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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
36c44edededcc255b4ce3fec24fb02b986f8a68b | dcf093fda1f51c094394c50e182cfb9dec39635a | /rel_set.lean | 9c95909644ff76a45ac7741934ac74eb39e6e6d6 | [] | no_license | dselsam/cs103 | 7ac496d0293befca95d3045add91c5270a5d291f | 31ab9784a6f65f226efb702a0da52f907c616a71 | refs/heads/master | 1,611,092,644,140 | 1,492,571,015,000 | 1,492,571,015,000 | 88,693,969 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,799 | lean | import data.set classical algebra.order data.nat
open set eq.ops
namespace relations
variable {T : Type}
/- [KS]
Given a set S, a partition of S is a set X ⊆ ℘(S) (that is, a set of subsets of S) with the following properties:
1. The union of all sets in X is equal to S.
2. For any S1, S2 ∈ X with S1 ≠ S2, we have t... |
6fa4720428ba6b623c0f37fac4e69082e4d4f4cb | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /archive/imo/imo1972_b2.lean | 722405f8ccf673393f2966b7b88f57a85cacafbd | [
"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 | 4,273 | lean | /-
Copyright (c) 2020 Ruben Van de Velde, Stanislas Polu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ruben Van de Velde, Stanislas Polu
-/
import data.real.basic
import analysis.normed_space.basic
/-!
# IMO 1972 B2
Problem: `f` and `g` are real-valued functions ... |
57f099c2c44ad8342851b30e3c043dfb19074ed0 | 137c667471a40116a7afd7261f030b30180468c2 | /src/measure_theory/arithmetic.lean | 7372b6fb316d9ff42b197c148e61df2a3b5f7714 | [
"Apache-2.0"
] | permissive | bragadeesh153/mathlib | 46bf814cfb1eecb34b5d1549b9117dc60f657792 | b577bb2cd1f96eb47031878256856020b76f73cd | refs/heads/master | 1,687,435,188,334 | 1,626,384,207,000 | 1,626,384,207,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 25,562 | 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 ... |
db285d0f64e14b72231c63547f21c50415c60cdf | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/data/polynomial/ring_division.lean | e48446cbde56a3b53335779a74a6fe532a9e1161 | [
"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 | 24,122 | 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, Johan Commelin
-/
import data.polynomial.basic
import data.polynomial.div
import data.polynomial.algebra_map
import data.se... |
1d658fab514ba9796fdb3029b255cbb8b729c394 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/algebra/direct_sum/algebra.lean | c192b1b12f302bc5c69606d092e27cdca354b73a | [
"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 | 5,649 | lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import algebra.direct_sum.ring
import algebra.direct_sum.module
/-! # Additively-graded algebra structures on `⨁ i, A i`
This file provides `R`-algebra structures on exte... |
550fe915539196ac67149f9adb84db71f7085550 | f57749ca63d6416f807b770f67559503fdb21001 | /hott/types/function.hlean | 1eb9e48554a6e1f3e42aa14c718da7f96ba0294b | [
"Apache-2.0"
] | permissive | aliassaf/lean | bd54e85bed07b1ff6f01396551867b2677cbc6ac | f9b069b6a50756588b309b3d716c447004203152 | refs/heads/master | 1,610,982,152,948 | 1,438,916,029,000 | 1,438,916,029,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,973 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Floris van Doorn
Ported from Coq HoTT
Theorems about embeddings and surjections
-/
import hit.trunc .pi .fiber .equiv
open equiv sigma sigma.ops eq trunc is_trunc pi is_equiv fiber... |
cf5e625472d4aa50500bba302a64f0abf7dc3ba7 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/set_theory/cardinal/continuum.lean | 370883c8c72e3887999fded17a4e29082a58e27a | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 4,057 | 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 set_theory.cardinal.ordinal
/-!
# Cardinality of continuum
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR... |
b11ddcd2bcae7942e86f83bab84af3896b90dc4e | 3b15c7b0b62d8ada1399c112ad88a529e6bfa115 | /src/Init/Prelude.lean | f53b6093a62e28a2190befdb51108c01bb949c03 | [
"Apache-2.0"
] | permissive | stephenbrady/lean4 | 74bf5cae8a433e9c815708ce96c9e54a5caf2115 | b1bd3fc304d0f7bc6810ec78bfa4c51476d263f9 | refs/heads/master | 1,692,621,473,161 | 1,634,308,743,000 | 1,634,310,749,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 77,651 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
universe u v w
@[inline] def id {α : Sort u} (a : α) : α := a
abbrev Function.comp {α : Sort u} {β : Sort v} {δ : Sort w} (f : β → δ) (g : α → β)... |
e39cbf53fa6602ed1d9e3ffe286318eba3c79170 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/tactic/fresh_names.lean | aa55f0c317340baee6cbf58da1d4761ddf358e65 | [
"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 | 5,482 | lean | /-
Copyright (c) 2020 Jannis Limperg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jannis Limperg
-/
import data.sum.basic
import tactic.dependencies
/-!
# Tactics for giving hypotheses fresh names
When introducing hypotheses, we often want to make sure that their ... |
5268e393cd97b8caec5d9d407b6762264c06d26a | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/computability/regular_expressions.lean | da9c7d23a3bc7fcffc09436ad97221475f85df43 | [
"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 | 9,771 | lean | /-
Copyright (c) 2020 Fox Thomson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fox Thomson
-/
import tactic.rcases
import computability.language
/-!
# Regular Expressions
This file contains the formal definition for regular expressions and basic lemmas. Note these... |
67330461a0d3643806fa4a13b9041495d2f38c4f | 2d34dfb0a1cc250584282618dc10ea03d3fa858e | /src/normed_group_hom.lean | f574eb453423f7753f719b9ef9afe7d91c1a8b92 | [] | no_license | zeta1999/lean-liquid | 61e294ec5adae959d8ee1b65d015775484ff58c2 | 96bb0fa3afc3b451bcd1fb7d974348de2f290541 | refs/heads/master | 1,676,579,150,248 | 1,610,771,445,000 | 1,610,771,445,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,622 | lean | import analysis.normed_space.basic
open_locale nnreal big_operators
set_option old_structure_cmd true
/-- A morphism of normed abelian groups is a bounded group homomorphism. -/
structure normed_group_hom (V W : Type*) [normed_group V] [normed_group W]
extends add_monoid_hom V W :=
(bound' : ∃ C, ∀ v, ∥to_fun v∥ ≤... |
a526f565ae59a26cc33bfc3414ceb969ed25afb4 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/category_theory/limits/shapes/biproducts.lean | e103165ce5f4b81a329a320b7bd9dda8d530b90f | [
"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 | 84,718 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Jakob von Raumer
-/
import algebra.group.ext
import category_theory.limits.shapes.finite_products
import category_theory.limits.shapes.binary_products
import category_t... |
6d67affe013247ff531d812dfe1958a7a5c80ade | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/1234.lean | 9815f6ea14a36a3bf85c633d84ca723910503eb9 | [
"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 | 1,213 | lean | theorem le_of_not_lt {a b : Nat} (_: ¬ a < b): b ≤ a := sorry
theorem lt_of_succ_lt (_: a + 1 < b): a < b := sorry
theorem succ_pred_eq_of_pos (_: 0 < v): v - 1 + 1 = v := sorry
set_option trace.Meta.Tactic.simp true
--set_option trace.Debug.Meta.Tactic.simp true
example (h₁: k ≤ v - 1) (h₂: 0 < v):
... |
5f3c5050d3176e1adfcd8fb093522c3da26ad258 | c45b34bfd44d8607a2e8762c926e3cfaa7436201 | /uexp/src/uexp/rules/pullConstantThroughUnion2.lean | fa6385c31447ffe29647c2e26360d9103b0ffdfd | [
"BSD-2-Clause"
] | permissive | Shamrock-Frost/Cosette | b477c442c07e45082348a145f19ebb35a7f29392 | 24cbc4adebf627f13f5eac878f04ffa20d1209af | refs/heads/master | 1,619,721,304,969 | 1,526,082,841,000 | 1,526,082,841,000 | 121,695,605 | 1 | 0 | null | 1,518,737,210,000 | 1,518,737,210,000 | null | UTF-8 | Lean | false | false | 2,079 | lean | import ..sql
import ..tactics
import ..u_semiring
import ..extra_constants
import ..ucongr
import ..TDP
-- set_option profiler true
open Expr
open Proj
open Pred
open SQL
open tree
notation `int` := datatypes.int
variable integer_1: const datatypes.int
variable integer_2: const datatypes.int
theorem rule:
forall ... |
edcc805c931263e8ece23b12b773d37b9cce763a | 97f752b44fd85ec3f635078a2dd125ddae7a82b6 | /hott/types/list.hlean | 8158114f36abe032750ad1870e8f9c5667628f44 | [
"Apache-2.0"
] | permissive | tectronics/lean | ab977ba6be0fcd46047ddbb3c8e16e7c26710701 | f38af35e0616f89c6e9d7e3eb1d48e47ee666efe | refs/heads/master | 1,532,358,526,384 | 1,456,276,623,000 | 1,456,276,623,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 36,106 | hlean | /-
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
Basic properties of lists.
