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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
e15dc8bab7b9f06641717a2cadb8907c9962ebe0 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/order/hom/complete_lattice.lean | fb0163c8fe28f5ad46f1658b396494999f62e399 | [
"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 | 26,955 | lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import data.set.lattice
import order.hom.lattice
/-!
# Complete lattice homomorphisms
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a co... |
c97f8f3a4d3dbe0af9d515d5cd2cca74858623ae | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/algebra/module/submodule.lean | 5bf48ebf4adf698bdfdd20080e59a909f338ef5a | [
"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 | 13,492 | 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
-/
import algebra.module.linear_map
import group_theory.group_action.sub_mul_action
/-!
# Submodules of a module
In ... |
cbf7b645024ab52eefa4b9c6ca892f7c2a9698e8 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/number_theory/quadratic_reciprocity.lean | a9ba7764a71911a26d19faa6486f7a2a2977ec30 | [
"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 | 24,988 | 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 field_theory.finite.basic
import data.zmod.basic
import data.nat.parity
/-!
# Quadratic reciprocity.
This file contains results about quadratic residues modulo ... |
3e8bb905a65e7d97b0cec95b70e710c830daee5f | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/topology/instances/ennreal.lean | 3929f95e8318de25462115c06860137bfbc5c682 | [
"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 | 54,868 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import topology.instances.nnreal
import topology.algebra.ordered.liminf_limsup
/-!
# Extended non-negative reals
-/
noncomputable theory
open classical set filter m... |
b797566b0dec853dc7a100b63be82d250219c70f | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/nat/basic.lean | 0494de6740b60dcde8d8196ed671c9c9684d2d3e | [] | 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 | 58,862 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebr... |
1b9ce89e4d7976f991128f7b9b10298fbfb4725b | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/topology/category/Top/opens.lean | 251221c85dcbea66c8bb6378f576e546734374b4 | [
"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 | 11,665 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.category.preorder
import category_theory.eq_to_hom
import topology.category.Top.epi_mono
import topology.sets.opens
/-!
# The category of open... |
15ec2a92431cb5d13e175754adc879c8c3e11ac7 | 3dd1b66af77106badae6edb1c4dea91a146ead30 | /tests/lean/run/coe2.lean | b2fbd3fb979fbaf13e73f9792e58ece4de9ed645 | [
"Apache-2.0"
] | permissive | silky/lean | 79c20c15c93feef47bb659a2cc139b26f3614642 | df8b88dca2f8da1a422cb618cd476ef5be730546 | refs/heads/master | 1,610,737,587,697 | 1,406,574,534,000 | 1,406,574,534,000 | 22,362,176 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 479 | lean | import standard
namespace setoid
inductive setoid : Type :=
| mk_setoid: Π (A : Type), (A → A → Prop) → setoid
definition carrier (s : setoid)
:= setoid_rec (λ a eq, a) s
definition eqv {s : setoid} : carrier s → carrier s → Prop
:= setoid_rec (λ a eqv, eqv) s
infix `≈`:50 := eqv
coercion carrier
... |
4a39c0245e18bac796a7644a1e4e47d580f32275 | 947b78d97130d56365ae2ec264df196ce769371a | /src/Lean/Exception.lean | ab1e2c07def80f67261e6bbe97a2d7d580545a8e | [
"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 | 3,585 | 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.Message
import Lean.InternalExceptionId
import Lean.Data.Options
namespace Lean
/- Exception type used in most Lean monads -/
inductive Except... |
a2415fb7ed2e422cb34487d177918e5b2de883d2 | 92b50235facfbc08dfe7f334827d47281471333b | /library/theories/number_theory/bezout.lean | 152f34c02cffdd86f64e0bbe86518901370875e5 | [
"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 | 3,821 | lean | /-
Copyright (c) 2015 William Peterson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: William Peterson, Jeremy Avigad
Extended gcd, Bezout's theorem, chinese remainder theorem.
-/
import data.nat.div data.int .primes
/- Bezout's theorem -/
section Bezout
open nat ... |
84abe6872019019ad288e30e2909106d956f0304 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/group_theory/specific_groups/dihedral.lean | 5f187ff794f92bef3cec66ee6bf984b432388f08 | [
"Apache-2.0"
] | permissive | AntoineChambert-Loir/mathlib | 64aabb896129885f12296a799818061bc90da1ff | 07be904260ab6e36a5769680b6012f03a4727134 | refs/heads/master | 1,693,187,631,771 | 1,636,719,886,000 | 1,636,719,886,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,498 | lean | /-
Copyright (c) 2020 Shing Tak Lam. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shing Tak Lam
-/
import data.fintype.card
import data.zmod.basic
import group_theory.order_of_element
/-!
