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9a11ad98f97e214b983b5217348a2798ca1c8c93 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /tests/lean/run/priority_test2.lean | 05f9121c4fc34d768170506ebbeb5c5a15ba192a | [
"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 | 692 | lean | open nat
structure foo [class] :=
(a : nat) (b : nat)
definition i1 [instance] [priority std.priority.default-2] : foo :=
foo.mk 1 1
example : foo.a = 1 :=
rfl
definition i2 [instance] [priority std.priority.default-1] : foo :=
foo.mk 2 2
example : foo.a = 2 :=
rfl
definition i3 [instance] : foo :=
foo.mk 3 3
ex... |
7312bac090f973eb7918ea99be801d51d272b64c | 07c76fbd96ea1786cc6392fa834be62643cea420 | /hott/homotopy/EM.hlean | 9a724d04c66882bb0880fd72826e6c79fc8dbac9 | [
"Apache-2.0"
] | permissive | fpvandoorn/lean2 | 5a430a153b570bf70dc8526d06f18fc000a60ad9 | 0889cf65b7b3cebfb8831b8731d89c2453dd1e9f | refs/heads/master | 1,592,036,508,364 | 1,545,093,958,000 | 1,545,093,958,000 | 75,436,854 | 0 | 0 | null | 1,480,718,780,000 | 1,480,718,780,000 | null | UTF-8 | Lean | false | false | 18,141 | hlean | /-
Copyright (c) 2016 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
Eilenberg MacLane spaces
-/
import hit.groupoid_quotient homotopy.hopf homotopy.freudenthal homotopy.homotopy_group
open algebra pointed nat eq category group is_... |
91baef365c676cf90ebc46ee7007e54ccee98150 | 367134ba5a65885e863bdc4507601606690974c1 | /src/category_theory/limits/shapes/equalizers.lean | 4994b98870ccf1b5976f24af0f71fb983520efec | [
"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 | 33,009 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Markus Himmel
-/
import category_theory.epi_mono
import category_theory.limits.limits
/-!
# Equalizers and coequalizers
This file defines (co)equalizers as special ca... |
73de7dc441ca47821df2a3447cbc6f42f98bd2ac | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/algebra/category/Module/change_of_rings.lean | fc8d97972b2a55538a9ecb857b28c7414ceef941 | [
"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 | 2,442 | lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
import algebra.category.Module.basic
/-!
# Change Of Rings
## Main definitions
* `category_theory.Module.restrict_scalars`: given rings `R, S` and a ring homomorphism ... |
a3836a158d9af8b80bd3817a771417b922a29fb9 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /04_Quantifiers_and_Equality.org.4.lean | c4e4eb1fbe5f8ee688d7635f2f0deb13dd5c97df | [] | 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 | 251 | lean | /- page 49 -/
import standard
variables (A : Type) (r : A → A → Prop)
variable (trans_r : ∀ {x y z}, r x y → r y z → r x z)
variables (a b c : A)
variables (Hab : r a b) (Hbc : r b c)
check trans_r
check trans_r Hab
check trans_r Hab Hbc
|
39d13b5d8f6c751174fbddd18ba16c33f06db1ed | 432d948a4d3d242fdfb44b81c9e1b1baacd58617 | /src/tactic/aesop/rule_builder.lean | 101df0d4a7e97317b7aa78bf9be4215546de0d73 | [
"Apache-2.0"
] | permissive | JLimperg/aesop3 | 306cc6570c556568897ed2e508c8869667252e8a | a4a116f650cc7403428e72bd2e2c4cda300fe03f | refs/heads/master | 1,682,884,916,368 | 1,620,320,033,000 | 1,620,320,033,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,043 | lean | /-
Copyright (c) 2021 Jannis Limperg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jannis Limperg
-/
import tactic.aesop.rule
namespace tactic
namespace aesop
meta inductive rule_builder_output
| rule (r : rule) (imode : indexing_mode)
| simp_lemmas (s : simp_lemm... |
db8936c06ea1df023a97102f44480b17e2bb8eb4 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/int/nat_prime_auto.lean | 0ec4dd83515ef1f85135cf20783c4f07902bf83f | [] | 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 | 611 | lean | /-
Copyright (c) 2020 Bryan Gin-ge Chen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker, Bryan Gin-ge Chen
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.nat.prime
import Mathlib.data.int.basic
import Mathlib.PostPort
n... |
b0797f91ea7e7252281873fc233ab96066ec4957 | 92b50235facfbc08dfe7f334827d47281471333b | /library/data/finset/partition.lean | cf74cc562bf25a24249c07baf8b170e9b8154ea7 | [
"Apache-2.0"
] | permissive | htzh/lean | 24f6ed7510ab637379ec31af406d12584d31792c | d70c79f4e30aafecdfc4a60b5d3512199200ab6e | refs/heads/master | 1,607,677,731,270 | 1,437,089,952,000 | 1,437,089,952,000 | 37,078,816 | 0 | 0 | null | 1,433,780,956,000 | 1,433,780,955,000 | null | UTF-8 | Lean | false | false | 5,764 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Haitao Zhang
Partitions of a type A into finite subsets of A. Such a partition is represented by
a function f : A → finset A which maps every element a : A to its equivalence cl... |
ae5f7931d4a3c278f5c63c021fe54b9094de09e3 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /src/Lean/Meta/Tactic/Replace.lean | 9e31d74f90732874b53cafa8734c943dea044f9a | [
"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 | 5,906 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Util.ForEachExpr
import Lean.Meta.AppBuilder
import Lean.Meta.MatchUtil
import Lean.Meta.Tactic.Util
import Lean.Meta.Tactic.Revert
import Lean.... |
4dba2f3a34d06bf1b7434e40dcfb19a18456abbf | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/inductionErrors.lean | 9bc246952fb7a8c47834b84bc24923e10972e8ea | [
"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 | 2,481 | lean | universe u
axiom elimEx (motive : Nat → Nat → Sort u) (x y : Nat)
(diag : (a : Nat) → motive a a)
(upper : (delta a : Nat) → motive a (a + delta.succ))
(lower : (delta a : Nat) → motive (a + delta.succ) a)
: motive y x
theorem ex1 (p q : Nat) : p ≤ q ∨ p > q := by
cases p, q using elimEx with
| lower d =... |
825859661a0ab9fa08d466a92c8215979edd24c6 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/group_theory/sylow.lean | 6340dc72ae90c9aaf42f58c2e9271797a1ba937f | [
"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 | 13,268 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import group_theory.group_action
import group_theory.quotient_group
import group_theory.order_of_element
import data.zmod.basic
import data.fintype.card
import data.list.... |
1de7a3e1235e28176d3033614138bd60a024c773 | d436468d80b739ba7e06843c4d0d2070e43448e5 | /src/algebra/category/Mon/basic.lean | 5b99dabb5f976e91f66759a66089e07604ea00ab | [
"Apache-2.0"
] | permissive | roro47/mathlib | 761fdc002aef92f77818f3fef06bf6ec6fc1a28e | 80aa7d52537571a2ca62a3fdf71c9533a09422cf | refs/heads/master | 1,599,656,410,625 | 1,573,649,488,000 | 1,573,649,488,000 | 221,452,951 | 0 | 0 | Apache-2.0 | 1,573,647,693,000 | 1,573,647,692,000 | null | UTF-8 | Lean | false | false | 6,350 | 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 category_theory.concrete_category
import algebra.group
import data.equiv.algebra
/-!