Ported from the standard library (list.basic and list.comb)
Some lemmas are commented... |
7c9f0d40f8772dc49e4a8f1925e3c2d1a99ed09b | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/topology/homeomorph.lean | c32965e632a54c26abeceaeea3684451a59e93da | [
"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 | 5,947 | lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Sébastien Gouëzel, Zhouhang Zhou, Reid Barton
-/
import topology.subset_properties topology.dense_embedding
open set
variables {α : Type*} {β : Type*} {γ... |
17af9c17040ee19999912476371b5ebd45ebd45a | a726f88081e44db9edfd14d32cfe9c4393ee56a4 | /src/game/world8/level6.lean | aa70077ad59527de62a724ebf21eba73e79d7ff6 | [] | no_license | b-mehta/natural_number_game | 80451bf10277adc89a55dbe8581692c36d822462 | 9faf799d0ab48ecbc89b3d70babb65ba64beee3b | refs/heads/master | 1,598,525,389,186 | 1,573,516,674,000 | 1,573,516,674,000 | 217,339,684 | 0 | 0 | null | 1,571,933,100,000 | 1,571,933,099,000 | null | UTF-8 | Lean | false | false | 801 | lean | import game.world8.level5 -- hide
namespace mynat -- hide
/-
# Advanced Addition World
## Level 5: `add_left_cancel`
The theorem `add_left_cancel` is the theorem that you can cancel on the left
when you're doing addition -- if `t + a = t + b` then `a = b`.
There is a three-line proof which ends in `exact add_right... |
4ab9bca8e2723a85a545cec325cd17d53f69dfc8 | 38ee9024fb5974f555fb578fcf5a5a7b71e669b5 | /Mathlib/Tactic/Ring.lean | 561e5e2ac80008c582ddc87525a02ecc97c59854 | [
"Apache-2.0"
] | permissive | denayd/mathlib4 | 750e0dcd106554640a1ac701e51517501a574715 | 7f40a5c514066801ab3c6d431e9f405baa9b9c58 | refs/heads/master | 1,693,743,991,894 | 1,636,618,048,000 | 1,636,618,048,000 | 373,926,241 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 18,092 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Aurélien Saue
-/
import Lean.Elab.Tactic.Basic
import Mathlib.Algebra.Ring.Basic
import Mathlib.Tactic.NormNum
/-!
# `ring`
Evaluate expressions in the language of co... |
141df226530c3ca54c4fcd51954ff5eadad0125c | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/topology/nhds_set.lean | cdd1a0a6f4150868c180707ba12755ef18cf40a9 | [
"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 | 2,990 | lean | /-
Copyright (c) 2022 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Patrick Massot
-/
import topology.basic
/-!
# Neighborhoods of a set
In this file we define the filter `𝓝ˢ s` or `nhds_set s` consisting of all neighborhoods of a... |
8aed1706dc15613214955c7d37001f81de6df3bd | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/star/big_operators.lean | 156f2f8f3ec943f4a42d71cda7125696a963ac66 | [
"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 | 826 | lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import algebra.big_operators.basic
import algebra.star.basic
/-! # Big-operators lemmas about `star` algebraic operations
These results are kept separate from `algebra.st... |
d755a12bef3fa7ef66e4fe8f98e6c8d00259f1be | ea5678cc400c34ff95b661fa26d15024e27ea8cd | /mod_inv.lean | bc7cbb3af327c8bcd43ac2bd8086d43a09fac4b3 | [] | 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 | 16,937 | lean | import data.nat.basic data.int.basic data.nat.modeq tactic.norm_num data.nat.prime
namespace nat
def mod_inv_aux : ℕ → ℕ → ℤ
| 0 p := 0
| (succ m) p := have (p%succ m)<succ m:=mod_lt p (succ_pos m),
(↑(gcd (succ m) p) - (mod_inv_aux (p%succ m) (succ m)*↑p))/↑(succ m)
def mod_inv : ℕ → ℕ → ℕ := λ m p, int.nat_a... |
2f1111974621fe7b2733837cf015317bfc51a4e7 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/imp.lean | 0a9721f681d916a207d8ce2f160f7101b3808654 | [
"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 | 580 | lean | constant N : Type.{1}
constants a b c : N
constant f : forall {a b : N}, N → N
check f
check @f
check @f a
check @f a b
check @f a b c
definition l1 : N → N → N → N := @f
definition l2 : N → N → N := @f a
definition l3 : N → N := @f a b
definition l4 : N := @f a b c
constant g : forall ⦃a b : N⦄, N → N
check g
chec... |
068e5492bf5fdf110e2d957362e6a34b5581be26 | c3de33d4701e6113627153fe1103b255e752ed7d | /data/list/basic.lean | 6f002729c0b78d30277064acf263a4623cc08318 | [] | no_license | jroesch/library_dev | 77d2b246ff47ab05d55cb9706a37d3de97038388 | 4faa0a45c6aa7eee6e661113c2072b8840bff79b | refs/heads/master | 1,611,281,606,352 | 1,495,661,644,000 | 1,495,661,644,000 | 92,340,430 | 0 | 0 | null | 1,495,663,344,000 | 1,495,663,344,000 | null | UTF-8 | Lean | false | false | 12,574 | 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
Basic properties of lists.
-/
import logic.basic ..nat.basic
open function nat
namespace list
universe variable... |
2be537faa609f147265472bd33d7d6a7d06a9a3a | 94e33a31faa76775069b071adea97e86e218a8ee | /src/algebra/char_zero/quotient.lean | ef5a28864312750901bf15ae67a99a72ccbe4b74 | [
"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 | 2,834 | lean | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import algebra.char_zero
import group_theory.quotient_group
/-!
# Lemmas about quotients in characteristic zero
-/
variables {R : Type*} [division_ring R] [char_zero R] {... |
753edc8c381616ff18a9f4481ca2a2aa2ba88a44 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/linear_algebra/matrix/charpoly/basic.lean | 36ab7df851783340b03c011dde8d75da3f93afa9 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 4,468 | 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 linear_algebra.matrix.adjugate
import ring_theory.polynomial_algebra
import tactic.apply_fun
import tactic.squeeze
/-!
# Characteristic polynomials and the Ca... |
c7cc0e281dc9423170178b4d397928519c8efe24 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/fin_enum.lean | 0bea45a72c8287d4e1e81a078b12e9c75a607033 | [
"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 | 8,905 | lean | /-
Copyright (c) 2019 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import control.monad.basic
import data.fintype.basic
/-!
