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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
f728201b9d339971acce95301eb499b6fa0bdc3d | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/topology/basic.lean | 7f8bb1528eb43aa1be7c195ab6c9acf726ac102a | [
"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 | 49,134 | 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 ... |
15469c5d276b1b864e32aed8e4711cd599ccd3fa | c777c32c8e484e195053731103c5e52af26a25d1 | /src/analysis/complex/conformal.lean | 895a1c2cc86c34e308e2cf39790fe15fa15f98b8 | [
"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 | 5,414 | lean | /-
Copyright (c) 2021 Yourong Zang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yourong Zang
-/
import analysis.complex.isometry
import analysis.normed_space.conformal_linear_map
import analysis.normed_space.finite_dimension
/-!
# Conformal maps between complex vec... |
8ceaa0fd5f99ef7f2763a6d254b4a6d86450f201 | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/data/int/parity.lean | 7594bf594b2b7e34df735adfb82afbedb2285719 | [
"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 | 3,609 | 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` and `odd` predicates on the integers.
-/
import data.int.modeq
import data.nat.parity
namespace int
@[simp] theorem mod_two_ne_one {n : ℤ} : ¬ n % 2 = 1 ↔ n ... |
9e68f8d4e2dc5b33425212f28dc06eb3e2c71870 | 618003631150032a5676f229d13a079ac875ff77 | /src/topology/sheaves/presheaf_of_functions.lean | 2fb6f2f12317c0486c2912c5e14704ddbc2f03d4 | [
"Apache-2.0"
] | permissive | awainverse/mathlib | 939b68c8486df66cfda64d327ad3d9165248c777 | ea76bd8f3ca0a8bf0a166a06a475b10663dec44a | refs/heads/master | 1,659,592,962,036 | 1,590,987,592,000 | 1,590,987,592,000 | 268,436,019 | 1 | 0 | Apache-2.0 | 1,590,990,500,000 | 1,590,990,500,000 | null | UTF-8 | Lean | false | false | 3,608 | 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 topology.sheaves.presheaf
import topology.category.TopCommRing
import topology.algebra.continuous_functions
universes v u
open category_theory
open topologic... |
8fcb7b4a5051fe5aec6a522392f33b5b5031adc3 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/ring_theory/non_zero_divisors.lean | 539d03416b96c56eb2bc4c3306fc565cafb874d6 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 6,785 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Devon Tuma
-/
import group_theory.submonoid.operations
import group_theory.submonoid.membership
/-!
# Non-zero divisors
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any change... |
760ba4af76d2953cc8603dfdcc967af7ec478b3a | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/algebra/star/pi.lean | b0089803f188802d5e7d3e699862177fc6ee9ec9 | [
"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 | 1,406 | 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.star.algebra
/-!
# `star` on pi types
We put a `has_star` structure on pi types that operates elementwise, such that it describes the
complex conjugation o... |
3cd583bf4a42592dc649a69186228b9507479c2e | 957a80ea22c5abb4f4670b250d55534d9db99108 | /library/init/algebra/ring.lean | 687eb709a7aec782dcf3229b94fc3c764d3ad7b7 | [
"Apache-2.0"
] | permissive | GaloisInc/lean | aa1e64d604051e602fcf4610061314b9a37ab8cd | f1ec117a24459b59c6ff9e56a1d09d9e9e60a6c0 | refs/heads/master | 1,592,202,909,807 | 1,504,624,387,000 | 1,504,624,387,000 | 75,319,626 | 2 | 1 | Apache-2.0 | 1,539,290,164,000 | 1,480,616,104,000 | C++ | UTF-8 | Lean | false | false | 12,594 | 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.algebra.group
/- Make sure instances defined in this file have lower priority than the ones
defined for concrete stru... |
26af6a21cea963fdee7bbe5f59d98dd3e46d0f66 | a4673261e60b025e2c8c825dfa4ab9108246c32e | /src/Lean/Elab/Binders.lean | 9fa5351ace78e411c4e1d733570bcfaa58f47225 | [
"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 | 25,602 | 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.Elab.Term
import Lean.Elab.Quotation
namespace Lean.Elab.Term
open Meta
/--
Given syntax of the forms
a) (`:` term)?
b) `:` term
r... |
6a9db98052141e98564472d2e3ae1e5e5708c0a8 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /stage0/src/Init/SizeOfLemmas.lean | 3c57afabef74b0e1e3eebbd0b61f42e8085f51c0 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | EdAyers/lean4 | 57ac632d6b0789cb91fab2170e8c9e40441221bd | 37ba0df5841bde51dbc2329da81ac23d4f6a4de4 | refs/heads/master | 1,676,463,245,298 | 1,660,619,433,000 | 1,660,619,433,000 | 183,433,437 | 1 | 0 | Apache-2.0 | 1,657,612,672,000 | 1,556,196,574,000 | Lean | UTF-8 | Lean | false | false | 1,127 | 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
-/
prelude
import Init.Meta
import Init.SizeOf
import Init.Data.Nat.Linear
@[simp] theorem Fin.sizeOf (a : Fin n) : sizeOf a = a.val + 1 := by
cases a; simp... |
5c8708002acd93de375f9b45ae5e3400045f47ab | 88892181780ff536a81e794003fe058062f06758 | /src/100_theorems/t022.lean | e1a7f3beeef99f2f4154a4de57f7d8e5aae7b317 | [] | no_license | AtnNn/lean-sandbox | fe2c44280444e8bb8146ab8ac391c82b480c0a2e | 8c68afbdc09213173aef1be195da7a9a86060a97 | refs/heads/master | 1,623,004,395,876 | 1,579,969,507,000 | 1,579,969,507,000 | 146,666,368 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 162 | lean | import data.real.cardinality
-- The Non-Denumerability of the Continuum
open set
lemma t022 : ¬ countable (set.univ : set ℝ) := cardinal.not_countable_real
|
1cefc369cfaf4722e9ba29b5b6c0f899e671150b | a4673261e60b025e2c8c825dfa4ab9108246c32e | /src/Init/Notation.lean | b0be3e21c3f7909e6efcb1ab366706ad012f2f81 | [
"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 | 7,094 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
Notation for operators defined at Prelude.lean
-/
prelude
import Init.Prelude
infixr:90 " ∘ " => Function.comp
infixr:35 " × " => Prod
infixl:65 " + " =>... |
50e297e560ab287c1df72f854a4585ac03dcd41a | 037dba89703a79cd4a4aec5e959818147f97635d | /src/2020/logic/bool_not.lean | 45c5f496ed7435f0b93bea65ca7584e1c0cc1023 | [] | no_license | ImperialCollegeLondon/M40001_lean | 3a6a09298da395ab51bc220a535035d45bbe919b | 62a76fa92654c855af2b2fc2bef8e60acd16ccec | refs/heads/master | 1,666,750,403,259 | 1,665,771,117,000 | 1,665,771,117,000 | 209,141,835 | 115 | 12 | null | 1,640,270,596,000 | 1,568,749,174,000 | Lean | UTF-8 | Lean | false | false | 3,380 | lean | import tactic
@[derive fintype] inductive bool2
| ff2 : bool2
| tt2 : bool2
namespace bool2
definition and2 : bool2 → bool2 → bool2
| ff2 P := ff2
| tt2 P := P
definition or2 : bool2 → bool2 → bool2
| tt2 P := tt2
| ff2 P := P
definition not2 : bool2 → bool2
| tt2 := ff2
| ff2 := tt2
definition xor2 (x y : bool2)... |
ef3e10d3d00151d1f99b61a970adc3626eae55a7 | a7dd8b83f933e72c40845fd168dde330f050b1c9 | /src/topology/basic.lean | 1111da7b418ab54b68c4b8dbcc233f03ae735eac | [
"Apache-2.0"
] | permissive | NeilStrickland/mathlib | 10420e92ee5cb7aba1163c9a01dea2f04652ed67 | 3efbd6f6dff0fb9b0946849b43b39948560a1ffe | refs/heads/master | 1,589,043,046,346 | 1,558,938,706,000 | 1,558,938,706,000 | 181,285,984 | 0 | 0 | Apache-2.0 | 1,568,941,848,000 | 1,555,233,833,000 | Lean | UTF-8 | Lean | false | false | 35,958 | 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
Theory of topological spaces.