# Category instances for monoid, add_monoid, comm_monoid, and add_comm_m... |
aeb36bda500f0980380385de54d4139e325b2a19 | 8e31b9e0d8cec76b5aa1e60a240bbd557d01047c | /scratch/inverse.lean | 2cffd4f03205e23dde43443497944c41f06313f2 | [] | no_license | ChrisHughes24/LP | 7bdd62cb648461c67246457f3ddcb9518226dd49 | e3ed64c2d1f642696104584e74ae7226d8e916de | refs/heads/master | 1,685,642,642,858 | 1,578,070,602,000 | 1,578,070,602,000 | 195,268,102 | 4 | 3 | null | 1,569,229,518,000 | 1,562,255,287,000 | Lean | UTF-8 | Lean | false | false | 1,127 | lean | import data.matrix data.rat.basic linear_algebra.determinant
variable {n : ℕ}
open matrix
local infix ` ⬝ `:70 := matrix.mul
local postfix `ᵀ` : 1500 := matrix.transpose
def comatrix (M : matrix (fin n) (fin n) ℚ) : matrix (fin n) (fin n) ℚ :=
begin
cases n,
{ exact fin.elim0 },
{ exact λ i j, (-1) ^ (i + j : ... |
4bb6b8df58d0f8726a450e95abda22c11557a5be | 75bd9c50a345718d735a7533c007cf45f9da9a83 | /src/data/mv_polynomial/comm_ring.lean | 33e77fb5768728e5bf43bacaa3e9893292cc9acd | [
"Apache-2.0"
] | permissive | jtbarker/mathlib | a1a3b1ddc16179826260578410746756ef18032c | 392d3e376b44265ef2dedbd92231d3177acc1fd0 | refs/heads/master | 1,671,246,411,096 | 1,600,801,712,000 | 1,600,801,712,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,940 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
-/
import data.mv_polynomial.variables
/-!
# Multivariate polynomials over a ring
Many results about polynomials hold when the coeffic... |
6f5cc4cf1ed545c4cd08154d0c2a5c516c6ca288 | 92b1c7f0343a6a5cd36bc0f623a7490da3f1e0f3 | /src/lib/attributed/to_mathlib.lean | f4ea964dbdc2031e1f98bcb048967a2414325dd4 | [
"Apache-2.0"
] | permissive | jtristan/stump-learnable | 717453eb590af16e60c7d3806cc9e66492fab091 | aa3c089f41602efa08d31ef6b41e549456186d57 | refs/heads/master | 1,625,630,634,360 | 1,607,552,106,000 | 1,607,552,106,000 | 218,629,406 | 15 | 2 | null | null | null | null | UTF-8 | Lean | false | false | 30,361 | lean | /-
Various lemmas intended for mathlib.
Some parts of this file are originally from
https://github.com/johoelzl/mathlib/blob/c9507242274ac18defbceb917f30d6afb8b839a5/src/measure_theory/measurable_space.lean
Authors: Johannes Holzl, John Tristan, Koundinya Vajjha
-/
import tactic.tidy
import measure_theory.giry_mon... |
707a7506f3155df0218bcc6ca935224bdb5b07b9 | 0c1546a496eccfb56620165cad015f88d56190c5 | /library/init/data/sigma/basic.lean | 25b13475cab27bcc9a3f472852deaee2ed07cdc0 | [
"Apache-2.0"
] | permissive | Solertis/lean | 491e0939957486f664498fbfb02546e042699958 | 84188c5aa1673fdf37a082b2de8562dddf53df3f | refs/heads/master | 1,610,174,257,606 | 1,486,263,620,000 | 1,486,263,620,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 737 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura, Jeremy Avigad, Floris van Doorn
-/
prelude
import init.logic init.wf
notation `Σ` binders `, ` r:(scoped p, sigma p) := r
notation `Σ'` binders `, ` r:(scoped... |
3c110f7dfb1263cad1086ac53e556545ef4bd40b | f3849be5d845a1cb97680f0bbbe03b85518312f0 | /tests/lean/num2.lean | 4b4dcf4bfd7901445c41f9acad4a4ca677790f5a | [
"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 | 354 | lean | prelude set_option pp.notation false
definition Prop := Sort 0
constant eq {A : Type} : A → A → Prop
infixl `=`:50 := eq
constant N : Type
constant z : N
constant o : N
constant b : N
notation 0 := z
notation 1 := o
#check 1
#check 0
constant G : Type
constant gz : G
constant a : G
notation 0 := gz
#check a = 0
... |
84750cf25145ab5ea3153005c2b30e2d64425817 | 4fa161becb8ce7378a709f5992a594764699e268 | /src/category_theory/single_obj.lean | e4e8eb88a8044fcb3f9da62f98b809331ff3f25a | [
"Apache-2.0"
] | permissive | laughinggas/mathlib | e4aa4565ae34e46e834434284cb26bd9d67bc373 | 86dcd5cda7a5017c8b3c8876c89a510a19d49aad | refs/heads/master | 1,669,496,232,688 | 1,592,831,995,000 | 1,592,831,995,000 | 274,155,979 | 0 | 0 | Apache-2.0 | 1,592,835,190,000 | 1,592,835,189,000 | null | UTF-8 | Lean | false | false | 5,294 | lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import category_theory.endomorphism
import category_theory.category.Cat
import algebra.category.Mon.basic
/-!
# Single-object category
Single object category with... |
3e49777bf66d8bb2d7a28221d3fe9a4df6d1dd82 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/deprecated/subring.lean | 9f7135caca873593f840ea3981f013b6dd895e94 | [
"Apache-2.0"
] | permissive | stjordanis/mathlib | 51e286d19140e3788ef2c470bc7b953e4991f0c9 | 2568d41bca08f5d6bf39d915434c8447e21f42ee | refs/heads/master | 1,631,748,053,501 | 1,627,938,886,000 | 1,627,938,886,000 | 228,728,358 | 0 | 0 | Apache-2.0 | 1,576,630,588,000 | 1,576,630,587,000 | null | UTF-8 | Lean | false | false | 8,077 | lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import deprecated.subgroup
import deprecated.group
import ring_theory.subring
universes u v
open group
variables {R : Type u} [ring R]
/-- `S` is a subring: a set... |
b4ff4276403d9b1f6794ec4e77bd67ce799df502 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/PrettyPrinter/Delaborator/SubExpr.lean | e09bddb5a62161f38573206dae8b31111e1ba05f | [
"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 | 3,912 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich, Daniel Selsam, Wojciech Nawrocki
-/
import Lean.Meta.Basic
import Lean.SubExpr
import Lean.Data.RBMap
/-!
# Subexpr utilities for delaborator.
This file defi... |
4b6ecc0e93a4247a6c797b9ef3bcdebb39968d99 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/meta/format_auto.lean | 1e61535bed1f3531710c3b4d034cae5b24489b9e | [] | 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 | 605 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.meta.options
import Mathlib.Lean3Lib.init.function
import Mathlib.Lean3Lib.init.data.to_string
universe... |
875a2f40f256f0deae5586b78d0e372caa0faa2d | b7f22e51856f4989b970961f794f1c435f9b8f78 | /library/tools/helper_tactics.lean | 0a1bf7fcc3ee4eb029271e25c1053852633fde3a | [
"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 | 391 | lean | -- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Author: Leonardo de Moura, Jeremy Avigad
-- tools.helper_tactics
-- ====================
-- Useful tactics.