Type class for finitely enumerable types. The property is stronger
than `fintype` in that it assigns each element ... |
27a9fc9da24c1a1fac558e2346cea23d873500b8 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/apply_fail.lean | d8e2ab4d7aeae955ce95d96b40246df9dbf9163b | [
"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 | 59 | lean | example (a b : Prop) : a ∧ b :=
begin
apply or.inr
end
|
a4725e4fcacf68b7fd2a50ad326ccd522b89f5c0 | e2c1ee9c02c59b832eb48536755242ce5f9b2c3e | /src/t2.lean | c6fb5f796c762ec694e4601d7eabccc5f14a2d1f | [] | no_license | yairgueta/Lean | cb5bb16d81674e8a07f85c9dbeb56dc2f543d4eb | af8a4fa24f76edfdd0dd33f013db194e611e6a86 | refs/heads/master | 1,676,275,529,938 | 1,610,289,661,000 | 1,610,289,661,000 | 328,405,309 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,370 | lean | /- Yair Gueta : 208624908 : t2
Exercise 2
-/
open classical
variables p q r s : Prop
-- commutativity of ∧ and ∨
example : p ∨ q ↔ q ∨ p :=
iff.intro
(assume hpq : p ∨ q,
or.elim hpq
(assume hp : p,
show q ∨ p, from or.inr hp)
(assume hq : q,
show q ∨ p, from or.inl hq))
(ass... |
b23cec561bb9d12bdfef6c2698dddea2f8c97d11 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/field_theory/separable_degree.lean | bc897af345ed3f8895cb4e6e48b23db142567cbe | [
"Apache-2.0"
] | permissive | kbuzzard/mathlib | 2ff9e85dfe2a46f4b291927f983afec17e946eb8 | 58537299e922f9c77df76cb613910914a479c1f7 | refs/heads/master | 1,685,313,702,744 | 1,683,974,212,000 | 1,683,974,212,000 | 128,185,277 | 1 | 0 | null | 1,522,920,600,000 | 1,522,920,600,000 | null | UTF-8 | Lean | false | false | 5,328 | lean | /-
Copyright (c) 2021 Jakob Scholbach. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob Scholbach
-/
import algebra.algebra.basic
import algebra.char_p.exp_char
import field_theory.separable
/-!
# Separable degree
This file contains basics about the separable de... |
9538dc8d41f199f214c1a7c6f2c1d0504bc73ce1 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /tests/lean/run/forest_height.lean | 574a55714692a683219f4ea22a23186dc832c9fc | [
"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 | 4,292 | lean | import data.nat data.sum data.sigma data.bool
open nat sigma
inductive tree (A : Type) : Type :=
| node : A → forest A → tree A
with forest : Type :=
| nil : forest A
| cons : tree A → forest A → forest A
namespace manual
check tree.rec_on
definition tree.height {A : Type} (t : tree A) : nat :=
tree.rec_on t
(λ (... |
26b693b12ebe2dfb7ec24cbb537cf2bd040d33cf | c777c32c8e484e195053731103c5e52af26a25d1 | /src/group_theory/subgroup/zpowers.lean | 6de48373ae8b7f1a9219f9d92f01a774f5592050 | [
"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 | 6,676 | lean | /-
Copyright (c) 2020 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import group_theory.subgroup.basic
/-!
# Subgroups generated by an element
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a correspondin... |
d4464b5618dce4868bea72952ea6fd11fb4c77f6 | 271e26e338b0c14544a889c31c30b39c989f2e0f | /src/Init/Lean/Compiler/IR/Boxing.lean | 2e4d89a6219e76aabb7ad453fd120b53a342cbee | [
"Apache-2.0"
] | permissive | dgorokho/lean4 | 805f99b0b60c545b64ac34ab8237a8504f89d7d4 | e949a052bad59b1c7b54a82d24d516a656487d8a | refs/heads/master | 1,607,061,363,851 | 1,578,006,086,000 | 1,578,006,086,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 12,973 | 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... |
9e2bd5b1ae6bf4f2a81d2fdcacab02c379e3ef22 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/ring_theory/adjoin/fg.lean | 29c97f8ff97dd5efd3e97abf18b16d3b59fe7985 | [
"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 | 6,904 | 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 ... |
a71f4f2c2ad7b36e74482841caa4a69f7049d883 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /counterexamples/quadratic_form.lean | 50214d8f685dd29833d95a78eab6cecb6a9bfeac | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 2,018 | lean | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import linear_algebra.quadratic_form.basic
import algebra.char_p.two
import data.zmod.basic
/-!
# `quadratic_form R M` and `subtype bilin_form.is_symm` are distinct notion... |
1e6decad5b5bbc69ea18127a49bad450233bdfca | 0845ae2ca02071debcfd4ac24be871236c01784f | /library/init/data/random.lean | 6bb3dc0946d50e3f5942d4d3e40db062fe5a7935 | [
"Apache-2.0"
] | permissive | GaloisInc/lean4 | 74c267eb0e900bfaa23df8de86039483ecbd60b7 | 228ddd5fdcd98dd4e9c009f425284e86917938aa | refs/heads/master | 1,643,131,356,301 | 1,562,715,572,000 | 1,562,715,572,000 | 192,390,898 | 0 | 0 | null | 1,560,792,750,000 | 1,560,792,749,000 | null | UTF-8 | Lean | false | false | 3,958 | 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.io init.data.int
universes u
/-
Basic random number generator support based on the one
available on the Haskell library
-/
/- Interfac... |
b2e0864213e8c189559d391244380d852a4535b5 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/finset/lattice.lean | 60a235f53593dc510fd4f251dc9fa124c8300dfb | [
"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 | 72,384 | 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.finset.option
import data.finset.pi
import data.finset.prod
import data.multiset.lattice
import order.complete_lattice
import orde... |
3b7e5e5e506fdf557d90df13904ecd2c4b647e5c | 86f6f4f8d827a196a32bfc646234b73328aeb306 | /examples/sets_functions_and_relations/unnamed_705.lean | f8d89ed6187492afd6777549700a849b9ca90359 | [] | no_license | jamescheuk91/mathematics_in_lean | 09f1f87d2b0dce53464ff0cbe592c568ff59cf5e | 4452499264e2975bca2f42565c0925506ba5dda3 | refs/heads/master | 1,679,716,410,967 | 1,613,957,947,000 | 1,613,957,947,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 479 | lean | import data.set.lattice
import data.nat.prime
open set nat
-- BEGIN
def primes : set ℕ := {x | prime x}
example : (⋃ p ∈ primes, {x | p^2 ∣ x}) = {x | ∃ p ∈ primes, p^2 ∣ x} :=
by { ext, rw mem_bUnion_iff, refl }
example : (⋃ p ∈ primes, {x | p^2 ∣ x}) = {x | ∃ p ∈ primes, p^2 ∣ x} :=
by { ext, simp }
example : (⋂... |
ee4f830a92e9f7112f64a83e6fa72e06ef5bdc82 | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /stage0/src/Std/Data/PersistentHashSet.lean | e5de05e8caa7af5c337abc651fe9093d05472800 | [
"Apache-2.0"
] | permissive | collares/lean4 | 861a9269c4592bce49b71059e232ff0bfe4594cc | 52a4f535d853a2c7c7eea5fee8a4fa04c682c1ee | refs/heads/master | 1,691,419,031,324 | 1,618,678,138,000 | 1,618,678,138,000 | 358,989,750 | 0 | 0 | Apache-2.0 | 1,618,696,333,000 | 1,618,696,333,000 | null | UTF-8 | Lean | false | false | 1,676 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
import Std.Data.PersistentHashMap
namespace Std
universes u v
structure PersistentHashSet (α : Type u) [BEq α] [Hashable α] where
(set : PersistentHashMa... |
28808ddde486e965b23019e8773902df8d8bc232 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /hott/types/sum.hlean | 98aaa85ebcf240719e2a5dae6f487bc5503e99d0 | [
"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 | 15,592 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Floris van Doorn
Theorems about sums/coproducts/disjoint unions
-/
import .pi .equiv logic
open lift eq is_equiv equiv prod prod.ops is_trunc sigma bool
namespace sum
universe v... |
5ca263703972692b01f92239fb55f2b184161a5e | 5c7fe6c4a9d4079b5457ffa5f061797d42a1cd65 | /src/exercises/src_22_set_equality.lean | eefdfc8cb9c5d43b7017c4a5291ac5c82baf07de | [] | no_license | gihanmarasingha/mth1001_tutorial | 8e0817feeb96e7c1bb3bac49b63e3c9a3a329061 | bb277eebd5013766e1418365b91416b406275130 | refs/heads/master | 1,675,008,746,310 | 1,607,993,443,000 | 1,607,993,443,000 | 321,511,270 | 3 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,106 | lean | import data.set
import data.finset
import logic.basic
namespace mth1001
open set
namespace set_membership
-- We use `finset ℕ` to denote the type of finite sets of elements of `ℕ`.
