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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
5b0df00e47b7879de347b3b0cc7c6be3b58cb2e6 | 94637389e03c919023691dcd05bd4411b1034aa5 | /src/zzz_junk/semigroup/semigroup.lean | 74d291bf5c02076b5873aadc6444f9f476363805 | [] | no_license | kevinsullivan/complogic-s21 | 7c4eef2105abad899e46502270d9829d913e8afc | 99039501b770248c8ceb39890be5dfe129dc1082 | refs/heads/master | 1,682,985,669,944 | 1,621,126,241,000 | 1,621,126,241,000 | 335,706,272 | 0 | 38 | null | 1,618,325,669,000 | 1,612,374,118,000 | Lean | UTF-8 | Lean | false | false | 497 | lean | import ..has_mul.has_mul
universe u
namespace hidden
/-
A semigroup is a set α (given by a type) with an associative
multiplication operator, mul. Many sets, α, can be treated as
semigroups. A set of any kind of objects is a semigroup as long
as it has an associative binary multiplication operator, mul.
-/
@[class... |
163d8c30226394b7e70bf8cfcc26c8f97c1f5121 | 3c453925e3aae41b20e0567130c33a61fb1c5854 | /src/subspace.lean | 2f549be3debf860107e73286277b1735ee60163f | [] | no_license | agusakov/vector_spaces | f7e272e9403a87a72b49d92ce759e4ebe9e4d55c | b23954c19b357a689e2a73e07fcf6c9e4a74713a | refs/heads/master | 1,670,493,487,137 | 1,596,908,778,000 | 1,596,908,778,000 | 283,599,211 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,107 | lean | import .vec_space
import group_theory.subgroup
import data.finset
import algebra.big_operators
import algebra.pointwise
--import ring_theory.polynomial.basic
open_locale big_operators classical
namespace vec_space
universes u v w x
open subgroup
structure subspace (F : Type u) (α : Type v) [field F] [add_comm_gro... |
62adad06437c863f56b28637b4effb02dc632dc1 | e39f04f6ff425fe3b3f5e26a8998b817d1dba80f | /data/list/basic.lean | 79237fbc338aaaf8c7e54861590f87942dd5a288 | [
"Apache-2.0"
] | permissive | kristychoi/mathlib | c504b5e8f84e272ea1d8966693c42de7523bf0ec | 257fd84fe98927ff4a5ffe044f68c4e9d235cc75 | refs/heads/master | 1,586,520,722,896 | 1,544,030,145,000 | 1,544,031,933,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 175,956 | lean | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
Basic properties of lists.
-/
import
tactic.interactive tactic.mk_iff_of_inductive_prop tactic... |
852371cfe3e2a1045cdf7141a54f5049e88056f7 | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/algebra/star/basic.lean | 6eb0d75ed515f4d519542f49f62dc3daa7326135 | [
"Apache-2.0"
] | permissive | ayush1801/mathlib | 78949b9f789f488148142221606bf15c02b960d2 | ce164e28f262acbb3de6281b3b03660a9f744e3c | refs/heads/master | 1,692,886,907,941 | 1,635,270,866,000 | 1,635,270,866,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 12,757 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import tactic.apply_fun
import algebra.field_power
import data.equiv.ring_aut
import group_theory.group_action.units
import algebra.ring.comp_typeclasses
/-!
# Star ... |
d0ce167c13323b27654eccba447ee1ddb664c1c2 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/pp_bug.lean | 552d59e1748f4089f71f6cea55bb168ee95a89ad | [
"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 | 211 | lean | variables p q : Prop
#check ¬(p → q)
#check ¬p → q
#check (¬p) → q
#check ¬(p → q)
#check p ↔ q
#check ¬(p ↔ q)
#check ¬p ↔ q
#check (¬p) ↔ q
#check (p → q) ↔ q
#check p → (q ↔ q)
|
16488d261e645d9ec075e82b9a96db8fe2b2ff73 | 3af272061d36e7f3f0521cceaa3a847ed4e03af9 | /src/fast_matrices.lean | 4d3f10d9e2f80b9a968b910a47cb79c5cb460911 | [] | no_license | semorrison/kbb | fdab0929d21dca880d835081814225a95f946187 | 229bd06e840bc7a7438b8fee6802a4f8024419e3 | refs/heads/master | 1,585,351,834,355 | 1,539,848,241,000 | 1,539,848,241,000 | 147,323,315 | 2 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 449 | lean | import data.vector
@[pattern] def vector.mk {α : Type*} {n : ℕ} (l : list α) (pr : l.length = n) :
vector α n := ⟨l, pr⟩
notation `![` l:(foldr `, ` (h t, list.cons h t) list.nil `]`) :=
vector.mk l rfl
def {u} fast_matrix (m n : ℕ) (α : Type u) : Type u := vector (vector α n) m
example : fast_matrix 2 3 ℤ :=
... |
093c01d836b3d61a0cde18ac424e1f5881baa406 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/linear_algebra/free_module_pid.lean | ab65e229491d7eaab8ca18e16413fc321c1f701a | [
"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 | 17,756 | 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
... |
f001f73a2145f025fd81713bae95020ae1ed12b9 | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/data/padics/padic_numbers.lean | 1ce981ff7081ed47f0ed3e4243332048a8b74246 | [
"Apache-2.0"
] | permissive | mcncm/mathlib | 8d25099344d9d2bee62822cb9ed43aa3e09fa05e | fde3d78cadeec5ef827b16ae55664ef115e66f57 | refs/heads/master | 1,672,743,316,277 | 1,602,618,514,000 | 1,602,618,514,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 38,341 | 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.padics.padic_norm
import analysis.normed_space.basic
/-!
# p-adic numbers
This file defines the p-adic numbers (rationals) `ℚ_p` as the completion of... |
38d050332e84084971b8f93de602542626326155 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/tactic/omega/int/main.lean | 05db7deacc85838bfeaff1f673b59a54fd7ede2b | [
"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 | 6,281 | lean | /- Copyright (c) 2019 Seul Baek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Seul Baek
Main procedure for linear integer arithmetic. -/
import tactic.omega.prove_unsats
import tactic.omega.int.dnf
open tactic
namespace omega
namespace int
open_locale omega.int
r... |
3754dc529b8b1ea6123fc5fca5720080d2d2916d | b7f22e51856f4989b970961f794f1c435f9b8f78 | /hott/homotopy/connectedness.hlean | 364905ed917a8c1c9ce6e46e2774018080cc0695 | [
"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 | 13,714 | hlean | /-
Copyright (c) 2015 Ulrik Buchholtz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ulrik Buchholtz, Floris van Doorn
Connectedness of types and functions
-/
import types.trunc types.arrow_2 types.lift
open eq is_trunc is_equiv nat equiv trunc function fiber funext... |
dad510e224321868e40a9568fed08553230418d4 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/linear_algebra/direct_sum/finsupp.lean | f099fe436e1984ef6182781e99e18fd799d49022 | [
"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 | 3,868 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import algebra.direct_sum.finsupp
import linear_algebra.finsupp
import linear_algebra.direct_sum.tensor_product
/-!
