio... |
aff0723d093fa6c386370ffa1b9db362b83b0c47 | 5d166a16ae129621cb54ca9dde86c275d7d2b483 | /library/tools/debugger/cli.lean | cac54e070ce60b0edbe206c6455d991dcc014855 | [
"Apache-2.0"
] | permissive | jcarlson23/lean | b00098763291397e0ac76b37a2dd96bc013bd247 | 8de88701247f54d325edd46c0eed57aeacb64baf | refs/heads/master | 1,611,571,813,719 | 1,497,020,963,000 | 1,497,021,515,000 | 93,882,536 | 1 | 0 | null | 1,497,029,896,000 | 1,497,029,896,000 | null | UTF-8 | Lean | false | false | 8,276 | 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
Simple command line interface for debugging Lean programs and tactics.
-/
import tools.debugger.util
namespace debugger
inductive mode
| init | step | run |... |
636005e1b94e4a5438da5e3d1582ae10f784f0a9 | b328e8ebb2ba923140e5137c83f09fa59516b793 | /src/Lean/Meta/Tactic/ElimInfo.lean | d35bc80c8fc5e8f5b110edc1228893ee59a4d642 | [
"Apache-2.0"
] | permissive | DrMaxis/lean4 | a781bcc095511687c56ab060e816fd948553e162 | 5a02c4facc0658aad627cfdcc3db203eac0cb544 | refs/heads/master | 1,677,051,517,055 | 1,611,876,226,000 | 1,611,876,226,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,994 | 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.Meta
structure ElimAltInfo where
name : Name
numFields : Nat
structure ElimInfo where
motivePos : Nat
... |
ec18cc87d92176597547b0f9867a8f6305f7b63d | a047a4718edfa935d17231e9e6ecec8c7b701e05 | /src/topology/uniform_space/basic.lean | aa8b76b2b2b880078c71f987883c8506f2132fdc | [
"Apache-2.0"
] | permissive | utensil-contrib/mathlib | bae0c9fafe5e2bdb516efc89d6f8c1502ecc9767 | b91909e77e219098a2f8cc031f89d595fe274bd2 | refs/heads/master | 1,668,048,976,965 | 1,592,442,701,000 | 1,592,442,701,000 | 273,197,855 | 0 | 0 | null | 1,592,472,812,000 | 1,592,472,811,000 | null | UTF-8 | Lean | false | false | 61,584 | 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, Patrick Massot
-/
import order.filter.lift
import topology.separation
/-!
# Uniform spaces
Uniform spaces are a generalization of metric spaces and top... |
fb445251415db20a1c3c6e8ef7d3f19f3f995f2a | bb31430994044506fa42fd667e2d556327e18dfe | /src/linear_algebra/affine_space/basis.lean | 56ad63b78851ce8a45f31bdde7566ed422b3b6b9 | [
"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 | 10,345 | lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import linear_algebra.affine_space.independent
import linear_algebra.basis
/-!
# Affine bases and barycentric coordinates
Suppose `P` is an affine space modelled on the m... |
971349b497624342fae81cbdb41f2129fd68a752 | 8f83e52da30f74edd26b394c8cbbaa68b2ac41aa | /06-formalizacija-dokazov/vaje-imp.lean | 6a468b23ac36a063941c8a29af59a9fcbb63f2ac | [] | no_license | petrapodlogar/teorija-programskih-jezikov | ec790e2a6cd293d54b6c1bdd48cbb8bd7e2b2421 | def21623d0b6bf1090e5d05e7c1d391aacdc70f2 | refs/heads/master | 1,599,611,534,895 | 1,574,856,756,000 | 1,574,856,756,000 | 221,290,046 | 0 | 0 | null | 1,573,585,033,000 | 1,573,585,033,000 | null | UTF-8 | Lean | false | false | 8,266 | lean | -- ==================== Syntax ====================
def loc := string
inductive aexp : Type
| Lookup : loc -> aexp
| Int : int -> aexp
| Plus : aexp -> aexp -> aexp
| Minus : aexp -> aexp -> aexp
| Times : aexp -> aexp -> aexp
inductive bexp : Type
| Bool : bool -> bexp
| Equal : aexp -> aexp -> bexp
| Less : aexp... |
cc75084b2b07e0e8efa5fd93965501049b79c3d1 | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /tests/lean/run/tactic1.lean | 76df973beb61b42527d9defef99470c1c76e93ce | [
"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 | 1,128 | lean |
theorem ex1 (x : Nat) (y : { v // v > x }) (z : Nat) : Nat :=
by {
clear y x;
exact z
}
theorem ex2 (x : Nat) (y : { v // v > x }) (z : Nat) : Nat :=
by {
clear x y;
exact z
}
theorem ex3 (x y z : Nat) (h₁ : x = y) (h₂ : z = y) : x = z :=
by {
have y = z from h₂.symm;
apply Eq.trans;
exact h₁;
assum... |
089de7d08d573f166784c599897fd80001d77a0c | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/analysis/special_functions/sqrt.lean | e33567aaa02f46998ef3c4865b42e8ff33aa3367 | [
"Apache-2.0"
] | permissive | abentkamp/mathlib | d9a75d291ec09f4637b0f30cc3880ffb07549ee5 | 5360e476391508e092b5a1e5210bd0ed22dc0755 | refs/heads/master | 1,682,382,954,948 | 1,622,106,077,000 | 1,622,106,077,000 | 149,285,665 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,633 | lean | /-
Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import data.real.sqrt
import analysis.calculus.inverse
import measure_theory.borel_space
/-!
# Smoothness of `real.sqrt`
In this file we prove that `real.sq... |
ef7721f5c594c08ed7e990e3f86e4f20b80bd5b1 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/tactic/to_additive.lean | c0aa488aa028cfc3ea355fdb5e611b140399cfcd | [
"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 | 28,515 | 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, Floris van Doorn
-/
import tactic.transform_decl
import tactic.algebra
import tactic.lint.basic
import tactic.alias
/-!