# Dihedral Groups
We define the dihedral groups `dihedral_group n`, with elem... |
82f4414febac8347b3db60bf9de6dc42de217804 | da23b545e1653cafd4ab88b3a42b9115a0b1355f | /src/tidy/tidy_attributes.lean | 98c765eeceeb76ceeaf14528d33688135984edec | [] | no_license | minchaowu/lean-tidy | 137f5058896e0e81dae84bf8d02b74101d21677a | 2d4c52d66cf07c59f8746e405ba861b4fa0e3835 | refs/heads/master | 1,585,283,406,120 | 1,535,094,033,000 | 1,535,094,033,000 | 145,945,792 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 845 | lean | -- Copyright (c) 2017 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Scott Morrison
import .at_least_one
open tactic
meta def tidy_attribute : user_attribute := {
name := `tidy,
descr := "A tactic that should be called by tidy."
}
run_cmd ... |
0e01fd88a927c8db8044979b93052a92b4fd391f | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/category_theory/action.lean | b54d36e94489854296129891f0f16cec4e24fee3 | [
"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 | 6,655 | lean | /-
Copyright (c) 2020 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
import category_theory.elements
import category_theory.is_connected
import category_theory.single_obj
import group_theory.group_action.basic
import group_theory.semidirect_pr... |
e08e192893aadd77ee1b2c52dc01592f9972357f | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/data/list/indexes.lean | d1db0d604c871f73c9ec34b60b1e342067cf1677 | [
"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 | 5,623 | lean | /-
Copyright (c) 2020 Jannis Limperg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jannis Limperg
-/
import data.list.basic
import data.list.defs
import logic.basic
universes u v
open function
namespace list
variables {α : Type u} {β : Type v}
section foldr_wi... |
03822604067bfa52a3f025dbb30143ce6164a2a4 | 367134ba5a65885e863bdc4507601606690974c1 | /src/category_theory/equivalence.lean | c5fb20d8763d85c8eb1a421345c1e9f751621718 | [
"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 | 23,396 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tim Baumann, Stephen Morgan, Scott Morrison, Floris van Doorn
-/
import category_theory.fully_faithful
import category_theory.whiskering
import category_theory.essential_image
import t... |
13dc4e13314fbde13095c5aa2a69a489e63d8981 | 00de0c30dd1b090ed139f65c82ea6deb48c3f4c2 | /src/data/int/basic.lean | 368ffa56c1987a77a4c0a57db3f424d791b341d8 | [
"Apache-2.0"
] | permissive | paulvanwamelen/mathlib | 4b9c5c19eec71b475f3dd515cd8785f1c8515f26 | 79e296bdc9f83b9447dc1b81730d36f63a99f72d | refs/heads/master | 1,667,766,172,625 | 1,590,239,595,000 | 1,590,239,595,000 | 266,392,625 | 0 | 0 | Apache-2.0 | 1,590,257,277,000 | 1,590,257,277,000 | null | UTF-8 | Lean | false | false | 53,291 | 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
... |
5eac837302939a6437a55eb08038947e8427333f | 94e33a31faa76775069b071adea97e86e218a8ee | /src/computability/primrec.lean | 1a29b1ea672bfb144b12531135426349de81087b | [
"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 | 51,901 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.list.join
import logic.equiv.list
import logic.function.iterate
/-!
