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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
583bbdb56bc77b8ea794afd651e9581237754d3c | f00cc9c04d77f9621aa57d1406d35c522c3ff82c | /tests/lean/run/monad_error_problem.lean | 0afdf2359162ee06655e33873060fb71cfcd5989 | [
"Apache-2.0"
] | permissive | shonfeder/lean | 444c66a74676d74fb3ef682d88cd0f5c1bf928a5 | 24d5a1592d80cefe86552d96410c51bb07e6d411 | refs/heads/master | 1,619,338,440,905 | 1,512,842,340,000 | 1,512,842,340,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 623 | lean | namespace issue
universes u v w
class monad_error (ε : inout Type u) (m : Type w → Type v) :=
[monad_m : monad m]
(fail : Π {α : Type w}, ε → m α)
set_option pp.all true
def unreachable {α} {m} [monad_error string m] : m α :=
monad_error.fail m "unreachable"
#check @unreachable
end issue
namespace original_issue
un... |
c41284a8724ac215965dbb0d8aeb26d09dae4ede | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /tests/lean/run/reduce3.lean | 61e110204823863aa6acb8736fc68db0e9b14096 | [
"Apache-2.0"
] | permissive | williamdemeo/lean4 | 72161c58fe65c3ad955d6a3050bb7d37c04c0d54 | 6d00fcf1d6d873e195f9220c668ef9c58e9c4a35 | refs/heads/master | 1,678,305,356,877 | 1,614,708,995,000 | 1,614,708,995,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 762 | lean |
def fact : Nat → Nat
| 0 => 1
| (n+1) => (n+1)*fact n
#check fact 6
#eval fact 10
-- set_option pp.all true
theorem tst1 : 100000000000 + 200000000000 = 300000000000 :=
rfl
theorem tst2 : 100000000000 * 200000000000 = 20000000000000000000000 :=
rfl
theorem tst3 : fact 7 = 5040 :=
rfl
theorem tst4 : fact 10 =... |
0424e65c2db30915555c7a0faaf68bb86f008117 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/int/nat_prime.lean | 4579ccc4dea978e0976cde637d2b4b2a1f6e0ac4 | [
"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 | 1,499 | 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 data.nat.prime
/-!
# Lemmas about nat.prime using `int`s
-/
open nat
namespace int
lemma not_prime_of_int_mul {a b : ℤ} {c : ℕ}
(ha :... |
2bc838788fef6a5fe735a040631f8ee1fa67537c | e514e8b939af519a1d5e9b30a850769d058df4e9 | /src/tactic/rewrite_search/tactic.lean | 10bc9c92d8aaeaba9c5c98e75ae62633cf66e7b9 | [] | no_license | semorrison/lean-rewrite-search | dca317c5a52e170fb6ffc87c5ab767afb5e3e51a | e804b8f2753366b8957be839908230ee73f9e89f | refs/heads/master | 1,624,051,754,485 | 1,614,160,817,000 | 1,614,160,817,000 | 162,660,605 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 8,893 | lean |
-- This file almost qualifies for inclusion in the `core` dir, but
-- the hooks into non-core pieces, i.e. providing defaults, and also
-- the external interface it exports is enough to keep it out here.
import .core
import .module
-- Default strategy, metric, and tracer used as a fallback by the engine
-- (so must ... |
dd7e0822efd182a3d4f64602f1ee1ecb98fcb552 | 7da5ceac20aaab989eeb795a4be9639982e7b35a | /src/tactic/fattribute.lean | 6b3bda84e2972e88d05f2b2f5bc39650cf717632 | [
"MIT"
] | permissive | formalabstracts/formalabstracts | 46c2f1b3a172e62ca6ffeb46fbbdf1705718af49 | b0173da1af45421239d44492eeecd54bf65ee0f6 | refs/heads/master | 1,606,896,370,374 | 1,572,988,776,000 | 1,572,988,776,000 | 96,763,004 | 165 | 28 | null | 1,555,709,319,000 | 1,499,680,948,000 | Lean | UTF-8 | Lean | false | false | 2,125 | lean | /-
Copyright (c) 2019 Koundinya Vajjha. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Koundinya Vajjha
The fabstract user attribute.
-/
import tactic.metadata
import system.io
open interactive interactive.types lean.parser tactic native io
@[user_attribute]
meta d... |
3ed63c483a41b73e5f96234b639fe0ff8591bf9b | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /src/Init/Lean/Meta/Tactic/Induction.lean | 70b960820499d47968a0c95e9a2d1b376c33b558 | [
"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 | 10,915 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import Init.Lean.Meta.RecursorInfo
import Init.Lean.Meta.SynthInstance
import Init.Lean.Meta.Tactic.Util
import Init.Lean.Meta.Tactic.Revert
import ... |
22fe6d1a5b7259a6d25232a3066a55033a1c7ba0 | 36938939954e91f23dec66a02728db08a7acfcf9 | /lean/deps/decodex86/src/decodex86.lean | fca8f38fe3e402b1014935927d47730b5d76e9ec | [
"Apache-2.0"
] | permissive | pnwamk/reopt-vcg | f8b56dd0279392a5e1c6aee721be8138e6b558d3 | c9f9f185fbefc25c36c4b506bbc85fd1a03c3b6d | refs/heads/master | 1,631,145,017,772 | 1,593,549,019,000 | 1,593,549,143,000 | 254,191,418 | 0 | 0 | null | 1,586,377,077,000 | 1,586,377,077,000 | null | UTF-8 | Lean | false | false | 2,928 | lean |
import system.io
import .instruction
import .sexp -- debugging
namespace decodex86
/- A decoder is an ADT with the ability to decode instructions given
an address. A decoder is parameterised by the path of the decoder
executable, and the details of the text segment of interest (the
file is most likely an ... |
3de44232f3933211a3526226b9d974e6c585e4f0 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/tactic/omega/int/preterm.lean | 7bdf5987831d0b2223e1774b3b542b6eb64ac00b | [
"Apache-2.0"
] | permissive | gebner/mathlib | eab0150cc4f79ec45d2016a8c21750244a2e7ff0 | cc6a6edc397c55118df62831e23bfbd6e6c6b4ab | refs/heads/master | 1,625,574,853,976 | 1,586,712,827,000 | 1,586,712,827,000 | 99,101,412 | 1 | 0 | Apache-2.0 | 1,586,716,389,000 | 1,501,667,958,000 | Lean | UTF-8 | Lean | false | false | 2,825 | lean | /- Copyright (c) 2019 Seul Baek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Seul Baek
Linear integer arithmetic terms in pre-normalized form. -/
import tactic.split_ifs tactic.omega.term
namespace omega
namespace int
/-- The shadow syntax for arithmetic terms. A... |
30ce86c30be93253a05144e3477284d0d7aa3248 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/concrete_instance.lean | 46b4535d433dc9846dc097d2cb0d029eb280970f | [
"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 | 177 | lean | variables a b : nat
set_option pp.all true
#check a * b
#check a + b
-- instance : semigroup nat := sorry
-- instance : add_semigroup nat := sorry
#check a * b
#check a + b
|
9b574a5085040c00d01bab0f1be9b139e32bfc76 | 78630e908e9624a892e24ebdd21260720d29cf55 | /src/logic_first_order/fol_09.lean | 215a5bdc1b1ffcfdda124105fcac84be97db6a60 | [
"CC0-1.0"
] | permissive | tomasz-lisowski/lean-logic-examples | 84e612466776be0a16c23a0439ff8ef6114ddbe1 | 2b2ccd467b49c3989bf6c92ec0358a8d6ee68c5d | refs/heads/master | 1,683,334,199,431 | 1,621,938,305,000 | 1,621,938,305,000 | 365,041,573 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 456 | lean | namespace fol_09
variable A : Type
variables P Q : A → Prop
theorem fol_09 : ((∀ x, P x → Q x) ∧ (∃ x, P x)) → ∃ x, Q x :=
assume h1: (∀ x, P x → Q x) ∧ (∃ x, P x),
have h2: ∀ x, P x → Q x, from and.left h1,
have h3: ∃ x, P x, from and.right h1,
show ∃ x, Q x, from exists.elim h3
(assume t (h4: P t),
have h5: P ... |
46bcf4035ae88234a31e92c5ae8e42f96751b0e8 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/topology/instances/real.lean | 6d3a1566d23d558747284e7d76406fce61b96238 | [
"Apache-2.0"
] | permissive | gebner/mathlib | eab0150cc4f79ec45d2016a8c21750244a2e7ff0 | cc6a6edc397c55118df62831e23bfbd6e6c6b4ab | refs/heads/master | 1,625,574,853,976 | 1,586,712,827,000 | 1,586,712,827,000 | 99,101,412 | 1 | 0 | Apache-2.0 | 1,586,716,389,000 | 1,501,667,958,000 | Lean | UTF-8 | Lean | false | false | 14,892 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
The real numbers ℝ.