Parts of the formalization is based on the books:
N. Bourbaki: General Topology
I. M. James: Topologies and Uniformit... |
b949d8d8cd2257bc2c12052b2c6265ec3c1f8d45 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /archive/imo/imo1994_q1.lean | 05f5f08dcd8e43869c183b1c6ad381fe8b0c643e | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 3,937 | lean | /-
Copyright (c) 2021 Antoine Labelle. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Labelle
-/
import algebra.big_operators.basic
import algebra.big_operators.order
import data.fintype.card
import data.finset.sort
import data.fin.interval
import tactic.linari... |
1f5732ec3d30ce9380ee5e5f87ffc7c0e847d05d | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /tests/lean/run/coesec.lean | 30bea8630ce075af69a54724454409b8d24d85c1 | [
"Apache-2.0"
] | permissive | codyroux/lean | 7f8dff750722c5382bdd0a9a9275dc4bb2c58dd3 | 0cca265db19f7296531e339192e9b9bae4a31f8b | refs/heads/master | 1,610,909,964,159 | 1,407,084,399,000 | 1,416,857,075,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 195 | lean | inductive func (A B : Type) :=
mk : (A → B) → func A B
section
variables {A B : Type}
definition to_function (F : func A B) : A → B :=
func.rec (λf, f) F
coercion to_function
end
|
9fb85f926c95a4e143ad230aab27730b3bc011f8 | a7eef317ddec01b9fc6cfbb876fe7ac00f205ac7 | /src/category_theory/limits/shapes/biproducts.lean | 9b5b3ef5dce4fa819c0f76f4b882486dbfb130a1 | [
"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 | 30,925 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.epi_mono
import category_theory.limits.shapes.binary_products
import category_theory.preadditive
import algebra.big_operators
/-!
# Biproducts... |
f14c1b10a3b2b1a987077e652222f95aca468347 | 1437b3495ef9020d5413178aa33c0a625f15f15f | /meta/rb_map.lean | 986eaa3e65248f83e87be7224171f1ca14c00dae | [
"Apache-2.0"
] | permissive | jean002/mathlib | c66bbb2d9fdc9c03ae07f869acac7ddbfce67a30 | dc6c38a765799c99c4d9c8d5207d9e6c9e0e2cfd | refs/heads/master | 1,587,027,806,375 | 1,547,306,358,000 | 1,547,306,358,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,811 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Robert Y. Lewis
Additional operations on native rb_maps and rb_sets.
-/
import data.option.defs
namespace native
namespace rb_set
meta def filter {key} (s : rb_set key) ... |
4aef56bc83d9198848cb012b8d4c5a78f27e2883 | 6b2a480f27775cba4f3ae191b1c1387a29de586e | /group_rep1/programmation/contant_group_scheme.lean | e3ab68f745353aaf4f390d6c35065d3468b6596e | [] | no_license | Or7ando/group_representation | a681de2e19d1930a1e1be573d6735a2f0b8356cb | 9b576984f17764ebf26c8caa2a542d248f1b50d2 | refs/heads/master | 1,662,413,107,324 | 1,590,302,389,000 | 1,590,302,389,000 | 258,130,829 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 1,458 | lean | import ring_theory.algebra
import ring_theory.ideals
/-!
Galois algebra : B : Algebra A.
G →* Aut (B / A)
est-ce que le groupe des automorphismes d'algebre est ok !
`A →ₐ[R] B`
-/
namespace prio
variables (k : Type)[comm_ring k] (B : Type)[comm_ring B][algebra k B](G : Type)[group G][fintype G... |
1022763c3a8f47460ef10723af613501322220cb | 618003631150032a5676f229d13a079ac875ff77 | /src/algebraic_geometry/stalks.lean | 780f921034fc2e3900923cba603b7bfff35c0377 | [
"Apache-2.0"
] | permissive | awainverse/mathlib | 939b68c8486df66cfda64d327ad3d9165248c777 | ea76bd8f3ca0a8bf0a166a06a475b10663dec44a | refs/heads/master | 1,659,592,962,036 | 1,590,987,592,000 | 1,590,987,592,000 | 268,436,019 | 1 | 0 | Apache-2.0 | 1,590,990,500,000 | 1,590,990,500,000 | null | UTF-8 | Lean | false | false | 2,094 | 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.sheaves.stalks
/-!
# Stalks for presheaved spaces
This file lifts constructions of stalks and pushforward... |
6bd3029599de6eab7dc46089985ad0bdf4c9b9ff | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/category_theory/subobject/limits.lean | 3bc6056120a1c2a30673d447df6b3b9174412080 | [
"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 | 16,314 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Scott Morrison
-/
import category_theory.subobject.lattice
/-!
# Specific subobjects
We define `equalizer_subobject`, `kernel_subobject` and `image_subobject`, which ar... |
cb2cd5500b3929c7b72334760483e40999a9d9ff | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/data/polynomial/derivative.lean | fbc1819285c936d61a50a738e54599e4bdbe9cc5 | [
"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 | 15,076 | 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 algebra.hom.iterate
import data.polynomial.eval
/-!
# The derivative map on polynomials
## Main definitions
* `p... |
8668c979773790244c912884c8caae696cb6153b | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/multiset/fold.lean | 39d9d0602a6307ae0e7f7b24d35822accda3f509 | [
"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 | 3,795 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
-/
import data.multiset.erase_dup
/-!
# The fold operation for a commutative associative operation over a multiset.
-/
namespace multiset
variables {α β : Type*}
/-! #... |
442e0916afe62dd4387f532a98de86bfe975ac61 | e07b1aca72e83a272dd59d24c6e0fa246034d774 | /src/tutorials/05_sequence_limits.lean | 0858cb9591fff9d23e83fb4649e9714789b70c09 | [
"Apache-2.0",
"LicenseRef-scancode-unknown-license-reference"
] | permissive | pedrominicz/learn | 637a343bd4f8669d76819ac660a2d2d3e0958710 | b79b802a9846c86c21d4b6f3e17af36e7382f0ef | refs/heads/master | 1,671,746,990,402 | 1,670,778,113,000 | 1,670,778,113,000 | 265,735,177 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,097 | lean | import data.real.basic
import algebra.pi_instances
import tuto_lib
notation `|`x`|` := abs x
/-
In this file we manipulate the elementary definition of limits of
sequences of real numbers.
mathlib has a much more general definition of limits, but here
we want to practice using the logical operators and relations
cov... |
bba40451be75d1b6cd667d30ef164484d38641b9 | 87a08a8e9b222ec02f3327dca4ae24590c1b3de9 | /src/topology/stone_cech.lean | 6c3f628c83df257fbb8677e4565d5e8bcfa9a651 | [
"Apache-2.0"
] | permissive | naussicaa/mathlib | 86d05223517a39e80920549a8052f9cf0e0b77b8 | 1ef2c2df20cf45c21675d855436228c7ae02d47a | refs/heads/master | 1,592,104,950,080 | 1,562,073,069,000 | 1,562,073,069,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,793 | lean | /-
Copyright (c) 2018 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton
Construction of the Stone-Čech compactification using ultrafilters.
Parts of the formalization are based on "Ultrafilters and Topology"
by Marius Stekelenburg, particularly ... |
1a4ed02cbd8ea18b9131f4c5bf749159471c0518 | 137c667471a40116a7afd7261f030b30180468c2 | /src/analysis/normed_space/units.lean | 1f051533bec9c1a7aa833c754628e796f55fa1b8 | [
"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 | 12,260 | lean | /-
Copyright (c) 2020 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import analysis.specific_limits
import analysis.asymptotics.asymptotics
/-!
# The group of units of a complete normed ring
This file contains the basic theory for... |
6565937b7ba9bc7aee03364b676beb2583c5b202 | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /hott/init/function.hlean | eb2af4e3df7daca6b5c0e5324aee8852cee826f0 | [
"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 | 1,485 | hlean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
General operations on functions.