def A := ({1, 2, 3, 4} : finset ℕ) -- This defines `A` to be `{1, 2, 3, 4}`.
def B := ({1, 3, 5, 6} : finset ℕ)
def C := ({5, 7, 9} : ... |
fe4907854080464eddbc8c68568c04c9715e1341 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/testing/slim_check/sampleable.lean | 51f6843770b7c6f6da84bd9c9723ee02a9cd4321 | [
"Apache-2.0"
] | permissive | agjftucker/mathlib | d634cd0d5256b6325e3c55bb7fb2403548371707 | 87fe50de17b00af533f72a102d0adefe4a2285e8 | refs/heads/master | 1,625,378,131,941 | 1,599,166,526,000 | 1,599,166,526,000 | 160,748,509 | 0 | 0 | Apache-2.0 | 1,544,141,789,000 | 1,544,141,789,000 | null | UTF-8 | Lean | false | false | 10,720 | lean | /-
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author(s): Simon Hudon
-/
import data.lazy_list
import data.lazy_list2
import data.tree
import tactic.linarith
import testing.slim_check.gen
/-!
# `sampleable` Class
This class permits the creat... |
81a08934fa06f3f82e51a129e7c6b5cd8ec61f65 | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/data/real/hyperreal.lean | 4b097cf4d58c2b6e48c487b2354c13b849fd43c8 | [
"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 | 36,545 | lean | /-
Copyright (c) 2019 Abhimanyu Pallavi Sudhir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Abhimanyu Pallavi Sudhir
Construction of the hyperreal numbers as an ultraproduct of real sequences.
-/
import data.real.basic algebra.field order.filter.filter_product anal... |
ce6e85c8f693b4c48b3bd07730eb3deb59c52b9e | bdb33f8b7ea65f7705fc342a178508e2722eb851 | /data/int/order.lean | afd80499a87825d088e96dffe5dd44830a58dd98 | [
"Apache-2.0"
] | permissive | rwbarton/mathlib | 939ae09bf8d6eb1331fc2f7e067d39567e10e33d | c13c5ea701bb1eec057e0a242d9f480a079105e9 | refs/heads/master | 1,584,015,335,862 | 1,524,142,167,000 | 1,524,142,167,000 | 130,614,171 | 0 | 0 | Apache-2.0 | 1,548,902,667,000 | 1,524,437,371,000 | Lean | UTF-8 | Lean | false | false | 7,722 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
The order relation on the integers.
-/
import data.int.basic
namespace int
lemma of_nat_le_of_nat_of_le {n m : ℕ} (h : n ≤ m) : of_nat n ≤ of_nat m :=
coe_nat_le_coe_na... |
396b9dcd64e3327225cbb4df806fcad2d8939319 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/computability/encoding.lean | 1b481befec16b7860c6320e87b33eb78b8c2a035 | [] | 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 | 5,516 | lean | /-
Copyright (c) 2020 Pim Spelier, Daan van Gent. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pim Spelier, Daan van Gent.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.fintype.basic
import Mathlib.data.num.lemmas
import Mathlib.t... |
637c411771b6090f9281c98a7716dbbf7e2fa121 | fe84e287c662151bb313504482b218a503b972f3 | /src/exercises/tactics_list.lean | f4f81b39bd50776b3b0aae15f4f88eb1a9574f3b | [] | 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 | 11,631 | lean | import tactic.interactive
import tactic.monotonicity
import data.finset
/-
To do: also document derive_handlers
-/
#check tactic.interactive.ac_mono
-- Deduce inequalities using known monotonicity properties of functions
#check tactic.interactive.abstract
-- Tactical to record the argument used as a lemma, as well as... |
0a12a5fec96f3b329baf1894a888dc2054cb213b | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/linear_algebra/matrix/absolute_value.lean | 38a7a0881fffeabfcda3c6d97b6159242a16b8f1 | [
"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 | 3,092 | lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import data.int.absolute_value
import linear_algebra.matrix.determinant
/-!
# Absolute values and matrices
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to thi... |
60c5ff25b0246e691e8c608ff535e7d9958305d2 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /stage0/src/Init/System/Platform.lean | 64c5d4f8cb4293ea7261bca2125433f45055c8b1 | [
"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 | 616 | lean | /-
Copyright (c) 2018 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import Init.Data.Nat.Basic
namespace System
namespace Platform
@[extern "lean_system_platform_windows"] constant getIsWindows : Unit → Bool
@[exte... |
d94656589cec125e609c474869bb7a708ca823c9 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/topology/nhds_set.lean | 9a215090a215ba50139f5d95ee2039b85a7865e7 | [
"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 | 3,099 | lean | /-
Copyright (c) 2022 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Patrick Massot
-/
import topology.basic
/-!
# Neighborhoods of a set
In this file we define the filter `𝓝ˢ s` or `nhds_set s` consisting of all neighborhoods of a... |
d17d476cb6175e9344c7b88aa6ba199342a28192 | e2c1ee9c02c59b832eb48536755242ce5f9b2c3e | /src/t9.lean | 3039f9f79161235ccbcb7dcb50f0c1323f8922e9 | [] | no_license | yairgueta/Lean | cb5bb16d81674e8a07f85c9dbeb56dc2f543d4eb | af8a4fa24f76edfdd0dd33f013db194e611e6a86 | refs/heads/master | 1,676,275,529,938 | 1,610,289,661,000 | 1,610,289,661,000 | 328,405,309 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,431 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
-/
import data.finset.basic
/-!
# The powerset of a finset
-/
namespace finset
open multiset
variables {α : Type*}
/-! ### powerset -/
section powerset
/-- When `s` ... |
11c6a602fe64d51bcbad3e9ceb6ec0028f6abd71 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/lake/Lake/Util/Cli.lean | 9c05b8580777a32706217f086b18fe608972d7e8 | [
"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 | 5,794 | lean | /-
Copyright (c) 2021 Mac Malone. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mac Malone
-/
namespace Lake
/-!
Defines the abstract CLI interface for Lake.
-/
/-! # Types -/
def ArgList := List String
@[inline] def ArgList.mk (args : List String) : ArgList :=
... |
e26d66a568f66291355fb52d7e9b3a2a6ba48e65 | 5e3548e65f2c037cb94cd5524c90c623fbd6d46a | /src_icannos_totilas/aops/2004-IMO_Shortlist-A2.lean | 4d4e437bb85b3dfd6526032163d20150932500bc | [] | no_license | ahayat16/lean_exos | d4f08c30adb601a06511a71b5ffb4d22d12ef77f | 682f2552d5b04a8c8eb9e4ab15f875a91b03845c | refs/heads/main | 1,693,101,073,585 | 1,636,479,336,000 | 1,636,479,336,000 | 415,000,441 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 593 | lean | import data.real.basic
import data.polynomial.basic
import data.polynomial.eval
import topology.continuous_function.bounded
-- A sequence of real numbers $\{a_n\}_n$ is called a bs sequence if $a_n = |a_{n+1} - a_{n+2}|$, for all $n\geq 0$. Prove that a bs sequence is bounded if and only if the function $f$ given by $... |
85930b951c25b41cc0d8a8ad283682fcf224ca82 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/data/quot.lean | 25f6b4d4ed8049f294c2c4b6648352c21d0e0294 | [
"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 | 19,444 | 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 logic.relator
/-!