import logic.eq
open tactic
namespace helper_tactics
definition a... |
f2d3ee2d64d244562e3617834d33cf608d1b253d | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/run/overload2.lean | cc9408d80ef44e75f93ec24d9d3f450f2a32e227 | [
"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 | 715 | lean | inductive F2 : Type
| O : F2
| I : F2
namespace F2
definition add : F2 → F2 → F2
| O O := O
| O I := I
| I O := I
| I I := O
infix + := F2.add
end F2
open F2 nat
#reduce (1 : nat) + 1
#reduce (1 : nat) + (1 : nat)
example : true :=
begin
have H : (1 : nat) + (1 : nat) = 2,
reflexivity,
constructor
end
examp... |
64f86cd2189be7df260515ffe951436d4e599a34 | 88fb7558b0636ec6b181f2a548ac11ad3919f8a5 | /tests/lean/run/1315b.lean | a72fab19d667068ec10664d14ad024c87adefc5c | [
"Apache-2.0"
] | permissive | moritayasuaki/lean | 9f666c323cb6fa1f31ac597d777914aed41e3b7a | ae96ebf6ee953088c235ff7ae0e8c95066ba8001 | refs/heads/master | 1,611,135,440,814 | 1,493,852,869,000 | 1,493,852,869,000 | 90,269,903 | 0 | 0 | null | 1,493,906,291,000 | 1,493,906,291,000 | null | UTF-8 | Lean | false | false | 1,069 | lean | open nat
def k : ℕ := 0
def fails : Π (n : ℕ) (m : ℕ), ℕ
| 0 m := 0
| (succ n) m :=
match k with
| 0 := 0
| (succ i) :=
let val := m+1 in
match fails n val with
| 0 := 0
| (succ l) := 0
end
end
def test (k : ℕ) : Π (n : ℕ) (m : ℕ), ℕ
| 0 m := 0
| (succ n) m :=
match k with
| 0 := 1
... |
0b8ed06cbe671912e7387feea9dce7509f54708c | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/topology/subset_properties.lean | 627d55a1d3044ff58ff8e1448a6ce81168335231 | [
"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 | 84,214 | 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, Yury Kudryashov
-/
import order.filter.pi
import topology.bases
import data.finset.order
import data.set.accumulate
import tactic.tfae
import topology.b... |
f0840e6163ff5b41a93b2f4fe5512aa55e4e906d | ac89c256db07448984849346288e0eeffe8b20d0 | /stage0/src/Lean/Elab/Structure.lean | 9ffeb64ceb8f9e8e9e0c26c3e555cf0014167f0b | [
"Apache-2.0"
] | permissive | chepinzhang/lean4 | 002cc667f35417a418f0ebc9cb4a44559bb0ccac | 24fe2875c68549b5481f07c57eab4ad4a0ae5305 | refs/heads/master | 1,688,942,838,326 | 1,628,801,942,000 | 1,628,801,995,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 44,112 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Parser.Command
import Lean.Meta.Closure
import Lean.Meta.SizeOf
import Lean.Meta.Injective
import Lean.Meta.Structure
import Lean.Meta.AppBuilde... |
d35c6950f2196519aabfb3bb3e59d4c01c1a5632 | 618003631150032a5676f229d13a079ac875ff77 | /src/data/int/basic.lean | 1ce1347e4ea04b2f32c935f692c966dd06866762 | [
"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 | 53,716 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
The integers, with addition, multiplication, and subtraction.
-/
import algebra.char_zero
import init_.data.int.order
import algebra.ring
import data.list.range
open nat
... |
73f3c2bd4933eb2f67aaa452f5bbe2b57995439d | 6582544781b11aaa14da20f1d34bead608be4a10 | /lean/love01_definitions_and_statements_demo.lean | 16525f7e07332845bf6f68401a6f6aa8a592c300 | [] | no_license | jpablo/logical_verification_2020 | f34e4945f788d5097d80364a49b518ce92b18194 | 55d9ecde1d7c8ff127f3c13da346e0bc04a3cef5 | refs/heads/master | 1,672,293,528,924 | 1,602,693,572,000 | 1,602,693,572,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,703 | lean | import .lovelib
/- # LoVe Demo 1: Definitions and Statements
We introduce the basics of Lean and proof assistants, without trying to carry
out actual proofs yet. We focus on specifying objects and statements of their
intended properties. -/
set_option pp.beta true
set_option pp.generalized_field_notation false
set... |
b3ce7de6b95c92d9b9085127be0629a713d6d2d9 | 4f9ca1935adf84f1bae9c5740ec1f2ad406716fa | /src/analysis/normed_space/operator_norm.lean | 0fbda4d9160937f5e3fc7f46456771d0a88a19e8 | [
"Apache-2.0"
] | permissive | matthew-hilty/mathlib | 36fd7db866365e9ee4a0ba1d6f8ad34d068cec6c | 585e107f9811719832c6656f49e1263a8eef5380 | refs/heads/master | 1,607,100,509,178 | 1,578,151,707,000 | 1,578,151,707,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 22,164 | lean | /-
Copyright (c) 2019 Jan-David Salchow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo
Operator norm on the space of continuous linear maps
Define the operator norm on the space of continuous linear maps between normed s... |
837e83e6fb4ed9a50905d2bffc85f7a7b3deb4e0 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/analysis/specific_limits/basic.lean | b69227c9b8cf94df1e8c766386ed23578f0c704a | [
"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 | 24,647 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Johannes Hölzl, Yury G. Kudryashov, Patrick Massot
-/
import algebra.geom_sum
import order.filter.archimedean
import order.iterate
import topology.instances.ennreal
... |
8207a558effabbaa0b24567ab7338c119e97d9d0 | 5d166a16ae129621cb54ca9dde86c275d7d2b483 | /tests/lean/unfold1.lean | 9845efef3232929a372fc23892f9a011af256575 | [
"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 | 404 | lean | open tactic
meta definition rewriteH (Hname : name) : tactic unit :=
do get_local Hname >>= rewrite_core reducible tt tt occurrences.all ff,
try reflexivity
example (l : list nat) : list.append l [] = l :=
by do
get_local `l >>= λ H, induction H [`h, `t, `iH],
--
dunfold [`list.append],
trace_state,
trac... |
82c83efccf927a4afdbee6d4d6394c024bfe74d9 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/calculus/deriv/add.lean | c199f455536e6e34fee143320c8cf5cfc0015aa7 | [
"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 | 11,333 | lean | /-
Copyright (c) 2019 Gabriel Ebner All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner, Sébastien Gouëzel, Yury Kudryashov, Anatole Dedecker
-/
import analysis.calculus.deriv.basic
import analysis.calculus.fderiv.add
/-!
# One-dimensional derivatives of sums... |
6d739a21a180baf991de601dd47c8782a62ef1e3 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/run/sigma_match.lean | 31f85efb8c4fb416acc60f14839f268a9942b7e3 | [
"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 | 758 | lean | open sigma
constant {l₁ l₂} hom {A : Type l₁} {B : Type l₂} (a : A) (b : B) : Type (max l₁ l₂)
attribute [reducible]
noncomputable definition arrow_ob (A B : Type) : Type :=
Σ (a : A) (b : B), hom a b
noncomputable definition src1 {A B : Type} (x : arrow_ob A B) : A :=
match x with
(sigma.mk a (sigma.mk b h)) := a... |
cad2e99a553d420cea31c421aa926ebd3ab5a1aa | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/funParen.lean | 75397f4b2a1b15023c4caed3182cc5de7eb33505 | [
"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 | 129 | lean | #check fun (α) [Repr α] => repr (α := α)
#check fun (x y) => x
-- conservatively interpret as pattern
#check fun (x id) => x
|
36b455ff03ccb7347abac4cf6d73fc369853feba | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/sec_notation.lean | 8e037eaac327c94b45b0539204947160c84731a3 | [
"Apache-2.0"
] | permissive | leanprover-community/lean | 12b87f69d92e614daea8bcc9d4de9a9ace089d0e | cce7990ea86a78bdb383e38ed7f9b5ba93c60ce0 | refs/heads/master | 1,687,508,156,644 | 1,684,951,104,000 | 1,684,951,104,000 | 169,960,991 | 457 | 107 | Apache-2.0 | 1,686,744,372,000 | 1,549,790,268,000 | C++ | UTF-8 | Lean | false | false | 197 | lean | open nat
section
parameter (A : Type)
definition f (a b : A) : A := a
definition add2 (a : nat) : nat := a + 2
postfix `+.2`:100 := add2
#reduce 3 +.2
end
example : 3 +.2 = 5 :=
rfl
|
153f0bcab9da13f89f71da067d05f4b811998110 | 36c7a18fd72e5b57229bd8ba36493daf536a19ce | /library/data/encodable.lean | 319fba650c8497b249d3b19aab4c0ba656207455 | [
"Apache-2.0"
] | permissive | YHVHvx/lean | 732bf0fb7a298cd7fe0f15d82f8e248c11db49e9 | 038369533e0136dd395dc252084d3c1853accbf2 | refs/heads/master | 1,610,701,080,210 | 1,449,128,595,000 | 1,449,128,595,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,698 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
Type class for encodable types.