# Results on finitely supported functions.
The t... |
14ac18187129381511a144a5d32ad6562f55735b | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/run/termElab.lean | 7ad3f8e72e921cdc34bf0c6a37d1048e5080d398 | [
"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 | 671 | lean | import Lean
open Lean
open Lean.Elab
open Lean.Elab.Term
def tst1 : TermElabM Unit := do
let opt ← getOptions;
let stx ← `(forall (a b : Nat), Nat);
IO.println "message 1"; -- This message goes direct to stdio. It will be displayed before trace messages.
let e ← elabTermAndSynthesize stx none;
logDbgTrace m!">>> {e}... |
5ae6d1566f3d934fbcd988bbbce544f1fbf687d1 | 4fa161becb8ce7378a709f5992a594764699e268 | /src/data/pnat/xgcd.lean | 477a6db12deb45cb6d1224082ec888d474462cd8 | [
"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 | 13,398 | lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Neil Strickland
This file sets up a version of the Euclidean algorithm that works
only with natural numbers. Given a, b > 0, it computes the unique
system (w, x, y, z, d) such that ... |
d3a2182bfbf506eb98589041d850ea6a5433c88e | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /tests/lean/run/eq24.lean | c5d3b7b974057ecc59160ece1d0658a925a9501a | [
"Apache-2.0"
] | permissive | tjiaqi/lean | 4634d729795c164664d10d093f3545287c76628f | d0ce4cf62f4246b0600c07e074d86e51f2195e30 | refs/heads/master | 1,622,323,796,480 | 1,422,643,069,000 | 1,422,643,069,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,121 | lean | open nat
inductive tree (A : Type) :=
leaf : A → tree A,
node : tree_list A → tree A
with tree_list :=
nil : tree_list A,
cons : tree A → tree_list A → tree_list A
namespace tree
open tree_list
definition size {A : Type} : tree A → nat
with size_l : tree_list A → nat,
size (leaf a) := 1,
size (no... |
7e700ff6a1a3f72f348069f0e795e971d96e015e | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/number_theory/padics/padic_numbers.lean | 630940e8b804ec934fc1724944debd1783d35d22 | [
"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 | 38,978 | 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 number_theory.padics.padic_norm
import analysis.normed.field.basic
/-!
# p-adic numbers
This file defines the `p`-adic numbers (rationals) `ℚ_[p]` as
the c... |
d9525194ce7a6bc1d19d92856d4026e0e3ecb7d5 | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/data/nat/gcd.lean | 2e5caff35b3ecc61491dd7e0da58035bb108fc55 | [
"Apache-2.0"
] | permissive | fpvandoorn/mathlib | b21ab4068db079cbb8590b58fda9cc4bc1f35df4 | b3433a51ea8bc07c4159c1073838fc0ee9b8f227 | refs/heads/master | 1,624,791,089,608 | 1,556,715,231,000 | 1,556,715,231,000 | 165,722,980 | 5 | 0 | Apache-2.0 | 1,552,657,455,000 | 1,547,494,646,000 | Lean | UTF-8 | Lean | false | false | 13,494 | 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
Definitions and properties of gcd, lcm, and coprime.
-/
import data.nat.basic
namespace nat
/- gcd -/
theorem gcd_dvd (m n : ℕ) : (gcd m n ∣ m) ∧ (g... |
a7b220a81798435229da87858f616dce2f2bba96 | a7eef317ddec01b9fc6cfbb876fe7ac00f205ac7 | /archive/100-theorems-list/73_ascending_descending_sequences.lean | f315ed4a925d66f9ca5018c511fcf9342e5a2617 | [
"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 | 8,096 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import data.fintype.basic
/-!
# Erdős–Szekeres theorem
This file proves Theorem 73 from the [100 Theorems List](https://www.cs.ru.nl/~freek/100/), also
known as the Erd... |
091c2b164aa8b3bb66f1528ddfc25f743ff7c5a9 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/number_theory/modular_forms/slash_actions.lean | 25b616b3bd5b09b986c75122d3c63d16a0c8fce6 | [
"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 | 8,036 | lean | /-
Copyright (c) 2022 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
import analysis.complex.upper_half_plane.basic
import linear_algebra.general_linear_group
import linear_algebra.special_linear_group
/-!
# Slash actions
This file de... |
b03cf4f80995c53ed748bad0bc62defbdcf39a41 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/probability/conditional_expectation.lean | ec903d56ad21d8bf1d7789a71ddf2c4cadb4abd5 | [
"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 | 3,414 | lean | /-
Copyright (c) 2022 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import probability.notation
import probability.independence
/-!
# Probabilistic properties of the conditional expectation
This file contains some properties about the co... |
fb51116d14282b1b618815d35755a08e551948c9 | ec5a7ae10c533e1b1f4b0bc7713e91ecf829a3eb | /ijcar16/examples/group.lean | 0784991bec25f44e876efa1201b77331678f2da9 | [
"MIT"
] | permissive | leanprover/leanprover.github.io | cf248934af7c7e9aeff17cf8df3c12c5e7e73f1a | 071a20d2e059a2c3733e004c681d3949cac3c07a | refs/heads/master | 1,692,621,047,417 | 1,691,396,994,000 | 1,691,396,994,000 | 19,366,263 | 18 | 27 | MIT | 1,693,989,071,000 | 1,399,006,345,000 | Lean | UTF-8 | Lean | false | false | 22,181 | lean | /-
This is a file from the Lean standard library.
We use it to demonstrate/test the congruence closure procedure
described in the paper:
"Congruence Closure for Intensional Type Theory"
Daniel Selsam and Leonardo de Moura
The lemmas proved using `by inst_simp` are using the congruence closure
procedure described ... |
580be37cb48e0dcbf6c996366f8a732a662a5d3d | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/data/polynomial/monic.lean | c74c31e11f5019d606792729a6cb985419a5e6f5 | [
"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 | 9,361 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
-/
import data.polynomial.degree
import algebra.associated
import tactic.omega
/-!
# Theory of monic polynomials
We give se... |
a6404256fc9ba2d1ef4b2b0b9abab531b982df29 | 02005f45e00c7ecf2c8ca5db60251bd1e9c860b5 | /src/ring_theory/polynomial/chebyshev/basic.lean | a74366049ce527cd8443d51ab8492720559df771 | [
"Apache-2.0"
] | permissive | anthony2698/mathlib | 03cd69fe5c280b0916f6df2d07c614c8e1efe890 | 407615e05814e98b24b2ff322b14e8e3eb5e5d67 | refs/heads/master | 1,678,792,774,873 | 1,614,371,563,000 | 1,614,371,563,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,189 | 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 ring_theory.polynomial.chebyshev.defs
import ring_theory.polynomial.chebyshev.dickson
import analysis.special_functions.trigonometric
import ring_theory.local... |
c4055d2c0ae93b7c369fb127d19dfe349c9b18c1 | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /library/init/num.lean | c20d55bc516ef92fef472d787e66f8ce02bbd901 | [
"Apache-2.0"
] | permissive | tjiaqi/lean | 4634d729795c164664d10d093f3545287c76628f | d0ce4cf62f4246b0600c07e074d86e51f2195e30 | refs/heads/master | 1,622,323,796,480 | 1,422,643,069,000 | 1,422,643,069,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,657 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.num
Authors: Leonardo de Moura
-/
prelude
import init.logic init.bool
open bool
definition pos_num.is_inhabited [instance] : inhabited pos_num :=
inhabited.mk pos_num.one
... |
5dd67fd6ec986093987348a21789ecf8c6e2b9ca | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/measure_theory/covering/besicovitch.lean | 34435f1851700eab09af2e1dbb47c75b6e722767 | [
"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 | 60,311 | 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.covering.differentiation
import measure_theory.covering.vitali_family
import measure_theory.integral.lebesgue
import measure_theory.measur... |
b1cfd97e196f4fd62cd423d5dc03bc30420aa78c | 4727251e0cd73359b15b664c3170e5d754078599 | /src/analysis/normed/group/completion.lean | a5feedcfe3f580e8919156dc0d42d8cf3164f580 | [
"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 | 1,313 | lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import analysis.normed.group.basic
import topology.algebra.group_completion
import topology.metric_space.completion
/-!