-/
prelude
import init.reserved_notation
namespace function
variables {A : Type} {B : Type} {C : Type} {D : Type} {E : Type}... |
e27b597adde27d4bc361a86b564c6738d6e80685 | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /tests/lean/unzip_error.lean | 183e26ada0de3897f42451a92e133d397aeda3f9 | [
"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 | 353 | lean | import data.vector
open nat vector prod
variables {A B : Type}
definition unzip : Π {n : nat}, vector (A × B) n → vector A n × vector B n,
unzip nil := (nil, nil),
unzip ((a, b) :: v) :=
match unzip v with
(va, vb) := (a :: va, b :: vb)
end
example : unzip ((1, 20) :: (2, 30) :: nil) = (1 :: 2 :: n... |
2db11fffb306b856110b6f59fd967004cc8d19a2 | f3849be5d845a1cb97680f0bbbe03b85518312f0 | /tests/lean/run/record1.lean | ebc730e5b3532333acc4180f0f04ea68cec64487 | [
"Apache-2.0"
] | permissive | bjoeris/lean | 0ed95125d762b17bfcb54dad1f9721f953f92eeb | 4e496b78d5e73545fa4f9a807155113d8e6b0561 | refs/heads/master | 1,611,251,218,281 | 1,495,337,658,000 | 1,495,337,658,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 786 | lean | structure point (A : Type) (B : Type) :=
mk :: (x : A) (y : B)
#check point
#check @ point.rec
#check point.mk
#check point.x
#check point.y
#check point.rec_on
inductive color
| red | green | blue
structure color_point (A : Type) (B : Type) extends point A B :=
mk :: (c : color)
#check @color_point.rec_on
#check c... |
36f7fb5e79a5b4bbd9e59718059c013090c8b1db | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/real/conjugate_exponents.lean | 9a13b6d17e943baf7f43d9200c5737f7d3a13982 | [
"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 | 3,686 | lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Yury Kudryashov
-/
import data.real.ennreal
/-!
# Real conjugate exponents
`p.is_conjugate_exponent q` registers the fact that the real numbers `p` and `q` are ... |
299ea2b6bdca781ee003e8c35040f070335a75c4 | f3a5af2927397cf346ec0e24312bfff077f00425 | /src/game/world3/level2.lean | 3e7685768568b74a8f714dd292bbf387ee381494 | [
"Apache-2.0"
] | permissive | ImperialCollegeLondon/natural_number_game | 05c39e1586408cfb563d1a12e1085a90726ab655 | f29b6c2884299fc63fdfc81ae5d7daaa3219f9fd | refs/heads/master | 1,688,570,964,990 | 1,636,908,242,000 | 1,636,908,242,000 | 195,403,790 | 277 | 84 | Apache-2.0 | 1,694,547,955,000 | 1,562,328,792,000 | Lean | UTF-8 | Lean | false | false | 795 | lean | import game.world3.level1 -- hide
import mynat.mul -- hide
namespace mynat -- hide
/-
# Multiplication World
## Level 2: `mul_one`
Remember that you can see everything you have proved so far about multiplication in
the drop-down box on the left (and that this list will grow as we proceed).
In this level we'll need... |
d0591b5395272de8bd9f91a66abe846fd652a4f3 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/playground/pldi/do2.lean | ebba3165db6b09d3c44e07ef04bdd78c8f918707 | [
"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 | 912 | lean | open Lean
/-
inductive Syntax
| missing : Syntax
| node (kind : SyntaxNodeKind) (args : Array Syntax) : Syntax
| atom (info : SourceInfo) (val : String) : Syntax
| ident (info : SourceInfo) (rawVal : Substring) (val : Name) (preresolved : List (Name × List String)) : Syntax
-/
partial def expandHash : Syntax → S... |
320a69d6021f4722e77c4d107259c26e47ef9cda | 26ac254ecb57ffcb886ff709cf018390161a9225 | /src/algebra/lie_algebra.lean | 16beef4aae4c45f1ff9c72e46eca1fea205f9072 | [
"Apache-2.0"
] | permissive | eric-wieser/mathlib | 42842584f584359bbe1fc8b88b3ff937c8acd72d | d0df6b81cd0920ad569158c06a3fd5abb9e63301 | refs/heads/master | 1,669,546,404,255 | 1,595,254,668,000 | 1,595,254,668,000 | 281,173,504 | 0 | 0 | Apache-2.0 | 1,595,263,582,000 | 1,595,263,581,000 | null | UTF-8 | Lean | false | false | 40,809 | lean | /-
Copyright (c) 2019 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import ring_theory.algebra
import linear_algebra.linear_action
import linear_algebra.bilinear_form
import tactic.noncomm_ring
/-!
# Lie algebras
This file defines Lie rin... |
2f4e448fcff3b2b63faf67d33b22640746842a5f | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/linear_algebra/special_linear_group.lean | 77c18d981b620fd58f04aaf6579e0bf150499c62 | [
"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 | 8,212 | 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.matrix.adjugate
import linear_algebra.matrix.to_lin
/-!
# The Special Linear group $SL(n, R)$
This file defines the elements of the Special Linear g... |
36a78ae3d26eb2130292a8e93fc92547b99c055c | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/eoi.lean | 8050e8d1aa936ff829f5d16b196ed2d38030aae9 | [
"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 | 14 | lean | def foo : Nat
|
0797f8823856090e4554396dbe294980101e0788 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/finmap.lean | 0518cbb1a88c7f980b30e0da348828eca2563fcd | [
"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 | 22,220 | lean | /-
Copyright (c) 2018 Sean Leather. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sean Leather, Mario Carneiro
-/
import data.list.alist
import data.finset.sigma
import data.part
/-!
# Finite maps over `multiset`
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any chang... |
810ebb517d09c06a899ca77ed08a3740e760beda | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/toFieldNameIssue.lean | abd3f37eb4e149545b9c8aacf08c59331706d4fb | [
"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 | 646 | lean | structure Foo.A where
x : Nat
structure Boo.A extends Foo.A where
y : Nat
structure B extends Boo.A where
z : Nat
def f1 (x y z : Nat) : B :=
{ x, y, z }
theorem ex1 (x y z : Nat) : f1 x y z = ⟨⟨⟨x⟩, y⟩, z⟩ :=
rfl
theorem ex2 (x y z : Nat) : f1 x y z = B.mk (Boo.A.mk (Foo.A.mk x) y) z :=
rfl
#check { ... |
5927ceeea3e59d401afadee18fa848ada736f094 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/ring_theory/unique_factorization_domain.lean | d4c443fe63a912bb1a1dbc810bab7834ea27e91c | [
"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 | 82,851 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker, Aaron Anderson
-/
import algebra.big_operators.associated
import algebra.gcd_monoid.basic
import data.finsupp.multiset
import ring_theory.noetherian
im... |
6d43b29568f230ea3f5872d7ef90e7cf7f2e06ba | e5c11e5a7d990ce404047c2bd848eeafac3c0a85 | /src/power_basis.lean | 9237221f0b96374bf8000c9479d0ad06c8a56133 | [
"LPPL-1.3c"
] | permissive | lean-forward/class-number | 9ec63c24845e46efc8fa8b15324d0815918292c7 | 4fccf36d5e0e16accae84c16df77a3839ad964e4 | refs/heads/main | 1,686,927,014,542 | 1,624,886,724,000 | 1,624,886,724,000 | 327,319,245 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 22,004 | 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 field_theory.minpoly
import linear_algebra.free_module
import ring_theory.adjoin
import ring_theory.adjoin_root
import ring_theory.algebraic
/-!
# Power basis
This... |
ec64869f11b77e1732c85499e315eca076b2f066 | 037dba89703a79cd4a4aec5e959818147f97635d | /src/2021/sets/sheet7.lean | 1524c9948c549fdcd820adc17a4707147d4e1086 | [] | no_license | ImperialCollegeLondon/M40001_lean | 3a6a09298da395ab51bc220a535035d45bbe919b | 62a76fa92654c855af2b2fc2bef8e60acd16ccec | refs/heads/master | 1,666,750,403,259 | 1,665,771,117,000 | 1,665,771,117,000 | 209,141,835 | 115 | 12 | null | 1,640,270,596,000 | 1,568,749,174,000 | Lean | UTF-8 | Lean | false | false | 5,073 | lean | /-
Copyright (c) 2021 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author : Kevin Buzzard
-/
import tactic -- imports all the Lean tactics
/-!