# The primitive recursive functions
The primitive recursive functions are the least ... |
38989e315bc2a60288277d00c84ce4c9b83c8adf | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/logic/unique.lean | d37e460f49e62d7b1a7dd0a1f22164f75790d307 | [
"Apache-2.0"
] | permissive | fpvandoorn/mathlib | b21ab4068db079cbb8590b58fda9cc4bc1f35df4 | b3433a51ea8bc07c4159c1073838fc0ee9b8f227 | refs/heads/master | 1,624,791,089,608 | 1,556,715,231,000 | 1,556,715,231,000 | 165,722,980 | 5 | 0 | Apache-2.0 | 1,552,657,455,000 | 1,547,494,646,000 | Lean | UTF-8 | Lean | false | false | 1,232 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
universes u v w
variables {α : Sort u} {β : Sort v} {γ : Sort w}
structure unique (α : Sort u) extends inhabited α :=
(uniq : ∀ a:α, a = default)
attribute [class... |
4d0cf58d613a4d58c6a33fbe2f3fbc97da75bdcd | 36c7a18fd72e5b57229bd8ba36493daf536a19ce | /tests/lean/run/blast_ematch4.lean | 7e39afb0440c4b0eaed2c072b7aa352935961642 | [
"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 | 273 | lean | import data.nat
open algebra nat
section
open nat
set_option blast.simp false
set_option blast.subst false
set_option blast.ematch true
attribute add.comm [forward]
attribute add.assoc [forward]
example (a b c : nat) : a + b + b + c = c + b + a + b :=
by blast
end
|
efec03180f50f8fb7a7f46c73b93552edf14b991 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /test/transport/basic.lean | 434e5798a6a7c988047ccfaf0a9b1c9fecf10ed1 | [
"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 | 2,591 | lean | import tactic.transport
import order.bounded_lattice
import algebra.lie.basic
-- We verify that `transport` can move a `semiring` across an equivalence.
-- Note that we've never even mentioned the idea of addition or multiplication to `transport`.
def semiring.map {α : Type} [semiring α] {β : Type} (e : α ≃ β) : semir... |
ca68f3df6242b9a70258cc8a94603ffa28a43123 | d3aa99b88d7159fbbb8ab10d699374ab7be89e03 | /src/data/list/basic.lean | 64391412adbe17fa1dca5c74a8da0ee7ac004978 | [
"Apache-2.0"
] | permissive | mzinkevi/mathlib | 62e0920edaf743f7fc53aaf42a08e372954af298 | c718a22925872db4cb5f64c36ed6e6a07bdf647c | refs/heads/master | 1,599,359,590,404 | 1,573,098,221,000 | 1,573,098,221,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 218,600 | lean | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
Basic properties of lists.
-/
import
tactic.interactive tactic.mk_iff_of_inductive_prop
logi... |
1833e36ca7057b2cc946fd65212a4798df156629 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/ring_theory/dedekind_domain/selmer_group.lean | adcbbfc9e1fb39003619e30841c8667e914dd114 | [
"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 | 9,854 | lean | /-
Copyright (c) 2022 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-/
import algebra.hom.equiv.type_tags
import data.zmod.quotient
import ring_theory.dedekind_domain.adic_valuation
import ring_theory.norm
/-!
# Selm... |
9f1b3f6baec9337e2e8bf78ee4f4060d341e7439 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/group_theory/submonoid/basic.lean | 34d40b22dea98e39a7d433503c090e2b608cbbd2 | [
"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 | 21,981 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard,
Amelia Livingston, Yury Kudryashov
-/
import algebra.hom.group -- Only needed for notation
import algebra.gro... |
0a502bb17a3c15e2423496390786aa880a6affa5 | ebf7140a9ea507409ff4c994124fa36e79b4ae35 | /src/solutions/thursday/category_theory/exercise3.lean | 1690bbac305fa4fcbe31603bdccba060c3da3c3d | [] | 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 | 1,023 | lean | import category_theory.equivalence
open category_theory
variables {C : Type*} [category C]
variables {D : Type*} [category D]
lemma equiv_reflects_mono {X Y : C} (f : X ⟶ Y) (e : C ≌ D)
(hef : mono (e.functor.map f)) : mono f :=
-- Hint: when `e : C ≌ D`, `e.functor.map_injective` says
-- `∀ f g, e.functor.map f... |
d7ecb0320404b15eecc273920059d96a59b995ef | aa5a655c05e5359a70646b7154e7cac59f0b4132 | /stage0/src/Lean/Elab/Tactic/Simp.lean | be6e9e7f690fb74be2216c76aed9ab96890cdd2a | [
"Apache-2.0"