# Completion of a normed group
In this file ... |
454f306b43bb7f7a8c7ab85c592ffb89ab86e7f1 | a4673261e60b025e2c8c825dfa4ab9108246c32e | /stage0/src/Lean/Elab/Tactic/Binders.lean | 1d760cdc87bd69a4c319755737d8ed42f314b3ce | [
"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 | 1,238 | 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.Tactic.Basic
namespace Lean.Elab.Tactic
private def liftTermBinderSyntax : Macro := fun stx => do
let hole ← `(?_)
match stx.getKind w... |
9bf9fe297794225700abcc81fe42463a52098ce6 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/topology/separation.lean | cec0988e408501540ec39a8afffebb4bc6e6a86e | [
"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 | 57,622 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import topology.subset_properties
import topology.connected
/-!
# Separation properties of topological spaces.
This file defines the predicate `sepa... |
199019e3f5e616af710cd2ca8ddcebfd5c1e71f4 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/topology/uniform_space/separation.lean | 4c5393d07fdac4079875011e2db49dafbea057c8 | [
"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 | 23,447 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot
-/
import tactic.apply_fun
import data.set.pairwise
import topology.uniform_space.basic
import topology.separation
/-!
# Hausdorff properties of unifor... |
aa12412f96279ae01b98a833628280a01483a376 | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/data/finsupp.lean | dfe7323bb4021a67a045f89e29c5ea5fe47fe392 | [
"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 | 64,065 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Type of functions with finite support.
Functions with finite support provide the basis for the following concrete instances:
* ℕ →₀ α: Polynomials (where α is a ring... |
bbbd0ed977e9355dfcc7e30c5df3c286e509cb0b | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/char_p/quotient_auto.lean | eb14ceaba81218ffc389de86f6ff4e05c5411571 | [] | 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 | 936 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Eric Wieser
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.char_p.basic
import Mathlib.algebra.ring_quot
import Mathlib.PostPort
universes... |
ed5dc9db6835479d2a50895958644216bedf11b6 | 9cb9db9d79fad57d80ca53543dc07efb7c4f3838 | /src/system_of_complexes/completion.lean | e6756ce5520d847ab15d7ac900c544db9fac352a | [] | no_license | mr-infty/lean-liquid | 3ff89d1f66244b434654c59bdbd6b77cb7de0109 | a8db559073d2101173775ccbd85729d3a4f1ed4d | refs/heads/master | 1,678,465,145,334 | 1,614,565,310,000 | 1,614,565,310,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,450 | lean | import analysis.specific_limits
import system_of_complexes.basic
import locally_constant.Vhat
open finset filter
open_locale nnreal big_operators topological_space
namespace system_of_complexes
universe variables u
variables (C C₁ C₂ : system_of_complexes.{u})
variables {k k' K K' : ℝ≥0} {m m' : ℤ} {c₀ c₀' : ℝ≥0} [f... |
616679baa0ec83443a3d9ffde946d02e249745ca | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/deprecated/group.lean | d35677e64572d46cd242c7fd0aee7bd1c676f9a0 | [
"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 | 13,579 | 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 algebra.group.type_tags
import algebra.group.units_hom
import algebra.ring.basic
import data.equiv.mul_add
/-!
# Unbundled monoid and group homomorphisms (d... |
461874940bf431ae22e6209346700cc8e8354631 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/tactic/ring.lean | 4704d1e3e274a4144246eb19d4c39cce4ef20146 | [
"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 | 28,581 | 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 tactic.norm_num
import data.int.range
/-!
# `ring`
Evaluate expressions in the language of commutative (semi)rings.
Based on <http://www.cs.ru.nl/~freek/cour... |
cc13827bcdb28a2eed00449be060c955f01c972c | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Compiler/LCNF/DependsOn.lean | 8eb7fb69890933119145ee199f3b014f643969a3 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 1,957 | 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.Compiler.LCNF.Basic
namespace Lean.Compiler.LCNF
private abbrev M := ReaderT FVarIdSet Id
private def fvarDepOn (fvarId : FVarId) : M Bool :=... |
fa792a5dddf485f913f427b9448cb444727c6257 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/data/mv_polynomial/variables.lean | 78c4a4d5667dd7ca670759cc6d4a8d5eb15f3beb | [
"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 | 24,380 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
-/
import algebra.big_operators.order
import data.mv_polynomial.monad
import data.set.pairwise
/-!
# Degrees and variables of polynomial... |
2335dd968b12a3188cc775fa184d87e7c8af0937 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/pnat/basic.lean | fdbc7a75516364eb15b73017ac8edc163a913c63 | [
"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 | 11,685 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Neil Strickland
-/
import data.pnat.defs
import data.nat.bits
import data.nat.order.basic
import data.set.basic
import algebra.group_with_zero.divisibility
impor... |
3a3925e83821c1eb7f2d67ac9994e60322ac8197 | c56b090bd37dca8992124f0b09c22340ef7e27bc | /src/lecture10.lean | 7d8f46cec070f3307c97783431037ced7a04944a | [] | no_license | stjordanis/math135 | df113ed7ae9f81b27316cc5b000f88b385391a81 | e270f3a9cae435c066c0d2574f03a8adbe40b7b5 | refs/heads/master | 1,677,069,951,721 | 1,611,905,122,000 | 1,611,905,122,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,152 | lean | import tactic
import data.nat.basic
import data.nat.prime
import data.real.basic
import data.nat.gcd
import data.real.sqrt
import data.nat.parity
import tactic.slim_check
namespace lecture10
open nat
def irrational (r : ℝ) := ∀ (n d : ℕ), (d ≠ 0) -> coprime n d -> ¬ coe n / coe d = r
lemma not_coprime_if_even {a b ... |
aeaa75b33c8399edca055b267061fd0fd46dafd1 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/eqnsAtSimp3.lean | d6341123898f45ff8105c51dea2cc9dceab31200 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 1,761 | lean | def f (x y : Nat) : Nat :=
match x, y with
| 0, 0 => 1
| 0, y => y
| x+1, 5 => 2 * f x 0
| x+1, y => 2 * f x y
theorem ex1 (x : Nat) (y : Nat) (h : y ≠ 5) : ∃ z, f (x+1) y = 2 * z := by
simp [f, h]
trace_state
apply Exists.intro
rfl
@[simp] def g (x y : Nat) : Nat :=
match x, y with
| 0, 0... |
0f86c9e8a5f4aba1cf1953ff71b2db3f4a828b78 | c8d830ce6c7de4840cf0c892d8b58e7e8df97e37 | /src/main.lean | 9922f37fb8271f39758738b74b0eb6d3a754e177 | [] | no_license | loganrjmurphy/lean-strategies | 4b8dd54771bb421c929a8bcb93a528ce6c1a70f1 | 020e2a65dc2ab475696dfea5ad8935a0a4085918 | refs/heads/main | 1,682,732,168,860 | 1,614,820,630,000 | 1,614,820,630,000 | 278,458,841 | 3 | 0 | null | 1,613,755,728,000 | 1,594,324,763,000 | Lean | UTF-8 | Lean | false | false | 2,396 | lean | import justification common_meta property_catalogue.LTL
import fcs
open interactive S A
variable {α : Type}
set_option pp.structure_instances_qualifier true
def local_input_name : string := "fcs_input_1"
def local_strat_name : string := "fcs_strat_1"
def local_prf_name : string := "fcs_prf_1"
def preamble : strin... |
fd1ad24a04368ccd49b97ea44386f6575e2a02c4 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/CompilerConstantFold.lean | 1dcd0da5ab217ccf61ea7d6bb51615d00d937c6f | [
"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 | 431 | lean | set_option trace.Compiler.result true in
def mulDivShift (a : Nat) (b : UInt8) (c : UInt16) (d : UInt32) (e : UInt64) : Nat :=
let a1 := a / 32
let a2 := a * 32
let b1 := b / 32
let b2 := b * 32
let c1 := c / 32
let c2 := c * 32
let d1 := d / 32
let d2 := d * 32
let e1 := e / 32
let e2 := e * 32
a... |
cdd860ba156ee499969da289102e36d0828c82cd | 8e6cad62ec62c6c348e5faaa3c3f2079012bdd69 | /src/algebra/lie/submodule.lean | e788ac6eab374f01a2e48b00148f18dfe35d145e | [
"Apache-2.0"
] | permissive | benjamindavidson/mathlib | 8cc81c865aa8e7cf4462245f58d35ae9a56b150d | fad44b9f670670d87c8e25ff9cdf63af87ad731e | refs/heads/master | 1,679,545,578,362 | 1,615,343,014,000 | 1,615,343,014,000 | 312,926,983 | 0 | 0 | Apache-2.0 | 1,615,360,301,000 | 1,605,399,418,000 | Lean | UTF-8 | Lean | false | false | 28,727 | 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 algebra.lie.subalgebra
import ring_theory.noetherian
/-!