# Sets in Lean, sheet 7 : the sets API
It might have occurred to you that if you had a prove
things like commutati... |
17fd3f1792a4f9f984bb451a91ccf910f1638ea5 | e030b0259b777fedcdf73dd966f3f1556d392178 | /library/init/meta/smt/smt_tactic.lean | 373a9e3f53f95084e0150e015009fee9710dc9f5 | [
"Apache-2.0"
] | permissive | fgdorais/lean | 17b46a095b70b21fa0790ce74876658dc5faca06 | c3b7c54d7cca7aaa25328f0a5660b6b75fe26055 | refs/heads/master | 1,611,523,590,686 | 1,484,412,902,000 | 1,484,412,902,000 | 38,489,734 | 0 | 0 | null | 1,435,923,380,000 | 1,435,923,379,000 | null | UTF-8 | Lean | false | false | 13,788 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.meta.simp_tactic
import init.meta.smt.congruence_closure
import init.meta.smt.ematch
universe variables u
run_command mk_simp_attr `pr... |
b4f1f4fa9543d5dca2f4710a90a2824ce51c7996 | 5ffb8080b18aa71638631832811ab18c0aec5879 | /src/group/basic.lean | 371a27622e1d4525c21911598b6694baec2a8414 | [
"Apache-2.0"
] | permissive | isabella232/group-theory-game | 805ba8f473af58e3b0437121712dfc36f535b71a | 152ec4a92ad67b6174a3d240c63fa56a6df6017e | refs/heads/master | 1,679,206,314,315 | 1,611,521,951,000 | 1,611,521,951,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,501 | lean | import tactic
/-!
Basic definitions in group theory.
Source:
https://xenaproject.wordpress.com/2018/04/30/group-theory-revision/
-/
set_option old_structure_cmd true -- it's better for this kind of stuff
-- We're overwriting inbuilt group theory here so we always work in
-- a namespace
namespace mygroup
-- def... |
73170fcc025bfc8381d3c8598be8878de362b7bd | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/dfinsupp/lex.lean | 3f52398c4be954291b69440d7ee7ce945eac1815 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 6,910 | lean | /-
Copyright (c) 2022 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa, Junyan Xu
-/
import data.dfinsupp.order
import data.dfinsupp.ne_locus
import order.well_founded_set
/-!
# Lexicographic order on finitely supported dependent functions
> TH... |
932bc682d531b688d0ddc4ee69ed9a9d7564ed7a | e151e9053bfd6d71740066474fc500a087837323 | /src/hott/init/meta/instances.lean | b6f579ee0f0020549b7fcebd8d41b9d3ac48eca4 | [
"Apache-2.0"
] | permissive | daniel-carranza/hott3 | 15bac2d90589dbb952ef15e74b2837722491963d | 913811e8a1371d3a5751d7d32ff9dec8aa6815d9 | refs/heads/master | 1,610,091,349,670 | 1,596,222,336,000 | 1,596,222,336,000 | 241,957,822 | 0 | 0 | Apache-2.0 | 1,582,222,839,000 | 1,582,222,838,000 | null | UTF-8 | Lean | false | false | 3,028 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
open lean
open lean.parser
local postfix `?`:9001 := optional
local postfix *:9001 := many
namespace tactic
/-- Reset the instance cache for the main goal. -/
meta... |
c74158cfd550459f59920dd04869be1778a96523 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/bad_eqns.lean | 640a59f3a0b20c7f0fdfffd784d481907e1cb54b | [
"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 | 863 | lean | open nat
definition foo1 : nat → nat
| foo1 (0 + x) := x
definition foo2 : nat → nat → nat
| foo2 0 _ := 0
| foo2 x ⌞y⌟ := x
definition foo3 : nat → nat → nat
| foo3 0 _ := 0
| foo3 ⌞x⌟ x := x
inductive tree (A : Type) :=
| node : tree_list A → tree A
| leaf : A → tree A
with tree_list :=
| nil {} : tree_li... |
404d695f6b555bf47c8c093de3e144d52f490aab | 86f6f4f8d827a196a32bfc646234b73328aeb306 | /examples/basics/unnamed_155.lean | 20e060616be7f5d66b376dffa43b0403c6ea4150 | [] | 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 | 182 | lean | import data.real.basic
-- BEGIN
example (a b c : ℝ) : a * (b * c) = b * (c * a) :=
begin
sorry
end
example (a b c : ℝ) : a * (b * c) = b * (a * c) :=
begin
sorry
end
-- END |
9845f3b31e91270d55cd1b50aaa1f3028bc75de0 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/vars_anywhere.lean | 8b1206012e25f0ae05409dd4b89d6edcdede557b | [
"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 | 107 | lean | variable {A : Type}
check @id
inductive List
| nil : List
| cons : A → List → List
check @List.cons
|
433719a35de5c6f1fa89f3b4790b14634811eb38 | 9e90bb7eb4d1bde1805f9eb6187c333fdf09588a | /src/stump/algorithm_properties.lean | 8cabf960e497ef0170d7ce516343ba8344aa912a | [
"Apache-2.0"
] | permissive | alexjbest/stump-learnable | 6311d0c3a1a1a0e65ce83edcbb3b4b7cecabb851 | f8fd812fc646d2ece312ff6ffc2a19848ac76032 | refs/heads/master | 1,659,486,805,691 | 1,590,454,024,000 | 1,590,454,024,000 | 266,173,720 | 0 | 0 | Apache-2.0 | 1,590,169,884,000 | 1,590,169,883,000 | null | UTF-8 | Lean | false | false | 4,136 | lean | /-
Copyright © 2019, Oracle and/or its affiliates. All rights reserved.
-/
import .algorithm_definition
import .setup_properties
namespace stump
variables (μ: probability_measure ℍ) (target: ℍ) (n: ℕ)
lemma label_sample_correct_2:
∀ n, ∀ v: vec ℍ n, ∀ i: dfin (nat.succ n), (kth_projn (label_sample target n v) i... |
e5ced43418247355837432b8d743fec095aceb2c | 947b78d97130d56365ae2ec264df196ce769371a | /tests/lean/run/array1.lean | 246e3901c8d793b558ae0e544b344692f605c337 | [
"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 | 2,389 | lean | new_frontend
#check @Array.mk
def v : Array Nat := @Array.mk Nat 10 (fun ⟨i, _⟩ => i)
def w : Array Nat :=
(mkArray 9 1).push 3
#check @Array.casesOn
def f : Fin w.sz → Nat :=
@Array.casesOn _ (fun w => Fin w.sz → Nat) w (fun _ f => f)
def arraySum (a : Array Nat) : Nat :=
a.foldl Nat.add 0
#eval mkArray 4 1
#ev... |
2b2091bc732a8fe1619a73591df3e7ee7691a0a3 | 9ad8d18fbe5f120c22b5e035bc240f711d2cbd7e | /src/combinatorics/falling.lean | da3d093a75cf4e3ab5ed1dd7c832e6680d39c2b5 | [] | no_license | agusakov/lean_lib | c0e9cc29fc7d2518004e224376adeb5e69b5cc1a | f88d162da2f990b87c4d34f5f46bbca2bbc5948e | refs/heads/master | 1,642,141,461,087 | 1,557,395,798,000 | 1,557,395,798,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,929 | lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Neil Strickland
This is about the function falling n k = n (n - 1) ... (n - k + 1)
Note that the above formula involves subtraction but we give a
different recursive definition that ... |
bb36b5b3b32637d9e822c9d46cd10b0d4e90ffe9 | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /tests/lean/run/KyleAlg.lean | 10fb741b21ee2da1be5c1114379d5110bcf69cba | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | tobiasgrosser/lean4 | ce0fd9cca0feba1100656679bf41f0bffdbabb71 | ebdbdc10436a4d9d6b66acf78aae7a23f5bd073f | refs/heads/master | 1,673,103,412,948 | 1,664,930,501,000 | 1,664,930,501,000 | 186,870,185 | 0 | 0 | Apache-2.0 | 1,665,129,237,000 | 1,557,939,901,000 | Lean | UTF-8 | Lean | false | false | 8,442 | lean | import Lean
/- from core:
class OfNat (α : Type u) (n : Nat) where
ofNat : α
class Mul (α : Type u) where
mul : α → α → α
class Add (α : Type u) where
add : α → α → α
-/
class Inv (α : Type u) where
inv : α → α
postfix:max "⁻¹" => Inv.inv
class One (α : Type u) where
one : α
export One (one)
instance... |
1460faccb9fcef081ae5bd7d9db4e15358a744c5 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/1020.lean | 8fbea6469711da5fed7df0a80e548ad33f690726 | [
"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 | 684 | lean | def allPairs (xs : List α) (ys : List β) : List (α × β) :=
let rec aux
| [], r => r
| x::xs, r =>
let rec aux₂
| [], r => r
| y::ys, r => (x, y) :: r
aux₂ ys (aux xs r)
aux xs []
def allPairsFixed (xs : List α) (ys : List β) : List (α × β) :=
let rec aux
| [], r => r
| x::xs, r =>
let... |
e6bc2ed8d8fae50ac5bfc19007396c7439c6c86e | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/calculus/inverse.lean | f84292e53e6335d8ff6a69b6a92c1d55f1ddb432 | [
"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 | 37,385 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Heather Macbeth, Sébastien Gouëzel
-/
import analysis.calculus.cont_diff
import analysis.normed_space.banach
/-!