# Transport multiplicative to ... |
68e7f0fc963fc3c8a7de11d3fe0f5b2d33fa3869 | acc85b4be2c618b11fc7cb3005521ae6858a8d07 | /data/nat/basic.lean | d4303d2d6ea32a77d27900d6a4f04ddf5c89d409 | [
"Apache-2.0"
] | permissive | linpingchuan/mathlib | d49990b236574df2a45d9919ba43c923f693d341 | 5ad8020f67eb13896a41cc7691d072c9331b1f76 | refs/heads/master | 1,626,019,377,808 | 1,508,048,784,000 | 1,508,048,784,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 15,775 | lean | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
Basic operations on the natural numbers.
-/
import logic.basic algebra.order
universe u
namespace nat
variables ... |
a1d1b231aa63bc70f276dff6a2de2240b74cd9ae | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/data/fintype/basic.lean | 455b5ad7999b52f310e5263d95027a0dd8241498 | [
"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 | 9,216 | lean | /-
Copyright (c) 2015 Leonardo de Moura. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
Finite type (type class).
-/
import data.list.perm data.list.as_type data.bool data.equiv
open list bool unit decidable option function
structure fintype [class]... |
47e6a09b6fae9fb95863cfa199664cda0138a66e | ad0c7d243dc1bd563419e2767ed42fb323d7beea | /analysis/measure_theory/lebesgue_measure.lean | da2fa93af2b3fbddc360766bf1c777c58b3e8ebd | [
"Apache-2.0"
] | permissive | sebzim4500/mathlib | e0b5a63b1655f910dee30badf09bd7e191d3cf30 | 6997cafbd3a7325af5cb318561768c316ceb7757 | refs/heads/master | 1,585,549,958,618 | 1,538,221,723,000 | 1,538,221,723,000 | 150,869,076 | 0 | 0 | Apache-2.0 | 1,538,229,323,000 | 1,538,229,323,000 | null | UTF-8 | Lean | false | false | 10,864 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Lebesgue measure on the real line
-/
import analysis.measure_theory.measure_space analysis.measure_theory.borel_space
noncomputable theory
open classical set lattice fi... |
b6e7afd3e23ea22872a4f629f8ec87b082bb452d | d1a52c3f208fa42c41df8278c3d280f075eb020c | /stage0/src/Lean/Elab/Mixfix.lean | 8c26c72f7f531a1ad17086ae1d10cd4a237ef704 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | cipher1024/lean4 | 6e1f98bb58e7a92b28f5364eb38a14c8d0aae393 | 69114d3b50806264ef35b57394391c3e738a9822 | refs/heads/master | 1,642,227,983,603 | 1,642,011,696,000 | 1,642,011,696,000 | 228,607,691 | 0 | 0 | Apache-2.0 | 1,576,584,269,000 | 1,576,584,268,000 | null | UTF-8 | Lean | false | false | 1,752 | 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.Elab.Attributes
namespace Lean.Elab.Command
@[builtinMacro Lean.Parser.Command.mixfix] def expandMixfix : Macro := fun stx =>
withAttrKindGl... |
130c55f1faa00c21d228f5a5f43890f3009476b4 | 853df553b1d6ca524e3f0a79aedd32dde5d27ec3 | /src/data/complex/exponential.lean | 1ffae819a8a6cc8721f73754e886ea15d8fe57f9 | [
"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 | 49,791 | 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
-/
import algebra.geom_sum
import data.nat.choose
import data.complex.basic
/-!
# Exponential, trigonometric and hyperbolic trigonometric functions... |
d27144763fec2bd7b42622fdf68b574afc210704 | e61a235b8468b03aee0120bf26ec615c045005d2 | /src/Init/Lean/Compiler/IR/Boxing.lean | 87b1bb0cf501aa642134072edb2e938634d833d4 | [
"Apache-2.0"
] | permissive | SCKelemen/lean4 | 140dc63a80539f7c61c8e43e1c174d8500ec3230 | e10507e6615ddbef73d67b0b6c7f1e4cecdd82bc | refs/heads/master | 1,660,973,595,917 | 1,590,278,033,000 | 1,590,278,033,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 12,980 | 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
-/
prelude
import Init.Control.EState
import Init.Control.Reader
import Init.Data.AssocList
import Init.Data.Nat
import Init.Lean.Runtime
import Init.Lean.Comp... |
0eb9ae830b5c5d2a71733d6e915d33c05ea6d7d0 | 510e96af568b060ed5858226ad954c258549f143 | /topology/topological_space.lean | 11edf5515bc57f0f009280599a06182c3db35258 | [] | no_license | Shamrock-Frost/library_dev | cb6d1739237d81e17720118f72ba0a6db8a5906b | 0245c71e4931d3aceeacf0aea776454f6ee03c9c | refs/heads/master | 1,609,481,034,595 | 1,500,165,215,000 | 1,500,165,347,000 | 97,350,162 | 0 | 0 | null | 1,500,164,969,000 | 1,500,164,969,000 | null | UTF-8 | Lean | false | false | 26,017 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Theory of topological spaces.