] | permissive | lambdaxymox/lean4 | ae943c960a42247e06eff25c35338268d07454cb | 278d47c77270664ef29715faab467feac8a0f446 | refs/heads/master | 1,677,891,867,340 | 1,612,500,005,000 | 1,612,500,005,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,100 | 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.Tactic.Simp
import Lean.Elab.Tactic.Basic
import Lean.Elab.Tactic.ElabTerm
import Lean.Elab.Tactic.Location
import Lean.Meta.Tactic.Replace... |
506ada8acb25c9ba6739c44df37081d2d23b0df6 | f68ef9a599ec5575db7b285d4960e63c5d464ccc | /Exercises/cantor.lean | 88a569723fb66e8c8807e97c44ef8b8883964a0e | [] | no_license | lucasmoschen/discrete-mathematics | a38d5970cc571b0b9d202bf6a43efeb8ed6f66e3 | 0f1945cc5eb094814c926cd6ae4a8b4c5c579a1e | refs/heads/master | 1,677,111,757,003 | 1,611,500,097,000 | 1,611,500,097,000 | 205,903,359 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 821 | lean | import data.set
variables X Y: Type
def surjective {X: Type} {Y: Type} (f : X → Y) : Prop := ∀ y, ∃ x, f x = y
theorem Cantor : ∀ (A: set X), ¬ ∃ (f: A → set A), surjective f :=
begin
intro A,
intro h,
cases h with f h1,
have h2: ∃ x, f x = {t : A | ¬ (t ∈ f t)}, from h1 {t : A... |
a34aadc1a012457c9d228a119ca145668dd78098 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/monoidal/discrete.lean | f32ed6597d3198aecd2838197ea1930186fd55e9 | [
"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 | 2,238 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import algebra.hom.group
import category_theory.discrete_category
import category_theory.monoidal.natural_transformation
/-!
# Monoids as discrete monoidal categorie... |
0308f27467df0e132a47e3ef6f76b72787993a43 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/data/real/cau_seq.lean | ff4f3327c78f5fd618a5381cd956b8a7271106d2 | [
"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 | 25,971 | 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.big_operators.order
/-!
# Cauchy sequences
A basic theory of Cauchy sequences, used in the construction of the reals and p-adic numbers. Where
applic... |
92e2dc226296779ecf508b9a9927d51d5d88e0a8 | 737dc4b96c97368cb66b925eeea3ab633ec3d702 | /src/Lean/Meta/LevelDefEq.lean | 05298df335447ad9edc23b3c501dfdca2fd4f844 | [
"Apache-2.0"
] | permissive | Bioye97/lean4 | 1ace34638efd9913dc5991443777b01a08983289 | bc3900cbb9adda83eed7e6affeaade7cfd07716d | refs/heads/master | 1,690,589,820,211 | 1,631,051,000,000 | 1,631,067,598,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,935 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Util.CollectMVars
import Lean.Util.ReplaceExpr
import Lean.Meta.Basic
import Lean.Meta.InferType
namespace Lean.Meta
private partial def decAu... |
5823248d81d43b7dd321288fd849da7840f79045 | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/field_theory/adjoin.lean | 36ab02ab7b3eec5af6ddc6bcf0a0eaa91b2321db | [
"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 | 33,305 | 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.intermediate_field
import field_theory.splitting_field
import field_theory.separable
import ring_theory.adjoin_root... |
c2d39a6d091e50c3c3bee08618df140abc55993b | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/data/equiv/fin.lean | 67c35fd52b49eb86a421b0a2a06cb406ee42ffbe | [
"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 | 14,091 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import data.fin
import data.equiv.basic
import tactic.norm_num
/-!
# Equivalences for `fin n`
-/
universe variables u
variables {m n : ℕ}
/-- Equivalence between `fin 0` an... |
0d69c5538d255d5615dcc1393cd629fa98c98559 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/category_theory/limits/shapes/wide_pullbacks.lean | c7edbed3b3aeaa0dc73a1d4827d328fafdfa7ea2 | [
"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 | 5,289 | 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.limits.limits
import category_theory.sparse
/-!
# Wide pullbacks
We define the category `wide_pullback_shape`, (resp. `wide_pushout_shape`) which... |
0b05c06ba4f49f9938cc03e763726bcecb0a2201 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/information_theory/hamming.lean | c1aacfc128e444d6d4d8a3a15df0dfab352ef9f3 | [
"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 | 14,135 | lean | /-
Copyright (c) 2022 Wrenna Robson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wrenna Robson
-/
import analysis.normed.group.basic
/-!