Note that every encodable type is countable.
-/
import data.fintype data.list data.list.sort data.sum data.nat.div data.countab... |
e121a5f3cb09b0960ee3404a23dca0492b1d28ab | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/ring/regular.lean | e34a13b1a68e8a67b81dcffbb5f38812854a9e00 | [
"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 | 3,374 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Yury Kudryashov, Neil Strickland
-/
import algebra.regular.basic
import algebra.ring.defs
/-!
# Lemmas about regular elements in rin... |
eeba95a62e05654188d0e8825bdbb0276ffd1258 | 432d948a4d3d242fdfb44b81c9e1b1baacd58617 | /src/algebraic_geometry/structure_sheaf.lean | 90d345beb739957435a1d926dd2ecb86cc0dae5d | [
"Apache-2.0"
] | permissive | JLimperg/aesop3 | 306cc6570c556568897ed2e508c8869667252e8a | a4a116f650cc7403428e72bd2e2c4cda300fe03f | refs/heads/master | 1,682,884,916,368 | 1,620,320,033,000 | 1,620,320,033,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 21,292 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Scott Morrison
-/
import algebraic_geometry.prime_spectrum
import algebra.category.CommRing.colimits
import algebra.category.CommRing.limits
import topology.sheaves.loc... |
5a10e86ea537ae84f4bab58641fb06306b44e3c0 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/coe4.lean | f1b2b2f063867b1b185e68cb4bd5856aa6fe8e17 | [
"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 | 837 | lean | import logic
namespace setoid
inductive setoid : Type :=
mk_setoid: Π (A : Type'), (A → A → Prop) → setoid
set_option pp.universes true
check setoid
definition test : Type.{2} := setoid.{0}
definition carrier (s : setoid)
:= setoid.rec (λ a eq, a) s
definition eqv {s : setoid} : carrier s → carrier... |
eb6edfd3aa968b0b3214370e30ccf44e80af44b9 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/list/fin_range.lean | cf9423b635b5f3bdb07127a45b2310b71cb8d661 | [
"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 | 2,999 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kenny Lau, Scott Morrison
-/
import data.list.of_fn
import data.list.perm
/-!
# Lists of elements of `fin n`
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes ... |
b742a66245b93a5b11779f667a60cdbd1e3cc050 | 8d65764a9e5f0923a67fc435eb1a5a1d02fd80e3 | /src/topology/algebra/ring.lean | 5d666760ca3a12ec3ab1689d1947b95ca21d2efa | [
"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 | 7,673 | 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
Theory of topological rings.
-/
import topology.algebra.group
import ring_theory.ideal.basic
import ring_theory.subring
import algebra.ring.prod
/-!
#... |
d87a3e2f72e71e6c52237c3b2ba50eb4b5198867 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /test/generalizes.lean | 9019e8ccf3bd3fc4fb4185098298af2a9021d2d8 | [
"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 | 3,547 | lean | /-
Copyright (c) 2020 Jannis Limperg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jannis Limperg
-/
import tactic.generalizes
universes u
lemma example_from_docs₁ (P : ∀ n, fin n → Prop) (n : ℕ) (f : fin n)
(p : ∀ n xs, P n xs) : P (nat.succ n) (fin.succ f) :=
b... |
024cc6cec2d11be3f89d5e74e3a930c6855c5a64 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/fintype/pi.lean | cee402273dd3e1a82ba3e025e4812bc7c15a5182 | [
"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 | 3,590 | 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.fintype.basic
import data.finset.pi
/-!
# fintype instances for pi types
-/
variables {α : Type*}
open finset
namespace fintype
variables [decidable_... |
78ad783bf547800fea146b204534d200f8149083 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/algebra/star/chsh.lean | e6a99191a1fd3026e0044470c9d776dcbe76d4fb | [
"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 | 10,051 | 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.star.basic
import analysis.special_functions.pow
/-!
# The Clauser-Horne-Shimony-Holt inequality and Tsirelson's inequality.
We establish a version o... |
43775103413ef984fcb569fc75936b5e1de0e566 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/data/set/finite.lean | 0a65e12bc734afb8ed592f514f3d1f2e5d44f5b8 | [
"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 | 34,843 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import data.finset.sort
/-!
# Finite sets
This file defines predicates `finite : set α → Prop` and `infinite : set α → Prop` and proves some
basic f... |
b5ec09dbd1e51feb4489c67a7586b35f9d7e9570 | 9b9a16fa2cb737daee6b2785474678b6fa91d6d4 | /src/tactic/fin_cases.lean | efbf72b7f7a8ddc946f9f8bd5356acdcd1618028 | [
"Apache-2.0"
] | permissive | johoelzl/mathlib | 253f46daa30b644d011e8e119025b01ad69735c4 | 592e3c7a2dfbd5826919b4605559d35d4d75938f | refs/heads/master | 1,625,657,216,488 | 1,551,374,946,000 | 1,551,374,946,000 | 98,915,829 | 0 | 0 | Apache-2.0 | 1,522,917,267,000 | 1,501,524,499,000 | Lean | UTF-8 | Lean | false | false | 1,954 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Scott Morrison
Case bashing on `fin n`, for explicit numerals `n`.
-/
import data.fin
namespace tactic
open lean.parser
open interactive interactive.types expr
meta def fin_cases_at ... |
be92edb70bf60b3cc473c688e176f8d86fdaef68 | d320d01276642370017b4ce56793b5f73e0016f9 | /lean projects and notes/finalreview.lean | c85d0eea22314f60e8278d679b364c5a1d9fcca3 | [] | no_license | samiazam00/my-work | 388d815ddc7e47860375959ba31be2530be7f11e | e9a8218b2441dce00bf117d3d985d00e6ee14ec0 | refs/heads/master | 1,608,518,076,248 | 1,580,268,523,000 | 1,580,268,523,000 | 236,280,156 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,973 | lean | --** Writing functions, recursion:
--see HW 3 for more examples
-- ex. recursive sum function:
def sumto : ℕ → ℕ
| 0 := 0
| (nat.succ n') := (nat.succ n') + sumto n'
-- ex. function that creates a list of string s repeated n times
def repeat : string → ℕ → list string
| s 0 := list.nil
| s (nat.succ n') := ... |
3dd67a870bbe43bd19dc5e4c0662abc14b66d5e3 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/category_theory/concrete_category/basic.lean | 6de88da5ec5a96983efbdef42af1599aff6ba20e | [
"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 | 6,586 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Johannes Hölzl, Reid Barton, Sean Leather, Yury Kudryashov
-/
import category_theory.types
import category_theory.full_subcategory
/-!
# Concrete categories
A concret... |
539cf8be4ade017c48cb0cf4d7ab4a9647eee693 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/list/zip.lean | 137526647df63cf2075c8419d71f127020f8788d | [
"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 | 15,894 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kenny Lau
-/
import data.list.big_operators
/-!
# zip & unzip
This file provides results about `list.zip_with`, `list.zip` and `list.unzip` (definitions are in
core L... |
a30db2864b010f9834760225201c67bd44204881 | 4fa161becb8ce7378a709f5992a594764699e268 | /src/analysis/convex/cone.lean | 74e490e4618dc769ac79537c7c9ca5f7eefaf807 | [
"Apache-2.0"
] | permissive | laughinggas/mathlib | e4aa4565ae34e46e834434284cb26bd9d67bc373 | 86dcd5cda7a5017c8b3c8876c89a510a19d49aad | refs/heads/master | 1,669,496,232,688 | 1,592,831,995,000 | 1,592,831,995,000 | 274,155,979 | 0 | 0 | Apache-2.0 | 1,592,835,190,000 | 1,592,835,189,000 | null | UTF-8 | Lean | false | false | 18,763 | lean | /-
Copyright (c) 2020 Yury Kudryashov All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import linear_algebra.linear_pmap
import analysis.convex.basic
import order.zorn
/-!