# Quotients -- extends the core library
-/
variables {α : Sort*} {β : Sort*}
namespace setoid
lemma ext {α : Sort*} :
∀{s t : setoid α}... |
8c22758015497a37fc975550b6cc510cc70856ff | 2a70b774d16dbdf5a533432ee0ebab6838df0948 | /_target/deps/mathlib/src/ring_theory/noetherian.lean | 81d1c0f054b7f17a64fa69ec63efc3e3f1ad5484 | [
"Apache-2.0"
] | permissive | hjvromen/lewis | 40b035973df7c77ebf927afab7878c76d05ff758 | 105b675f73630f028ad5d890897a51b3c1146fb0 | refs/heads/master | 1,677,944,636,343 | 1,676,555,301,000 | 1,676,555,301,000 | 327,553,599 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 27,637 | 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 algebraic_geometry.prime_spectrum
import data.multiset.finset_ops
import linear_algebra.linear_independent
import order.order_... |
faca5019888316b64261c7656d77306843e1a67f | 94e33a31faa76775069b071adea97e86e218a8ee | /src/group_theory/group_action/conj_act.lean | b371a48913d10c53916285e84d12ef3ff04110e2 | [
"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 | 7,599 | lean | /-
Copyright (c) 2021 . All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import group_theory.group_action.basic
import group_theory.subgroup.basic
import algebra.group_ring_action
/-!
# Conjugation action of a group on itself
This file defines the conjug... |
e35364a1b2b68bd55d129cc7e86226487e1819a2 | 2f8bf12144551bc7d8087a6320990c4621741f3d | /library/init/lean/compiler/ir/default.lean | b505d472900ef211f7ca3273315f6b7b4e997157 | [
"Apache-2.0"
] | permissive | jesse-michael-han/lean4 | eb63a12960e69823749edceb4f23fd33fa2253ce | fa16920a6a7700cabc567aa629ce4ae2478a2f40 | refs/heads/master | 1,589,935,810,594 | 1,557,177,860,000 | 1,557,177,860,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,081 | 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.lean.compiler.ir.basic
import init.lean.compiler.ir.format
import init.lean.compiler.ir.pushproj
import init.lean.compiler.ir.elimdead
i... |
b56b548660b18e0679b430a314e9d76c6921c177 | 592ee40978ac7604005a4e0d35bbc4b467389241 | /Library/generated/mathscheme-lean/LeftShelfSig.lean | 761baf5c967d7c5f0d952ca51cada48c60612b59 | [] | no_license | ysharoda/Deriving-Definitions | 3e149e6641fae440badd35ac110a0bd705a49ad2 | dfecb27572022de3d4aa702cae8db19957523a59 | refs/heads/master | 1,679,127,857,700 | 1,615,939,007,000 | 1,615,939,007,000 | 229,785,731 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,869 | lean | import init.data.nat.basic
import init.data.fin.basic
import data.vector
import .Prelude
open Staged
open nat
open fin
open vector
section LeftShelfSig
structure LeftShelfSig (A : Type) : Type :=
(linv : (A → (A → A)))
open LeftShelfSig
structure Sig (AS : Type) : Type :=
(linvS : (AS → (... |
776df7441d324378fdbb06b1b50c2fe8fdf1d2f1 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/char_p/local_ring.lean | d189ae2f98cf96aef5b2349d1bee5960fae24a2d | [
"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 | 2,937 | lean | /-
Copyright (c) 2022 Jon Eugster. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jon Eugster
-/
import algebra.char_p.basic
import ring_theory.ideal.local_ring
import algebra.is_prime_pow
import data.nat.factorization.basic
/-!
# Characteristics of local rings
## Ma... |
30e224e64fb1d0d065ec57a590bdb8937b356bd2 | 82b86ba2ae0d5aed0f01f49c46db5afec0eb2bd7 | /src/Lean/Compiler/InitAttr.lean | dff0b95ae9c7abfcb3bc507ee9f2af8e66db4dbe | [
"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 | 4,403 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Environment
import Lean.Attributes
namespace Lean
private def getIOTypeArg : Expr → Option Expr
| Expr.app (Expr.const `IO _ _) arg _ => som... |
1cd8573e7bcaba47ec7b12fb6375c1385749ea5c | a7602958ab456501ff85db8cf5553f7bcab201d7 | /Notes/Logic_and_Proof/Chapter4/4.13.lean | bf0628338456429831728f674d31cb1bc0671e2a | [] | 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 | 693 | lean | -- So far we've seen things like:
-- - How to prove (¬ B ∧ A) from the premise (A ∧ ¬ B)
-- - How to apply one hypothesis to another that contains an implication
--
-- What we haven't quite seen yet is how to do an implication introduction
-- ourselves. We can do this with the "assume" or lambda syntax. Consider
-... |
4b7cb79c9f4c5d7e5a295510f77f953e7102d988 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/data/finsupp/pointwise.lean | 62d95d1c5e332924cdfd7747dd7a4180fb153626 | [
"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 | 2,294 | 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 data.finsupp.basic
/-!
# The pointwise product on `finsupp`.
TODO per issue #1864:
We intend to remove the convolution product on finsupp, and define
it only... |
9b79b1e42b75e3b482d58f145299106c380711fc | 968e2f50b755d3048175f176376eff7139e9df70 | /examples/prop_logic_lean_summary/unnamed_468.lean | 9a98fa593187cef13cbab89d74058e273510f763 | [] | no_license | gihanmarasingha/mth1001_sphinx | 190a003269ba5e54717b448302a27ca26e31d491 | 05126586cbf5786e521be1ea2ef5b4ba3c44e74a | refs/heads/master | 1,672,913,933,677 | 1,604,516,583,000 | 1,604,516,583,000 | 309,245,750 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 277 | lean | variables p q : Prop
-- BEGIN
example (h₁ : p → q) (h₂ : q → p) : p ↔ q :=
begin
split, -- This replaces the goal `p ↔ q` with 1. p → q and 2. q → p.
{ exact h₁, }, -- Closes the goal `p → q`.
{ exact h₂, }, -- Closes the goal `q → p`.
end
-- END |
3f7f7d94c41ab494d2b7e6690a1fc6dc21428127 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/topology/metric_space/emetric_space_auto.lean | 15e62c23995e9b1405c544084e30c54c47510d8a | [] | 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 | 34,991 | lean | /-
Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.real.ennreal
i... |
c95e512b220eee5e2421e872fd1529308dc43672 | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/algebra/free.lean | 1bb7eee7a7bbe131116f5ac411958ac8be6dcdac | [
"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 | 17,097 | lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