# Hamming spaces
The Hamming metric counts the number of places two members of a (finite) Pi type
differ. The Hamming norm is ... |
a395fe0858d0e639e7c7ecae2872ebcb084b83ca | 41ed4e6eacdd37c176d4ecf70193b40b9f9e1a93 | /src/thomaes_function.lean | 168b722300c3a41079c20bc5be9010c379aa68f0 | [] | no_license | FrickHazard/thomaes-function | ae67a4a0d01cf00d128639eec4740879a057240d | 260ba849187a5a1867ec988370010e6aebc31f00 | refs/heads/main | 1,689,771,900,819 | 1,631,674,532,000 | 1,631,674,532,000 | 392,437,647 | 2 | 0 | null | 1,628,695,346,000 | 1,628,020,204,000 | Lean | UTF-8 | Lean | false | false | 7,273 | lean | /-
Copyright (c) 2015, 2017 Ender Doe. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ender Doe, Kevin Buzzard
-/
import data.real.irrational
local notation `|` x `|` := abs x
open_locale classical
/--
The thomae's function on reals also known as the "Popcorn" fun... |
af7026e0369d53d205db10a238999226f1d1307e | f3849be5d845a1cb97680f0bbbe03b85518312f0 | /library/init/algebra/ordered_ring.lean | 911695d701b487224a64edf489cd63ccf8280fc2 | [
"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 | 16,048 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
-/
prelude
import init.algebra.ordered_group init.algebra.ring
/- Make sure instances defined in this file have lower priority than the ones
... |
80ecbb87b943dced2baf6c7adc36b8506fdae301 | bb31430994044506fa42fd667e2d556327e18dfe | /src/data/fin/basic.lean | 2be427042b55460c383daab4d80f0bc6928f69c4 | [
"Apache-2.0"
] | permissive | sgouezel/mathlib | 0cb4e5335a2ba189fa7af96d83a377f83270e503 | 00638177efd1b2534fc5269363ebf42a7871df9a | refs/heads/master | 1,674,527,483,042 | 1,673,665,568,000 | 1,673,665,568,000 | 119,598,202 | 0 | 0 | null | 1,517,348,647,000 | 1,517,348,646,000 | null | UTF-8 | Lean | false | false | 72,477 | lean | /-
Copyright (c) 2017 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Keeley Hoek
-/
import algebra.ne_zero
import algebra.order.with_zero
import order.rel_iso.basic
import data.nat.order.basic
import order.hom.set
/-!
# The finite typ... |
4445562f059a9bbb6e2a4f9fb4c341408db1fd5a | 7c2dd01406c42053207061adb11703dc7ce0b5e5 | /src/exercises/05_sequence_limits.lean | 2c68967e243af16a123a8e3e2863ecc319c3c894 | [
"Apache-2.0"
] | permissive | leanprover-community/tutorials | 50ec79564cbf2ad1afd1ac43d8ee3c592c2883a8 | 79a6872a755c4ae0c2aca57e1adfdac38b1d8bb1 | refs/heads/master | 1,687,466,144,386 | 1,672,061,276,000 | 1,672,061,276,000 | 189,169,918 | 186 | 81 | Apache-2.0 | 1,686,350,300,000 | 1,559,113,678,000 | Lean | UTF-8 | Lean | false | false | 5,894 | lean | import data.real.basic
import algebra.group.pi
import tuto_lib
notation `|`x`|` := abs x
/-
In this file we manipulate the elementary definition of limits of
sequences of real numbers.
mathlib has a much more general definition of limits, but here
we want to practice using the logical operators and relations
covered... |
cafafbae96cd1838554a93ec466204e15721128f | 618003631150032a5676f229d13a079ac875ff77 | /src/field_theory/perfect_closure.lean | 959ef695c52c790c5a64f657b099d7e2ff3fb8f1 | [
"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 | 16,682 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov
-/
import algebra.char_p
import data.equiv.ring
import algebra.group_with_zero_power
import algebra.iterate_hom
/-!
# The perfect closure of a field
-/
universe... |
589bd4233ef5a6f71cc396181f3894a6dba84a9b | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/topology/separation.lean | 2474f8efbb18c18ae2d0acfcf10d210fc2d42e9a | [
"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 | 16,717 | 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
Separation properties of topological spaces.