# Convex cones
In a vector space `E` over `ℝ`, we define a convex cone as a su... |
8a4fca12917a7bc9331fa57c35b28381ff1032c0 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/monoidal/limits.lean | 930b3912659abcad2b80f7cadf0ef8bba4784394 | [
"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 | 3,961 | 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 category_theory.monoidal.functorial
import category_theory.monoidal.functor_category
import category_theory.limits.has_limits
/-!
# `lim : (J ⥤ C) ⥤ C` is lax... |
6842c9713255df2fd21554b28ca0bb1751f028b6 | 675b8263050a5d74b89ceab381ac81ce70535688 | /src/data/real/ennreal.lean | e2fc19bfadff4482d8cd8ce93267d5b6698736e2 | [
"Apache-2.0"
] | permissive | vozor/mathlib | 5921f55235ff60c05f4a48a90d616ea167068adf | f7e728ad8a6ebf90291df2a4d2f9255a6576b529 | refs/heads/master | 1,675,607,702,231 | 1,609,023,279,000 | 1,609,023,279,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 55,948 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl, Yury Kudryashov
-/
import data.real.nnreal
import data.set.intervals
/-!
# Extended non-negative reals
We define `ennreal := with_no ℝ≥0` to be the type of extended no... |
9093f6c18e22b023d552103c6e7f044862778bf2 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/limits/shapes/equalizers.lean | 750dc84ea4f73c4f17d39146b3ae07d337ddea1e | [
"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 | 45,892 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Markus Himmel
-/
import category_theory.epi_mono
import category_theory.limits.has_limits
/-!
# Equalizers and coequalizers
This file defines (co)equalizers as specia... |
a4384428eacd2495e621372518e987c120ea07f9 | 46125763b4dbf50619e8846a1371029346f4c3db | /src/algebra/module.lean | 076027745fc900e317a90ef62c4dc0c1c64f0454 | [
"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 | 18,407 | lean | /-
Copyright (c) 2015 Nathaniel Thomas. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nathaniel Thomas, Jeremy Avigad, Johannes Hölzl, Mario Carneiro
Modules over a ring.
## Implementation notes
Throughout the `linear_map` section implicit `{}` brackets are often ... |
ec6d01b78e3a389d633800a6de51c8fa25422991 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /07_Induction_and_Recursion.org.21.lean | d1aaf5862f7da22206f5189a44ea93f4ab805cdc | [] | 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 | 471 | lean | /- page 108 -/
import standard
import data.list
open nat bool list
-- BEGIN
definition is_not_zero (a : nat) : bool :=
match a with
| zero := ff
| succ _ := tt
end
-- We can use recursive equations and match
variable {A : Type}
variable p : A → bool
definition filter : list A → list A
| filter nil := nil
| f... |
45d4f5d7fcd239a4e092c581eacb8606b89f420b | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/group_theory/order_of_element.lean | 2b148145624fc4c9526a45d155a9e3c30f5089c5 | [
"Apache-2.0"
] | permissive | jumpy4/mathlib | d3829e75173012833e9f15ac16e481e17596de0f | af36f1a35f279f0e5b3c2a77647c6bf2cfd51a13 | refs/heads/master | 1,693,508,842,818 | 1,636,203,271,000 | 1,636,203,271,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 28,707 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Julian Kuelshammer
-/
import algebra.pointwise
import group_theory.coset
import dynamics.periodic_pts
import algebra.iterate_hom
/-!
# Order of an element
This file d... |
36560d4f5085b6ce58fe3905ed84a998f7dd65b0 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/preadditive/schur.lean | 72adf4c71242d1bd33a2216c492676303a11cac7 | [] | 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 | 1,811 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Scott Morrison
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.simple
import Mathlib.category_theory.preadditive.default
im... |
9fe781b2162ae681ccd0c9dd84104bd390b91ba6 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/ring_theory/witt_vector/frobenius_fraction_field.lean | e9cd65c73af4f49789074aab6002b93ed192c2a1 | [
"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 | 11,970 | lean | /-
Copyright (c) 2022 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Heather Macbeth
-/
import data.nat.cast.with_top
import field_theory.is_alg_closed.basic
import ring_theory.witt_vector.discrete_valuation_ring
/-!
# Solving equatio... |
696d61f7e163c13c2b85dc4a25c0497e1d0d67a6 | 46125763b4dbf50619e8846a1371029346f4c3db | /src/topology/metric_space/basic.lean | ad4e772fafe0caea1e64c02a2728692dd91df76d | [
"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 | 66,301 | lean | /-
Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Metric spaces.
Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
Many definitions and theorems expected on metric spaces are already introduced o... |
ba8abfae5e7f136a589d007b379b10428c5a2f7c | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/ring_theory/localization/away.lean | 1ca217eb416a16e9070e79e688563d7c3b454e5e | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 7,043 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen
-/
import ring_theory.adjoin_root
import ring_theory.localization.basic
/-!
# Localizations away from an element
... |
da5ac26b1f27cd0123a304436af85541a83f4eb4 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/ring_theory/algebra_tower.lean | 13995f4ff684d88a3b7d37d947822047beb4ace0 | [
"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 | 14,131 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import algebra.algebra.restrict_scalars
import algebra.algebra.tower
import algebra.invertible
import linear_algebra.basis
import ring_theory.adjoin.fg
import ring_theory.polyn... |
9a0fc613332f2dcba5838d70e4366541efc4ee1d | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/quotient.lean | 3cd044c5b6bf8caa129009776098e1ab8fc7f02b | [
"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 | 2,223 | 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 tactic.basic
/-!
# Algebraic quotients
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> https://github.com/leanprover-community/mathlib4/pull/643
> Any changes to this... |
845c4569af648a98d58a07236cab7b1169153cdf | 130c49f47783503e462c16b2eff31933442be6ff | /stage0/src/Lean/Parser/Extension.lean | 784a8e0d7121d9aa35dd7b6640bfd8fae19ba1f0 | [
"Apache-2.0"
] | permissive | Hazel-Brown/lean4 | 8aa5860e282435ffc30dcdfccd34006c59d1d39c | 79e6732fc6bbf5af831b76f310f9c488d44e7a16 | refs/heads/master | 1,689,218,208,951 | 1,629,736,869,000 | 1,629,736,896,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 26,212 | 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
-/
import Lean.ScopedEnvExtension
import Lean.Parser.Basic
import Lean.Parser.StrInterpolation
import Lean.KeyedDeclsAttribute
/-! Extensib... |
7f3497aa5f01445a25ee0e17342e38d946f33d01 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/graded_object.lean | 80fe7b9126dc9cc7422c0fed9fdbea2debbcc93f | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 6,819 | 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.group_power.lemmas
import category_theory.pi.basic
import category_theory.shift
import category_theory.concrete_category.basic
/-!
# The category of g... |
bd8b92f8f18799faa280750df9dd2e700a234697 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/measure_theory/function/uniform_integrable.lean | 12a46e9d26327c9b3e1fb3b8ebbafc786c960b90 | [
"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 | 48,623 | lean | /-
Copyright (c) 2022 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import measure_theory.function.convergence_in_measure
/-!
# Uniform integrability
This file contains the definitions for uniform integrability (both in the measure theory... |
ead9f395f70377f2aee597621b356dba35e6a77f | 63abd62053d479eae5abf4951554e1064a4c45b4 | /test/norm_digits.lean | 6a6ba62e59fd88bc862fa34845efc8b2bd0d30e2 | [
"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 | 674 | lean | import data.nat.digits
example : nat.digits 0 0 = [] := by norm_digits
example : nat.digits 1 0 = [] := by norm_digits
example : nat.digits 2 0 = [] := by norm_digits
example : nat.digits 10 0 = [] := by norm_digits
example : nat.digits 0 1 = [1] := by norm_digits
example : nat.digits 0 1000 = [1000] := by norm_digits... |
64abe6fce3452f56dca9dc136d1fa1bc3d6e100c | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/analysis/convex/exposed.lean | 2d4650d67dedcae84d60ad1a8939c44edd308131 | [
"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 | 8,889 | lean | /-
Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import analysis.convex.extreme
/-!