They are constructed as the topological completion of ℚ. With the following steps:
(1) prove that ℚ forms a uniform space.
(2) subt... |
5ae5edd772f6d27d62b901ac1c557059984f30f1 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/analysis/box_integral/partition/filter.lean | 269041acca025d560029abd19eaddb0d9516ab23 | [
"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 | 27,739 | lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import analysis.box_integral.partition.subbox_induction
import analysis.box_integral.partition.additive
/-!
# Filters used in box-based integrals
First we define ... |
6eefa4d9506551abde4ca9dbf86ae81c1669f868 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/natlit.lean | c3b5654da3ac71d8f683b3fbbb221286acb6f09a | [
"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 | 176 | lean |
def tst1 : 0 + 1 = 1 := rfl
def tst2 : 2 + 3 = 5 := rfl
def tst3 : 4 + 3 = 7 := rfl
def tst4 : 0 + 3 = 3 := rfl
def tst5 : 1 + 3 = 4 := rfl
def tst6 : 100 + 100 = 200 := rfl
|
2e4eeada6dbf19fc5ce380cd9fd8928a63555e75 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/algebraic_geometry/Scheme.lean | 3ea0aafa989bafbf44b5a724d5ee48b56b4cb8e2 | [
"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 | 3,814 | 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 algebraic_geometry.Spec
/-!
# The category of schemes
A scheme is a locally ringed space such that every point is contained in some open set
where there is a... |
309fc326f8fee45d4dd49378741dd7d744a46c73 | 626e312b5c1cb2d88fca108f5933076012633192 | /src/algebra/smul_with_zero.lean | 440139f4738a3e500cd387823f52c10d034deab5 | [
"Apache-2.0"
] | permissive | Bioye97/mathlib | 9db2f9ee54418d29dd06996279ba9dc874fd6beb | 782a20a27ee83b523f801ff34efb1a9557085019 | refs/heads/master | 1,690,305,956,488 | 1,631,067,774,000 | 1,631,067,774,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,877 | lean | /-
Copyright (c) 2021 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import algebra.group_power.basic
import algebra.opposites
/-!
# Introduce `smul_with_zero`
In analogy with the usual monoid action on a Type `M`, we introduce an acti... |
0d6c3c5f6f5eaa85f21c590baec16de9f3e0044a | 618003631150032a5676f229d13a079ac875ff77 | /src/algebra/category/Group/adjunctions.lean | 21e584cd8ceb89b70c0c9aaa80a45e8e3ce4d822 | [
"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 | 1,809 | 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.Group
import group_theory.free_abelian_group
/-!
The free abelian group on a type is the left adjoint of the
forgetful functo... |
4470be711ab9649e51f13db874d370da7a44a84e | b19a1b7dc79c802247fdce4c04708e070863b4d2 | /propositional-assertions.lean | e1d2c5447df599017df645e2bea4c96d0feca499 | [] | no_license | utanapishtim/promethazine | 99a1e80311fb20251a54ba78a534b23852b88c40 | 08a6f9bd6dd08feb3df8d4697e19ffc8d333b249 | refs/heads/master | 1,653,595,504,487 | 1,480,129,933,000 | 1,480,129,933,000 | 74,801,596 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,269 | lean | open classical
variables p q r s : Prop
-- commutativity of ∧ and ∨
example : p ∧ q ↔ q ∧ p := _
example : p ∨ q ↔ q ∨ p := _
-- associativity of ∧ and ∨
example : (p ∧ q) ∧ r ↔ p ∧ (q ∧ r) := _
example : (p ∨ q) ∨ r ↔ p ∨ (q ∨ r) := _
-- distributivity
example : p ∧ (q ∨ r) ↔ (p ∧ q) ∨ (p ∧ r) := _
example : p ∨... |
3d5dc5256db98ac64f429769cad30a750c6636f6 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/analysis/convex/specific_functions.lean | e539611bc0e54c369874040e978806c74c226cae | [
"Apache-2.0"
] | permissive | gebner/mathlib | eab0150cc4f79ec45d2016a8c21750244a2e7ff0 | cc6a6edc397c55118df62831e23bfbd6e6c6b4ab | refs/heads/master | 1,625,574,853,976 | 1,586,712,827,000 | 1,586,712,827,000 | 99,101,412 | 1 | 0 | Apache-2.0 | 1,586,716,389,000 | 1,501,667,958,000 | Lean | UTF-8 | Lean | false | false | 4,214 | 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.mean_value data.nat.parity analysis.complex.exponential
/-!
# Collection of convex functions
In this file we prove that the following fun... |
88a8a32360f731462ad50340beeac38159114934 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/data/fin/ops.lean | 8dc6c79cf691be9f7abbf838791e845109aa2ec0 | [] | 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 | 2,394 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.data.nat.default
import Mathlib.Lean3Lib.init.data.fin.basic
namespace Mathlib
namespace fin
protec... |
f2a0d3a30b1135418878f2985d7cb10d4d1c1bbf | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/field_theory/finite_card.lean | a7e3572629e231633260f5abb5c97e4ed2b66c84 | [
"Apache-2.0"
] | permissive | ChrisHughes24/mathlib | 98322577c460bc6b1fe5c21f42ce33ad1c3e5558 | a2a867e827c2a6702beb9efc2b9282bd801d5f9a | refs/heads/master | 1,583,848,251,477 | 1,565,164,247,000 | 1,565,164,247,000 | 129,409,993 | 0 | 1 | Apache-2.0 | 1,565,164,817,000 | 1,523,628,059,000 | Lean | UTF-8 | Lean | false | false | 1,120 | lean | /-
Copyright (c) 2019 Casper Putz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joey van Langen, Casper Putz
-/
import algebra.char_p data.zmod.basic linear_algebra.basis
universes u
variables (α : Type u) [discrete_field α] [fintype α]
namespace finite_field
the... |
d8abc46a22744e1f40d87eb5e7aaf81d1122d004 | 5e3548e65f2c037cb94cd5524c90c623fbd6d46a | /src_icannos_totilas/aops/2008-IMO-Problem_4.lean | e4193350f104191d8ca30fc845274b00e98477e6 | [] | no_license | ahayat16/lean_exos | d4f08c30adb601a06511a71b5ffb4d22d12ef77f | 682f2552d5b04a8c8eb9e4ab15f875a91b03845c | refs/heads/main | 1,693,101,073,585 | 1,636,479,336,000 | 1,636,479,336,000 | 415,000,441 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 309 | lean | import data.real.basic
theorem exo (f: real -> real) :
(forall x, f x > 0)
-> (forall x y z w: real, x > 0 /\ y > 0 /\ z > 0 /\ w > 0 /\ w*x = y*z ->
((f w)^2 + (f x)^2) / (f y^2 + f z^2) = (w^2 + x^2) / (y^2 + z^2)
)
-> (forall x > 0, f(x) = x) \/ (forall x > 0, f(x) = 1/x)
:= sorry |
57da4d6a69bc36ed9ef9b7a372e8e2212993d7b4 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/hott/krewrite_bug.hlean | e34259247115b5f3a35ed3a7f3442ed239b5a267 | [
"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 | 1,314 | hlean | import algebra.category.functor
open function category eq prod prod.ops equiv is_equiv sigma sigma.ops is_trunc funext iso
open pi
namespace functor
variables {A B C D E : Precategory}
definition compose_pentagon_test (K : D ⇒ E) (H : C ⇒ D) (G : B ⇒ C) (F : A ⇒ B) :
(calc K ∘f H ∘f G ∘f F = (K ∘f H) ∘f G ∘f... |
fbd444b197a9ee6f40e5457a7146fd2807e75e2f | b70031c8e2c5337b91d7e70f1e0c5f528f7b0e77 | /src/order/filter/basic.lean | 129067c47a3c56d3ebcd1de83faf6e25a884b1a1 | [
"Apache-2.0"
] | permissive | molodiuc/mathlib | cae2ba3ef1601c1f42ca0b625c79b061b63fef5b | 98ebe5a6739fbe254f9ee9d401882d4388f91035 | refs/heads/master | 1,674,237,127,059 | 1,606,353,533,000 | 1,606,353,533,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 99,607 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jeremy Avigad
-/
import order.zorn
import order.copy
import data.set.finite
import tactic.monotonicity
/-!