-/
import algebra.lattice.filter
open set filter lattice
universes u v w
structure topological_space (α : Type u) :=
(open' : set ... |
32354accb55a269f5078f2e21e2f2ff6a486992c | 07f5f86b00fed90a419ccda4298d8b795a68f657 | /library/init/meta/injection_tactic.lean | d647a724324b1acba18158c6f177592dd7d8be58 | [
"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 | 2,970 | 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.function
namespace tactic
open nat tactic environment expr list
private meta def at_end₂ (e₁ e₂ : expr) : ℕ → tactic ... |
43e32fb47ba447067b94abc78a187844228c383a | 6094e25ea0b7699e642463b48e51b2ead6ddc23f | /library/data/set/basic.lean | 0d346ffd103f315f9d42ae4c9f95fc1ed74871c4 | [
"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 | 23,728 | 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 logic.connectives logic.identities algebra.binary
open eq.ops binary function
definition set (X : Type) := X → Prop
namespace set
variable {... |
d727eb955eb7c15c669bb7e60c027cde1ea70fb0 | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /tests/lean/run/doNotation3.lean | 58ec09e97e8ba4013d86c9fe44d81f52721ba5b3 | [
"Apache-2.0"
] | permissive | williamdemeo/lean4 | 72161c58fe65c3ad955d6a3050bb7d37c04c0d54 | 6d00fcf1d6d873e195f9220c668ef9c58e9c4a35 | refs/heads/master | 1,678,305,356,877 | 1,614,708,995,000 | 1,614,708,995,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,623 | lean | theorem zeroLtOfLt : {a b : Nat} → a < b → 0 < b
| 0, _, h => h
| a+1, b, h =>
have a < b from Nat.ltTrans (Nat.ltSuccSelf _) h
zeroLtOfLt this
def fold {m α β} [Monad m] (as : Array α) (b : β) (f : α → β → m β) : m β := do
let rec loop : (i : Nat) → i ≤ as.size → β → m β
| 0, h, b => b
| i+1, h, b => do
... |
ffc592f0e74ca9999c85a27121042f0b32d7301c | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/linear_algebra/affine_space/finite_dimensional.lean | a8d31e4dd08ab99373eb4e668b6c6a984eefa362 | [
"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 | 29,371 | lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import linear_algebra.affine_space.independent
import linear_algebra.finite_dimensional
/-!
# Finite-dimensional subspaces of affine spaces.
This file provides a few re... |
6df78a4b3b461e9d43a2f601daf50356b04ba876 | 08bd4ba4ca87dba1f09d2c96a26f5d65da81f4b4 | /src/Lean/Compiler/IR/LLVMBindings.lean | 8e6a2aad53a20208738d97cbda8bdbd81b48e17e | [
"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",
"Apache-2.0",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | gebner/lean4 | d51c4922640a52a6f7426536ea669ef18a1d9af5 | 8cd9ce06843c9d42d6d6dc43d3e81e3b49dfc20f | refs/heads/master | 1,685,732,780,391 | 1,672,962,627,000 | 1,673,459,398,000 | 373,307,283 | 0 | 0 | Apache-2.0 | 1,691,316,730,000 | 1,622,669,271,000 | Lean | UTF-8 | Lean | false | false | 14,502 | lean | /-
Copyright (c) 2022 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Siddharth Bhat
-/
namespace LLVM
/-!
This file defines bindings for LLVM. The main mechanisms
are to:
- Mirror the values of C enumerations.
- Create opaque values for LLVM's p... |
0abfb512109f4a7bfb9fe358f250c3237226cf01 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/reverts_tac.lean | 33fb4b37315a730a40d148148738d7780fec9b49 | [
"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 | 570 | lean | import logic
theorem tst {a b c : Prop} : a → b → c → a ∧ b :=
begin
intros [Ha, Hb, Hc],
reverts [Hb, Ha],
intros [Hb2, Ha2],
apply (and.intro Ha2 Hb2),
end
theorem foo1 {A : Type} (a b c : A) (P : A → Prop) : P a → a = b → P b :=
begin
intros [Hp, Heq],
reverts [Heq, Hp],
intro Heq,
eapply (eq.rec_... |
93425a63691de4e3f38b7820ea39002931dbd34f | d450724ba99f5b50b57d244eb41fef9f6789db81 | /src/homework/hw1and2.lean | c68f4b494e220044a0f92d75b8c31dcdd973eef8 | [] | no_license | jakekauff/CS2120F21 | 4f009adeb4ce4a148442b562196d66cc6c04530c | e69529ec6f5d47a554291c4241a3d8ec4fe8f5ad | refs/heads/main | 1,693,841,880,030 | 1,637,604,848,000 | 1,637,604,848,000 | 399,946,698 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,247 | lean | /-
EQUALITY
-/
/- #1
Suppose that x, y, z, and w are arbitrary objects of some type,
T; and suppose further that we know (have proofs of the facts)
that x = y, y = z, and w = z. Give a very, very short English
proof of the conjecture that z = w. You can use not only the
axioms of equality, but either of the theo... |
a736eba7cf8561c3ffeb8b6e7e36b3becdad2b9d | 59b654f4ee2fef898a3487dc03554a569051b63a | /src/old/twcube_graph.lean | 484ca29bc3d42b482d9a725bb7bf24975a6bc6cd | [] | no_license | gunpinyo/twisted_cube_formalisation | 180c9157478b66ec2b11ca47c8ff998a3e978a88 | f78206ac495e84bd43a9b820fa10b6c94722e0ec | refs/heads/master | 1,624,501,222,992 | 1,607,081,624,000 | 1,607,081,624,000 | 166,885,106 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 586 | lean | import generic_cube_graph
def twprism_graph : graph → graph := prism_graph tt
def twcube_graph (n : ℕ) : graph := cube_graph tt n
def twcube_graph_alt (n : ℕ) : graph := cube_graph_alt tt n
section
variable n : ℕ
def twcg_to_twcg' : graph_cat.hom (twcube_graph n) (twcube_graph_alt n)
:= cg_to_cg'... |
a2e4fb229f79313bbc0591ea1d45ff21a464de53 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/noncomp_thm.lean | d31bf82c759af8b6d97a16a3a217f4345d68d9a6 | [
"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 | 44 | lean | noncomputable theorem foo : true := trivial
|
2b1621db410daf28a02454e2c3b32b7f071cc0e2 | 43390109ab88557e6090f3245c47479c123ee500 | /src/M3P14/Arithmetic_functions/mobius.lean | 70c3c41d9fcfcf76eca7f8ce2def6797a6d14747 | [
"Apache-2.0"
] | permissive | Ja1941/xena-UROP-2018 | 41f0956519f94d56b8bf6834a8d39473f4923200 | b111fb87f343cf79eca3b886f99ee15c1dd9884b | refs/heads/master | 1,662,355,955,139 | 1,590,577,325,000 | 1,590,577,325,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,233 | lean | import data.nat.prime algebra.big_operators M3P14.Arithmetic_functions.sum_over_divisors
open nat
-- mobius function