# Inverse function theorem
> THIS FILE IS SYNCHRONI... |
515d9c87ddcdb02183a6743ab4cc51b583e2e731 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/category_theory/limits/shapes/equalizers.lean | b953dc4b3fe2d7feed3decc10140c2a0cfaf75e6 | [
"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 | 7,094 | 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
import category_theory.limits.limits
open category_theory
namespace category_theory.limits
local attribute [tidy] tactic.case_bash
universes v... |
65e44d5f65a361f1d55b2148851ae5949e97c98c | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/simpPrefixIssue.lean | 3cea8940324baab0f7f3e4f20326602cefa64748 | [
"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 | 168 | lean | universe u
axiom f {α : Sort u} (a : α) : α
axiom f_eq {α : Sort u} (a : α) : f a = a
example (a : Nat) : f id a = a := by
simp only [f_eq]
trace_state
rfl
|
0e69993c383dcf65d93d93b31a974a6b4a5842b5 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/data/quot.lean | 50c0a4138b3a5002d1cb70eab957db7c7d42dee8 | [
"Apache-2.0"
] | permissive | Lix0120/mathlib | 0020745240315ed0e517cbf32e738d8f9811dd80 | e14c37827456fc6707f31b4d1d16f1f3a3205e91 | refs/heads/master | 1,673,102,855,024 | 1,604,151,044,000 | 1,604,151,044,000 | 308,930,245 | 0 | 0 | Apache-2.0 | 1,604,164,710,000 | 1,604,163,547,000 | null | UTF-8 | Lean | false | false | 20,070 | 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
/-!
# Quotient types
This module extensd the core library's treatment of quotient types (`init.data.quot`).
## Tags
quotient
-/
variables {α... |
d804ac5df27ff14f0aa2794f8889220e96e04f50 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /02_Dependent_Type_Theory.org.39.lean | d90dae6f873464b5c342c755a06dd48dd73b2fdf | [] | 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 | 227 | lean | /- page 30 -/
import standard
definition id {A : Type} (x : A) := x
check id -- ?A → ?A
variables A B : Type
variables (a : A) (b : B)
check id -- ?A A B a b → ?A A B a b
check id a -- A
check id b -- B
|
4df06254130f10e7ac07998565e2f59b594f01f7 | ce6917c5bacabee346655160b74a307b4a5ab620 | /src/ch3/ex0311.lean | 71f2aacc2d7c8d68ca6d45dc872b3f8c44c42fb0 | [] | no_license | Ailrun/Theorem_Proving_in_Lean | ae6a23f3c54d62d401314d6a771e8ff8b4132db2 | 2eb1b5caf93c6a5a555c79e9097cf2ba5a66cf68 | refs/heads/master | 1,609,838,270,467 | 1,586,846,743,000 | 1,586,846,743,000 | 240,967,761 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 200 | lean | variables p q : Prop
example (h : p ∨ q) : q ∨ p :=
or.elim h
(assume hp : p,
show q ∨ p, from or.intro_right q hp)
(assume hq : q,
show q ∨ p, from or.intro_left p hq)
|
a1a177fc4c56afe7c057c359aba51bac99700863 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/number_theory/pell.lean | 8978a09bf54300da34b66efabc13394d59b433b7 | [
"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 | 39,426 | 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.nat.modeq
import data.zsqrtd.basic
/-!
# Pell's equation and Matiyasevic's theorem
This file solves Pell's equation, i.e. integer solutions to `x ^ 2 -... |
b145f43d7268b88fa6fed121d9e99dec0201b2dc | 0003047346476c031128723dfd16fe273c6bc605 | /src/group_theory/perm/cycles.lean | 666199cdab3890cdb5f10d12c7a8c2fbb56042da | [
"Apache-2.0"
] | permissive | ChandanKSingh/mathlib | d2bf4724ccc670bf24915c12c475748281d3fb73 | d60d1616958787ccb9842dc943534f90ea0bab64 | refs/heads/master | 1,588,238,823,679 | 1,552,867,469,000 | 1,552,867,469,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,480 | 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 group_theory.perm.sign group_theory.order_of_element
namespace equiv.perm
open equiv function finset
variables {α : Type*} {β : Type*} [decidable_eq α]
def same_... |
ad44310af6bac1aaf2ea9667e149c4346fa6a369 | 98beff2e97d91a54bdcee52f922c4e1866a6c9b9 | /src/sheaf.lean | 46b01c3d5894d45ebc40c726b6b9fdc917fd6f00 | [] | no_license | b-mehta/topos | c3fc43fb04ba16bae1965ce5c26c6461172e5bc6 | c9032b11789e36038bc841a1e2b486972421b983 | refs/heads/master | 1,629,609,492,867 | 1,609,907,263,000 | 1,609,907,263,000 | 240,943,034 | 43 | 3 | null | 1,598,210,062,000 | 1,581,877,668,000 | Lean | UTF-8 | Lean | false | false | 49,370 | lean | import category_theory.full_subcategory
import category_theory.limits.creates
import category_theory.reflects_isomorphisms
import category_theory.limits.preserves.shapes.binary_products
import category_theory.limits.preserves.shapes.terminal
import category_theory.adjunction.fully_faithful
import category_theory.closed... |
9bd0c4934a64d94fa854988bb988caedc0a5327f | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/topology/order.lean | 4b15e7b6953bcbf11eefa1864f5616db46853c7d | [
"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 | 33,788 | 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.tactic
/-!
# Ordering on topologies and (co)induced topologies
Topologies on a fixed type `α` are ordered, by reverse inclusion.
Tha... |
4b4c43c72f4b9497836f2acaf9e4625729c0b2fa | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/simp15.lean | 020401f6e6ffaf0c9612f853fe96d8865773dc8b | [
"Apache-2.0"
] | permissive | codyroux/lean0.1 | 1ce92751d664aacff0529e139083304a7bbc8a71 | 0dc6fb974aa85ed6f305a2f4b10a53a44ee5f0ef | refs/heads/master | 1,610,830,535,062 | 1,402,150,480,000 | 1,402,150,480,000 | 19,588,851 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 444 | lean | rewrite_set simple
add_rewrite and_truer and_truel and_falser and_falsel or_falsel : simple
(*
add_congr_theorem("simple", "and_congr")
add_congr_theorem("simple", "or_congr")
*)
variables a b c : Nat
(*
local opts = options({"simplifier", "contextual"}, false)
local t = parse_lean([[a = 1 ∧ (¬ b = 0 ∨ c ≠ 0 ∨ b ... |
706eafdac2c72fe28a867da8fc7bb9eb83ab973e | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /tests/lean/hott/noc_list.hlean | d61ccbfc63957bdf06aa6aac7201b67cddd76ecc | [
"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 | 645 | hlean | inductive list (A : Type) : Type :=
nil {} : list A,
cons : A → list A → list A
namespace list
open lift
theorem nil_ne_cons {A : Type} (a : A) (v : list A) : nil ≠ cons a v :=
λ H, down (no_confusion H)
theorem cons.inj₁ {A : Type} (a₁ a₂ : A) (v₁ v₂ : list A) : cons a₁ v₁ = cons a₂ v₂ → a₁ = a₂ :=
λ H,... |
31ede306f01a4262b11178e56ab8460ff003153a | 46125763b4dbf50619e8846a1371029346f4c3db | /src/group_theory/monoid_localization.lean | d762ce6b554778f4704b82d0be913674b4830af3 | [
"Apache-2.0"
] | permissive | thjread/mathlib | a9d97612cedc2c3101060737233df15abcdb9eb1 | 7cffe2520a5518bba19227a107078d83fa725ddc | refs/heads/master | 1,615,637,696,376 | 1,583,953,063,000 | 1,583,953,063,000 | 246,680,271 | 0 | 0 | Apache-2.0 | 1,583,960,875,000 | 1,583,960,875,000 | null | UTF-8 | Lean | false | false | 14,015 | lean | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
import group_theory.congruence
import algebra.associated
import algebra.punit_instances
/-!