# Theory of filters on sets
## Main definitions
* `filter`... |
f385025c2ab77a8380ea05755c1ca4e280a75489 | 7cdf3413c097e5d36492d12cdd07030eb991d394 | /src/game/world4/level3.lean | 4765d3e64d08c9c8e13d8e1551fcc1cbb00618cc | [] | no_license | alreadydone/natural_number_game | 3135b9385a9f43e74cfbf79513fc37e69b99e0b3 | 1a39e693df4f4e871eb449890d3c7715a25c2ec9 | refs/heads/master | 1,599,387,390,105 | 1,573,200,587,000 | 1,573,200,691,000 | 220,397,084 | 0 | 0 | null | 1,573,192,734,000 | 1,573,192,733,000 | null | UTF-8 | Lean | false | false | 331 | lean | import game.world4.level2 -- hide
namespace mynat -- hide
/-
# World 4 : Power World
## Level 3: `pow_one`
-/
/- Lemma
For all naturals $a$, $a ^ 1 = a$.
-/
lemma pow_one (a : mynat) : a ^ (1 : mynat) = a :=
begin [less_leaky]
rw one_eq_succ_zero,
rw pow_succ,
rw pow_zero,
rw one_mul,
refl,
end
end myn... |
6d59a9da150ea4ff82ab99b01dd4b7004dc1e412 | 7a76361040c55ae1eba5856c1a637593117a6556 | /src/exercises/love02_backward_proofs_exercise_solution.lean | edcbee63437f9595a3ffd306259f42c2ffe7260d | [] | no_license | rgreenblatt/fpv2021 | c2cbe7b664b648cef7d240a654d6bdf97a559272 | c65d72e48c8fa827d2040ed6ea86c2be62db36fa | refs/heads/main | 1,692,245,693,819 | 1,633,364,621,000 | 1,633,364,621,000 | 407,231,487 | 0 | 0 | null | 1,631,808,608,000 | 1,631,808,608,000 | null | UTF-8 | Lean | false | false | 4,704 | lean | import ..lectures.love02_backward_proofs_demo
/-! # LoVe Exercise 2: Backward Proofs -/
set_option pp.beta true
set_option pp.generalized_field_notation false
namespace LoVe
namespace backward_proofs
/-! ## Question 1: Connectives and Quantifiers
1.1. Carry out the following proofs using basic tactics.
Hint: S... |
b1883b6067dc07817746bfe94d00d78afa57758b | 8930e38ac0fae2e5e55c28d0577a8e44e2639a6d | /algebra/ordered_group.lean | 623e5f858c69d4f0ec18f7d1cce01dd6a06724c6 | [
"Apache-2.0"
] | permissive | SG4316/mathlib | 3d64035d02a97f8556ad9ff249a81a0a51a3321a | a7846022507b531a8ab53b8af8a91953fceafd3a | refs/heads/master | 1,584,869,960,527 | 1,530,718,645,000 | 1,530,724,110,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 19,941 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl
Ordered monoids and groups.
-/
import algebra.group order.bounded_lattice tactic.basic
universe u
variable {α : Type u}
section old_structure_cmd
set... |
182b8833f4853fd0a4b91c478284d04b183c9db8 | 36c7a18fd72e5b57229bd8ba36493daf536a19ce | /tests/lean/run/415.hlean | 34bcc3fb1d6df3f38f017ba6decc4b48df400656 | [
"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 | 326 | hlean | import algebra.group
open path_algebra
variable {A : Type}
variable [s : add_comm_group A]
include s
theorem add_minus_cancel_left1 (a b c : A) : (c + a) - (c + b) = a - b :=
begin
rotate_left 1,
apply sorry
end
theorem add_minus_cancel_left2 (a b c : A) : (c + a) - (c + b) = a - b :=
by rotate_left 1;
apply ... |
be49d6e3b3d2b6a31afce089fb163825b2df1f8b | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/category/Group/limits.lean | 0878a696a834b887b4da45481b9aa3261a96cb35 | [
"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 | 12,318 | 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.category.Mon.limits
import algebra.category.Group.preadditive
import category_theory.over
import category_theory.limits.concrete_category
import catego... |
a9641cb1b785e6f78a26045bb77387dc131d39a3 | a4673261e60b025e2c8c825dfa4ab9108246c32e | /stage0/src/Init/Data/Fin/Basic.lean | 3973bd7168b10fda31dc70b0fbbb0a93f24a5ca6 | [
"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 | 2,316 | 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.Data.Nat.Div
import Init.Data.Nat.Bitwise
import Init.Coe
open Nat
namespace Fin
instance coeToNat {n} : Coe (Fin n) Nat :=
⟨fun v =... |
4ef96ede37634d9ceb2b9257d4d38e82705eced3 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/topology/list.lean | 15693259043742fc52d791147123cbfc4873321f | [
"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 | 8,729 | lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import topology.constructions
import topology.algebra.monoid
/-!
# Topology on lists and vectors
-/
open topological_space set filter
open_locale topological_space filt... |
a2abd57114e731219948e29293ac97a565d7b5fc | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/topology/omega_complete_partial_order.lean | 22abd1a899e0beaad93abcf4e6d547292c04a83c | [
"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 | 5,195 | lean | /-
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Simon Hudon
-/
import topology.basic
import order.omega_complete_partial_order
/-!
# Scott Topological Spaces
A type of topological spaces whose notion
of continuity is equivalent to con... |
71d37e9164408681dcb567bbeccef532925f8ecd | ea4aee6b11f86433e69bb5e50d0259e056d0ae61 | /src/tidy/tactic_states.lean | 079f51322a2f6cabfa24dec9347e95ff662d5324 | [] | no_license | timjb/lean-tidy | e18feff0b7f0aad08c614fb4d34aaf527bf21e20 | e767e259bf76c69edfd4ab8af1b76e6f1ed67f48 | refs/heads/master | 1,624,861,693,182 | 1,504,411,006,000 | 1,504,411,006,000 | 103,740,824 | 0 | 0 | null | 1,505,553,968,000 | 1,505,553,968,000 | null | UTF-8 | Lean | false | false | 5,689 | lean | -- Copyright (c) 2017 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Scott Morrison
open tactic
universe variables u v w
-- TODO surely this should be in the standard library
meta definition interaction_monad.result.map { α σ σ' : Type } (r : i... |
795797d819fdff10d2c044125cbadd969aa8d693 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/equiv/transfer_instance_auto.lean | c62ec30b6709a2a109ca1679e8b50bb228236466 | [] | 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 | 11,652 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.equiv.basic
import Mathlib.algebra.field
import Mathlib.algebra.module.default
import ... |
c1e10b7b3eef57983d339b56898d89a122c5c307 | 77c5b91fae1b966ddd1db969ba37b6f0e4901e88 | /src/ring_theory/roots_of_unity.lean | d174c752f77749413c74dd3ace7d24d7e9a4e8c6 | [
"Apache-2.0"
] | permissive | dexmagic/mathlib | ff48eefc56e2412429b31d4fddd41a976eb287ce | 7a5d15a955a92a90e1d398b2281916b9c41270b2 | refs/heads/master | 1,693,481,322,046 | 1,633,360,193,000 | 1,633,360,193,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 40,421 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import data.nat.parity
import data.polynomial.ring_division
import group_theory.specific_groups.cyclic
import ring_theory.integral_domain
import number_theory.diviso... |
b69e4750f166020aadce513544d14ec0baf07caa | 9338c56dfd6ceacc3e5e63e32a7918cfec5d5c69 | /src/spectrum_of_a_ring/induced_continuous_map.lean | 5955f334524d8da685424400431123f0d62dc4c7 | [] | no_license | Project-Reykjavik/lean-scheme | 7322eefce504898ba33737970be89dc751108e2b | 6d3ec18fecfd174b79d0ce5c85a783f326dd50f6 | refs/heads/master | 1,669,426,172,632 | 1,578,284,588,000 | 1,578,284,588,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,492 | lean | /-
Induced map from Spec(B) to Spec(A).
https://stacks.math.columbia.edu/tag/00E2
-/
import topology.basic
import ring_theory.ideal_operations
import spectrum_of_a_ring.zariski_topology
open lattice
universes u v
variables {α : Type u} {β : Type v} [comm_ring α] [comm_ring β]
variables (f : α → β) [is_ring_hom... |
d1f0596dd5b6dd022ae091eee09577b8d5456804 | 80746c6dba6a866de5431094bf9f8f841b043d77 | /src/algebra/group_power.lean | 57997eea4ba045efb6b4b3f867d5148d80d27017 | [
"Apache-2.0"
] | permissive | leanprover-fork/mathlib-backup | 8b5c95c535b148fca858f7e8db75a76252e32987 | 0eb9db6a1a8a605f0cf9e33873d0450f9f0ae9b0 | refs/heads/master | 1,585,156,056,139 | 1,548,864,430,000 | 1,548,864,438,000 | 143,964,213 | 0 | 0 | Apache-2.0 | 1,550,795,966,000 | 1,533,705,322,000 | Lean | UTF-8 | Lean | false | false | 24,902 | lean | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis
The power operation on monoids and groups. We separate this from group, because it depends on
nat, which in turn depends on other parts of algebra.