1. Free magma of a type (traversable, decidable equality).
2. Free semigroup of a magma.
3. Free semigroup of a type (traversable, decidable equality).
4. Free monoid of a semigr... |
a43a96ee4b41b60caabd2b2e17b61d5345104f8a | e61a235b8468b03aee0120bf26ec615c045005d2 | /stage0/src/Init/Lean/Elab/Level.lean | 23cba79426d7539c635ed1283f4be6ea242701a1 | [
"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 | 2,676 | 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.Lean.Meta.LevelDefEq
import Init.Lean.Elab.Exception
import Init.Lean.Elab.Log
namespace Lean
namespace Elab
namespace Level
structure... |
ebf2765762a6af6c45e7f6f8f362ca56f6616d82 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/super.lean | 0226943fa2c11547a00dbcd8ad8656534dc5ce31 | [
"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 | 75 | lean | constant f : nat → nat
notation a `²` := f a
variable a : nat
check a²
|
029a4c8818aeb213150635584a6afed2511c5d89 | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /src/Lean/Meta/Basic.lean | e40718bd116971aece494bedecfadde454090372 | [
"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 | 39,636 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Data.LOption
import Lean.Environment
import Lean.Class
import Lean.ReducibilityAttrs
import Lean.Util.Trace
import Lean.Util.RecDepth
import Lea... |
5ad13426c41ff8cfd700966f05177ae6a48fa60d | 3dc4623269159d02a444fe898d33e8c7e7e9461b | /.github/workflows/geo/src/comm_ring_sieves.lean | 01d24cd765101d9936959a6c039b54d34452f18e | [] | no_license | Or7ando/lean | cc003e6c41048eae7c34aa6bada51c9e9add9e66 | d41169cf4e416a0d42092fb6bdc14131cee9dd15 | refs/heads/master | 1,650,600,589,722 | 1,587,262,906,000 | 1,587,262,906,000 | 255,387,160 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 594 | lean |
import category_theory.comma
import category_theory.limits.shapes.finite_limits
import category_theory.yoneda
import order.complete_lattice
import data.set.lattice
import .comma
import algebra.category.CommRing
import category_theory.types
universes u
local notation `Ring` := CommRing.{u}
local notation `Set` := ... |
a68ff64d80fa47d799fe6a9a371f34f6aac7c68f | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/combinatorics/set_family/kleitman.lean | 9c8e39d497dcfd0223c77c62b2a7c2fabcfb9721 | [
"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 | 3,768 | lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import combinatorics.set_family.harris_kleitman
import combinatorics.set_family.intersecting
/-!
# Kleitman's bound on the size of intersecting families
An intersecting... |
f42c71cabe5cb50d227c1e6be4e8965d3b8457fb | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/monoidal/discrete.lean | 45a90c545cf464a73aba5479569a1ed4c5b1d12c | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 2,349 | 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 algebra.hom.group
import category_theory.discrete_category
import category_theory.monoidal.natural_transformation
/-!
# Monoids as discrete monoidal categorie... |
53c777ff0bfd939e9a6d2c237ff389a04635392a | 947b78d97130d56365ae2ec264df196ce769371a | /tests/lean/run/evalconst.lean | 487d3d0d566f5d935715816bc95f269c82290806 | [
"Apache-2.0"
] | permissive | shyamalschandra/lean4 | 27044812be8698f0c79147615b1d5090b9f4b037 | 6e7a883b21eaf62831e8111b251dc9b18f40e604 | refs/heads/master | 1,671,417,126,371 | 1,601,859,995,000 | 1,601,860,020,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 345 | lean | import Lean
new_frontend
open Lean
def x := 10
unsafe def tst : CoreM Unit := do
let env ← getEnv;
IO.println $ env.evalConst Nat `x;
pure ()
#eval tst
def f (x : Nat) := x + 1
unsafe def tst2 : CoreM Unit := do
let env ← getEnv;
let f ← liftIO $ IO.ofExcept $ env.evalConst (Nat → Nat) `f;
IO.println $ (f 10);
pur... |
4d33fcb6fd00b89e777219d0633414229cd2697c | ff5230333a701471f46c57e8c115a073ebaaa448 | /tests/lean/float.lean | e55893427c8457a6f5ae9fb66d836cec78485bf8 | [
"Apache-2.0"
] | permissive | stanford-cs242/lean | f81721d2b5d00bc175f2e58c57b710d465e6c858 | 7bd861261f4a37326dcf8d7a17f1f1f330e4548c | refs/heads/master | 1,600,957,431,849 | 1,576,465,093,000 | 1,576,465,093,000 | 225,779,423 | 0 | 3 | Apache-2.0 | 1,575,433,936,000 | 1,575,433,935,000 | null | UTF-8 | Lean | false | false | 3,129 | lean |
open native native.float
meta def close_enough (a b : float) : bool := abs (a - b) < 10 * epsilon
local infixr ` ≃ `:2 := close_enough
meta def floats := [0,1,-1,pi,epsilon, 1/epsilon, pi / 2, pi / 4, -pi]
meta def floats2 := list.bind floats (λ x, floats.map (λ y, (x,y)))
meta def check1 (prop : float → bool) :=... |
e6adebcc372f7bcc424ac5715e27a948cf1f2f81 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/asymptotics/asymptotics.lean | 77c2586c1dc1dabef01105bbd72682f51963f087 | [
"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 | 73,755 | lean | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Yury Kudryashov
-/
import analysis.normed.group.infinite_sum
import analysis.normed_space.basic
import topology.algebra.order.liminf_limsup
import topology.local_homeomor... |
5b335f5e966882d1275c536a8601e43fee3cdb9d | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /13_More_Tactics.org.5.lean | 04e1f0e078d78eb18047c365e426004749c66e2e | [] | no_license | cjmazey/lean-tutorial | ba559a49f82aa6c5848b9bf17b7389bf7f4ba645 | 381f61c9fcac56d01d959ae0fa6e376f2c4e3b34 | refs/heads/master | 1,610,286,098,832 | 1,447,124,923,000 | 1,447,124,923,000 | 43,082,433 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 514 | lean | import standard
variables p q : Prop
example (Hp : p) (Hq : q) : p ∧ q :=
by split; exact Hp; exact Hq
example (Hp : p) (Hq : q) : p ∧ q :=
by split; repeat assumption
example (Hp : p) : p ∨ q :=
by constructor; assumption
example (Hq : q) : p ∨ q :=
by constructor; assumption
example (Hp : p) : p ∨ q :=
by const... |
71314a45aa5d9e7d82aaaaf05b55cba1f5bb3bce | c777c32c8e484e195053731103c5e52af26a25d1 | /src/analysis/convex/measure.lean | e2366037f71342268a166a669271188120b7c4a7 | [
"Apache-2.0"
] | permissive | kbuzzard/mathlib | 2ff9e85dfe2a46f4b291927f983afec17e946eb8 | 58537299e922f9c77df76cb613910914a479c1f7 | refs/heads/master | 1,685,313,702,744 | 1,683,974,212,000 | 1,683,974,212,000 | 128,185,277 | 1 | 0 | null | 1,522,920,600,000 | 1,522,920,600,000 | null | UTF-8 | Lean | false | false | 4,354 | lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import analysis.convex.topology
import analysis.normed_space.add_torsor_bases
import measure_theory.measure.haar_lebesgue
/-!
# Convex sets are null-measurable
Le... |
9d81a5d81e3bbad9bfdca49e55f6e8fd49585ae7 | 2a70b774d16dbdf5a533432ee0ebab6838df0948 | /_target/deps/mathlib/src/topology/basic.lean | 0966e88ac77e23a1f71043ae409543cf87375fa5 | [
"Apache-2.0"
] | permissive | hjvromen/lewis | 40b035973df7c77ebf927afab7878c76d05ff758 | 105b675f73630f028ad5d890897a51b3c1146fb0 | refs/heads/master | 1,677,944,636,343 | 1,676,555,301,000 | 1,676,555,301,000 | 327,553,599 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 51,991 | 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, Jeremy Avigad
-/
import order.filter.ultrafilter
import order.filter.partial
noncomputable theory
/-!