# Exposed sets
This file defines exposed sets and exposed points for sets in a real vector space.
An exp... |
2c8c4e37ecda1247327c83b82a3ccdfda26ec176 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/run/cc_ac_bug.lean | 386f8fb533c1fc47c48b57ff28234dffd89d4b0b | [
"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 | 110 | lean | example (a b c : nat) (f : nat → nat → nat) : f (b * c) (c * b * a) = f (c * b) (a * c * b) :=
by ac_refl
|
36495f8133cdef4a26f281bd2578a3bbaa654672 | 92b50235facfbc08dfe7f334827d47281471333b | /library/logic/instances.lean | e9ac41a61f10eee562e4e4f67dd845bec4a379d0 | [
"Apache-2.0"
] | permissive | htzh/lean | 24f6ed7510ab637379ec31af406d12584d31792c | d70c79f4e30aafecdfc4a60b5d3512199200ab6e | refs/heads/master | 1,607,677,731,270 | 1,437,089,952,000 | 1,437,089,952,000 | 37,078,816 | 0 | 0 | null | 1,433,780,956,000 | 1,433,780,955,000 | null | UTF-8 | Lean | false | false | 3,767 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
Class instances for iff and eq.
-/
import logic.connectives algebra.relation
namespace relation
/- logical equivalence relations -/
theorem is_equivalence_eq [... |
69551b544997a1285ae83cc2142a1b82baa84f81 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/category_theory/pi/basic.lean | e0dfb43d1a61a504cfb4db17c2daf1b0a272f1e2 | [
"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 | 4,369 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Scott Morrison
-/
import category_theory.natural_isomorphism
import category_theory.eq_to_hom
/-!
# Categories of indexed families of objects.
We define the pointwise ca... |
125edf360b471b68737e2540ef3f70752fcc787c | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/eq1.lean | 5d3f426e6f0e0c86746e03b15563d379f35d1ab7 | [
"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 | 82 | lean | import Int.
variable i : Int
check i = 0
set_option pp::coercion true
check i = 0
|
620fd98f0ac879130a707c706e224a6e3d56e78d | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/analysis/calculus/implicit.lean | 622726d32387ca0a5c62000ec597907cebdc56ef | [
"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 | 20,211 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import analysis.calculus.inverse
import analysis.normed_space.complemented
/-!
# Implicit function theorem
We prove three versions of the implicit function theore... |
a00666136654471e4edf38c02d2e5b863cc8707a | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/category_theory/category/Kleisli.lean | 736b45987fc722ad6c180c4605224eee1f286437 | [
"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 | 1,621 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import category_theory.category.basic
/-!
# The Kleisli construction on the Type category
Define the Kleisli category for (control) monads.
`category_theory/monad/kleisli... |
5930ac340bcdbb9b81275ff06753f9fb231cb516 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /doc/examples/NFM2022/nfm3.lean | 3db250777703108b3c641cdfd2de34aa9119af06 | [
"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 | 1,357 | lean | /- Enumerated types -/
inductive Weekday where
| sunday | monday | tuesday | wednesday
| thursday | friday | saturday
#check Weekday.sunday
-- Weekday
open Weekday
#check sunday
def natOfWeekday (d : Weekday) : Nat :=
match d with
| sunday => 1
| monday => 2
| tuesday => 3
| wednesday => 4
|... |
ab575e2013835d36074546fb06f0b83a7a1472ba | f3849be5d845a1cb97680f0bbbe03b85518312f0 | /tests/lean/run/calc.lean | 8fae77820940041adea25036b4e9e798e231a605 | [
"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 | 356 | lean | namespace foo
constant le : num → num → Prop
axiom le_trans {a b c : num} : le a b → le b c → le a c
attribute [trans] le_trans
infix `<<`:50 := le
end foo
namespace foo
theorem T {a b c d : num} : a << b → b << c → c << d → a << d
:= assume H1 H2 H3,
calc a << b : H1
... << c : H2
... |
b9ad73e3dfa11ba30bc637caa6e50d6f03da3fb4 | 05d69962fb9deab19838de9bbcf33ebdbf8faa57 | /mul_aux.lean | 59d3e7e25253d73a6ee036106ee83e0867dda8c5 | [] | no_license | pj0y1/polynom | 6eb7c96dbf34960be5721a232a67f7a592aedf7a | 9e198cc9104017fae7774574f141197bb295ee66 | refs/heads/master | 1,611,193,417,139 | 1,501,472,138,000 | 1,501,472,138,000 | 64,856,946 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 17,155 | lean | import finsupp alg_aux
open classical set prod.ops eq.ops
open function comm_cancel_monoid
set_option max_memory 2048
namespace function_aux
variables {A B:Type}
section commutativity --1
variables [comm_semigroup A][comm_semiring B]
/- for polynoms to be commutative, B has to be comm_ring-/
theorem mul_co... |
6870a4a8d1bf2b48abb6e012666eaf56e649eb3f | ce6917c5bacabee346655160b74a307b4a5ab620 | /src/ch5/ex0602.lean | 82fcf5c912ec5bfc3b0266eb00505cddc637834c | [] | 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 | 128 | lean | example (x y : ℕ) (p : ℕ → Prop) (q : Prop) (h : q → x = y) (h' : p y) (hq : q) : p x :=
by { rw (h hq), assumption }
|
8dce62e66f2ec730cbe6b234c8d9ad2332d3bbf6 | a721fe7446524f18ba361625fc01033d9c8b7a78 | /src/principia/topology/connectedness.lean | 7911b259feaf7138cb2c0e52016ec974c980fbbc | [] | no_license | Sterrs/leaning | 8fd80d1f0a6117a220bb2e57ece639b9a63deadc | 3901cc953694b33adda86cb88ca30ba99594db31 | refs/heads/master | 1,627,023,822,744 | 1,616,515,221,000 | 1,616,515,221,000 | 245,512,190 | 2 | 0 | null | 1,616,429,050,000 | 1,583,527,118,000 | Lean | UTF-8 | Lean | false | false | 15,263 | lean | import .topological_space
import .continuity
namespace hidden
namespace topological_space
variables {α β : Type}
open classical
local attribute [instance] classical.prop_decidable
structure disconnects (X : topological_space α) (U V: myset α): Prop :=
(neq_empty_left: U ≠ ∅) (neq_empty_right: V ≠ ∅)
(open_left: X... |
111685b5b5a39102b919d2b022092d1e840b5f14 | 6b02ce66658141f3e0aa3dfa88cd30bbbb24d17b | /src/Lean/Parser/Tactic.lean | 96ed2925c54e27a30890e558941668acb2c63010 | [
"Apache-2.0"
] | permissive | pbrinkmeier/lean4 | d31991fd64095e64490cb7157bcc6803f9c48af4 | 32fd82efc2eaf1232299e930ec16624b370eac39 | refs/heads/master | 1,681,364,001,662 | 1,618,425,427,000 | 1,618,425,427,000 | 358,314,562 | 0 | 0 | Apache-2.0 | 1,618,504,558,000 | 1,618,501,999,000 | null | UTF-8 | Lean | false | false | 1,215 | 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
-/
import Lean.Parser.Term
namespace Lean
namespace Parser
namespace Tactic
builtin_initialize
register_parser_alias "tacticSeq" tact... |
76a42edba8517e14f937a15ecfc958f076c1c443 | efce24474b28579aba3272fdb77177dc2b11d7aa | /src/homotopy_theory/formal/cofibrations/brown.lean | 5729bb3fb1fd05ee38d1ec2bfc95d890f74b8b8c | [
"Apache-2.0"
] | permissive | rwbarton/lean-homotopy-theory | cff499f24268d60e1c546e7c86c33f58c62888ed | 39e1b4ea1ed1b0eca2f68bc64162dde6a6396dee | refs/heads/lean-3.4.2 | 1,622,711,883,224 | 1,598,550,958,000 | 1,598,550,958,000 | 136,023,667 | 12 | 6 | Apache-2.0 | 1,573,187,573,000 | 1,528,116,262,000 | Lean | UTF-8 | Lean | false | false | 10,435 | lean | import .arrow
import .cofibration_category
import tactic.slice
/- Brown factorization, aka "Ken Brown's lemma", and a relative version.