We h... |
5180065a077d891da03034b7477fde551c22fbd8 | f98c49f30cbc7120b78f92246f22dedad3f11f62 | /lean/book/Logic_and_Proof/LP_03_Natural_Deduction_for_Propositional_Logic.lean | 32b1063c56e9865fe7e46b0e7a463fa56f9c3cdf | [
"Unlicense"
] | permissive | haroldcarr/learn-haskell-coq-ml-etc | 5a88bbbb0e0f435798ee9cab29d9e9da854174e2 | a7247caa22097573cbfa1e95fa81debeb146c12a | refs/heads/master | 1,683,755,751,897 | 1,682,914,556,000 | 1,682,914,556,000 | 12,350,346 | 36 | 9 | null | null | null | null | UTF-8 | Lean | false | false | 347 | lean | -- Give a natural deduction proof of 𝐴∧𝐵 from hypothesis 𝐵∧𝐴.
example (A B : Prop) : B ∧ A → A ∧ B := λ (h : B ∧ A), and.intro h.right h.left
-- Give a natural deduction proof of (𝑄→𝑅)→𝑅 from hypothesis 𝑄.
example (Q R : Prop) : Q ∧ (Q → R) → R := λ (h₁ : Q ∧ (Q → R)), h₁.right h₁.left
|
d8f3f574e8ed0c823fd605b3d47e53f1841abf76 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/probability/notation.lean | 882efd388369cdbef292ac7e328fe9693469db73 | [
"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 | 1,878 | lean | /-
Copyright (c) 2021 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import measure_theory.function.conditional_expectation.real
/-! # Notations for probability theory
This file defines the following notations, for functions `X,Y`, measu... |
b566e395aff15ac633804b30ffe8f61dec031e33 | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /tests/lean/run/unifhint3.lean | 8e341c26eb59601cf31463776c49d17cfa65ca31 | [
"Apache-2.0"
] | permissive | collares/lean4 | 861a9269c4592bce49b71059e232ff0bfe4594cc | 52a4f535d853a2c7c7eea5fee8a4fa04c682c1ee | refs/heads/master | 1,691,419,031,324 | 1,618,678,138,000 | 1,618,678,138,000 | 358,989,750 | 0 | 0 | Apache-2.0 | 1,618,696,333,000 | 1,618,696,333,000 | null | UTF-8 | Lean | false | false | 1,379 | lean | /- Coercion pullback example from the paper "Hints in Unification" -/
universes u
structure Monoid where
α : Type u
op : α → α → α
unit : α
structure Group where
α : Type u
op : α → α → α
unit : α
inv : α → α
structure Ring where
α : Type u
mul : α → α → α
add : α → α → α
neg :... |
2959947b6b833dd3fdbe0cb32775808cdfd4b39d | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /03_Propositions_and_Proofs.org.17.lean | 99629636a14d93e763d198ed9dbd71f76f588fc9 | [] | 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 | 131 | lean | /- page 38 -/
import standard
variables p q : Prop
check p → q → p ∧ q
check ¬p → p ↔ false
check p ∨ q → q ∨ p
|
a668154429ffd88679a932b0c4bfb4a2184d2ed9 | ce89339993655da64b6ccb555c837ce6c10f9ef4 | /inf_prime.lean | 172644f8e099ce1993e652ab95cb14dbbba40cf8 | [] | no_license | zeptometer/LearnLean | ef32dc36a22119f18d843f548d0bb42f907bff5d | bb84d5dbe521127ba134d4dbf9559b294a80b9f7 | refs/heads/master | 1,625,710,824,322 | 1,601,382,570,000 | 1,601,382,570,000 | 195,228,870 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 723 | lean | def eudclid : ∀ k l m : ℕ, (l ∣ m ∧ l ∣ (m + k)) → l ∣ m ∧ l ∣ k :=
begin
intros k l m,
intros h,
cases h with lm lmk,
apply and.intro,
exact lm,
apply (nat.dvd_add_iff_right lm).mpr,
exact lmk
end
def factorial_n : ∀ n : ℕ, ∃ m : ℕ, ∀ l : ℕ, l ≤ n → l ∣ m :=
begin
apply nat.rec,
apply (exists.int... |
9cfd176e9ac3fb1c1fb1419cb233af35b190031e | 6e9cd8d58e550c481a3b45806bd34a3514c6b3e0 | /src/ring_theory/fractional_ideal.lean | b9bada9c8386026b933757875cf27b43c371b700 | [
"Apache-2.0"
] | permissive | sflicht/mathlib | 220fd16e463928110e7b0a50bbed7b731979407f | 1b2048d7195314a7e34e06770948ee00f0ac3545 | refs/heads/master | 1,665,934,056,043 | 1,591,373,803,000 | 1,591,373,803,000 | 269,815,267 | 0 | 0 | Apache-2.0 | 1,591,402,068,000 | 1,591,402,067,000 | null | UTF-8 | Lean | false | false | 20,348 | 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 ring_theory.localization
import ring_theory.principal_ideal_domain
/-!
# Fractional ideals
This file defines fractional ideals of an integral domain and proves bas... |
1512d686a9d0f2dd66e0cefefd6b1debd5d52abc | 43390109ab88557e6090f3245c47479c123ee500 | /src/Banach spaces.lean | 008a1723fcf291784f486be8dc2df71a486b3869 | [
"Apache-2.0"
] | permissive | Ja1941/xena-UROP-2018 | 41f0956519f94d56b8bf6834a8d39473f4923200 | b111fb87f343cf79eca3b886f99ee15c1dd9884b | refs/heads/master | 1,662,355,955,139 | 1,590,577,325,000 | 1,590,577,325,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 548 | lean | import analysis.metric_space algebra.module inner_product_spaces.basic
import inner_product_spaces.norm_space
universes u v
variables V W : Type
section norm_space
-- Banach space is a complete normed space.
class banach_space (V : Type) extends norm_space V: Type :=
(complete: complete_space ℝ)
noncomputable insta... |
98119978e238fa292946953ebd34d39fe91044df | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/set/pointwise/big_operators.lean | 5460c2512846cc04fbb0eee32ecc1256ea18e22f | [
"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 | 6,955 | lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import algebra.big_operators.basic
import data.set.pointwise.basic
/-!
# Results about pointwise operations on sets and big operators.
> THIS FILE IS SYNCHRONIZED WITH MA... |
dd6bb25938260d984d9cc4eae33529076d2cebb5 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/category_theory/limits/shapes/regular_mono.lean | f4dd9f2e2ebf9a9d8f827337a90acebf7f90c5e5 | [
"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 | 14,863 | 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.preserves.basic
import category_theory.limits.shapes.kernels
import category_theory.limits.shapes.strong_epi
import catego... |
74801515999c92d8a4c1adad006c86ede48f3298 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/ring_theory/matrix_algebra.lean | 323fc9aae3d16a999b6cf6ab80c3170708078b3e | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 5,224 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Eric Wieser
-/
import data.matrix.basis
import ring_theory.tensor_product
/-!
We show `matrix n n A ≃ₐ[R] (A ⊗[R] matrix n n R)`.
-/
universes u v w
open_locale tens... |
5e1c4bd868a6fb0efb4932c4448e6ff47459184c | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/control/fold.lean | 674d41339585f4ab453bbfa8fbdf1cf2a8e15709 | [
"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 | 14,975 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Sean Leather
-/
import algebra.free_monoid
import algebra.opposites
import control.traversable.instances
import control.traversable.lemmas
import category_theory.endomorphism... |
3c2f6a063e1223560abf3b76cff8dba90f8542a0 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/analysis/normed_space/operator_norm.lean | 1ae5c3a806ab7b8e32ba7663dc3127649e91c323 | [
"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 | 57,506 | 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
-/
import linear_algebra.finite_dimensional
import analysis.normed_space.linear_isometry
import analysis.normed_space.riesz_lemma
impor... |
771c7f09cbd0912c75dcfaa8c7a28d7ce919dba9 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/number_theory/cyclotomic/discriminant.lean | ef6c2e982b731fd20eabe92f9f6322a1f2ad7a48 | [
"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 | 11,889 | lean | /-
Copyright (c) 2022 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
import number_theory.cyclotomic.primitive_roots
import ring_theory.discriminant
/-!