-/
import topology.subset_properties
open set filter
open_locale topological_space
local attribute [insta... |
b307520da7f08b3178e9272640aa7729679505e5 | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/algebra/big_operators/pi.lean | ba1408cdb6d068c02670e65cb5df7bc3bf3d3b2b | [
"Apache-2.0"
] | permissive | hamdysalah1/mathlib | b915f86b2503feeae268de369f1b16932321f097 | 95454452f6b3569bf967d35aab8d852b1ddf8017 | refs/heads/master | 1,677,154,116,545 | 1,611,797,994,000 | 1,611,797,994,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,429 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot
-/
import algebra.ring.pi
import algebra.big_operators.basic
import data.fintype.basic
import algebra.group.prod
/-!
# Big operators for Pi Types
This file co... |
4d7e851a4febd5a2472c60e1d9c7f7d6698e3a64 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/field_theory/polynomial_galois_group.lean | d522d1b6ba71fd98b76d9c2dc8a7f906ab42dae8 | [
"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 | 21,925 | 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 analysis.complex.polynomial
import field_theory.galois
import group_theory.perm.cycle.type
/-!
# Galois Groups of Polynomials
>... |
482d4b50925e16bd467500bf06a37dd821d0e83f | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/compiler/534.lean | 4dad681ac2b0fca1db2a4ed60271a20482c75979 | [
"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 | 252 | lean | def foo (array : Array Nat) : Nat -> Nat
| 0 => 0
| n + 1 =>
let array := array.filter (!.==5)
if array.isEmpty then
0
else
let arrayOfLast := #[array.back]
foo arrayOfLast n
def main : IO Unit :=
IO.println ("hi")
|
1fd03cb565131a8b994f054677f30118752ed319 | 969dbdfed67fda40a6f5a2b4f8c4a3c7dc01e0fb | /src/linear_algebra/nonsingular_inverse.lean | e4ccbb77e7ed5c3c6252bcaf2d32ed51cba53eee | [
"Apache-2.0"
] | permissive | SAAluthwela/mathlib | 62044349d72dd63983a8500214736aa7779634d3 | 83a4b8b990907291421de54a78988c024dc8a552 | refs/heads/master | 1,679,433,873,417 | 1,615,998,031,000 | 1,615,998,031,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 16,376 | lean | /-
Copyright (c) 2019 Tim Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Tim Baanen.
-/
import algebra.associated
import linear_algebra.determinant
import tactic.linarith
import tactic.ring_exp
/-!
# Nonsingular inverses
In this file, we define an inverse for ... |
ccb9583c07600b3da26208a3ac421fa5defc6804 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/algebra/nonarchimedean/adic_topology.lean | 3190120464aac9b57f9b004b239455b2603e34c9 | [
"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 | 9,307 | lean | /-
Copyright (c) 2021 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import ring_theory.ideal.operations
import topology.algebra.nonarchimedean.bases
import topology.uniform_space.completion
import topology.algebra.uniform_ring
/-!
#... |
5bd7f3e66d2c68cc2a6f053efd72181b811342ba | ad0c7d243dc1bd563419e2767ed42fb323d7beea | /number_theory/pell.lean | b264f897e356338f4d9080d8fe6eac7227183193 | [
"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 | 62,380 | 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.int.basic data.nat.prime data.nat.modeq
/-- The ring of integers adjoined with a square root of `d`.
These have the form `a + b √d` where `a b : ℤ`. Th... |
6b938d678a396801e655c9bd3e470faae657e0fb | 74d9d5f45c6ce5c4f2faf215c04a68eab55fe525 | /src/operator_norm.lean | 3770ec19943047093e3b42063d94f1594da8559d | [] | no_license | joshpoll/differential_geometry | 290bb8a934ca3b3b6b707d810e6d4b941710b710 | 57e00a7e37b7c4c73c847429171ff63d3a48def5 | refs/heads/master | 1,584,551,626,391 | 1,527,747,643,000 | 1,527,747,643,000 | 135,014,993 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,359 | lean | /-
The operator norm is the natural norm for linear operators between normed vector spaces. One can think of it as how much a map stretches unit vectors or as the smallest value that guarantees Cauchy-Schwarz (i.e. ∥L v∥ ≤ ∥L∥ * ∥v∥).
The derivative of f : E → F is f' : E → continuous_linear_map E F.