Following Rădulescu-Banu, Cofibrations in Homotopy Theory, section 1.3. -/
universes v u
namespace homotopy_theory.cofibrations
open category_theory
open category_theory.categ... |
a3afd46f6ae6585795e99e0acca3f41b96e8a37c | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/analysis/inner_product_space/rayleigh.lean | a85ca67aafd3c14d6a81c16c7ba935faba49d3ac | [
"Apache-2.0"
] | permissive | jumpy4/mathlib | d3829e75173012833e9f15ac16e481e17596de0f | af36f1a35f279f0e5b3c2a77647c6bf2cfd51a13 | refs/heads/master | 1,693,508,842,818 | 1,636,203,271,000 | 1,636,203,271,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 12,313 | lean | /-
Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth, Frédéric Dupuis
-/
import analysis.inner_product_space.calculus
import analysis.inner_product_space.dual
import analysis.calculus.lagrange_multipliers
import linear_a... |
fb519176c9c088266d95801cc536cac8c9dbf8c9 | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/linear_algebra/finsupp_vector_space.lean | cccfd64c0873b315872d194c89c1d4f1acaf4f12 | [
"Apache-2.0"
] | permissive | ilitzroth/mathlib | ea647e67f1fdfd19a0f7bdc5504e8acec6180011 | 5254ef14e3465f6504306132fe3ba9cec9ffff16 | refs/heads/master | 1,680,086,661,182 | 1,617,715,647,000 | 1,617,715,647,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,092 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import data.mv_polynomial
import linear_algebra.dimension
import linear_algebra.direct_sum.finsupp
import linear_algebra.finite_dimensional
/-!
# Linear structures ... |
46256b05bc217d6eb97d8365371ad0210c690580 | 9dd3f3912f7321eb58ee9aa8f21778ad6221f87c | /library/init/category/combinators.lean | d034302bc04048055f9e44e63cffcbe6d0151a12 | [
"Apache-2.0"
] | permissive | bre7k30/lean | de893411bcfa7b3c5572e61b9e1c52951b310aa4 | 5a924699d076dab1bd5af23a8f910b433e598d7a | refs/heads/master | 1,610,900,145,817 | 1,488,006,845,000 | 1,488,006,845,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,609 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
Monad combinators, as in Haskell's Control.Monad.
-/
prelude
import init.category.monad init.data.list.basic
universes u v w
def mmap {m : Type u → Type v} [mona... |
1486d015cd836c9dfda900569196ef8ed6db2ec5 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/reader.lean | 7aadc489ed365a5fb9dcf610c2bac67ed92f3597 | [
"Apache-2.0"
] | permissive | leanprover-community/lean | 12b87f69d92e614daea8bcc9d4de9a9ace089d0e | cce7990ea86a78bdb383e38ed7f9b5ba93c60ce0 | refs/heads/master | 1,687,508,156,644 | 1,684,951,104,000 | 1,684,951,104,000 | 169,960,991 | 457 | 107 | Apache-2.0 | 1,686,744,372,000 | 1,549,790,268,000 | C++ | UTF-8 | Lean | false | false | 298 | lean | import system.io
def lifted_test : state_t ℕ (reader_t ℕ io) unit :=
do 0 ← get,
1 ← read,
adapt_reader (λ n, (n, 2)) ((do p ← read,
put p.2) : state_t ℕ (reader_t (ℕ × ℕ) io) _),
2 ← get,
pure ()
#eval (lifted_test.run 0).run 1
|
7e96df9726bbc606e832fe25bc7a8457bb569cbe | 6214e13b31733dc9aeb4833db6a6466005763162 | /src/soundness.lean | a4c81d92ec35f77feb1a0d36dfab14b622c7a892 | [] | no_license | joshua0pang/esverify-theory | 272a250445f3aeea49a7e72d1ab58c2da6618bbe | 8565b123c87b0113f83553d7732cd6696c9b5807 | refs/heads/master | 1,585,873,849,081 | 1,527,304,393,000 | 1,527,304,393,000 | 154,901,199 | 1 | 0 | null | 1,540,593,067,000 | 1,540,593,067,000 | null | UTF-8 | Lean | false | false | 3,779 | lean | import .definitions3 .progress .preservation
lemma true_true_freevars: FV (prop.term value.true ⋀ prop.term value.true) = FV (prop.term value.true) :=
have h1: FV (prop.term value.true ⋀ prop.term value.true) = ∅, from set.eq_empty_of_forall_not_mem (
assume x: var,
assume : x ∈ FV (prop.term value.true ⋀ pr... |
d91bdce38f15d5e7522069b42e6deae147451fd6 | c1a29ca460720df88ab68dc42d9a1a02e029d505 | /examples/introduction/unnamed_111.lean | 91ebd546cb8a9c2df8e51a63d55280052bfbb537 | [] | no_license | agusakov/mathematics_in_lean | acb5b3d659e4522ae4b4836ea550527f03f6546c | 2539562e4d91c858c73dbecb5b282ce1a7d38b6d | refs/heads/master | 1,665,963,365,241 | 1,592,080,022,000 | 1,592,080,022,000 | 272,078,062 | 0 | 0 | null | 1,592,078,772,000 | 1,592,078,772,000 | null | UTF-8 | Lean | false | false | 141 | lean | #check 2 + 2 = 4
def fermat_last_theorem :=
∀ x y z n : ℕ, n > 2 → x * y * z ≠ 0 → x^n + y^n ≠ z^n
#check fermat_last_theorem |
2bc84d1502db4c448828a2b721ef2bac026b444a | 130c49f47783503e462c16b2eff31933442be6ff | /stage0/src/Init/WF.lean | de9c3ff473299e269f924c6b6fa0c8b1565fee8d | [
"Apache-2.0"
] | permissive | Hazel-Brown/lean4 | 8aa5860e282435ffc30dcdfccd34006c59d1d39c | 79e6732fc6bbf5af831b76f310f9c488d44e7a16 | refs/heads/master | 1,689,218,208,951 | 1,629,736,869,000 | 1,629,736,896,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,166 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import Init.SizeOf
import Init.Data.Nat.Basic
universe u v
set_option codegen false
inductive Acc {α : Sort u} (r : α → α → Prop) : α → Prop where... |
f9ab594fb7a58d3444eb75239a4daed7473d3f38 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/stream/init.lean | d48687ae32734224390ce07189632bb9a899cdfc | [
"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 | 22,037 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
/-!