# Discriminant of cyclotomic fields
We compute the discriminant of a `p ^ n`-t... |
416c79bb2d332dce7fa4a9212901421ff60c934f | b70031c8e2c5337b91d7e70f1e0c5f528f7b0e77 | /src/field_theory/adjoin.lean | 43c3545b296167889e31775c31b8fd09358b100c | [
"Apache-2.0"
] | permissive | molodiuc/mathlib | cae2ba3ef1601c1f42ca0b625c79b061b63fef5b | 98ebe5a6739fbe254f9ee9d401882d4388f91035 | refs/heads/master | 1,674,237,127,059 | 1,606,353,533,000 | 1,606,353,533,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 20,422 | lean | /-
Copyright (c) 2020 Thomas Browning and Patrick Lutz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning and Patrick Lutz
-/
import field_theory.intermediate_field
import field_theory.splitting_field
import field_theory.fixed
/-!
# Adjoining Elements to... |
fa00ef618ce38d86f33ca0e592a7d87adad63811 | 471bedbd023d35c9d078c2f936dd577ace7f5813 | /library/init/wf.lean | c75d08c1a0434a22a482d8736da21e6b5524a1d1 | [
"Apache-2.0"
] | permissive | lambdaxymox/lean | e06f0fa503666df827edd9867d7f49ca017aae64 | fc13c8c72a15dab71a2c2b31410c2cadc3526bd7 | refs/heads/master | 1,666,785,407,985 | 1,666,153,673,000 | 1,666,153,673,000 | 310,165,986 | 0 | 0 | Apache-2.0 | 1,604,542,096,000 | 1,604,542,095,000 | null | UTF-8 | Lean | false | false | 7,103 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import init.data.nat.basic init.data.prod
universes u v
/-- A value `x : α` is accessible from `r` when every value that's lesser under `r` is also... |
a00b2afbe2e13ab7e28f96df7e95c5d627d9f728 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/data/nat/pow.lean | 68a6541c08376f53d54877e686f1a841b5733548 | [
"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 | 11,570 | lean | /-
Copyright (c) 2014 Floris van Doorn (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
import algebra.group_power.order
/-! # `nat.pow`
Results on the power operation... |
d5f8348340323f847862e060f3ed285b70b6e3b1 | 8eeb99d0fdf8125f5d39a0ce8631653f588ee817 | /src/topology/instances/nnreal.lean | 63ab24436bfad2df2f6594c6c719322aa0228fa6 | [
"Apache-2.0"
] | permissive | jesse-michael-han/mathlib | a15c58378846011b003669354cbab7062b893cfe | fa6312e4dc971985e6b7708d99a5bc3062485c89 | refs/heads/master | 1,625,200,760,912 | 1,602,081,753,000 | 1,602,081,753,000 | 181,787,230 | 0 | 0 | null | 1,555,460,682,000 | 1,555,460,682,000 | null | UTF-8 | Lean | false | false | 3,724 | lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
Nonnegative real numbers.
-/
import topology.algebra.infinite_sum
noncomputable theory
open set topological_space metric
open_locale topological_space
namespace nnreal... |
b423e2137bc44c6625b53686400406c357da3aa1 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/calc_heq_symm.lean | a5a51c3375a7864dd207f2d59869d216ad126311 | [
"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 | 314 | lean | theorem tst {A B C D : Type} {a₁ a₂ : A} {b : B} {c : C} {d : D}
(H₀ : a₁ = a₂) (H₁ : a₂ == b) (H₂ : b == c) (H₃ : c == d) : d == a₁ :=
calc d == c : heq.symm H₃
... == b : heq.symm H₂
... == a₂ : heq.symm H₁
... = a₁ : eq.symm H₀
#print definition tst
|
ca0b235c7cc1dda465a920185309daa7771dde60 | 246309748072bf9f8da313401699689ebbecd94d | /src/data/fintype/basic.lean | 9524db98b509a47d7c85310f1be83006853b4972 | [
"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 | 44,554 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
Finite types.
-/
import tactic.wlog
import data.finset.powerset
import data.finset.lattice
import data.finset.pi
import data.array.lemmas
universes u v
variables {α : ... |
6a01411b9b7a4f36fd8305636958c9758cb91290 | 137c667471a40116a7afd7261f030b30180468c2 | /src/category_theory/skeletal.lean | c711d5a02edf93831f553b23d5c7c491a91ebf41 | [
"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 | 10,570 | 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 category_theory.isomorphism_classes
import category_theory.thin
/-!
# Skeleton of a category
Define skeletal categories as categories in which any two isomorphic... |
4029f30f19aa0b9c4a652b68c32072b2c366d1cf | 9a0b1b3a653ea926b03d1495fef64da1d14b3174 | /algebra/field.lean | 55af3fb0c700f6716649ad126dda8891de22be0a | [
"Apache-2.0"
] | permissive | khoek/mathlib-tidy | 8623b27b4e04e7d598164e7eaf248610d58f768b | 866afa6ab597c47f1b72e8fe2b82b97fff5b980f | refs/heads/master | 1,585,598,975,772 | 1,538,659,544,000 | 1,538,659,544,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,207 | 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 algebra.ring logic.basic
open set
universe u
variables {α : Type u}
instance division_ring.to_domain [s : division_ring α] : domain α :=
{ eq... |
4b7ef79edc29721333536429020cf4aea31005ef | 75db7e3219bba2fbf41bf5b905f34fcb3c6ca3f2 | /hott/types/prod.hlean | 8e5375340d92e86975126ad16f939ed9655d9270 | [
"Apache-2.0"
] | permissive | jroesch/lean | 30ef0860fa905d35b9ad6f76de1a4f65c9af6871 | 3de4ec1a6ce9a960feb2a48eeea8b53246fa34f2 | refs/heads/master | 1,586,090,835,348 | 1,455,142,203,000 | 1,455,142,277,000 | 51,536,958 | 1 | 0 | null | 1,455,215,811,000 | 1,455,215,811,000 | null | UTF-8 | Lean | false | false | 8,717 | hlean | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Jakob von Raumer
Ported from Coq HoTT
Theorems about products
-/
open eq equiv is_equiv is_trunc prod prod.ops unit equiv.ops
variables {A A' B B' C D : Type} {P... |
4b04fd3f0b549278f7e2e5e8545e45e956b5bca2 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/set/intervals/unordered_interval.lean | 61410b54b796e87b8e9352b6f606823d81db74ab | [
"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 | 10,014 | lean | /-
Copyright (c) 2020 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
-/
import order.bounds.basic
import data.set.intervals.basic
/-!