# Lie submodules of a Lie algebra
In this file we define Lie submodules and Lie ideals, we construct the l... |
4532444755a52f0dace2c19b30dc0ba812e64b4d | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/tactic/rcases.lean | ffb00957dcb0ec55662e34df5f82dea13c1dcbc1 | [
"Apache-2.0"
] | permissive | mcncm/mathlib | 8d25099344d9d2bee62822cb9ed43aa3e09fa05e | fde3d78cadeec5ef827b16ae55664ef115e66f57 | refs/heads/master | 1,672,743,316,277 | 1,602,618,514,000 | 1,602,618,514,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 37,222 | 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.dlist
import tactic.core
import tactic.clear
/-!
# Recursive cases (`rcases`) tactic and related tactics
`rcases` is a tactic that will perform `cases`... |
7853cf4b2cb9d27a1d6cfc9a505c62b947f983b2 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/deprecated/group.lean | 01f35b136cfff20935453d0bea65556df94d4ba9 | [
"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 | 12,328 | lean | import algebra.group.type_tags algebra.group.is_unit
/-!
# Unbundled monoid and group homomorphisms (deprecated)
This file defines typeclasses for unbundled monoid and group homomorphisms. Though these classes are
deprecated, they are still widely used in mathlib, and probably will not go away before Lean 4
because L... |
86559bf125247186b36fcab3b632ddf821ef6c49 | 367134ba5a65885e863bdc4507601606690974c1 | /archive/imo/imo1962_q4.lean | 1532f103af0a1db7ddeff1619707fd2f9ec9ee5e | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 4,143 | lean | /-
Copyright (c) 2020 Kevin Lacker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker, Heather Macbeth
-/
import analysis.special_functions.trigonometric
/-!
# IMO 1962 Q4
Solve the equation `cos x ^ 2 + cos (2 * x) ^ 2 + cos (3 * x) ^ 2 = 1`.
Since Lean ... |
4140f17911a909b6552a627e0a0d6a4919576ded | 4727251e0cd73359b15b664c3170e5d754078599 | /src/tactic/fin_cases.lean | 6e0a575cd81c69bdb9d7fbd0b2a860f8eb141856 | [
"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 | 5,851 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import data.fintype.basic
import tactic.norm_num
/-!
# Case bash
This file provides the tactic `fin_cases`. `fin_cases x` performs case analysis on `x`, that is
cre... |
b070fe7da2ee93d66baaa173f546b3b8bf8a3412 | e22cb3c96cab3b1635ab1f31bcc6f998a4cab507 | /test/conjunction.lean | ac631bbb8c7887ef57d2559c4cd153315e0f1f3a | [
"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 | 68 | lean | import advice
lemma conj (P Q : Prop)
(P ∧ Q) : P :=
{! !}
|
6b155376621238d46ba009e1c1bd2c5afdeafc5a | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/category_theory/monoidal/functor.lean | 6f3630b5a3abbaca22c93852be8ae7fa0198d86c | [
"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 | 17,609 | 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, Bhavik Mehta
-/
import category_theory.monoidal.category
import category_theory.adjunction.basic
import category_theory.products.basic
/-!
# (Lax... |
3d24aca930e4600b24e3dc22194e3c5ba4289f61 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/rec_meta_issue.lean | 24722d2b59a57226550c4c28ebd5eb8b91364265 | [
"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 | 329 | lean | open tactic
meta def left_right_search (tac := assumption) : tactic unit :=
tac
<|> (left >> left_right_search)
<|> (right >> left_right_search)
example (p q r : Prop) : r → p ∨ q ∨ r :=
begin intros, left_right_search end
example (a b c : nat) : a = b ∨ b = c ∨ a = a :=
begin left_right_search reflexivity end
|
fe5c79133fd96d3c19373d4a17e0db0cae5cdbad | 9dd3f3912f7321eb58ee9aa8f21778ad6221f87c | /library/init/algebra/group.lean | 93d9903eb8d6df3ab66fcc19681cda3d49d95124 | [
"Apache-2.0"
] | permissive | bre7k30/lean | de893411bcfa7b3c5572e61b9e1c52951b310aa4 | 5a924699d076dab1bd5af23a8f910b433e598d7a | refs/heads/master | 1,610,900,145,817 | 1,488,006,845,000 | 1,488,006,845,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 15,279 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
-/
prelude
import init.logic init.algebra.ac init.meta init.meta.decl_cmds init.meta.smt.rsimp
/- Make sure instances defined in this file have... |
dafd996d3ee05a1091bb27c57e43263ab28e5cf9 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/set2.lean | 6ac0045d5e0d6e35334fbbaa04a6644209aca49a | [
"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 | 373 | lean | import logic data.bool
open bool
namespace set
definition set (T : Type) := T → bool
definition mem {T : Type} (a : T) (s : set T) := s a = tt
infix `∈` := mem
section
variable {T : Type}
definition empty : set T := λx, ff
notation `∅` := empty
theorem mem_empty (x : T) : ¬ (x ∈ ∅)
:= not.intro (λH : x ∈... |
c3b9a54cd22ee602220da197acdd8ce2d08a220f | b2c4bd81ed12cc14c20704365f094339d4c894a2 | /src/graph_theory/tree.lean | 24a1c890c6b0166a53e2e1fba2abc676cd055810 | [] | no_license | agusakov/graph_theory_2020 | 711639d9d9b25fd83899620da11ae1753d11d48b | 83a8afc31aa28dbec39a768d6042d3cb515f7a16 | refs/heads/master | 1,669,901,277,114 | 1,596,931,643,000 | 1,596,931,643,000 | 285,154,458 | 5 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,656 | lean | import .path
import .graph_induction
-- from math 688 notes, lec-19
universe u
variables (V : Type u)
-- TO DO:
-- define components (they are used twice here), give them some lemmas
-- prove that removing a vertex from a tree results in a graph whose components are trees with smaller size
-- concrete de... |
28aba80d89f168c12266944a4fd0170bc78dbb15 | 3aad12fe82645d2d3173fbedc2e5c2ba945a4d75 | /src/data/sigma/fst.lean | d1105193bb062e42f8bca85ac5627f18062fa421 | [] | no_license | seanpm2001/LeanProver-Community_MathLIB-Nursery | 4f88d539cb18d73a94af983092896b851e6640b5 | 0479b31fa5b4d39f41e89b8584c9f5bf5271e8ec | refs/heads/master | 1,688,730,786,645 | 1,572,070,026,000 | 1,572,070,026,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,672 | lean | import data.sigma.basic
import tactic.ext
namespace sigma
universes u v
section
variables {α : Type u} {β β' : α → Type v}
theorem eq_fst {s₁ s₂ : sigma β} : s₁ = s₂ → s₁.1 = s₂.1 :=
by cases s₁; cases s₂; cc
theorem eq_snd {s₁ s₂ : sigma β} : s₁ = s₂ → s₁.2 == s₂.2 :=
by cases s₁; cases s₂; cc
end
section
variab... |
7e1c9fa748f6edfa880b283951bde6403e46a549 | 7a76361040c55ae1eba5856c1a637593117a6556 | /src/exercises/love03_forward_proofs_exercise_sheet.lean | 084807a9c7139c23a0e78e73cd8346ebfe396bd5 | [] | no_license | rgreenblatt/fpv2021 | c2cbe7b664b648cef7d240a654d6bdf97a559272 | c65d72e48c8fa827d2040ed6ea86c2be62db36fa | refs/heads/main | 1,692,245,693,819 | 1,633,364,621,000 | 1,633,364,621,000 | 407,231,487 | 0 | 0 | null | 1,631,808,608,000 | 1,631,808,608,000 | null | UTF-8 | Lean | false | false | 3,172 | lean | import ..lovelib
/-! # LoVe Exercise 3: Forward Proofs -/
set_option pp.beta true
set_option pp.generalized_field_notation false
namespace LoVe
/-! ## Question 1: Connectives and Quantifiers
1.1. Supply structured proofs of the following lemmas. -/
lemma I (a : Prop) :
a → a :=
sorry
lemma K (a b : Prop) :
... |
9736b312a70c7e6ef9093adb743c9ec8846db9bd | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Meta/Match/Match.lean | 53af4b8688e1d061b366e4c45dd061042ebc016f | [
"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 | 43,857 | 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.Check
import Lean.Meta.Closure
import Lean.Meta.Tactic.Cases
import Lean.Meta.Tactic.Contradiction
import Lean.Meta.GeneralizeTelescope
imp... |
3d0127f5d638723353debf8fd9d1003003974d82 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/concrete_category/unbundled_hom.lean | f2b1a5869d3b953a8bf7723292fdb386b2b69e55 | [] | 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 | 2,503 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.concrete_category.bundled_hom
import Mathlib.PostPort
universes u l
na... |
31ae3ef1bdd4d80fa1f33a9cb61fafc6192da0da | 367134ba5a65885e863bdc4507601606690974c1 | /src/order/fixed_points.lean | e4556eff11ba384c9b376a288a2fd7f82da4673d | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 8,754 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau
-/
import order.complete_lattice
import dynamics.fixed_points.basic
/-!