# Localizations of commutative monoids
Localizing a commutative r... |
8ab95404d584b9081810b65c92b4fd8f205316b1 | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /library/data/num/default.lean | 4fdc6da6c5d13d9d3b7166f67cc311fd676dafbf | [
"Apache-2.0"
] | permissive | codyroux/lean | 7f8dff750722c5382bdd0a9a9275dc4bb2c58dd3 | 0cca265db19f7296531e339192e9b9bae4a31f8b | refs/heads/master | 1,610,909,964,159 | 1,407,084,399,000 | 1,416,857,075,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 416 | 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
-----------------------------------------------------... |
a659b3dafd902f9c75a56bd6e0da923795f23e5e | 38ee9024fb5974f555fb578fcf5a5a7b71e669b5 | /Mathlib/Lean/LocalContext.lean | f2352397965a8b877f2f3b0478c4d399ee740644 | [
"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 | 864 | lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Scott Morrison
-/
import Lean.Meta.Tactic.Apply
namespace Lean.LocalContext
universe u v
variable {m : Type u → Type v} [Monad m] [Alternative m]
variable {β : Type u}
/-- Return the... |
df3ac4f6eaadeffa0ca8be18d74b858856ae2b6f | 8d65764a9e5f0923a67fc435eb1a5a1d02fd80e3 | /src/ring_theory/polynomial/dickson.lean | c68f397c179a84e0d2d50270cb1756963aac707e | [
"Apache-2.0"
] | permissive | troyjlee/mathlib | e18d4b8026e32062ab9e89bc3b003a5d1cfec3f5 | 45e7eb8447555247246e3fe91c87066506c14875 | refs/heads/master | 1,689,248,035,046 | 1,629,470,528,000 | 1,629,470,528,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,534 | 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 ring_theory.polynomial.chebyshev
import ring_theory.localization
import data.zmod.basic
import algebra.char_p.invertible
/-!
# Dickson polynomials
... |
fc7066f5c2e8536cffc539a65d266779e45d9ccc | d436468d80b739ba7e06843c4d0d2070e43448e5 | /src/ring_theory/algebra.lean | a28caf80a60f149333c64be51a7f044d8c72f461 | [
"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 | 20,487 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
Algebra over Commutative Ring (under category)
-/
import data.polynomial data.mv_polynomial
import data.complex.basic
import data.matrix.basic
import linear_algebra.tensor_produ... |
37446757b2ee6486a4fb47610c46b30f73d94495 | 5d166a16ae129621cb54ca9dde86c275d7d2b483 | /library/init/meta/rec_util.lean | f7e00acfe1e1f693586c874df2edf82f1ca4fc65 | [
"Apache-2.0"
] | permissive | jcarlson23/lean | b00098763291397e0ac76b37a2dd96bc013bd247 | 8de88701247f54d325edd46c0eed57aeacb64baf | refs/heads/master | 1,611,571,813,719 | 1,497,020,963,000 | 1,497,021,515,000 | 93,882,536 | 1 | 0 | null | 1,497,029,896,000 | 1,497,029,896,000 | null | UTF-8 | Lean | false | false | 4,662 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
Helper tactic for showing that a type has decidable equality.
-/
prelude
import init.meta.tactic init.data.option.instances
namespace tactic
open expr
/- Re... |
06442887d9b44e034f525d2b422b7328b448cafc | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/playground/hashable.lean | 185faf32f2e675a6f2346b86c90b0e10f70eba76 | [
"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 | 2,089 | lean | set_option trace.Elab.Deriving.hashable true
inductive SimpleInd
| A
| B
deriving Hashable
theorem «inductive fields have different base hashes» : ∀ x, hash x =
match x with
| SimpleInd.A => 0
| SimpleInd.B => 1 := λ x => rfl
mutual
inductive Foo : Type → Type
| A : Int → (3 = 3) → String → Foo Int
| B : Bar → Foo St... |
dd7d9d90e8a0a34b499717e67a2aad6dd5362c8b | 076f5040b63237c6dd928c6401329ed5adcb0e44 | /instructor-notes/2019.11.12.Proofs.lean | d6b521bbd5db916f26953ca7eeaf49beadd52ae4 | [] | no_license | kevinsullivan/uva-cs-dm-f19 | 0f123689cf6cb078f263950b18382a7086bf30be | 09a950752884bd7ade4be33e9e89a2c4b1927167 | refs/heads/master | 1,594,771,841,541 | 1,575,853,850,000 | 1,575,853,850,000 | 205,433,890 | 4 | 9 | null | 1,571,592,121,000 | 1,567,188,539,000 | Lean | UTF-8 | Lean | false | false | 5,346 | lean | /-
There are two key things we do with proofs.
(1) We build them
(2) We use them
In logic, the basic rules for building,
or constructing, proofs go by the name
of introduction rules. The basic rules
for using proofs are called elimination
rules.
Each *form* of proposition has its own
introduction and elimination rul... |
37412a146d65b9278586ac25732f90eca01f7955 | 2a70b774d16dbdf5a533432ee0ebab6838df0948 | /_target/deps/mathlib/src/analysis/convex/integral.lean | 3a5aa3e7f265b1003cd12e5327cfc087a94fde3f | [
"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 | 7,685 | lean | /-
Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Yury G. Kudryashov
-/
import analysis.convex.basic
import measure_theory.set_integral
/-!
# Jensen's inequality for integrals
In this file we prove four theorems:
* `convex.smul_... |
8f87e5af2a7cc51b302b6e91e45898b2a72ad810 | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /stage0/src/Lean/Compiler/LCNF/Types.lean | c1c37e9097ffc2d4dc813303b5a7ccb3c10c4f81 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | tobiasgrosser/lean4 | ce0fd9cca0feba1100656679bf41f0bffdbabb71 | ebdbdc10436a4d9d6b66acf78aae7a23f5bd073f | refs/heads/master | 1,673,103,412,948 | 1,664,930,501,000 | 1,664,930,501,000 | 186,870,185 | 0 | 0 | Apache-2.0 | 1,665,129,237,000 | 1,557,939,901,000 | Lean | UTF-8 | Lean | false | false | 10,870 | 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.Meta.InferType
namespace Lean.Compiler
scoped notation:max "◾" => lcErased
scoped notation:max "⊤" => lcAny
namespace LCNF
structure LCNFTyp... |
779abc89c54def00f133dff2ef01aa44e2007078 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/algebra/ordered_field.lean | 6d672f58ef58ef79468034f410dda4060ce63da8 | [
"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 | 23,904 | lean | /-
Copyright (c) 2014 Robert Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Lewis, Leonardo de Moura, Mario Carneiro, Floris van Doorn
-/
import algebra.ordered_ring
import algebra.field
/-!