# Intervals without endpoints ordering
In any decidable linear order `α`, we define the set of elements ... |
1fa7f7319e0283877424e52b900cfef8a40f0513 | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /tests/lean/run/expr_maps.lean | e8b78370f3931b67cc21b02ee15e32e17b6425cb | [
"Apache-2.0"
] | permissive | walterhu1015/lean4 | b2c71b688975177402758924eaa513475ed6ce72 | 2214d81e84646a905d0b20b032c89caf89c737ad | refs/heads/master | 1,671,342,096,906 | 1,599,695,985,000 | 1,599,695,985,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,929 | lean | import Lean.Expr
open Lean
def exprType : Expr := mkSort levelOne
def biDef := BinderInfo.default
def exprNat := mkConst `Nat []
-- Type -> Type
def TypeArrowType := mkForall `α biDef exprType exprType
-- Type -> Type
def TypeArrowType2 := mkForall `β biDef exprType exprType
-- fun (x : Nat) => x
... |
e0515050977a41f55984204abece0e8ce36be99f | ea5678cc400c34ff95b661fa26d15024e27ea8cd | /simplex.lean | c26cd3c3b0dd03632acb400aa30c06ff11679736 | [] | no_license | ChrisHughes24/leanstuff | dca0b5349c3ed893e8792ffbd98cbcadaff20411 | 9efa85f72efaccd1d540385952a6acc18fce8687 | refs/heads/master | 1,654,883,241,759 | 1,652,873,885,000 | 1,652,873,885,000 | 134,599,537 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,884 | lean | import data.matrix data.rat linear_algebra.basis data.fintype tactic.omega algebra.associated
import linear_algebra.determinant
open matrix fintype finset
variables {m n : ℕ}
variables (A : matrix (fin m) (fin n) ℚ)
notation `rvec` n := matrix (fin 1) (fin n) ℚ
notation `cvec` m := matrix (fin m) (fin 1) ℚ
def colu... |
ff8194dd0413077034653a382507da3d7e1c96fd | ebf7140a9ea507409ff4c994124fa36e79b4ae35 | /src/exercises_sources/wednesday/algebraic_hierarchy.lean | 4c2a9870eb352f3a9b4bb9c652baa7a4f2503258 | [] | no_license | fundou/lftcm2020 | 3e88d58a92755ea5dd49f19c36239c35286ecf5e | 99d11bf3bcd71ffeaef0250caa08ecc46e69b55b | refs/heads/master | 1,685,610,799,304 | 1,624,070,416,000 | 1,624,070,416,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 19,138 | lean | /-
This is a sorry-free file covering the material on Wednesday afternoon
at LFTCM2020. It's how to build some algebraic structures in Lean
-/
import data.rat.basic -- we'll need the rationals at the end of this file
/-
As a mathematician I essentially always start my Lean files with the following line:
-/
import tac... |
c998020e403f52832308cb6e8e6ffe33dcf10ae2 | 649957717d58c43b5d8d200da34bf374293fe739 | /src/topology/algebra/uniform_group.lean | b3a53d035a9586ab6d2332df1ea4c1c583b487e2 | [
"Apache-2.0"
] | permissive | Vtec234/mathlib | b50c7b21edea438df7497e5ed6a45f61527f0370 | fb1848bbbfce46152f58e219dc0712f3289d2b20 | refs/heads/master | 1,592,463,095,113 | 1,562,737,749,000 | 1,562,737,749,000 | 196,202,858 | 0 | 0 | Apache-2.0 | 1,562,762,338,000 | 1,562,762,337,000 | null | UTF-8 | Lean | false | false | 19,997 | 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
Uniform structure on topological groups:
* `topological_add_group.to_uniform_space` and `topological_add_group_is_uniform` can be used to
construct a... |
9a6a125507d0bcd129d39ea365f638cf4c08f137 | 9ad8d18fbe5f120c22b5e035bc240f711d2cbd7e | /src/commutative_algebra/ring_hom_extra.lean | b02a366266dd71d4512b45882640522621209f73 | [] | 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 | 958 | lean | import algebra.ring data.nat.cast data.int.basic
universes u v
variables {α : Type u} {β : Type v} [semiring α] [semiring β]
variables (f : α → β) [is_semiring_hom f]
lemma is_semiring_hom.map_cast (n : ℕ) : f (n : α) = (n : β) :=
begin
apply nat.eq_cast (λ n, f (n : α)),
{change f ((0 : ℕ) : α) = 0,rw[nat.cast_z... |
6f8dc3a21e0c9b3ff638c244ccce0def815fec3a | 94e33a31faa76775069b071adea97e86e218a8ee | /src/algebra/order/with_zero.lean | 5f191f7ff070ace9771f9838004735c5e880e6c4 | [
"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 | 14,297 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Johan Commelin, Patrick Massot
-/
import algebra.order.group
import tactic.abel
/-!
# Linearly ordered commutative groups and monoids with a zero element adjoined
This file se... |
9cc1e8edebeb32a8369b5fb9bba50d8c3d984547 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/measure_theory/measurable_space_def.lean | 7f0a406e3fdb7ec824937c489d0d5cb3abc2508f | [
"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 | 19,774 | 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.set.countable
import logic.encodable.lattice
import order.conditionally_complete_lattice
import order.disjointed
import order.symm_diff
/... |
902e75bdb0b00c20358cc0a073034156b95fff22 | 08bd4ba4ca87dba1f09d2c96a26f5d65da81f4b4 | /src/Init/Data/Array/Basic.lean | 4c13b9e5b0139d8708bfc5934b8bfee429cfa109 | [
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"Apache-2.0",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | gebner/lean4 | d51c4922640a52a6f7426536ea669ef18a1d9af5 | 8cd9ce06843c9d42d6d6dc43d3e81e3b49dfc20f | refs/heads/master | 1,685,732,780,391 | 1,672,962,627,000 | 1,673,459,398,000 | 373,307,283 | 0 | 0 | Apache-2.0 | 1,691,316,730,000 | 1,622,669,271,000 | Lean | UTF-8 | Lean | false | false | 28,721 | lean | /-
Copyright (c) 2018 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import Init.WFTactics
import Init.Data.Nat.Basic
import Init.Data.Fin.Basic
import Init.Data.UInt.Basic
import Init.Data.Repr
import Init.Data.ToStr... |
39a60dd1683d3c50f0a00711a414298543b7e82c | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/analysis/special_functions/integrals.lean | 5c9265092f5d447d38b23e0ac44100c7dd0d1172 | [
"Apache-2.0"
] | permissive | waynemunro/mathlib | e3fd4ff49f4cb43d4a8ded59d17be407bc5ee552 | 065a70810b5480d584033f7bbf8e0409480c2118 | refs/heads/master | 1,693,417,182,397 | 1,634,644,781,000 | 1,634,644,781,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 20,462 | lean | /-
Copyright (c) 2021 Benjamin Davidson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Benjamin Davidson
-/
import measure_theory.integral.interval_integral
/-!
# Integration of specific interval integrals
This file contains proofs of the integrals of various specif... |
2cf805b3277c6e430ff4ecdc9579e43d6a050446 | 2c096fdfecf64e46ea7bc6ce5521f142b5926864 | /src/Lean/Elab/PreDefinition/Eqns.lean | a419993c3b24827614b6c5830c7f26da3f7e7e78 | [
"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 | Kha/lean4 | 1005785d2c8797ae266a303968848e5f6ce2fe87 | b99e11346948023cd6c29d248cd8f3e3fb3474cf | refs/heads/master | 1,693,355,498,027 | 1,669,080,461,000 | 1,669,113,138,000 | 184,748,176 | 0 | 0 | Apache-2.0 | 1,665,995,520,000 | 1,556,884,930,000 | Lean | UTF-8 | Lean | false | false | 16,180 | 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.Eqns
import Lean.Util.CollectFVars
import Lean.Meta.Tactic.Split
import Lean.Meta.Tactic.Apply
import Lean.Meta.Tactic.Refl
import Lean.Met... |
3b1eb583d5c18c66e5a6b311b80c735c0956bbfe | ad0c7d243dc1bd563419e2767ed42fb323d7beea | /algebra/ordered_field.lean | 5701536a7f9cc96320c1876c84ed74a8d0a98d4e | [
"Apache-2.0"
] | permissive | sebzim4500/mathlib | e0b5a63b1655f910dee30badf09bd7e191d3cf30 | 6997cafbd3a7325af5cb318561768c316ceb7757 | refs/heads/master | 1,585,549,958,618 | 1,538,221,723,000 | 1,538,221,723,000 | 150,869,076 | 0 | 0 | Apache-2.0 | 1,538,229,323,000 | 1,538,229,323,000 | null | UTF-8 | Lean | false | false | 8,375 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import algebra.ordered_ring algebra.field
section linear_ordered_field
variables {α : Type*} [linear_ordered_field α] {a b c d : α}
def div_pos := @div_pos_of_pos_o... |
45c4d3b111b36a1982b8a27d2bd612ea55b08109 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/data/padics/padic_integers.lean | 732dbeebd41b59b55d32a03c8874cfc77e1dd721 | [
"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 | 10,584 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Mario Carneiro
-/
import data.int.modeq
import data.padics.padic_numbers
/-!