-- taken from M3P14 sheet 1
def square_free_int (n : ℕ) := ∀ p : ℕ, prime p ∧ (p ∣ n → ¬ (p^2 ∣ n))
-- number of prime divisors of n, not counting multiplicities
def primes_div_nodup (n : ℕ) := n.fa... |
828e24f1a7837a4b2d10df241dea5535e292da10 | 8e381650eb2c1c5361be64ff97e47d956bf2ab9f | /src/Kenny/sites/lattice.lean | aded717b3dd5c7a31f8ea658aa50da388254e104 | [] | no_license | alreadydone/lean-scheme | 04c51ab08eca7ccf6c21344d45d202780fa667af | 52d7624f57415eea27ed4dfa916cd94189221a1c | refs/heads/master | 1,599,418,221,423 | 1,562,248,559,000 | 1,562,248,559,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,624 | lean | import Kenny.sites.basic order.complete_lattice
universes u v
namespace lattice
class Sup_lattice (X : Type u) extends lattice X, has_Sup X :=
(le_Sup : ∀ {s : set X} {a : X}, a ∈ s → a ≤ Sup s)
(Sup_le : ∀ {s : set X} {a : X}, (∀ (b : X), b ∈ s → b ≤ a) → Sup s ≤ a)
class Sup_distrib_lattice (X : Type u) extends S... |
ee2adab43b7a81267fa1937903bf81f66f214ffa | 22e97a5d648fc451e25a06c668dc03ac7ed7bc25 | /src/ring_theory/algebra_operations.lean | e727f0f9fd93d3c0f4a66bb3cad23a903ed8353a | [
"Apache-2.0"
] | permissive | keeferrowan/mathlib | f2818da875dbc7780830d09bd4c526b0764a4e50 | aad2dfc40e8e6a7e258287a7c1580318e865817e | refs/heads/master | 1,661,736,426,952 | 1,590,438,032,000 | 1,590,438,032,000 | 266,892,663 | 0 | 0 | Apache-2.0 | 1,590,445,835,000 | 1,590,445,835,000 | null | UTF-8 | Lean | false | false | 8,918 | lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
Multiplication and division of submodules of an algebra.
-/
import ring_theory.algebra
import ring_theory.ideals
import algebra.pointwise
universes u v
open algebra
local attr... |
52ad7798749fb96067d1d5f209385ebef0f39008 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/tactic/ring.lean | 9dbdd0dd188ae07fcfc36b711d266246ecf961c3 | [
"Apache-2.0"
] | permissive | rmitta/mathlib | 8d90aee30b4db2b013e01f62c33f297d7e64a43d | 883d974b608845bad30ae19e27e33c285200bf84 | refs/heads/master | 1,585,776,832,544 | 1,576,874,096,000 | 1,576,874,096,000 | 153,663,165 | 0 | 2 | Apache-2.0 | 1,544,806,490,000 | 1,539,884,365,000 | Lean | UTF-8 | Lean | false | false | 21,105 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
Evaluate expressions in the language of commutative (semi)rings.
Based on <http://www.cs.ru.nl/~freek/courses/tt-2014/read/10.1.1.61.3041.pdf> .
-/
import algebra.group... |
33bda3aa4c5799f480978bb17296b62e90891dd5 | 59b654f4ee2fef898a3487dc03554a569051b63a | /src/graph.lean | 9fb1b94ea649dc3d45bac6163676280c08393d8e | [] | no_license | gunpinyo/twisted_cube_formalisation | 180c9157478b66ec2b11ca47c8ff998a3e978a88 | f78206ac495e84bd43a9b820fa10b6c94722e0ec | refs/heads/master | 1,624,501,222,992 | 1,607,081,624,000 | 1,607,081,624,000 | 166,885,106 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,421 | lean | import utils
structure graph : Type 1 :=
(node : Type)
(edge : Type)
(src : edge → node)
(trg : edge → node)
namespace graph
protected def ext (G G' : graph)
(node : G.node = G'.node)
(edge : G.edge = G'.edge)
(src : G.src == G'.src)
... |
f4c1fa83065dc594e98b8f59162003efe705edbd | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/measure_theory/covering/vitali.lean | 7836842778ca8ad9b8ebb1176a3ea51ee2218ff0 | [
"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 | 29,621 | lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import topology.metric_space.basic
import measure_theory.constructions.borel_space
import measure_theory.covering.vitali_family
/-!
# Vitali covering theorems
... |
8db86d29c13fa10d2dd88953a3c1969bfd5f8803 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/elab13.lean | 810d83813a06b63ae7d5487357466edf6872ab01 | [
"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 | 255 | lean | open tactic list
#check
assume c : name,
(
do {
env ← get_env,
decl ← returnex (environment.get env c),
num ← return (length (declaration.univ_params decl)),
ls ← mk_num_meta_univs 2,
return (expr.const c ls)
} : tactic expr)
|
814765cbff6734a59663c72d81602d221f819b68 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/measure_theory/bochner_integration.lean | f36a5e6966bb0a71591e51e5704b33326f39672e | [
"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 | 64,770 | 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... |
ec1e8524f4331ec94a4af26cc7ca592c865fef8b | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/ring_theory/adjoin/fg.lean | bcc8bfa719413dc7a2e40673fa50d2f1587ae80b | [
"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 | 6,902 | 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 develops ... |
ee9a784a6fb7b68d98e36453fbaef5655f8de19a | dc15192b741b5d1c22cea8d65d6eb38bce3d838d | /src/finset.lean | 007c14d9f4ed76027f8ec182d2c187ee27717c52 | [] | no_license | VArtem/lean-matroids | 86910241ac8d1a5ec7b35adb77c1cc9969480fb9 | a8969b1cb2456820ccbdce65e2e168c48c30d9bf | refs/heads/main | 1,678,556,999,525 | 1,614,537,008,000 | 1,614,537,008,000 | 338,915,729 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 2,668 | lean | import data.finset.basic
import tactic
variables {X : Type*} [fintype X] [decidable_eq X]
namespace finset
open finset
lemma card_erase_of_mem' {A : finset X} {x} (h : x ∈ A) : (A.erase x).card + 1 = A.card :=
begin
rw [card_erase_of_mem h, nat.add_one, nat.succ_pred_eq_of_pos],
rw [gt_iff_lt, pos_iff_ne_zero],... |
0ba6da62480a2a7bb8da632dd81e1b34065b433f | e4d500be102d7cc2cf7c341f360db71d9125c19b | /src/data/zmod/basic.lean | bb5d3c068516507ed203c09cb818ba746d34b6b9 | [
"Apache-2.0"
] | permissive | mgrabovsky/mathlib | 3cbc6c54dab5f277f0abf4195a1b0e6e39b9971f | e397b4c1266ee241e9412e17b1dd8724f56fba09 | refs/heads/master | 1,664,687,987,155 | 1,591,255,329,000 | 1,591,255,329,000 | 269,361,264 | 0 | 0 | Apache-2.0 | 1,591,275,784,000 | 1,591,275,783,000 | null | UTF-8 | Lean | false | false | 25,974 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Chris Hughes
-/
import data.int.modeq
import algebra.char_p
import data.nat.totient
/-!