# Fixed point construction on complete lattices
-/
universes u v w
variables {α : Ty... |
08031b2a032e200cdf70ccec3b692d29a121d283 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/analysis/convex/extreme.lean | 9757be2358c11098dcc9755071528929a03ce181 | [
"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 | 9,613 | lean | /-
Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import analysis.convex.hull
/-!
# Extreme sets
This file defines extreme sets and extreme points for sets in a module.
An extreme set of `A... |
1b64fd3a4b3e899cd61d8cf3e1e354cebf13015d | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/data/real/basic.lean | 2cf7891903364deaed703f93a9b0c2e4beaca57a | [
"Apache-2.0"
] | permissive | vaibhavkarve/mathlib | a574aaf68c0a431a47fa82ce0637f0f769826bfe | 17f8340912468f49bdc30acdb9a9fa02eeb0473a | refs/heads/master | 1,621,263,802,637 | 1,585,399,588,000 | 1,585,399,588,000 | 250,833,447 | 0 | 0 | Apache-2.0 | 1,585,410,341,000 | 1,585,410,341,000 | null | UTF-8 | Lean | false | false | 25,986 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Floris van Doorn
The (classical) real numbers ℝ. This is a direct construction
from Cauchy sequences.
-/
import order.conditionally_complete_lattice data.real.cau_seq_... |
f49e6ee30cbec06882dbaba5618493dd18660392 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/topology/sheaves/presheaf.lean | 509dd24158d6aa1160da688d882df0cca6d098e9 | [
"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 | 2,583 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Mario Carneiro, Reid Barton
-/
import topology.category.Top.opens
/-!
# Presheaves on a topological space
We define `presheaf C X` simply as `(opens X)ᵒᵖ ⥤ C`,
and in... |
662c44c18649407caf299442e62d145002dc0a18 | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/ring_theory/polynomial/symmetric.lean | 435f21ff0a3cd001ed2cb74f3652a005d4e98c97 | [
"Apache-2.0"
] | permissive | hamdysalah1/mathlib | b915f86b2503feeae268de369f1b16932321f097 | 95454452f6b3569bf967d35aab8d852b1ddf8017 | refs/heads/master | 1,677,154,116,545 | 1,611,797,994,000 | 1,611,797,994,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,579 | lean | /-
Copyright (c) 2020 Hanting Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Hanting Zhang, Johan Commelin
-/
import tactic
import data.mv_polynomial.rename
import data.mv_polynomial.comm_ring
/-!
# Symmetric Polynomials and Elementary Symmetric Polynomials
Th... |
0b7cd725167fe0fb0861bdb118337a698b04ad3b | 367134ba5a65885e863bdc4507601606690974c1 | /src/measure_theory/borel_space.lean | 4ffb428c742c472ab4c9ee9e393e31ed5f1da20c | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 65,857 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov
-/
import measure_theory.measure_space
import measure_theory.ae_measurable_sequence
import analysis.complex.basic
import analysis.normed_space.finite_di... |
5d485e30a32979c60c21a6f2c1f4563cb8609784 | e4a7c8ab8b68ca0e53d2c21397320ea590fa01c6 | /src/data/polya/field/norm.lean | 99da39d6052f1f69e256db074e0cb62e632bdbe8 | [] | no_license | lean-forward/field | 3ff5dc5f43de40f35481b375f8c871cd0a07c766 | 7e2127ad485aec25e58a1b9c82a6bb74a599467a | refs/heads/master | 1,590,947,010,909 | 1,563,811,881,000 | 1,563,811,881,000 | 190,415,651 | 1 | 0 | null | 1,563,643,371,000 | 1,559,746,688,000 | Lean | UTF-8 | Lean | false | false | 9,970 | lean | import .sterm .pterm
namespace list
theorem subset_union_left {α : Type*} [decidable_eq α]
{l1 l2 : list α} : l1 ⊆ l1 ∪ l2 :=
by {intros a ha, apply list.mem_union_left, exact ha}
end list
namespace polya.field
inductive alt (γ) [const_space γ] : bool → Type
| sform : list (nterm γ) → sterm γ → alt tt
| pform : ... |
6b0a8de32477f7d5db21586083ef65b6fb3e5c4a | a4673261e60b025e2c8c825dfa4ab9108246c32e | /stage0/src/Lean/Meta/Match/Basic.lean | 90ec8e3d13472eee5ca1aac4032ff8eddd7dc043 | [
"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 | 10,952 | 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.Match.MatcherInfo
import Lean.Meta.Match.CaseArraySizes
namespace Lean.Meta.Match
inductive Pattern : Type :=
| inaccessible (e : Expr)... |
7da7a789e537b681b44dd974ddb63033cfe12a6d | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/int/range.lean | e6ddc1b1fbeaa6176723af0f358db2f4e53291e0 | [] | 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 | 1,408 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro and Kenny Lau
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.int.basic
import Mathlib.data.list.range
import Mathlib.PostPort
namespace M... |
bca912568bbead349868ac88377bbac496a0ee04 | 4fa161becb8ce7378a709f5992a594764699e268 | /src/data/pequiv.lean | edb967c494e73fe71a4df635422a263002a63f79 | [
"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 | 11,183 | lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import data.set.lattice
universes u v w x
/-- A `pequiv` is a partial equivalence, a representation of a bijection between a subset
of `α` and a subset of `β` -/
stru... |
c30d327707528858a08a13b2d27d80b25034aaea | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/topology/algebra/group.lean | 45fb9ce21877f33803b4854159af553873e7db86 | [
"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 | 29,644 | 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.pointwise
import group_theory.quotient_group
import topology.algebra.monoid
import topology.homeomorph
import top... |
86ee0b137fb2cb8fdb5cda0cfeb1ba2e7efeea25 | ce89339993655da64b6ccb555c837ce6c10f9ef4 | /bluejam/chap4_exercise4.lean | d487b82100486e9eb0c1344835243cfdf8d65ec2 | [] | no_license | zeptometer/LearnLean | ef32dc36a22119f18d843f548d0bb42f907bff5d | bb84d5dbe521127ba134d4dbf9559b294a80b9f7 | refs/heads/master | 1,625,710,824,322 | 1,601,382,570,000 | 1,601,382,570,000 | 195,228,870 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 932 | lean | namespace hidden
def divides (m n : ℕ) : Prop := ∃ k, m * k = n
instance : has_dvd nat := ⟨divides⟩
def even (n : ℕ) : Prop := 2 ∣ n
def prime (n : ℕ) : Prop := n > 1 ∧ ¬ ∃ m : ℕ, m ≠ n ∧ m ∣ n
def infinitely_many_primes : Prop := ∀ n : ℕ, ∃ p : ℕ, p > n ∧ prime p
def Fermat_prime (n : ℕ) : Prop := ∃ k : ℕ, n = ... |
db1cff28263d0925b7769b6c2ed60646be17ef16 | d0f9af2b0ace5ce352570d61b09019c8ef4a3b96 | /notes/2020.02.06-implicit_args.lean | 8f77c2a8f2a2de49c2ece47fddb2b49575229302 | [] | no_license | jngo13/Discrete-Mathematics | 8671540ef2da7c75915d32332dd20c02f001474e | bf674a866e61f60e6e6d128df85fa73819091787 | refs/heads/master | 1,675,615,657,924 | 1,609,142,011,000 | 1,609,142,011,000 | 267,190,341 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,817 | lean | /-
Explicit type arguments
-/
/-
A polymorphic type, poly, with one type
parameter, here named alpha. Objects of
this type represent ordered pairs where
both elements are of the same type, e.g.,
ordered pairs of natural numbers, ordered
pairs of strings, etc.