# p-adic integers
This file defines the p-adic integers ℤ_p as the subtype of ℚ_p with ... |
8612bb5751d6919cd34f5afafcb9cf7a881825fd | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/field_theory/subfield.lean | 9c83fa7561b6d5794abb00a3ba97068a5c68290f | [
"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 | 4,969 | lean | /-
Copyright (c) 2018 Andreas Swerdlow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andreas Swerdlow
-/
import ring_theory.subring
variables {F : Type*} [field F] (S : set F)
section prio
set_option default_priority 100 -- see Note [default priority]
class is_subf... |
191a6d7d2f44bd33510c3a885337d10167ebee75 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/topology/algebra/monoid_auto.lean | 5ef211ccdcce781380a0856eb53814dcc8f66eb1 | [] | 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 | 12,488 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.topology.continuous_on
import Mathlib.group_theory.submonoid.basic
import M... |
0f0176d73e8540859a2285347357e57ddb2c1890 | 6094e25ea0b7699e642463b48e51b2ead6ddc23f | /hott/types/nat/div.hlean | 280f6915545bd495e1322f0e4bbf22082b11d850 | [
"Apache-2.0"
] | permissive | gbaz/lean | a7835c4e3006fbbb079e8f8ffe18aacc45adebfb | a501c308be3acaa50a2c0610ce2e0d71becf8032 | refs/heads/master | 1,611,198,791,433 | 1,451,339,111,000 | 1,451,339,111,000 | 48,713,797 | 0 | 0 | null | 1,451,338,939,000 | 1,451,338,939,000 | null | UTF-8 | Lean | false | false | 26,379 | hlean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
Definitions prod properties of div prod mod. Much of the development follows Isabelle's library.
-/
import types.nat.sub
open eq.ops well_founded decid... |
707d358c8304f989465326509653e4ba4432b761 | 947b78d97130d56365ae2ec264df196ce769371a | /tests/lean/exitAfterParseError.lean | 8e3bf2e8c4869555e66dd6986d38e20d99c486bf | [
"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 | 39 | lean | new_frontend
def foo
#exit
def bla
|
eac535283154106507ee783888238b77065731ae | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/field_theory/primitive_element.lean | 91f9463c8f69e04e7cada34344c667c2fc10674e | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 8,776 | lean | /-
Copyright (c) 2020 Thomas Browning, Patrick Lutz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning, Patrick Lutz
-/
import field_theory.adjoin
import field_theory.is_alg_closed.basic
import field_theory.separable
import ring_theory.integral_domain
/-... |
941aac12567cc1192a64f1685128ff9836670fa2 | f3849be5d845a1cb97680f0bbbe03b85518312f0 | /library/init/meta/rec_util.lean | 487350e1de1f66f85315a7ac316017ab442f5631 | [
"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 | 2,820 | 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... |
c3c45d63c2c388f8f17d38096ee8c81a11049273 | 9ad8d18fbe5f120c22b5e035bc240f711d2cbd7e | /src/commutative_algebra/galois_field_4.lean | 8bbcc4390fc9ccf0f729d33082fc766715b8fd25 | [] | 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 | 993 | lean | import algebra.ring
@[derive decidable_eq]
inductive F4 : Type
| zero : F4
| one : F4
| alpha : F4
| beta : F4
namespace F4
def add : F4 → F4 → F4
| zero y := y
| x zero := x
| one one := zero
| one alpha := beta
| one beta := alpha
| alpha one := beta
| alpha alpha := zero
| alpha beta... |
33ad425df36daa12d9fc44e951d1998f27f421aa | 38bf3fd2bb651ab70511408fcf70e2029e2ba310 | /src/topology/opens.lean | ea45c71e6cea09d648ceedbe919983f73715c5df | [
"Apache-2.0"
] | permissive | JaredCorduan/mathlib | 130392594844f15dad65a9308c242551bae6cd2e | d5de80376088954d592a59326c14404f538050a1 | refs/heads/master | 1,595,862,206,333 | 1,570,816,457,000 | 1,570,816,457,000 | 209,134,499 | 0 | 0 | Apache-2.0 | 1,568,746,811,000 | 1,568,746,811,000 | null | UTF-8 | Lean | false | false | 6,360 | 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
Subtype of open subsets in a topological space.
-/
import topology.bases topology.subset_properties topology.constructions
open filter lattice
variable... |
805be627406fe21c463840c33135c7b0c0edbe05 | 54d7e71c3616d331b2ec3845d31deb08f3ff1dea | /library/init/category/applicative.lean | bb1841f17f7790c7d4fa554b1fa57ebc3730c897 | [
"Apache-2.0"
] | permissive | pachugupta/lean | 6f3305c4292288311cc4ab4550060b17d49ffb1d | 0d02136a09ac4cf27b5c88361750e38e1f485a1a | refs/heads/master | 1,611,110,653,606 | 1,493,130,117,000 | 1,493,167,649,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,766 | 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
-/
prelude
import init.category.functor
open function
universes u v
class has_pure (f : Type u → Type v) :=
(pure : Π {α : Type u}, α → f α... |
c4d7353e1b8ffc2a0030dfa9394620cb76b414ef | 5c7fe6c4a9d4079b5457ffa5f061797d42a1cd65 | /src/library/src_field_lemmas.lean | 803e7b113c09123540b12aef18e2eb8aadc0c9a8 | [] | no_license | gihanmarasingha/mth1001_tutorial | 8e0817feeb96e7c1bb3bac49b63e3c9a3a329061 | bb277eebd5013766e1418365b91416b406275130 | refs/heads/master | 1,675,008,746,310 | 1,607,993,443,000 | 1,607,993,443,000 | 321,511,270 | 3 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,989 | lean | import .src_field tactic
namespace mth1001
namespace myreal
section grouplaws
variables {R : Type} [comm_group R]
lemma add_comm (x y : R) : x + y = y + x := comm_group.add_comm x y
lemma add_assoc (x y z : R) : (x + y) + z = x + (y + z) := comm_group.add_assoc x y z
lemma add_zero (x : R) : x + 0 = x := comm_grou... |
343bd9cd3b8f922f00574f7351d7d6cd0950a497 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/pi/lex.lean | 847e495469617f591819e97508ef47b0503d1654 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 8,613 | 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 order.well_founded
import algebra.group.pi
import algebra.order.group.defs
/-!
# Lexicographic order on Pi types
This file defines the lexicographic order for P... |
91487b15448aeec37ecf8d66e80558acea17c2aa | 4fa118f6209450d4e8d058790e2967337811b2b5 | /src/Spa/space.lean | 8665b28bcda3e1ba0b108212e9d92971519b3d30 | [
"Apache-2.0"
] | permissive | leanprover-community/lean-perfectoid-spaces | 16ab697a220ed3669bf76311daa8c466382207f7 | 95a6520ce578b30a80b4c36e36ab2d559a842690 | refs/heads/master | 1,639,557,829,139 | 1,638,797,866,000 | 1,638,797,866,000 | 135,769,296 | 96 | 10 | Apache-2.0 | 1,638,797,866,000 | 1,527,892,754,000 | Lean | UTF-8 | Lean | false | false | 9,657 | lean | import continuous_valuations
import Huber_pair
/-!
# The adic spectrum as a topological space
In this file we define a structure (`rational_open_data`) that will parameterise
a basis for the topology on the adic spectrum of a Huber pair.
-/
open_locale classical
local attribute [instance] set.pointwise_mul_comm_semi... |
d4d989131c7f393c2d348f34efd41fef7ff9d3cb | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/analysis/special_functions/polar_coord.lean | 8b76bf9a13ab358f4e8a1cc422363e64008f58e1 | [
"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 | 6,701 | lean | /-
Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import measure_theory.function.jacobian
/-!
# Polar coordinates
We define polar coordinates, as a local homeomorphism in `ℝ^2` between `ℝ^2 - (-∞, 0]` and
`(0... |
53472510d2cb565c1fc8384cf8586e45fa626320 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/simp3.lean | 3e59f0bfec6c19727d95924967f7c86bf9109f09 | [
"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 | 623 | lean | opaque f (x : Nat) : Nat
@[simp] axiom fEq (x : Nat) : f x = x
theorem ex1 (x : Nat) : f (f x, x).fst = x := by simp
theorem ex2 (x : Nat) : f ((fun a => f (f a)) x) = x := by simp
opaque g (x : Nat) : Nat
@[simp] axiom gEq (x : Nat) : g x = match x with | 0 => 1 | x+1 => 2
@[simp] theorem add1 (x : Nat) : x + 1 = x... |
3aae7da231ea9f6377cca66fe69fc8576b368530 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/linear_algebra/dual.lean | 051e3416d7a0750674e365058c3741cd0d150504 | [
"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 | 24,711 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Fabian Glöckle
-/
import linear_algebra.finite_dimensional
import linear_algebra.projection
/-!
# Dual vector spaces
The dual space of an R-module M is the R-module o... |
42fe65da2a8a167959e4d7749ea103268dae3e70 | 77c5b91fae1b966ddd1db969ba37b6f0e4901e88 | /src/algebra/gcd_monoid/finset.lean | b376262d01eb1a6ae26c35f63f70db7eac6deb1f | [
"Apache-2.0"
] | permissive | dexmagic/mathlib | ff48eefc56e2412429b31d4fddd41a976eb287ce | 7a5d15a955a92a90e1d398b2281916b9c41270b2 | refs/heads/master | 1,693,481,322,046 | 1,633,360,193,000 | 1,633,360,193,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,881 | lean | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import data.finset.fold
import algebra.gcd_monoid.multiset
/-!