### Linear ordered fields
A linear ordered field is a field ... |
abb0e2acb01915807f853666aa714417d94d0a1d | 8cb37a089cdb4af3af9d8bf1002b417e407a8e9e | /library/init/meta/environment.lean | 800536aa50978410e4c6bab44c07c34c0b1276ff | [
"Apache-2.0"
] | permissive | kbuzzard/lean | ae3c3db4bb462d750dbf7419b28bafb3ec983ef7 | ed1788fd674bb8991acffc8fca585ec746711928 | refs/heads/master | 1,620,983,366,617 | 1,618,937,600,000 | 1,618,937,600,000 | 359,886,396 | 1 | 0 | Apache-2.0 | 1,618,936,987,000 | 1,618,936,987,000 | null | UTF-8 | Lean | false | false | 11,033 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.meta.declaration init.meta.exceptional init.data.option.basic
import init.meta.rb_map
/-- An __environment__ contains all of the declar... |
845bfc3c0356793cbcdfc44617f12c377f3324bf | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/topology/algebra/module.lean | ae7923f4395f119adb0b31b919a822b5db857879 | [
"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 | 41,765 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo, Yury Kudryashov
-/
import topology.algebra.ring
import topology.uniform_space.uniform_embedding
import ring_theory.algebra
import line... |
5b8b3c435fe7afa38fbd048b8df7af9d59058554 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/bitvec/basic.lean | 74c21d597dc6178abb89dfbb199062d5ee0bb044 | [] | 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 | 2,467 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.bitvec.core
import Mathlib.data.fin
import Mathlib.tactic.norm_num
import Mathlib.tactic.m... |
dbf2b5952e6c884de8ef63659a6623f15789306a | df7bb3acd9623e489e95e85d0bc55590ab0bc393 | /lean/love12_basic_mathematical_structures_demo.lean | d0e52552d1503de0c25af200ccf1ee217717ee48 | [] | no_license | MaschavanderMarel/logical_verification_2020 | a41c210b9237c56cb35f6cd399e3ac2fe42e775d | 7d562ef174cc6578ca6013f74db336480470b708 | refs/heads/master | 1,692,144,223,196 | 1,634,661,675,000 | 1,634,661,675,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 12,475 | lean | import .love05_inductive_predicates_demo
/- # LoVe Demo 12: Basic Mathematical Structures
We introduce definitions and proofs about basic mathematical structures such as
groups, fields, and linear orders. -/
set_option pp.beta true
set_option pp.generalized_field_notation false
namespace LoVe
/- ## Type Classes... |
f238f0b4cd5ca64976e8bf69b01dfc6e16514bd9 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/measure_theory/tactic.lean | 1db9e2a782ebc27351d93096b2426c4f309a9b89 | [
"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 | 6,436 | 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 tactic.auto_cases
import tactic.tidy
import tactic.with_local_reducibility
import tactic.show_term
import measure_theory.measure.measure_space_def
/-!
# Tactics fo... |
4bb7cbade4c832f327348cf7665f5234cbb71249 | 7b02c598aa57070b4cf4fbfe2416d0479220187f | /homotopy/EM.hlean | 33acbbe66e4ca2ecd6b0799c56debb6a255d53b4 | [
"Apache-2.0"
] | permissive | jdchristensen/Spectral | 50d4f0ddaea1484d215ef74be951da6549de221d | 6ded2b94d7ae07c4098d96a68f80a9cd3d433eb8 | refs/heads/master | 1,611,555,010,649 | 1,496,724,191,000 | 1,496,724,191,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 27,814 | hlean | -- Authors: Floris van Doorn
import homotopy.EM algebra.category.functor.equivalence types.pointed2 ..pointed_pi ..pointed
open eq equiv is_equiv algebra group nat pointed EM.ops is_trunc trunc susp function is_conn
namespace EM
definition EMadd1_functor_succ [unfold_full] {G H : AbGroup} (φ : G →g H) (n : ℕ) :
... |
4c54e93b94453d94897a9eeeac2d776e629b631b | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /src/Init/Lean/Elab/Declaration.lean | 52ef36fab775e02fe620ffbc833e636fefbe404c | [
"Apache-2.0"
] | permissive | mhuisi/lean4 | 28d35a4febc2e251c7f05492e13f3b05d6f9b7af | dda44bc47f3e5d024508060dac2bcb59fd12e4c0 | refs/heads/master | 1,621,225,489,283 | 1,585,142,689,000 | 1,585,142,689,000 | 250,590,438 | 0 | 2 | Apache-2.0 | 1,602,443,220,000 | 1,585,327,814,000 | C | UTF-8 | Lean | false | false | 6,356 | 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, Sebastian Ullrich
-/
prelude
import Init.Lean.Util.CollectLevelParams
import Init.Lean.Elab.Definition
namespace Lean
namespace Elab
namespace Command
def e... |
1b164b8c43b49714dd1560477dd0dbae77180d1d | bae21755a4a03bbe0a5c22e258db8633407711ad | /library/init/category/option.lean | 6ee2bc20876ecef617ad8940c356eacd695a3d9c | [
"Apache-2.0"
] | permissive | nor-code/lean | f437357a8f85db0f06f186fa50fcb1bc75f6b122 | aa306af3d7c47de3c7937c98d3aa919eb8da6f34 | refs/heads/master | 1,662,613,329,886 | 1,586,696,014,000 | 1,586,696,014,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,206 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
prelude
import init.category.alternative init.category.lift init.category.except
universes u v
structure option_t (m : Type u → Type v)... |
a5210d36b64efd31b5af382c8b32431fbcc363ff | da23b545e1653cafd4ab88b3a42b9115a0b1355f | /src/tidy/mk_apps.lean | e0cc2ddc783e9faf32e24c75922480da62837d96 | [] | no_license | minchaowu/lean-tidy | 137f5058896e0e81dae84bf8d02b74101d21677a | 2d4c52d66cf07c59f8746e405ba861b4fa0e3835 | refs/heads/master | 1,585,283,406,120 | 1,535,094,033,000 | 1,535,094,033,000 | 145,945,792 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,259 | lean | import data.list
import data.option
import .lock_tactic_state
open tactic
meta def mk_app_aux : expr → expr → expr → tactic expr
| f (expr.pi n binder_info.default d b) arg := do
infer_type arg >>= unify d,
return $ f arg
| f (expr.pi n binder_info.inst_implicit d b) arg := do
infer_type arg >>= unify d,
... |
1325118418662a8d327582856c7053ce29108df8 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/monad/coequalizer_auto.lean | be0203395814a0d4d8af6cdb319a4173bea2a0d5 | [] | 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 | 5,432 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.limits.shapes.reflexive
import Mathlib.category_theory.limits.preserves.shapes.... |
1571b609d0c04325718a789672e59d8bea023d9a | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /test/linarith.lean | 9caa1309e1fd81aa3d92bc59378df4862b3b0410 | [
"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 | 10,171 | lean | import tactic.linarith
example {α : Type} (_inst : Π (a : Prop), decidable a)
[linear_ordered_field α]
{a b c : α}
(ha : a < 0)
(hb : ¬b = 0)
(hc' : c = 0)
(h : (1 - a) * (b * b) ≤ 0)
(hc : 0 ≤ 0)
(this : -(a * -b * -b + b * -b + 0) = (1 - a) * (b * b))
(h : (1 - a) * (b * b) ≤ 0) :
0 < 1 - a :=
be... |
89f13fa160b6d966086be5fca277621c930b75d0 | 1446f520c1db37e157b631385707cc28a17a595e | /stage0/src/Init/Data/List/Basic.lean | 0a71a5396b57a3859f9504e26102d48eb2545390 | [
"Apache-2.0"
] | permissive | bdbabiak/lean4 | cab06b8a2606d99a168dd279efdd404edb4e825a | 3f4d0d78b2ce3ef541cb643bbe21496bd6b057ac | refs/heads/master | 1,615,045,275,530 | 1,583,793,696,000 | 1,583,793,696,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,165 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import Init.Core
import Init.Data.Nat.Basic
open Decidable List
universes u v w
instance (α : Type u) : Inhabited (List α) :=
⟨List.nil⟩
variables... |
590dae9368a9ed4f4986905073f1470bebd0c691 | 75c54c8946bb4203e0aaf196f918424a17b0de99 | /old/zfc.lean | 2d137ded6825958acddd7a2eb72dc6ad06312767 | [
"Apache-2.0"
] | permissive | urkud/flypitch | 261e2a45f1038130178575406df8aea78255ba77 | 2250f5eda14b6ef9fc3e4e1f4a9ac4005634de5c | refs/heads/master | 1,653,266,469,246 | 1,577,819,679,000 | 1,577,819,679,000 | 259,862,235 | 1 | 0 | Apache-2.0 | 1,588,147,244,000 | 1,588,147,244,000 | null | UTF-8 | Lean | false | false | 14,862 | lean | /-
Copyright (c) 2019 The Flypitch Project. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Han, Floris van Doorn, Andrew Tindall
-/
import .fol set_theory.zfc
open fol
namespace zfc
inductive ZFC_rel : ℕ → Type 1
| ϵ : ZFC_rel 2
def L_ZFC : Language.{1} :=
⟨... |
2ada9ad85bf9e7ab124c0c468c82354975cd0245 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /library/data/quotient/util.lean | 4122e004f4d0cd2751420dc9b4c906c705c6ae69 | [
"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 | 3,971 | lean | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Floris van Doorn
-/
import logic ..prod algebra.relation
open prod eq.ops
namespace quotient
/- auxiliary facts about products -/
variables {A B : Type}
/- flip -/
definiti... |
68de5cb9020368c2dd701060143eee0908514b53 | 05b503addd423dd68145d68b8cde5cd595d74365 | /src/data/prod.lean | 7915203e85a0243cd8222723ca95196f4895336c | [
"Apache-2.0"
] | permissive | aestriplex/mathlib | 77513ff2b176d74a3bec114f33b519069788811d | e2fa8b2b1b732d7c25119229e3cdfba8370cb00f | refs/heads/master | 1,621,969,960,692 | 1,586,279,279,000 | 1,586,279,279,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,045 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
/-!