-/
inductive my_prod (α : Type) : Type
| mk : α → α → my_p... |
64e68ef0b12b4b16b7ef1a5fc3f58fc2b1210475 | a76f677b87d42a9470ba3a0a78cfddd3063118e6 | /src/example.lean | e4154d6d116768e4000a06ab403bb3fb678bf681 | [] | no_license | Ja1941/hilberts-axioms | 50219c732ad5fa167408432e8c8baae259777a40 | 5b653a92e448b77da41c9893066b641bc4e6b316 | refs/heads/master | 1,693,238,884,856 | 1,635,702,120,000 | 1,635,702,120,000 | 385,546,384 | 9 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 64,117 | lean | /-
Copyright (c) 2021 Tianchen Zhao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tianchen Zhao
-/
import congruence.basic
import data.zmod.basic
import data.real.basic
import data.real.sqrt
import group_theory.group_action.defs
import analysis.normed_space.inner_pro... |
4c657e29c3e8674416097dbb39fdcd99f370d423 | d436468d80b739ba7e06843c4d0d2070e43448e5 | /src/category/basic.lean | 93f29e2eaacf26857c321f89cef066828ae7316e | [
"Apache-2.0"
] | permissive | roro47/mathlib | 761fdc002aef92f77818f3fef06bf6ec6fc1a28e | 80aa7d52537571a2ca62a3fdf71c9533a09422cf | refs/heads/master | 1,599,656,410,625 | 1,573,649,488,000 | 1,573,649,488,000 | 221,452,951 | 0 | 0 | Apache-2.0 | 1,573,647,693,000 | 1,573,647,692,000 | null | UTF-8 | Lean | false | false | 6,657 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Extends the theory on functors, applicatives and monads.
-/
universes u v w
variables {α β γ : Type u}
notation a ` $< `:1 f:1 := f a
section functor
variables {f : ... |
1a1686d2a32323de903550cfcea18c174b310932 | 3f7026ea8bef0825ca0339a275c03b911baef64d | /src/data/nat/gcd.lean | 5282ead7f3586e06c8ddbe4b33d45233b002559a | [
"Apache-2.0"
] | permissive | rspencer01/mathlib | b1e3afa5c121362ef0881012cc116513ab09f18c | c7d36292c6b9234dc40143c16288932ae38fdc12 | refs/heads/master | 1,595,010,346,708 | 1,567,511,503,000 | 1,567,511,503,000 | 206,071,681 | 0 | 0 | Apache-2.0 | 1,567,513,643,000 | 1,567,513,643,000 | null | UTF-8 | Lean | false | false | 15,497 | 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
Definitions and properties of gcd, lcm, and coprime.
-/
import data.nat.basic
namespace nat
/- gcd -/
theorem gcd_dvd (m n : ℕ) : (gcd m n ∣ m) ∧ (g... |
5cd96b864f4847c3e74304c5f01bf6cff11ee89b | b70031c8e2c5337b91d7e70f1e0c5f528f7b0e77 | /src/data/polynomial/div.lean | 315fd91266c24ac77498ed17e45e49f8c9cdd358 | [
"Apache-2.0"
] | permissive | molodiuc/mathlib | cae2ba3ef1601c1f42ca0b625c79b061b63fef5b | 98ebe5a6739fbe254f9ee9d401882d4388f91035 | refs/heads/master | 1,674,237,127,059 | 1,606,353,533,000 | 1,606,353,533,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 25,953 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
-/
import data.polynomial.monic
import ring_theory.euclidean_domain
import ring_theory.multiplicity
/-!
# Division of univar... |
4b08719e914d9d5b3702b975043b3e24ced4c97e | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/data/nat/parity.lean | 2f1ed7111f24789e7c6b67571aef787f750587bc | [
"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 | 3,705 | lean | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
The `even` predicate on the natural numbers.
-/
import .modeq algebra.group_power
namespace nat
@[simp] theorem mod_two_ne_one {n : nat} : ¬ n % 2 = 1 ↔ n % 2 = 0 :=
by... |
4472947eb820469fa7b754b9641ac9fc403e376d | 9c1ad797ec8a5eddb37d34806c543602d9a6bf70 | /monoidal_categories/lemmas/symmetry_in_terms_of_natural_transformations.lean | 12b249e179bc5a465718d1499ef30e8cb0346507 | [] | no_license | timjb/lean-category-theory | 816eefc3a0582c22c05f4ee1c57ed04e57c0982f | 12916cce261d08bb8740bc85e0175b75fb2a60f4 | refs/heads/master | 1,611,078,926,765 | 1,492,080,000,000 | 1,492,080,000,000 | 88,348,246 | 0 | 0 | null | 1,492,262,499,000 | 1,492,262,498,000 | null | UTF-8 | Lean | false | false | 4,494 | lean | -- Copyright (c) 2017 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Stephen Morgan, Scott Morrison
import ..braided_monoidal_category
open tqft.categories
open tqft.categories.functor
open tqft.categories.products
open tqft.categories.natural_tr... |
b1b82766bbf72f361670515ab232ba2f40d3551e | 4727251e0cd73359b15b664c3170e5d754078599 | /src/number_theory/basic.lean | 0accec3918f5b90c6a920294faa55977d83da21b | [
"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 | 1,407 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Kenny Lau
-/
import algebra.geom_sum
import ring_theory.ideal.quotient
/-!