# GCD and LCM operations on finsets
## Main definitions
- `finset.gcd` - the greatest common denomin... |
b8c91495d9b08762bdb8a72aedcbc2d8006161c9 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /hott/algebra/category/constructions/terminal.hlean | 24a40687ac27f4a955206a77b2685e81d42926e5 | [
"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 | 1,770 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
Terminal category
-/
import .indiscrete
open functor is_trunc unit eq
namespace category
definition terminal_precategory [constructor] : precategory unit :=
... |
4cb79c0132f28c73a7597b38ee80e7876a4bd6bc | 42c01158c2730cc6ac3e058c1339c18cb90366e2 | /M1F/2017-18/Example_Sheet_01/Question_05/solution_5.orig.lean | c366e4396ae8a0308ddcd41b24ef0e811e4e87c0 | [] | no_license | ChrisHughes24/xena | c80d94355d0c2ae8deddda9d01e6d31bc21c30ae | 337a0d7c9f0e255e08d6d0a383e303c080c6ec0c | refs/heads/master | 1,631,059,898,392 | 1,511,200,551,000 | 1,511,200,551,000 | 111,468,589 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,567 | lean | import data.set -- handy for proofs.
definition A : set ℕ := {1,2,3,4,5}
-- part (a) is true
theorem M1F_Sheet01_Q05a_is_true : 1 ∈ A :=
begin
simp [A]
end
-- part (b) does not even typecheck.
-- part (c) is true
theorem M1F_Sheet01_Q05c_is_true : {1} ⊆ A :=
begin
simp [A]
end
-- part (d) is true
-- set_optio... |
00d0b06a87b84c39ab24f76cf4fc532caac861a5 | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/category_theory/monad/limits.lean | 1f5329c3bd99d7d429984a4061a110ca00275570 | [
"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 | 13,974 | lean | /-
Copyright (c) 2019 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.monad.adjunction
import category_theory.adjunction.limits
import category_theory.limits.preserves.shapes.terminal
namespace cate... |
203d08baf250c03228d1f80701f9f6a4eeb08d98 | 9dd3f3912f7321eb58ee9aa8f21778ad6221f87c | /library/init/logic.lean | b8066cad71e626eeb6432f8a65800ce94ef65645 | [
"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 | 37,472 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Floris van Doorn
-/
prelude
import init.core
universes u v w
@[reducible] def id {α : Sort u} (a : α) : α := a
def flip {α : Sort u} {β : So... |
b9f5d87caac2ccb9c9568b12158ba744e076bf18 | a79fbdb1f19ad636f8d541f5560e562b96c24ffb | /src/D.lean | d4c7d685801a131a04ac048cb0c143d3830ed3cd | [] | no_license | bjoernkjoshanssen/jaccard | aa914e816097a3266d25efbd88426e34824802f8 | 7a1846fc617f0d59ee7c11f95f1bee8d3abce5fc | refs/heads/master | 1,686,417,342,281 | 1,685,329,727,000 | 1,685,329,727,000 | 325,476,041 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 24,493 | lean | /-
Copyright (c) 2020 Bjørn Kjos-Hanssen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Bjørn Kjos-Hanssen.
Zulip chat help from:
Alex J. Best, Johan Commelin, Kyle Miller, Pedro Minicz, Reid Barton, Scott Morrison, Heather Macbeth.
Code contribution and definition o... |
73bd04fc73dbe463e4c2f9fce12b15d5a18c978c | 4727251e0cd73359b15b664c3170e5d754078599 | /src/combinatorics/simple_graph/clique.lean | 87996e7e1e54eb48d8b3c250d7bd7ed5f8ce3b03 | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 5,324 | lean | /-
Copyright (c) 2022 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 combinatorics.simple_graph.basic
import data.finset.pairwise
/-!
# Graph cliques
This file defines cliques in simple graphs. A clique... |
ab3ac00446dd6922325c3c986744efb6dff5322f | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/955.lean | 07d5711a9c239a16e52ed04366e14e18b9e4724d | [
"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 | 462 | lean | namespace Ex2
mutual
def isEven : Nat → Bool
| 0 => true
| n+1 => isOdd n
def isOdd : Nat → Bool
| 0 => false
| n+1 => isEven n
end
termination_by _ n =>
match n with
| _ => n
end Ex2
namespace Ex3
mutual
def isEven : Nat → Bool
| 0 => true
| n+1 => isOdd n
def isOdd : Nat → Bool
... |
34bda46629e104219029fe9be04787c71126390d | 626e312b5c1cb2d88fca108f5933076012633192 | /src/data/set/function.lean | fba2409c4e0aaf698515fbd33c9b3d1690e33afb | [
"Apache-2.0"
] | permissive | Bioye97/mathlib | 9db2f9ee54418d29dd06996279ba9dc874fd6beb | 782a20a27ee83b523f801ff34efb1a9557085019 | refs/heads/master | 1,690,305,956,488 | 1,631,067,774,000 | 1,631,067,774,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 37,683 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Andrew Zipperer, Haitao Zhang, Minchao Wu, Yury Kudryashov
-/
import data.set.basic
import logic.function.conjugate
/-!
# Functions over sets
## Main definitions
### P... |
7f90c52fc7f47f8457c62793d85fd989d4f3f4e6 | 4727251e0cd73359b15b664c3170e5d754078599 | /test/linarith.lean | dc364a18a313e04e4db4b60afee4d87c05ba5bb8 | [
"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 | 10,592 | 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... |
d3464ba2b9111e97b9099fb3ad02bfc32d8d41a7 | 592ee40978ac7604005a4e0d35bbc4b467389241 | /Library/generated/mathscheme-lean/AddGroup_RingoidSig.lean | ae6b752f4fe04c847ac74846b8444e4363b068bd | [] | no_license | ysharoda/Deriving-Definitions | 3e149e6641fae440badd35ac110a0bd705a49ad2 | dfecb27572022de3d4aa702cae8db19957523a59 | refs/heads/master | 1,679,127,857,700 | 1,615,939,007,000 | 1,615,939,007,000 | 229,785,731 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,461 | lean | import init.data.nat.basic
import init.data.fin.basic
import data.vector
import .Prelude
open Staged
open nat
open fin
open vector
section AddGroup_RingoidSig
structure AddGroup_RingoidSig (A : Type) : Type :=
(plus : (A → (A → A)))
(zero : A)
(lunit_zero : (∀ {x : A} , (plus zero x) = x))
... |
79686d46e42c45d7d0996ff45b5d8e0b2333ef5b | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /09_Type_Classes.org.5.lean | 250b7a96a58caf25690798025cd700563b9488cd | [] | 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 | 537 | lean | import standard
namespace hide
inductive inhabited [class] (A : Type) : Type :=
mk : A → inhabited A
definition Prop.is_inhabited [instance] : inhabited Prop :=
inhabited.mk true
definition bool.is_inhabited [instance] : inhabited bool :=
inhabited.mk bool.tt
definition nat.is_inhabited [instance] : inhabited nat :... |
97c619f7f2b343d4b19a3b97e4c50c4f99a70aab | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/topology/maps.lean | 6bde07a224865be942b475162f68e3e06373d69b | [] | 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 | 18,692 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.topology.order
import Mathlib.PostPort
universes u_1 u_2 l... |
c260cb71722508336bdd237695685805db363773 | 968e2f50b755d3048175f176376eff7139e9df70 | /examples/prop_logic_theory/unnamed_1250.lean | 25578d0b89f837c0549111f24f56d48c22bc1b42 | [] | no_license | gihanmarasingha/mth1001_sphinx | 190a003269ba5e54717b448302a27ca26e31d491 | 05126586cbf5786e521be1ea2ef5b4ba3c44e74a | refs/heads/master | 1,672,913,933,677 | 1,604,516,583,000 | 1,604,516,583,000 | 309,245,750 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 330 | lean | variables (p : Prop)
-- BEGIN
example : p ↔ p :=
begin
split, -- By iff introduction, it suffices to prove `p → p` and `p → p`
{ show p → p, from id }, -- We show `p → p` from reflexivity of implication.
{ show p → p, from id }, -- We show `p → p` from reflexivity of implication.
end
-- END |
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