# Integers mod `n`
Definition of the integers mod n, and the field structure on the integers mod... |
4ad2bf845bc181a8617ce787391b8f472753c5e7 | ce6917c5bacabee346655160b74a307b4a5ab620 | /src/ch4/ex0409.lean | ad29cd97e8558f91354b1f5b10a4c8874cd61057 | [] | 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 | 420 | lean | def is_even (a : ℕ) := ∃ b, a = 2 * b
theorem even_plus_even {a b : ℕ} (h1 : is_even a) (h2 : is_even b) : is_even (a + b) :=
exists.elim h1
(assume w1,
assume hw1,
exists.elim h2
(assume w2,
assume hw2,
exists.intro (w1 + w2)
(calc
a + b = 2 ... |
200d9b4e7cdb6052fcb98928b0a6179087b4a31b | ba4794a0deca1d2aaa68914cd285d77880907b5c | /src/game/world10/level1.lean | f066829c7d24c4eda50562cf146cd2c384eca015 | [
"Apache-2.0"
] | permissive | ChrisHughes24/natural_number_game | c7c00aa1f6a95004286fd456ed13cf6e113159ce | 9d09925424da9f6275e6cfe427c8bcf12bb0944f | refs/heads/master | 1,600,715,773,528 | 1,573,910,462,000 | 1,573,910,462,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,381 | lean | import mynat.le -- import definition of ≤
import game.world9.level4
import game.world4.level8
namespace mynat -- hide
/- Axiom : le_iff_exists_add (a b : mynat)
a ≤ b ↔ ∃ (c : mynat), b = a + c
-/
/- Tactic : use
## Summary
`use` works on the goal. If your goal is `⊢ ∃ c : mynat, 1 + x = x + c`
then `use 1` will tu... |
eeb4961972d4d08ee82431cf593e9725b917f237 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/comma.lean | c78fa975d0b0ab7cb1be15934e97ce8c9f2560c7 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 8,904 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Johan Commelin, Bhavik Mehta
-/
import category_theory.isomorphism
import category_theory.functor.category
import category_theory.eq_to_hom
/-!
# Comma categories
> T... |
0c0ac92a57f63ae7ea1b3965db5fd507fb85b1fb | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/set_theory/ordinal/basic.lean | 6c36f67c2e29f8cd90085f474fcb6a71fbb882fa | [
"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 | 49,516 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Floris van Doorn
-/
import data.sum.order
import order.initial_seg
import set_theory.cardinal.basic
/-!
# Ordinals
Ordinals are defined as equivalences of well-ordere... |
6ad83b803559698942571c4c92bd5661a90142c8 | dc15192b741b5d1c22cea8d65d6eb38bce3d838d | /src/base_of.lean | a610672b3286799423343b24053a759eb0e5275c | [] | no_license | VArtem/lean-matroids | 86910241ac8d1a5ec7b35adb77c1cc9969480fb9 | a8969b1cb2456820ccbdce65e2e168c48c30d9bf | refs/heads/main | 1,678,556,999,525 | 1,614,537,008,000 | 1,614,537,008,000 | 338,915,729 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 2,088 | lean | import data.fintype.basic
import tactic
import matroid
import finset
variables {α : Type*} [fintype α] [decidable_eq α] {m : matroid α} {A B X: finset α}
open finset
namespace matroid
lemma base_of_refl_iff_ind : m.ind A ↔ m.base_of A A :=
begin
split, {
intro Aind,
refine ⟨subset.refl _, Aind, λ x hnx hx... |
b8be488407b5924aa669f8a23602d46ddbc46c77 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/number_theory/bertrand.lean | 27480499ca9b31167d3bc4c1f46653343101bc1f | [
"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 | 11,236 | lean | /-
Copyright (c) 2020 Patrick Stevens. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Stevens, Bolton Bailey
-/
import data.nat.choose.factorization
import number_theory.primorial
import analysis.convex.specific_functions
/-!
# Bertrand's Postulate
This file ... |
f3df667beca57c02780479ed2e9f50dde5a435d5 | c09f5945267fd905e23a77be83d9a78580e04a4a | /src/analysis/normed_space/deriv.lean | 436e522e7b4aa82ff93308a96fcce982af8a1fb0 | [
"Apache-2.0"
] | permissive | OHIHIYA20/mathlib | 023a6df35355b5b6eb931c404f7dd7535dccfa89 | 1ec0a1f49db97d45e8666a3bf33217ff79ca1d87 | refs/heads/master | 1,587,964,529,965 | 1,551,819,319,000 | 1,551,819,319,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,858 | lean | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
The Fréchet derivative.
Let `E` and `F` be normed spaces, and `f : E → F`. Then
`has_fderiv_at_within f f' x s`
says that the function `f' : E → F` is a bounded linea... |
5132e469f60d074934a139c19bd6a345d0c1283d | fe84e287c662151bb313504482b218a503b972f3 | /src/combinatorics/graph.lean | 7e0dd66981b90f1906e7bce3ea12b1a25d890daa | [] | 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 | 3,452 | lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Neil Strickland
This file gives some basic definitions for graph theory.
It supports only graphs with no loops or multiple edges.