# Basic results in number theory
This file should contain basic results in number theory. ... |
29a6492f9db1f9b9e5536215abdb0e3168d601b9 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /test/measurability.lean | aa16b6306a79ef74947ca5d0402a85ee014f6fa9 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 3,433 | 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.tactic
import measure_theory.function.special_functions.inner
import measure_theory.function.special_functions.basic
open_locale big_operators ennr... |
bfa89877d07cac98d84b81ab14f727944f27a4d3 | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/topology/algebra/infinite_sum.lean | d108a10e0c03f90e97a515861822868dc273964c | [
"Apache-2.0"
] | permissive | vaibhavkarve/mathlib | a574aaf68c0a431a47fa82ce0637f0f769826bfe | 17f8340912468f49bdc30acdb9a9fa02eeb0473a | refs/heads/master | 1,621,263,802,637 | 1,585,399,588,000 | 1,585,399,588,000 | 250,833,447 | 0 | 0 | Apache-2.0 | 1,585,410,341,000 | 1,585,410,341,000 | null | UTF-8 | Lean | false | false | 31,597 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Infinite sum over a topological monoid
This sum is known as unconditionally convergent, as it sums to the same value under all possible
permutations. For Euclidean spa... |
c6c9df7733fd7bfc151549b9526510956b63fe32 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/init/monad_combinators.lean | 5cbbb63ac7697574c69ffb4b10e329dc1f5e33de | [
"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 | 2,937 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
Monad combinators, as in Haskell's Control.Monad.
-/
prelude
import init.monad init.list
namespace monad
definition mapM {m : Type → Type} [monad m] {A B : Type}... |
b85c623f5f1b7fe92a8aa956960bb9aa24c5af06 | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /src/Lean/Elab/Frontend.lean | 88c80cfb944911e5c94ad68fb395f52e2511d00a | [
"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 | 4,797 | 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.Elab.Import
import Lean.Elab.Command
namespace Lean
namespace Elab
namespace Frontend
structure Context :=
(commandStateRef... |
b2a858f1525cf055d2e4b9daf181ddcec4a13e44 | 4b846d8dabdc64e7ea03552bad8f7fa74763fc67 | /library/init/wf.lean | 39a7592554b10b0463dbb5a89d74a22b83de4b9b | [
"Apache-2.0"
] | permissive | pacchiano/lean | 9324b33f3ac3b5c5647285160f9f6ea8d0d767dc | fdadada3a970377a6df8afcd629a6f2eab6e84e8 | refs/heads/master | 1,611,357,380,399 | 1,489,870,101,000 | 1,489,870,101,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,441 | 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
-/
prelude
import init.data.nat.basic init.data.prod
universes u v
inductive acc {α : Type u} (r : α → α → Prop) : α → Prop
| intro : ∀ x, (∀ y, r y x → acc y... |
c4465a0e90b4a7eacfc5da3d23cb5615d14a2621 | 38bf3fd2bb651ab70511408fcf70e2029e2ba310 | /src/tactic/reassoc_axiom.lean | 352099405fe218e3b124d836b36e2c5fde13178f | [
"Apache-2.0"
] | permissive | JaredCorduan/mathlib | 130392594844f15dad65a9308c242551bae6cd2e | d5de80376088954d592a59326c14404f538050a1 | refs/heads/master | 1,595,862,206,333 | 1,570,816,457,000 | 1,570,816,457,000 | 209,134,499 | 0 | 0 | Apache-2.0 | 1,568,746,811,000 | 1,568,746,811,000 | null | UTF-8 | Lean | false | false | 3,452 | lean | /-
Copyright (c) 2019 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author(s): Simon Hudon
-/
import category_theory.category
/-!
Reformulate category-theoretic axioms in a more associativity-friendly way.
## The `reassoc` attribute
The `reassoc` attribute can ... |
32b62cf46de4e54e205c1e2dc79e810be172759d | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/polynomial/iterated_deriv.lean | 627dbf083b9216f45e00cd573710605542810663 | [
"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 | 8,060 | lean | /-
Copyright (c) 2020 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
import data.polynomial.derivative
import logic.function.iterate
import data.finset.intervals
import tactic.ring
import tactic.linarith
/-!
# Theory of iterated derivati... |
22fde5d7ba050feecbc555685f8b839674837cb4 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Init/Data/Queue.lean | 8fe7f346bc4aa6a96a176ecb14c18346cbb58e20 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 1,955 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Selsam
Simple queue implemented using two lists.
Note: this is only a temporary placeholder.
-/
prelude
import Init.Data.List
namespace Std
/--
A functional queue data... |
5e1c481c4f5cc490ccd0b211f2813ed816cf7113 | a7602958ab456501ff85db8cf5553f7bcab201d7 | /Assignment4/9.5-homework.lean | e040226ffc7cbc7795b4281be0f557e0a83b5e79 | [] | no_license | enlauren/math-logic | 081e2e737c8afb28dbb337968df95ead47321ba0 | 086b6935543d1841f1db92d0e49add1124054c37 | refs/heads/master | 1,594,506,621,950 | 1,558,634,976,000 | 1,558,634,976,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,968 | lean | -- Assignment 4
-- Dom Farolino, farolidm@mail.uc.edu
-- Math Logic
-- Exercise 1
section
variable A: Type
variable f: A → A
variable P: A → Prop
variable h: ∀ x, P x → P (f x)
-- Show the following:
-- Scope of ∀ is maximal.
example: ∀ y, P y → P (f (f y)) :=
assume z: A, -- Arbitrary... |
97c8425cddf7d4ab7a3ccb4fa38f8c1782e6ab60 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/order/hom/basic.lean | deab8d48d7eb2d1139a2371d1136ce62c7f52f16 | [
"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 | 41,827 | 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 logic.equiv.option
import order.rel_iso
import tactic.monotonicity.basic
/-!
# Order homomorphisms
This file defines order homomorphisms, which are bundled m... |
10decf693f8cfc9731d90eeb528be1538d0e5075 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/analysis/box_integral/divergence_theorem.lean | a5c0acde4b54ed4053b7af15c6807eca40069238 | [
"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 | 16,363 | 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 analysis.box_integral.basic
import analysis.box_integral.partition.additive
import analysis.calculus.fderiv
/-!
# Divergence integral for Henstock-Kurzweil ... |
1df05c72e0fe66a5a77fb092baae12928d0a13f5 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/data/sigma/basic.lean | 9f9beb6811330e6fd66135ab00771048abdbb087 | [
"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 | 3,687 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
-/
import tactic.lint
section sigma
variables {α : Type*} {β : α → Type*}
instance [inhabited α] [inhabited (β (default α))] : inhabited (sigma β) :=
⟨⟨default α, defa... |
3fce92c371ae0bbacaa29d3a95e1eda814bf72c4 | b074a51e20fdb737b2d4c635dd292fc54685e010 | /src/algebraic_geometry/stalks.lean | 59b454ffd0b38c2f4a0b787c75d22ff57b14c87f | [
"Apache-2.0"
] | permissive | minchaowu/mathlib | 2daf6ffdb5a56eeca403e894af88bcaaf65aec5e | 879da1cf04c2baa9eaa7bd2472100bc0335e5c73 | refs/heads/master | 1,609,628,676,768 | 1,564,310,105,000 | 1,564,310,105,000 | 99,461,307 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,903 | 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 algebraic_geometry.presheafed_space
import topology.Top.stalks
/-!
# Stalks for presheaved spaces
This file lifts constructions of stalks and pushforwards... |
f21e27dad0ef96ab2a9c1ec1e7654888a0493193 | 36c7a18fd72e5b57229bd8ba36493daf536a19ce | /library/data/nat/fact.lean | c915f7f4562d3c2017b83a2bc2e0e8a2a2d4267f | [
"Apache-2.0"
] | permissive | YHVHvx/lean | 732bf0fb7a298cd7fe0f15d82f8e248c11db49e9 | 038369533e0136dd395dc252084d3c1853accbf2 | refs/heads/master | 1,610,701,080,210 | 1,449,128,595,000 | 1,449,128,595,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,440 | 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
Factorial
-/
import data.nat.div
open algebra
namespace nat
definition fact : nat → nat
| 0 := 1
| (succ n) := (succ n) * fact n
lemma fact_zero : fa... |
b749e514fd5a7f51bdf32dc5e08c548be6946ec0 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/calculus/deriv/slope.lean | 659b3e4190984ac2d063ecb4798627219523093c | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 7,703 | 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 analysis.calculus.deriv.basic
import linear_algebra.affine_space.slope
/-!