We need t... |
3e1474a36c3201f415b11a0b6638c07881d55e54 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/deprecated/ring_auto.lean | b775db0a6c6a1229f9c099c0108522cca4cbfa48 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,229 | lean | /-
Copyright (c) 2020 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.deprecated.group
import Mathlib.PostPort
universes u v l u_1 u_2
namespace Mathlib
/-!
#... |
81aca9961e46f6714b1473b7f1a5fa8a0b2e4f06 | 37da0369b6c03e380e057bf680d81e6c9fdf9219 | /hott/init/path.hlean | e8030805000e2f5acfb91e3f22d09c6caf2191c0 | [
"Apache-2.0"
] | permissive | kodyvajjha/lean2 | 72b120d95c3a1d77f54433fa90c9810e14a931a4 | 227fcad22ab2bc27bb7471be7911075d101ba3f9 | refs/heads/master | 1,627,157,512,295 | 1,501,855,676,000 | 1,504,809,427,000 | 109,317,326 | 0 | 0 | null | 1,509,839,253,000 | 1,509,655,713,000 | C++ | UTF-8 | Lean | false | false | 31,657 | hlean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Jakob von Raumer, Floris van Doorn
Ported from Coq HoTT
-/
prelude
import .function .tactic
open function eq
/- Path equality -/
namespace eq
variables {A ... |
eb0c211689177d77d8e61a60530ed5a18bb8ce7f | 1dd482be3f611941db7801003235dc84147ec60a | /test/linarith.lean | bbd989a049ae90f60ace9f36fb232bda6359754a | [
"Apache-2.0"
] | permissive | sanderdahmen/mathlib | 479039302bd66434bb5672c2a4cecf8d69981458 | 8f0eae75cd2d8b7a083cf935666fcce4565df076 | refs/heads/master | 1,587,491,322,775 | 1,549,672,060,000 | 1,549,672,060,000 | 169,748,224 | 0 | 0 | Apache-2.0 | 1,549,636,694,000 | 1,549,636,694,000 | null | UTF-8 | Lean | false | false | 3,593 | lean | import tactic.linarith
example (e b c a v0 v1 : ℚ) (h1 : v0 = 5*a) (h2 : v1 = 3*b) (h3 : v0 + v1 + c = 10) :
v0 + 5 + (v1 - 3) + (c - 2) = 10 :=
by linarith
example (ε : ℚ) (h1 : ε > 0) : ε / 2 + ε / 3 + ε / 7 < ε :=
by linarith
example (x y z : ℚ) (h1 : 2*x < 3*y) (h2 : -4*x + z/2 < 0)
(h3 : 12*y - z < ... |
3692e2a4dc411c388b70476eab364b3374730c57 | 22e97a5d648fc451e25a06c668dc03ac7ed7bc25 | /src/tactic/lean_core_docs.lean | ab5bb8aeab04131c20fc617ecbe88efb39ab3e94 | [
"Apache-2.0"
] | permissive | keeferrowan/mathlib | f2818da875dbc7780830d09bd4c526b0764a4e50 | aad2dfc40e8e6a7e258287a7c1580318e865817e | refs/heads/master | 1,661,736,426,952 | 1,590,438,032,000 | 1,590,438,032,000 | 266,892,663 | 0 | 0 | Apache-2.0 | 1,590,445,835,000 | 1,590,445,835,000 | null | UTF-8 | Lean | false | false | 22,847 | lean | /-
Copyright (c) 2020 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Bryan Gin-ge Chen, Robert Y. Lewis, Scott Morrison
-/
import tactic.doc_commands
/-!
# Core tactic documentation
This file adds the majority of the interactive tactics... |
9a84302db9d0c67c8d59168f8f7bf52786abf1a2 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/lake/Lake/Config/FacetConfig.lean | 36632967ed4bc0e37a7dfaea7b88824b34278346 | [
"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 | 2,714 | lean | /-
Copyright (c) 2022 Mac Malone. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mac Malone, Mario Carneiro
-/
import Lake.Build.Info
import Lake.Build.Store
namespace Lake
/-- A facet's declarative configuration. -/
structure FacetConfig (DataFam : Name → Type) (ι :... |
0e234423fa5017f83bbe98f36fcb1b46c0ab355e | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/ring_theory/ideal/over.lean | 9d4b4d8eab0a12aca569bc5725e0a35ce39ffd92 | [
"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 | 14,588 | 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.algebraic
import ring_theory.localization
/-!