# Streams a.k.a. infinite lists a.k.a. infinite sequences
This file used to be in the core library. It was moved to `mathlib` and renamed to `init` to... |
9ee5f1b8c9884fe0699ce2ba7f2ac60dfa762d82 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /src/Init/Data/HashSet.lean | ff9e65d498303540a8051b2a58f53bdf96c0f421 | [
"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 | 6,459 | 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
-/
prelude
import Init.Data.Array.Basic
import Init.Data.List.Control
import Init.Data.Option.Basic
import Init.Data.Hashable
universes u v w
def HashSetBucket... |
226e9cc68a7dcffe9397104f3c7756d194f28be3 | 1d265c7dd8cb3d0e1d645a19fd6157a2084c3921 | /src/other/int_vector3d_cross_full.lean | 28e8b90b677539372d3b8204eec31958c3994e4d | [
"MIT"
] | permissive | hanzhi713/lean-proofs | de432372f220d302be09b5ca4227f8986567e4fd | 4d8356a878645b9ba7cb036f87737f3f1e68ede5 | refs/heads/master | 1,585,580,245,658 | 1,553,646,623,000 | 1,553,646,623,000 | 151,342,188 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 7,194 | lean | -- theorem add_assoc' (a b c : ℤ) : a+b+c = a+(b+c) := add_assoc a b c
-- theorem add_comm' (a b : ℤ) : a + b = b + a := add_comm a b
-- theorem mul_assoc' (a b c : ℤ) : a*b*c = a*(b*c) := mul_assoc a b c
-- theorem mul_comm' (a b:ℤ) : a*b=b*a := mul_comm a b
-- theorem add_mul' (a b c : ℤ) : (a+b)*c = a*c+b*c := add_m... |
bed890a54bf626c4a1f06c2cb384c1914a6b6f55 | 947b78d97130d56365ae2ec264df196ce769371a | /src/Lean/Elab/PreDefinition/MkInhabitant.lean | 70fcd3aa706a16d81927d88160457d5c769e1654 | [
"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 | 1,607 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.AppBuilder
namespace Lean
namespace Elab
open Meta
private def mkInhabitant? (type : Expr) : MetaM (Option Expr) :=
catch
(do inh ← mkA... |
22904cfa241077ebf6b4285fed8ba4d264691819 | 8f209eb34c0c4b9b6be5e518ebfc767a38bed79c | /code/src/internal/Ant/implies.lean | 8dc11c3855a96dd56d0c0eeccbcd8a3e0efdd2ab | [] | no_license | hediet/masters-thesis | 13e3bcacb6227f25f7ec4691fb78cb0363f2dfb5 | dc40c14cc4ed073673615412f36b4e386ee7aac9 | refs/heads/master | 1,680,591,056,302 | 1,617,710,887,000 | 1,617,710,887,000 | 311,762,038 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 890 | lean | import tactic
import data.finset
import ..internal_definitions
import .rhss
import .map
variable [GuardModule]
open GuardModule
@[trans] lemma Ant.implies_trans (a b c : Ant bool) (h1: a ⟶ b) (h2: b ⟶ c): a ⟶ c :=
begin
induction h1 generalizing c;
cases h2,
{ refine Ant.implies.rhs _; tauto, },
{ ref... |
339cb00189c0d348d93e762c137bf537756348fd | 4d3f29a7b2eff44af8fd0d3176232e039acb9ee3 | /LAMR/Examples/using_lean/examples4.lean | 71b6ece15b948000539275605554a724203e4176 | [] | no_license | marijnheule/lamr | 5fc5d69d326ff92e321242cfd7f72e78d7f99d7e | 28cc4114c7361059bb54f407fa312bf38b48728b | refs/heads/main | 1,689,338,013,620 | 1,630,359,632,000 | 1,630,359,632,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,831 | lean |
-- textbook: List
import Init
open List
variable {α : Type}
variable (as bs cs : List α)
variable (a b c : α)
#check a :: as
#check as ++ bs
example : [] ++ as = as := nil_append as
example : (a :: as) ++ bs = a :: (as ++ bs) := cons_append a as bs
-- end textbook: List
-- textbook: append_nil'
theorem append_n... |
5c415ef8bf1fd4d39a604cbcbbda6c8e54dc35f8 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/2073.lean | 2ee5893bcf01c754c9468556d950baca0be2cd71 | [
"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 | 107 | lean | def Commute (a b : Nat) := a * b = b * a
example : Commute m n :=
calc m * n = n * m := Nat.mul_comm ..
|
9e673c48e29a27cd08bcea3f0924c45bba8dad40 | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/simp17.lean | 905907de54be5c5b0ce87c95a09356188ffa53c8 | [
"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 | 351 | lean | rewrite_set simple
add_rewrite and_truer and_truel and_falser and_falsel or_falsel Nat::add_zeror a_neq_a : simple
(*
add_congr_theorem("simple", "and_congrr")
*)
variables a b c : Nat
(*
local t = parse_lean([[c + 0 ≠ b + 1 ∧ b = 0 ∧ c = 1]])
local s, pr = simplify(t, "simple")
print(s)
print(pr)
print(get_environ... |
c03e8238b5391f14aca788841dd4a175a00fad1e | cf39355caa609c0f33405126beee2739aa3cb77e | /library/init/control/state.lean | ca00bbb040c29cb36306e1a1c1c229157fc26959 | [
"Apache-2.0"
] | permissive | leanprover-community/lean | 12b87f69d92e614daea8bcc9d4de9a9ace089d0e | cce7990ea86a78bdb383e38ed7f9b5ba93c60ce0 | refs/heads/master | 1,687,508,156,644 | 1,684,951,104,000 | 1,684,951,104,000 | 169,960,991 | 457 | 107 | Apache-2.0 | 1,686,744,372,000 | 1,549,790,268,000 | C++ | UTF-8 | Lean | false | false | 7,811 | 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, Sebastian Ullrich
The state monad transformer.
-/
prelude
import init.control.alternative init.control.lift
import init.control.id init.control.except
univer... |
80296a501d8caab6ee14ad54f6b27c297cb06567 | 246309748072bf9f8da313401699689ebbecd94d | /src/linear_algebra/eigenspace.lean | 42d0db932bee9879ecb6e23acbf5db6373dd21b7 | [
"Apache-2.0"
] | permissive | YJMD/mathlib | b703a641e5f32a996f7842f7c0043bab2b462ee2 | 7310eab9fa8c1b1229dca42682f1fa6bfb7dbbf9 | refs/heads/master | 1,670,714,479,314 | 1,599,035,445,000 | 1,599,035,445,000 | 292,279,930 | 0 | 0 | null | 1,599,050,561,000 | 1,599,050,560,000 | null | UTF-8 | Lean | false | false | 11,561 | 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 field_theory.algebraic_closure
import linear_algebra.finsupp
/-!
# Eigenvectors and eigenvalues
This file defines eigenspaces and eigenvalues.
An e... |
1d013240ce19ae80d1273692f53f35678541ac0c | 9dd3f3912f7321eb58ee9aa8f21778ad6221f87c | /tests/lean/notation4.lean | 8362f6a440ec734127245e7748c5f5c6f4e0ec0d | [
"Apache-2.0"
] | permissive | bre7k30/lean | de893411bcfa7b3c5572e61b9e1c52951b310aa4 | 5a924699d076dab1bd5af23a8f910b433e598d7a | refs/heads/master | 1,610,900,145,817 | 1,488,006,845,000 | 1,488,006,845,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 310 | lean | --
open sigma
inductive List (T : Type) : Type | nil {} : List | cons : T → List → List open List notation h :: t := cons h t notation `[` l:(foldr `,` (h t, cons h t) nil) `]` := l
check ∃ (A : Type) (x y : A), x = y
check ∃ (x : num), x = 0
check Σ' (x : num), x = 10
check Σ (A : Type), List A
|
60eb5a88580c5ccd6089058559df6ad6171e0625 | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /tests/lean/no_confusion_type.lean | aedb431274b08377aac9a528b3816d0c49b868f0 | [
"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 | 353 | lean | import logic data.nat.basic
open nat
inductive vector (A : Type) : nat → Type :=
vnil : vector A zero,
vcons : Π {n : nat}, A → vector A n → vector A (succ n)
check vector.no_confusion_type
constants a1 a2 : num
constants v1 v2 : vector num 2
constant P : Type₁
eval vector.no_confusion_type P (vector.vcons a1 v... |
ab8fca4951b8d387e7a9442b91540dd87715d2c5 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/tactic/omega/term.lean | 40f6f5b4cdc48b02b1fc88b5338d137743dd1b16 | [
"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 | 2,690 | lean | /-
Copyright (c) 2019 Seul Baek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Seul Baek
-/
/-
Normalized linear integer arithmetic terms.
-/
import tactic.omega.coeffs
namespace omega
/-- Shadow syntax of normalized terms. The first element
represents the cons... |
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