# Extra facts about `prod`
This file defines `prod.swap : α × β → β × α` and proves various simple lemmas about `prod`.
-/
variables {α : Type*} {β : Type*} {γ... |
b47d95acd70676bab1bed9790949b0fbc7dc57c3 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/linear_algebra/eigenspace_auto.lean | 985ca178008014f8929b73cf257bb1e22e02240a | [] | 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 | 12,504 | lean | /-
Copyright (c) 2020 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Alexander Bentkamp.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.field_theory.algebraic_closure
import Mathlib.linear_algebra.finsupp
import Mathlib... |
5a1c6334a2b06d63f144a982777d3c4d1dfb19df | 94e33a31faa76775069b071adea97e86e218a8ee | /src/data/dfinsupp/basic.lean | 590b1b7ec21d4086ba13cbc55a368835ce6a6ecb | [
"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 | 81,044 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau
-/
import algebra.module.pi
import algebra.module.linear_map
import algebra.big_operators.basic
import data.set.finite
import group_theory.submonoid.membership
imp... |
86ed94211b6f2902da2e0a56f83e05376154264e | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/algebra/big_operators/order.lean | 9191c85ad3fe08d2babd9eb3361132ba5d710adb | [
"Apache-2.0"
] | permissive | hikari0108/mathlib | b7ea2b7350497ab1a0b87a09d093ecc025a50dfa | a9e7d333b0cfd45f13a20f7b96b7d52e19fa2901 | refs/heads/master | 1,690,483,608,260 | 1,631,541,580,000 | 1,631,541,580,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 21,663 | 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 algebra.absolute_value
import algebra.big_operators.basic
/-!
# Results about big operators with values in an ordered algebraic structure.
Mostly monotonici... |
dcd17235b7c22b60d1f47f9aed178d92959dd2e9 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/number_theory/prime_counting.lean | b531b97019305e1a369413ce794f3111aeea6ee4 | [
"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 | 3,378 | lean | /-
Copyright (c) 2021 Bolton Bailey. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bolton Bailey
-/
import data.nat.prime_fin
import data.nat.totient
import data.finset.locally_finite
import data.nat.count
import data.nat.nth
/-!
# The Prime Counting Function
In th... |
f87649278fb51746e4f6285b9d1e3a4b9f544a60 | 4bcaca5dc83d49803f72b7b5920b75b6e7d9de2d | /src/Lean/Server/Utils.lean | f8fcc7e5bb32b7a7eb0d3429d26dd02b323d8a55 | [
"Apache-2.0"
] | permissive | subfish-zhou/leanprover-zh_CN.github.io | 30b9fba9bd790720bd95764e61ae796697d2f603 | 8b2985d4a3d458ceda9361ac454c28168d920d3f | refs/heads/master | 1,689,709,967,820 | 1,632,503,056,000 | 1,632,503,056,000 | 409,962,097 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,348 | lean | /-
Copyright (c) 2020 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki, Marc Huisinga
-/
import Lean.Data.Position
import Lean.Data.Lsp
import Lean.Server.InfoUtils
import Init.System.FilePath
namespace IO
def throwServerError (err... |
d716fe0a1f62f48095ea108ccdf3347c566dae61 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/category_theory/limits/shapes/regular_mono.lean | 7c8f7e3d4e8f56404ee8f4162938bef1402040ff | [
"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 | 12,913 | 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.kernels
import category_theory.limits.shapes.strong_epi
import category_theory.limits.shapes.pullbacks
/-!
# Defin... |
1fd9f2fcc5bd8c5efee02501ef766b4c4fbf4719 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/ring_theory/prime.lean | 2ac7f35dbe098ada776d513508a9967b3523129c | [] | 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 | 1,585 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.associated
import Mathlib.algebra.big_operators.basic
import Mathlib.PostPort
universe... |
011dcc9d8b6fa01dff0bb7e4ddd5963acd749526 | 076f5040b63237c6dd928c6401329ed5adcb0e44 | /assignments/hw5_higher_order_functions.lean | 7993b913d40874de10065b9e206c09721de0908d | [] | no_license | kevinsullivan/uva-cs-dm-f19 | 0f123689cf6cb078f263950b18382a7086bf30be | 09a950752884bd7ade4be33e9e89a2c4b1927167 | refs/heads/master | 1,594,771,841,541 | 1,575,853,850,000 | 1,575,853,850,000 | 205,433,890 | 4 | 9 | null | 1,571,592,121,000 | 1,567,188,539,000 | Lean | UTF-8 | Lean | false | false | 7,449 | lean | open list
/-
#1. You are to implement a function
that takes a "predicate" function and a
list and that returns a new list: namely
a list that contains all and only those
elements of the first list for which the
given predicate function returns true.
We start by giving you two predicate
functions. Each takes an argume... |
01839401ac8d7a1c33614a71667a69d8863a7ffc | 4f065978c49388d188224610d9984673079f7d91 | /proofs_by_induction.lean | 6a74cd7fbb9c3853d8c971c4eca5fba254e079ff | [] | 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 | 3,725 | lean | import algebra.big_operators data.fintype
import tactic.ring
-- https://xenaproject.wordpress.com/2018/03/30/proofs-by-induction/
open nat
def odd : ℕ → ℕ := λ i, 2 * i + 1
def square : ℕ → ℕ := λ i, i ^ 2
theorem odd_square_inductive_step (d : ℕ) :
square d + odd d = square (succ d) :=
by dsimp [square, odd, pow]... |
202065744bf3fd6ef816d511954b1967f93e7d99 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/data/int/parity.lean | 0684b9e46463c424befa2f057b6a9728c06fd320 | [
"Apache-2.0"
] | permissive | rmitta/mathlib | 8d90aee30b4db2b013e01f62c33f297d7e64a43d | 883d974b608845bad30ae19e27e33c285200bf84 | refs/heads/master | 1,585,776,832,544 | 1,576,874,096,000 | 1,576,874,096,000 | 153,663,165 | 0 | 2 | Apache-2.0 | 1,544,806,490,000 | 1,539,884,365,000 | Lean | UTF-8 | Lean | false | false | 2,951 | 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 integers.
-/
import .modeq data.nat.parity algebra.group_power
namespace int
@[simp] theorem mod_two_ne_one {n : int} : ¬ n % 2 = 1 ↔ n % 2 ... |
ce3bbbfabc9751a5d454e15cee8c4bb6645286d0 | 367134ba5a65885e863bdc4507601606690974c1 | /src/algebra/category/CommRing/adjunctions.lean | 2328a7b76fb0eb76204d229ac07637bd9154fe94 | [
"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 | 1,701 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Johannes Hölzl
-/
import algebra.category.CommRing.basic
import data.mv_polynomial
/-!
Multivariable polynomials on a type is the left adjoint of the
forgetful functor... |
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