It should be refactored to use definitions and resu... |
400e59d40898f7ce13a368ba4ab1eabda9c4dbfe | 037dba89703a79cd4a4aec5e959818147f97635d | /src/2020/problem_sheets/Part_II/sheet1_q3.lean | 4fbc3867c4ce32459313b2d5fdd02ba7e1febe4a | [] | no_license | ImperialCollegeLondon/M40001_lean | 3a6a09298da395ab51bc220a535035d45bbe919b | 62a76fa92654c855af2b2fc2bef8e60acd16ccec | refs/heads/master | 1,666,750,403,259 | 1,665,771,117,000 | 1,665,771,117,000 | 209,141,835 | 115 | 12 | null | 1,640,270,596,000 | 1,568,749,174,000 | Lean | UTF-8 | Lean | false | false | 775 | lean | import tactic
variables (x y : ℕ)
open nat
-- Q3 def
def is_pred (x y : ℕ) := x.succ = y
theorem Q3a : ¬ ∃ x : ℕ, is_pred x 0 :=
begin
sorry
end
theorem Q3b : y ≠ 0 → ∃! x, is_pred x y :=
begin
sorry
end
def aux : 0 < y → ∃ x, is_pred x y :=
begin
sorry
end
-- definition of pred' is "choose a random d such... |
fc1b94fe82c783f6fa5f2f1c4eda999f36e026c4 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/algebra/big_operators/basic.lean | c1bfa596b492759e86bc47cd453da5b741c24e1f | [
"Apache-2.0"
] | permissive | abentkamp/mathlib | d9a75d291ec09f4637b0f30cc3880ffb07549ee5 | 5360e476391508e092b5a1e5210bd0ed22dc0755 | refs/heads/master | 1,682,382,954,948 | 1,622,106,077,000 | 1,622,106,077,000 | 149,285,665 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 60,250 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import data.finset.fold
import data.equiv.mul_add
import tactic.abel
/-!
# Big operators
In this file we define products and sums indexed by finite sets (specifica... |
b8ab3293a1d54a2ecd4d5d9df795a84a4c797e16 | 82b86ba2ae0d5aed0f01f49c46db5afec0eb2bd7 | /stage0/src/Init/Data/List/Basic.lean | 5ed43828dec619a1cf675bad31e7e8f01beec324 | [
"Apache-2.0"
] | permissive | banksonian/lean4 | 3a2e6b0f1eb63aa56ff95b8d07b2f851072d54dc | 78da6b3aa2840693eea354a41e89fc5b212a5011 | refs/heads/master | 1,673,703,624,165 | 1,605,123,551,000 | 1,605,123,551,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,725 | 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.Core
import Init.Data.Nat.Basic
open Decidable List
universes u v w
instance (α : Type u) : Inhabited (List α) := ⟨List.nil⟩
variables... |
cc2da761007c8e4befe36820e649fcc1c2aa4716 | 6094e25ea0b7699e642463b48e51b2ead6ddc23f | /library/data/set/finite.lean | b5a791cff4f1639147a215466006c94db0c20448 | [
"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 | 7,029 | lean | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
The notion of "finiteness" for sets. This approach is not computational: for example, just because
an element s : set A satsifies finite s doesn't mean that we can com... |
6923c4bff8c0f8a50eaad5b2308547a7742c31b8 | 359199d7253811b032ab92108191da7336eba86e | /src/mywork/mid-term_review/hw-2_practice.lean | fab99013e2fb2f95938bf8d80a154453b5273b1c | [] | 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 | 1,693 | lean | -- 14
example : ∀ (P : Prop), P ∧ false ↔ false :=
begin
assume P,
apply iff.intro _ _,
-- forwards implication proof
assume p_and_false,
exact and.elim_right p_and_false,
-- backwards implication proof
assume f,
exact false.elim f, -- **How does the false elim rule work?**
end
-- 12
example : ∀ (P : P... |
963ce5e19d55885213d8e972a771a57378b77610 | b561a44b48979a98df50ade0789a21c79ee31288 | /stage0/src/Lean/PrettyPrinter/Formatter.lean | df2370c170b70d3904828f4bb891e94e30e9cb5e | [
"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 | 21,953 | lean | /-
Copyright (c) 2020 Sebastian Ullrich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
-/
import Lean.CoreM
import Lean.Parser.Extension
import Lean.KeyedDeclsAttribute
import Lean.ParserCompiler.Attribute
import Lean.PrettyPrinter.Basic
/-!
The for... |
b8743e3ddafa394a83aa3382cffcdf629062a1ec | 6094e25ea0b7699e642463b48e51b2ead6ddc23f | /library/algebra/group.lean | 10d6fbe31e6214918cfc6a407bd9d99333ad56c2 | [
"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 | 24,820 | 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
Various multiplicative and additive structures. Partially modeled on Isabelle's library.
-/
import logic.eq data.unit data.sigma data.prod
import alge... |
ba6be3e69d7bff09a2c0528ab24b25970c007b62 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/meta/smt/congruence_closure_auto.lean | 017886d49d67a0685c88e295149e3175669138be | [] | 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 | 574 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.meta.interactive_base
import Mathlib.Lean3Lib.init.meta.tactic
import Mathlib.Lean3Lib.init.meta.set_get... |
bb741376f6e8613c95c5cc105e67f2506124cbd5 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/analysis/special_functions/trigonometric/inverse_deriv.lean | c449c042d7303e4012186a50a564acee69b8a821 | [
"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 | 7,723 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-/
import analysis.special_functions.trigonometric.inverse
import analysis.special_functions.trigonometric... |
de5059573504dd6c5219eb6b71defcadac5f9d04 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/analysis/special_functions/bernstein.lean | f7532b07c6960ca607c1c844c4c19c21150f5578 | [
"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 | 12,756 | 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 algebra.order.field
import ring_theory.polynomial.bernstein
import topology.continuous_function.polynomial
/-!