# Derivative as the limit of the slope
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4... |
03870dab6e644f3cb3fa1637c5b90da2f2a59a58 | b32d3853770e6eaf06817a1b8c52064baaed0ef1 | /src/super/inferences/subsumption.lean | e7fb585a528c78b70e1ec179ea55c8aa7ac10c39 | [] | no_license | gebner/super2 | 4d58b7477b6f7d945d5d866502982466db33ab0b | 9bc5256c31750021ab97d6b59b7387773e54b384 | refs/heads/master | 1,635,021,682,021 | 1,634,886,326,000 | 1,634,886,326,000 | 225,600,688 | 4 | 2 | null | 1,598,209,306,000 | 1,575,371,550,000 | Lean | UTF-8 | Lean | false | false | 1,115 | lean | import super.prover_state super.subsume
namespace super
meta def simplification.forward_subsumption : simplification_rule | given := do
active ← get_active,
s ← tactic.read,
if active.values.existsb $ λ act : derived_clause, does_subsume_pure s act.cls given then
pure none
else
pure given
meta def preprocessing.... |
51015e044915263b31dca7957f1dfd9ecee2f93c | c777c32c8e484e195053731103c5e52af26a25d1 | /src/algebra/algebra/subalgebra/basic.lean | 9cc6730b0237d582c96f01b9718ac61d68c4d2b6 | [
"Apache-2.0"
] | permissive | kbuzzard/mathlib | 2ff9e85dfe2a46f4b291927f983afec17e946eb8 | 58537299e922f9c77df76cb613910914a479c1f7 | refs/heads/master | 1,685,313,702,744 | 1,683,974,212,000 | 1,683,974,212,000 | 128,185,277 | 1 | 0 | null | 1,522,920,600,000 | 1,522,920,600,000 | null | UTF-8 | Lean | false | false | 47,141 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov
-/
import algebra.algebra.basic
import data.set.Union_lift
import linear_algebra.finsupp
import ring_theory.ideal.operations
/-!
# Subalgebras over Commutative S... |
6c58deac4cb39d30cf1274064c3c3bb35d405bd4 | 4f065978c49388d188224610d9984673079f7d91 | /plus20181101q5.lean | 25dd3b4cb7da9216e4bcd68b01ca8fd3b2aad7bf | [] | no_license | kckennylau/Lean | b323103f52706304907adcfaee6f5cb8095d4a33 | 907d0a4d2bd8f23785abd6142ad53d308c54fdcb | refs/heads/master | 1,624,623,720,653 | 1,563,901,820,000 | 1,563,901,820,000 | 109,506,702 | 3 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 8,572 | lean | import data.polynomial ring_theory.associated
open finset
namespace polynomial
variables {α : Type*} [decidable_eq α]
theorem degree_add_eq_of_degree_gt [comm_semiring α]
{f g : polynomial α} (H : degree g < degree f) :
degree (f + g) = degree f :=
add_comm g f ▸ degree_add_eq_of_degree_lt H
theorem degree_sub... |
468a013ebeee4890088d42312c1b40006885458e | 367134ba5a65885e863bdc4507601606690974c1 | /src/ring_theory/witt_vector/verschiebung.lean | 73050f129c33a6145b59d229044bac3cf19c660b | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 5,944 | 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 ring_theory.witt_vector.basic
import ring_theory.witt_vector.is_poly
/-!
## The Verschiebung operator
## References
* [Hazewinkel, *Witt Vectors*][Haze09]... |
4a445ba98b8a33b5fea1f98639c7a4539d3c8a14 | d436468d80b739ba7e06843c4d0d2070e43448e5 | /src/data/analysis/topology.lean | c9a8d3e71f5dd33e42048080fff20768389e973e | [
"Apache-2.0"
] | permissive | roro47/mathlib | 761fdc002aef92f77818f3fef06bf6ec6fc1a28e | 80aa7d52537571a2ca62a3fdf71c9533a09422cf | refs/heads/master | 1,599,656,410,625 | 1,573,649,488,000 | 1,573,649,488,000 | 221,452,951 | 0 | 0 | Apache-2.0 | 1,573,647,693,000 | 1,573,647,692,000 | null | UTF-8 | Lean | false | false | 8,415 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
Computational realization of topological spaces (experimental).
-/
import topology.bases data.analysis.filter
open set
open filter (hiding realizer)
open_locale topolog... |
13a18386626d91d50504925e50bd748fa05803e1 | 3dd1b66af77106badae6edb1c4dea91a146ead30 | /tests/lean/run/e4.lean | 5265bad9b52b70b8ecbf0f07cd490328ad4cea2b | [
"Apache-2.0"
] | permissive | silky/lean | 79c20c15c93feef47bb659a2cc139b26f3614642 | df8b88dca2f8da1a422cb618cd476ef5be730546 | refs/heads/master | 1,610,737,587,697 | 1,406,574,534,000 | 1,406,574,534,000 | 22,362,176 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 636 | lean | definition Prop [inline] := Type.{0}
definition false : Prop := ∀x : Prop, x
check false
theorem false_elim (C : Prop) (H : false) : C
:= H C
definition eq {A : Type} (a b : A)
:= ∀ P : A → Prop, P a → P b
check eq
infix `=`:50 := eq
theorem refl {A : Type} (a : A) : a = a
:= λ P H, H
definition true : Prop
:= f... |
01f1845e7ec2b2f9fba9888b6be77b9f62507e3b | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/projDefEq2.lean | d6f44959dd70d2a906429ffe5e5444a1d16e14f7 | [
"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 | 266 | lean | structure Foo where
x : Nat
h : x > 1
theorem foo_gt_0 (foo : Foo) : foo.x > 0 :=
Nat.lt_of_succ_lt foo.h
example (x : Nat) (h : x > 1) : id { x, h : Foo }.x > 0 :=
foo_gt_0 { x, h }
example (x : Nat) (h : x > 1) : id { x, h : Foo }.x > 0 :=
foo_gt_0 _
|
2caec13a0e6bd293c7d569aa1f6bd5fae17787a1 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Data/Lsp/Client.lean | 4ac80a6e0e0fb27c2079940dc9a8f3079807aad0 | [
"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 | 491 | lean | /-
Copyright (c) 2021 Joscha Mennicken. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joscha Mennicken
-/
import Lean.Data.Lsp.Basic
import Lean.Data.Json
namespace Lean
namespace Lsp
open Json
structure Registration where
id : String
method : String
regist... |
41b01e938232a82db0a34a520e092a31c3093de8 | c9c1a27957d84c115a545c9f93aeaaa780279709 | /src/CTL.lean | 2f0ccb6af7891e5b07435636616fdb452346b275 | [] | no_license | loganrjmurphy/lean-temporal | 320475197f39afbea7e29b7de6cdd183e3f7c5de | 40c6ad1502fc4168dffe9f34ad2d2043d53af174 | refs/heads/main | 1,672,925,416,469 | 1,605,106,081,000 | 1,605,106,081,000 | 311,688,877 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,248 | lean | import data.stream tactic
open stream tactic
namespace CTL
variables AP : Type
mutual inductive state_formula, path_formula
with state_formula : Type
| T : state_formula
| atom (a : AP) : state_formula
| conj (Φ₁ Φ₂ : state_formula ) : state_formula
| neg (Φ : state_formula) : state_formula
| E (φ : pat... |
04696c44fefe5afc38be9f4cbe336b9bf7c04455 | a7eef317ddec01b9fc6cfbb876fe7ac00f205ac7 | /src/data/real/ennreal.lean | 4f6d25e50d11fa53b01d4972b9b17d6436e41a1f | [
"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 | 45,557 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl, Yury Kudryashov
Extended non-negative reals
-/
import data.real.nnreal
import data.set.intervals
noncomputable theory
open classical set
open_locale classical big_oper... |
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