# Basic theory of topological spaces.
The main ... |
580f7b6ac028d71d46f5fd2d29f44d7968510acf | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/simpZetaFalse.lean | 8e26af76e6027543fa3d0a5546452fa732c0c7ea | [
"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 | 894 | lean | constant f : Nat → Nat
axiom f_eq (x : Nat) : f (f x) = x
theorem ex1 (x : Nat) (h : f (f x) = x) : (let y := x*x; if f (f x) = x then 1 else y + 1) = 1 := by
simp (config := { zeta := false }) only [h]
trace_state
simp
#print ex1 -- uses let_congr
theorem ex2 (x z : Nat) (h : f (f x) = x) (h' : z = x) : (let ... |
7cb5b545b9d14cfbd9f493750734a8b86b4b6a47 | 976d2334b51721ddc405deb2e1754016d454286e | /lean_at_mc2020_source/infinitude_of_primes.lean | c838359c704013b2b6e012746bf0a85f3cb295ca | [] | no_license | kbuzzard/lean-at-MC2020 | 11bb6ac9ec38a6caace9d5d9a1705d6794d9f477 | 1f7ca65a7ba5cc17eb49f525c02dc6b0e65d6543 | refs/heads/master | 1,668,496,422,317 | 1,594,131,838,000 | 1,594,131,838,000 | 277,877,735 | 0 | 0 | null | 1,594,142,006,000 | 1,594,142,005,000 | null | UTF-8 | Lean | false | false | 1,885 | lean | import tactic
import data.nat.prime
open nat
#check @nat.dvd_sub
/-
dvd_sub : ∀ {k m n : ℕ}, n ≤ m → k ∣ m → k ∣ n → k ∣ m - n
-/
#check @nat.le.intro
#check nat.le.dest
theorem dvd_sub2 (p a b : ℕ) : (p ∣ a) → (p ∣ a + b) → (p ∣ b) :=
begin
have H : a ≤ a + b, {simp,},
have K : b = (a + b) - a, {simp,},
intr... |
93c80bfbbe7364e852ad408e5c8defe86acfcdfc | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/pempty_instances.lean | 4e43b22d9cb6dcc4968dd6dd080fb35ddf7cdfda | [
"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 | 526 | lean | /-
Copyright (c) 2021 Julian Kuelshammer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Kuelshammer
-/
import algebra.group.defs
import algebra.group.to_additive
/-!
# Instances on pempty
This file collects facts about algebraic structures on the (universe-p... |
5946089efcdeed264b74f4cc6d6fff17ec6d65d1 | 95dcf8dea2baf2b4b0a60d438f27c35ae3dd3990 | /src/group_theory/free_group.lean | 1bbe52dfcd435864391eba08f13b4373ced54bed | [
"Apache-2.0"
] | permissive | uniformity1/mathlib | 829341bad9dfa6d6be9adaacb8086a8a492e85a4 | dd0e9bd8f2e5ec267f68e72336f6973311909105 | refs/heads/master | 1,588,592,015,670 | 1,554,219,842,000 | 1,554,219,842,000 | 179,110,702 | 0 | 0 | Apache-2.0 | 1,554,220,076,000 | 1,554,220,076,000 | null | UTF-8 | Lean | false | false | 30,783 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
Free groups as a quotient over the reduction relation `a * x * x⁻¹ * b = a * b`.
First we introduce the one step reduction relation
`free_group.red.step`: w * x * x⁻¹ * v ~... |
d3e8999dad6d4e2b44c8cd8b74bb5d528c4b6c5c | ec5a7ae10c533e1b1f4b0bc7713e91ecf829a3eb | /ijcar16/examples/cc2.lean | 9c0c79a8498eec280c2489dd01c815a7e17417e2 | [
"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 | 901 | lean | /-
Example/test file for the congruence closure procedure described in the paper:
"Congruence Closure for Intensional Type Theory"
Daniel Selsam and Leonardo de Moura
The tactic `by blast` has been configured in this file to use just
the congruence closure procedure using the command
set_option blast.strategy... |
d7773bb6ee1fcfc431afc35426a31c9e6307db2f | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/analysis/normed_space/bounded_linear_maps.lean | af8cbd4355ee548b8a712805c74dce78452fe194 | [
"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 | 26,040 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
-/
import analysis.normed_space.multilinear
import analysis.normed_space.units
import analysis.asymptotics.asymptotics
/-!
# Bounded linear maps
This f... |
fef4e990b8e3167682f17d7969e62ef02687d1b3 | 968e2f50b755d3048175f176376eff7139e9df70 | /examples/prop_logic_theory/unnamed_1022.lean | 8609e1e9593f1f634d780ad9e602db73f10abfb7 | [] | no_license | gihanmarasingha/mth1001_sphinx | 190a003269ba5e54717b448302a27ca26e31d491 | 05126586cbf5786e521be1ea2ef5b4ba3c44e74a | refs/heads/master | 1,672,913,933,677 | 1,604,516,583,000 | 1,604,516,583,000 | 309,245,750 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 609 | lean | variables p q r : Prop
-- BEGIN
theorem imp_trans1 : (p → q) → (q → r) → (p → r) :=
begin
assume h₁ : p → q, -- Assume `h₁ : p → q`. By implication introduction, it suffices to prove `(q → r) → (p → r)`.
assume h₂ : q → r, -- Assume `h₂ : q → r`. By implication introduction, it suffices to prove `p → r`.
assume... |
fa8bd798872f13a91c11ac9a34e3b97c20a02224 | 437dc96105f48409c3981d46fb48e57c9ac3a3e4 | /src/algebra/char_p.lean | 2831ee2bad2f2ee1838d5f8a559b07725e45d4d8 | [
"Apache-2.0"
] | permissive | dan-c-k/mathlib | 08efec79bd7481ee6da9cc44c24a653bff4fbe0d | 96efc220f6225bc7a5ed8349900391a33a38cc56 | refs/heads/master | 1,658,082,847,093 | 1,589,013,201,000 | 1,589,013,201,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,755 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Kenny Lau, Joey van Langen, Casper Putz
Characteristic of semirings.
-/
import data.fintype.basic
import data.nat.choose
import algebra.module
universes u v
/-- The generator of the kern... |
011f23b891c2537638a129ec26da2f3278ced292 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/ring_theory/witt_vector/basic_auto.lean | 53fc485e43a001b58f92c6c66761950e8ee3cde1 | [] | 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 | 7,775 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.mv_polynomial.counit
import Mathlib.data.mv_polynomial.invertible
imp... |
d01bb12d8fc9358755265ae8d6815b52c973c15b | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/rat/denumerable_auto.lean | 55c856253bb1b36bfb7e6da30cc394439b6e8455 | [] | 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 | 940 | lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Chris Hughes
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.rat.default
import Mathlib.set_theory.cardinal
import Mathlib.PostPort
namespace Mathlib
... |
64599ddbb9d86e967ccda9e400c9331e9846e771 | 22e97a5d648fc451e25a06c668dc03ac7ed7bc25 | /src/geometry/manifold/real_instances.lean | f141af8e29c3f0e8d90c79110a3bce079a7797b2 | [
"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 | 14,167 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import geometry.manifold.smooth_manifold_with_corners
import linear_algebra.finite_dimensional
/-!
# Constructing examples of manifolds over ℝ
We introduce th... |
543c64a80b36c04722051a4c06e4a01962787283 | 680b0d1592ce164979dab866b232f6fa743f2cc8 | /hott/init/path.hlean | f3b3be710e5a19b381a3859e7ddb40bc1ab5fa9e | [
"Apache-2.0"
] | permissive | syohex/lean | 657428ab520f8277fc18cf04bea2ad200dbae782 | 081ad1212b686780f3ff8a6d0e5f8a1d29a7d8bc | refs/heads/master | 1,611,274,838,635 | 1,452,668,188,000 | 1,452,668,188,000 | 49,562,028 | 0 | 0 | null | 1,452,675,604,000 | 1,452,675,602,000 | null | UTF-8 | Lean | false | false | 25,800 | hlean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Jakob von Raumer, Floris van Doorn
Ported from Coq HoTT
-/
prelude
import .function .tactic
open function eq
/- Path equality -/
namespace eq
variables {A ... |
969d83cb72107bf39eb6bca059c6e52ae1375a5f | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/linear_algebra/clifford_algebra/equivs.lean | 8b9c752965015e83ed779433b392683366367cb5 | [
"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 | 13,479 | lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import algebra.quaternion_basis
import data.complex.module
import linear_algebra.clifford_algebra.conjugation
/-!