# Bernstein approximations and Weierstrass' the... |
a0911498fb4e5577d52b6c0858f4f4267135eb3c | ac1c2a2f522b0fdf854095ba00f882ca849669e7 | /leanpkg/leanpkg/toml.lean | b622b933fe029a23ea5549346e826ecb30694179 | [
"Apache-2.0"
] | permissive | abliss/lean | b8b336abc8d50dbb0726dcff9dd16793c23bfbe1 | fb24cc99573c153f97a1951ee94bbbdda300b6be | refs/heads/master | 1,611,536,584,520 | 1,497,811,981,000 | 1,497,811,981,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,823 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Gabriel Ebner
-/
import data.buffer.parser
-- I'd like to contribute a new naming convention:
-- CamelCase for non-terminals.
def join (sep : string) : list string → string
| [... |
3c8f1ee7c070fcbe24ba9339d39a1b23f141f25e | f5f7e6fae601a5fe3cac7cc3ed353ed781d62419 | /src/data/seq/seq.lean | 9a57ae3229da87ec57a98faa7cf47d9992ab72d7 | [
"Apache-2.0"
] | permissive | EdAyers/mathlib | 9ecfb2f14bd6caad748b64c9c131befbff0fb4e0 | ca5d4c1f16f9c451cf7170b10105d0051db79e1b | refs/heads/master | 1,626,189,395,845 | 1,555,284,396,000 | 1,555,284,396,000 | 144,004,030 | 0 | 0 | Apache-2.0 | 1,533,727,664,000 | 1,533,727,663,000 | null | UTF-8 | Lean | false | false | 25,101 | lean | import data.stream data.lazy_list data.seq.computation logic.basic tactic.interactive
universes u v w
/-
coinductive seq (α : Type u) : Type u
| nil : seq α
| cons : α → seq α → seq α
-/
/-- `seq α` is the type of possibly infinite lists (referred here as sequences).
It is encoded as an infinite stream of options s... |
a853931f203d57908c16f1c38d5fc496c528ea16 | 26ac254ecb57ffcb886ff709cf018390161a9225 | /src/linear_algebra/tensor_product.lean | 20bfd0b53177f98e3fcb7fe94e1823068865b9f2 | [
"Apache-2.0"
] | permissive | eric-wieser/mathlib | 42842584f584359bbe1fc8b88b3ff937c8acd72d | d0df6b81cd0920ad569158c06a3fd5abb9e63301 | refs/heads/master | 1,669,546,404,255 | 1,595,254,668,000 | 1,595,254,668,000 | 281,173,504 | 0 | 0 | Apache-2.0 | 1,595,263,582,000 | 1,595,263,581,000 | null | UTF-8 | Lean | false | false | 25,348 | 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
-/
import group_theory.congruence
import group_theory.free_abelian_group
import linear_algebra.direct_sum_module
/-!
# Tensor product of semimodules over commuta... |
056dc99503ad6d3a9ae9bf04dde74fd6a7ad7848 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/measure_theory/arithmetic.lean | 158072c5ffd782661f1706bfd1da465b55d60262 | [
"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 | 25,052 | 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.measure_space
/-!
# Typeclasses for measurability of operations
In this file we define classes `has_measurable_mul` etc and prove dot-style ... |
c81c699f41db5fe77998b5ae465a13bb03bde42f | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/linear_algebra/free_module/pid.lean | 468d3090f9ad85b5e05b88d34f9f2e05f7e79d05 | [
"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 | 36,355 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import linear_algebra.basis
import linear_algebra.finsupp_vector_space
import ring_theory.principal_ideal_domain
import ring_theory.finiteness
/-! # Free modules over PID
... |
9fca317d0e12800cf4527f57ddc9864a7b79045c | a19a4fce1e5677f4d20cbfdf60c04b6386ab8210 | /hott/init/tactic.hlean | b5ca7b6e369893404f6a142ff8e365bb1a5928ac | [
"Apache-2.0"
] | permissive | nthomas103/lean | 9c341a316e7d9faa00546462f90a8aa402e17eac | 04eaf184a92606a56e54d0d6c8d59437557263fc | refs/heads/master | 1,586,061,106,806 | 1,454,640,115,000 | 1,454,641,279,000 | 51,127,143 | 0 | 0 | null | 1,454,648,683,000 | 1,454,648,683,000 | null | UTF-8 | Lean | false | false | 7,084 | hlean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
This is just a trick to embed the 'tactic language' as a Lean
expression. We should view 'tactic' as automation that when execute
produces a term. tactic.buil... |
9998394e04d0e1c3b138fa94b9526418769d7084 | 22e97a5d648fc451e25a06c668dc03ac7ed7bc25 | /src/group_theory/submonoid.lean | 9e9340da01856ce247386d4e2c10a5024e1346f3 | [
"Apache-2.0"
] | permissive | keeferrowan/mathlib | f2818da875dbc7780830d09bd4c526b0764a4e50 | aad2dfc40e8e6a7e258287a7c1580318e865817e | refs/heads/master | 1,661,736,426,952 | 1,590,438,032,000 | 1,590,438,032,000 | 266,892,663 | 0 | 0 | Apache-2.0 | 1,590,445,835,000 | 1,590,445,835,000 | null | UTF-8 | Lean | false | false | 51,317 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard,
Amelia Livingston, Yury Kudryashov
-/
import algebra.big_operators
import algebra.free_monoid
import algebra.g... |
8a1ca0a728c7c0eb790476a19e8b2f2f60af1f5d | 22e97a5d648fc451e25a06c668dc03ac7ed7bc25 | /src/ring_theory/noetherian.lean | 86f8f9e3b743c2b93e793c5debc440c6e9490bd2 | [
"Apache-2.0"
] | permissive | keeferrowan/mathlib | f2818da875dbc7780830d09bd4c526b0764a4e50 | aad2dfc40e8e6a7e258287a7c1580318e865817e | refs/heads/master | 1,661,736,426,952 | 1,590,438,032,000 | 1,590,438,032,000 | 266,892,663 | 0 | 0 | Apache-2.0 | 1,590,445,835,000 | 1,590,445,835,000 | null | UTF-8 | Lean | false | false | 23,063 | lean | /-
Copyright (c) 2018 Mario Carneiro and Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kevin Buzzard
-/
import ring_theory.ideal_operations
import linear_algebra.basis
/-!
# Noetherian rings and modules
The following are equivalent for... |
eb31b7e56597f8f567347b787c361594ff71689c | 7cdf3413c097e5d36492d12cdd07030eb991d394 | /world_experiments/world7/level6andthreequarters.lean | 9dde5613b24c39703bd02e9a42ba2892d495a0c0 | [] | no_license | alreadydone/natural_number_game | 3135b9385a9f43e74cfbf79513fc37e69b99e0b3 | 1a39e693df4f4e871eb449890d3c7715a25c2ec9 | refs/heads/master | 1,599,387,390,105 | 1,573,200,587,000 | 1,573,200,691,000 | 220,397,084 | 0 | 0 | null | 1,573,192,734,000 | 1,573,192,733,000 | null | UTF-8 | Lean | false | false | 2,637 | lean | import mynat.definition -- hide
import mynat.add -- hide
import game.world2.level6andahalf -- hide
namespace mynat -- hide
/- Tactic : have
The `have` tactic is a way to prove an intermediate lemma,
in the middle of your proof.
If `h : A = B` is a hypothesis (i.e., a proof of `A = B`)
and your goal contains one or ... |
bdc373dce692f6dfcc5e3691428decb4c41359a4 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/measure_theory/function/simple_func_dense.lean | 524954f92c8c60db7c5098345b69716b61f0c1f5 | [
"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 | 7,373 | 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, Heather Macbeth
-/
import measure_theory.integral.lebesgue
/-!
# Density of simple functions
Show that each Borel measurable function can be approximat... |
b0edffad4c5ef241922246b165192714bf0edb97 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/linear_algebra/affine_space/independent.lean | db354ac1c5cda1cae66b352204feefc25c971fe9 | [
"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 | 28,394 | lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import data.finset.sort
import data.matrix.notation
import linear_algebra.affine_space.combination
import linear_algebra.affine_space.affine_equiv
import linear_algebra.b... |
9307a6a7ea0f9d3a999f8b13c76e84a0aab8a81b | ce6917c5bacabee346655160b74a307b4a5ab620 | /src/ch4/ex0405.lean | 1b17ed296f79238d45b6813e967489459100e4c0 | [] | 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 | 167 | lean | variables (α : Type) (p q : α → Prop)
example (h : ∃ x, p x ∧ q x) : ∃ x, q x ∧ p x :=
match h with ⟨w, hw⟩ :=
⟨w, hw.right, hw.left⟩
end
|
4ab0c89129e708eeb055eaaf1ab3275358303159 | bf532e3e865883a676110e756f800e0ddeb465be | /data/equiv.lean | 6a07cded1af45873dd797248db4b49ad020b354f | [
"Apache-2.0"
] | permissive | aqjune/mathlib | da42a97d9e6670d2efaa7d2aa53ed3585dafc289 | f7977ff5a6bcf7e5c54eec908364ceb40dafc795 | refs/heads/master | 1,631,213,225,595 | 1,521,089,840,000 | 1,521,089,840,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 28,131 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Mario Carneiro
In the standard library we cannot assume the univalence axiom.
We say two types are equivalent if they are isomorphic.
Two equivalent types h... |
886e26b0c12865e0b05f2d407c01ee8871c2a8d0 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /stage0/src/Lean/Meta/SynthInstance.lean | cac95fde45173722e2cf829c7675353ebe57293d | [
"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 | 34,745 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Selsam, Leonardo de Moura
Type class instance synthesizer using tabled resolution.
-/
import Lean.Meta.Basic
import Lean.Meta.Instances
import Lean.Meta.AbstractMVars
im... |
4f4d2610b18a61ed263a6c7b42a83d124697c783 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/data/prod_auto.lean | f70439edc0deead606fca4c859f05595b659b7d0 | [] | 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 | 1,865 | 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
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.logic
universes u v u₁ u₂ v₁ v₂
namespace Mathlib
@[simp] theorem prod.mk.eta {α : Typ... |
f1ddf3a1cb6d46a7a2130dbafd84e5a358111db5 | ad0c7d243dc1bd563419e2767ed42fb323d7beea | /data/nat/binomial.lean | aa66aa0bc5e03e55ed008ac9acff4887b51de24a | [
"Apache-2.0"
] | permissive | sebzim4500/mathlib | e0b5a63b1655f910dee30badf09bd7e191d3cf30 | 6997cafbd3a7325af5cb318561768c316ceb7757 | refs/heads/master | 1,585,549,958,618 | 1,538,221,723,000 | 1,538,221,723,000 | 150,869,076 | 0 | 0 | Apache-2.0 | 1,538,229,323,000 | 1,538,229,323,000 | null | UTF-8 | Lean | false | false | 1,565 | 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 data.nat.choose algebra.big_operators
open nat finset
/-- The binomial theorem -/
theorem add_pow {α : Type*} [comm_semiring α] (x y : α) : ∀ n : ℕ,
(x + y) ... |
d38060b64af7cdc4ed8d2b5ae1d5a6857dba980e | e30ff3aabdac29f8ea40ad76887544d0f9be9018 | /ircbot/modules/ping_pong.lean | deec0d5b12d2d16a24fc038438f79ba20c994a68 | [] | no_license | forked-from-1kasper/leanbot | bdef0efa3e4d0eb75b06c1707fb4e35086bb57fa | c61c8c7fdad7b05877e0d232719ce23d2999557f | refs/heads/master | 1,651,846,081,986 | 1,646,404,009,000 | 1,646,404,009,000 | 127,132,795 | 12 | 1 | null | 1,605,183,650,000 | 1,522,237,998,000 | Lean | UTF-8 | Lean | false | false | 1,554 | lean | import ircbot.types ircbot.support
open types support
namespace modules.ping_pong
def ping_pong_func (input : irc_text) : list irc_text :=
match input with
| irc_text.parsed_normal
{ object := some ~nick!ident, type := message.privmsg,
args := [subject], text := "\\ping" } :=
let new_subject :=
if subject... |
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