# Other constructions isomorphic to Clifford Algebras
Th... |
4cd96c4735a1de469a26b9a052f61b314755866b | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/list/func.lean | b43eda69369a4068ef5ff01c831cc51c1d7164e7 | [
"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 | 11,246 | lean | /-
Copyright (c) 2019 Seul Baek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Seul Baek
-/
import data.nat.order.basic
/-!
# Lists as Functions
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
Definition... |
a943ce6acd6523e5ab6570a57334634e24e24762 | b2fe74b11b57d362c13326bc5651244f111fa6f4 | /src/category_theory/limits/shapes/normal_mono.lean | f1053026aaec4d3b252478f4a40fdb04bc9d142c | [
"Apache-2.0"
] | permissive | midfield/mathlib | c4db5fa898b5ac8f2f80ae0d00c95eb6f745f4c7 | 775edc615ecec631d65b6180dbcc7bc26c3abc26 | refs/heads/master | 1,675,330,551,921 | 1,608,304,514,000 | 1,608,304,514,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,293 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Bhavik Mehta
-/
import category_theory.limits.shapes.regular_mono
import category_theory.limits.shapes.kernels
/-!
# Definitions and basic properties of normal monomor... |
ed7dac2a89c92a0ac8467f2d8131b797c52b7275 | 92e157ec9825b5e4597a6d715a8928703bc8e3b2 | /src/mywork/sep_3_2021.lean | 89c6fc5a8b31128af71911107b67c8cd6444708a | [] | no_license | exb3dg/cs2120f21 | 9e566bc508762573c023d3e70f83cb839c199ec8 | 319b8bf0d63bf96437bf17970ce0198d0b3525cd | refs/heads/main | 1,692,970,909,568 | 1,634,584,540,000 | 1,634,584,540,000 | 399,947,025 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 743 | lean | /-
prove equality is symmetric using reflextivity and substitution
-/
theorem eq.symm :
∀ (T : Type ) (x y : T), x = y → y = x :=
begin
assume (T : Type),
assume (x y : T),
assume (e : x = y),
rw e,
end
/-
Theorem: Equallity is symmetric. In other words
∀ (T : Type ) (x y : T), x = y → y = x :=... |
b5463e9d4806b771b76a12121992ea58cf94b24f | 437dc96105f48409c3981d46fb48e57c9ac3a3e4 | /src/data/complex/exponential.lean | b16c8bbb4fa624b34371738d24a517a8cbc1d017 | [
"Apache-2.0"
] | permissive | dan-c-k/mathlib | 08efec79bd7481ee6da9cc44c24a653bff4fbe0d | 96efc220f6225bc7a5ed8349900391a33a38cc56 | refs/heads/master | 1,658,082,847,093 | 1,589,013,201,000 | 1,589,013,201,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 47,763 | 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
local notation `abs'` := _root_.abs
open is_absolute_value
open_locale... |
5b47afa2a8aa4bebc8cb4deabfcf05fdedab02e5 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/set_theory/schroeder_bernstein.lean | 181c1c4b39b685e30d4d9d70d17e1565f3ab4a93 | [
"Apache-2.0"
] | permissive | dupuisf/mathlib | 62de4ec6544bf3b79086afd27b6529acfaf2c1bb | 8582b06b0a5d06c33ee07d0bdf7c646cae22cf36 | refs/heads/master | 1,669,494,854,016 | 1,595,692,409,000 | 1,595,692,409,000 | 272,046,630 | 0 | 0 | Apache-2.0 | 1,592,066,143,000 | 1,592,066,142,000 | null | UTF-8 | Lean | false | false | 5,062 | 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
The Schröder-Bernstein theorem, and well ordering of cardinals.
-/
import order.fixed_points
import order.zorn
open set classical
open_locale classical... |
da4c99586f5a7849845e518e124e95cd374ea8ef | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /tests/lean/run/eval_unboxed_const.lean | 8f44cac2e8721554237ccd11a6e741b927e10919 | [
"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 | 458 | lean | import Lean
open Lean
def c1 : Bool := true
unsafe def tst1 : CoreM Unit := do
env ← getEnv;
let v := env.evalConst Bool `c1;
IO.println v
#eval tst1 -- outputs incorrect value (ok false). Reason: the unboxed value `true` is `1`, but the boxed `false` value is also `1`.
def c2 : Bool := false
unsafe def tst2 : Cor... |
50119435c718597ce242fa6def1869d07a030faa | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/big_operators/fin.lean | 4182c72eeeb8ea51afbdbe10ea014fd6d1eda3ab | [
"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 | 18,955 | lean | /-
Copyright (c) 2020 Yury Kudryashov, Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Anne Baanen
-/
import data.fintype.big_operators
import data.fintype.fin
import data.list.fin_range
import logic.equiv.fin
/-!
# Big operators and `fin`... |
a676cca8c4bcc06a3cc1453af091f70c807d528e | 7a468d7c7c0949ab8b191bb62ff6d4d2af9f3917 | /test/de_morgans.lean | cc03fc5e868b1fb296d8365fdb781ca85c84248a | [
"Apache-2.0"
] | permissive | seanpm2001/LeanProver_SMT2_Interface | c15b2fba021c406d965655b182eef54a14121b82 | 7ff0ce248b68ea4db2a2d4966a97b5786da05ed7 | refs/heads/master | 1,688,599,220,366 | 1,547,825,187,000 | 1,547,825,187,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 249 | lean | import smt2
lemma negation_of_conj :
forall (P Q : Prop),
not (P ∧ Q) ↔ not P ∨ not Q :=
by intros; z3 "d1.log"
lemma negation_of_disj :
forall (P Q : Prop),
¬ (P ∨ Q) ↔ ¬ P ∧ ¬ Q :=
begin
intros, z3
end
|
6ef84427d2f2f3b1890d2bc76b4cfaf9add988fe | e30ff3aabdac29f8ea40ad76887544d0f9be9018 | /ircbot/parsing.lean | 4fa1b4665624e4a59c71a94c970c09a95fa6d7db | [] | 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 | 4,566 | lean | import data.buffer.parser
import ircbot.types ircbot.datetime
namespace string
def lf := char.of_nat 10
def cr := char.of_nat 13
def trim_sym (c : char) (s : string) := if s.back = c then string.pop_back s else s
def trim_nl := trim_sym cr ∘ trim_sym lf
end string
namespace char
def is_hex (ch : char) : b... |
fb9e0663d42c66a9201a5f6ca203a8a5c61d20a1 | ad0c7d243dc1bd563419e2767ed42fb323d7beea | /algebra/gcd_domain.lean | 3f75176265a2754c8d13f75da2952c0f189fc690 | [
"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 | 13,832 | 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
GCD domain and integral domains with normalization functions
TODO: abstract the domains to to semi domains (i.e. domains on semirings) to include ℕ and... |
70f0d69dcd9fa3455126d8b2aba9b34bff73b383 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/algebra/group/pi.lean | 479d647c836dea99bacd795e92091ad3aea4e966 | [
"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 | 5,844 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot
-/
import algebra.ordered_group
import tactic.pi_instances
/-!
# Pi instances for groups and monoids
This file defines instances for group, monoid, semigroup ... |
409d5216b6806c3943af319908e082c3acf58634 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/algebra/continued_fractions/continuants_recurrence.lean | 2e683fe46ef685c334b3a708fe3bd7302b39deda | [
"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 | 3,679 | lean | /-
Copyright (c) 2019 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import algebra.continued_fractions.translations
/-!
# Recurrence Lemmas for the `continuants` Function of Continued Fractions.
## Summary
Given a generalized co... |
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