# Ideals over/under ideals
This file concerns ideals lying over other ideals.
Let `f : R →+* S` be a rin... |
3f03f873b8deb98a7bc16dbcae4c351f9d60ba26 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /archive/imo/imo1994_q1.lean | 89b584ee3ebce936a67af877a5aa5309682efc16 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 4,287 | lean | /-
Copyright (c) 2021 Antoine Labelle. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Labelle
-/
import algebra.big_operators.basic
import algebra.big_operators.order
import data.fintype.big_operators
import data.finset.sort
import data.fin.interval
import tact... |
fd84d0a4479426e5c5f39848beb5051a25c760ce | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/ring_theory/polynomial/basic.lean | 95d18e95b496f15e3c5c8573505963c9bb8eeff2 | [
"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 | 43,802 | lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import algebra.char_p.basic
import data.mv_polynomial.comm_ring
import data.mv_polynomial.equiv
import ring_theory.principal_ideal_domain
import ring_theory.polynomial.content... |
dab2afe0a430a10e7ba9a977ff63be6a66c60f2a | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /src/builtin/specialfn.lean | 95f4e4e714a00dbde073a1ba0bab5b94e5f5eb0d | [
"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 | 571 | lean | import Real.
variable exp : Real → Real.
variable log : Real → Real.
variable pi : Real.
alias π : pi.
variable sin : Real → Real.
definition cos x := sin (x - π / 2).
definition tan x := sin x / cos x.
definition cot x := cos x / sin x.
definition sec x := 1 / cos x.
definition csc x := 1 / sin x.
definition sinh x... |
29caa1c13fe58dc08d2968e0a862f17144fef18a | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /tests/lean/run/revert1.lean | effc59863614e6ef5053430132d9f8d338b56e8a | [
"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 | 310 | lean | new_frontend
theorem tst1 (x y z : Nat) : y = z → x = x → x = y → x = z :=
begin
intros h1 h2 h3;
revert h2;
intro h2;
exact Eq.trans h3 h1
end
theorem tst2 (x y z : Nat) : y = z → x = x → x = y → x = z :=
begin
intros h1 h2 h3;
revert y;
intros y hb ha;
exact Eq.trans ha hb
end
|
1ff465bc6f1e61407a42427527e687aeaa66ef82 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /test/by_contra.lean | ddff6e807d1c944e2a8f060e96d1d8507efa203b | [
"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 | 606 | lean | import tactic.by_contra
import tactic.interactive
example : 1 < 2 :=
begin
by_contra' h,
guard_hyp' h : 2 ≤ 1,
revert h,
exact dec_trivial
end
example : 1 < 2 :=
begin
by_contra' h : 2 ≤ 1,
guard_hyp' h : 2 ≤ 1, -- this is not defeq to `¬ 1 < 2`
revert h,
exact dec_trivial
end
example : 1 < 2 :=
begi... |
510b3e894605025efb2d55cc1cbb1e205053a898 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/conv_tac1.lean | 583c14979c10fdc8e55f32105b98cdc0470bc1bb | [
"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 | 3,529 | lean | local attribute [simp] nat.add_comm nat.add_left_comm
example (a b : nat) : (λ x, a + x) 0 = b + 1 + a :=
begin
conv in (_ + 1) { change nat.succ b },
guard_target (λ x, a + x) 0 = nat.succ b + a,
admit
end
def Div : nat → nat → nat | x y :=
if h : 0 < y ∧ y ≤ x
then
have x - y < x, from sorry,
Div (x - y) y... |
e4197a53ced1ddc4a525c344c148d63db3d773b1 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Meta/Instances.lean | d3b784f965d6389cee5bfde0fb8564907c661c38 | [
"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 | 11,813 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.ScopedEnvExtension
import Lean.Meta.GlobalInstances
import Lean.Meta.DiscrTree
import Lean.Meta.CollectMVars
namespace Lean.Meta
register_buil... |
d5c90ec900a43aac2eb7d691dbfc7976354bf677 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /tests/lean/run/ack.lean | fd76f8e7cd13e5a3fe6252c550f8414a9fce4cbd | [
"Apache-2.0"
] | permissive | soonhokong/lean-osx | 4a954262c780e404c1369d6c06516161d07fcb40 | 3670278342d2f4faa49d95b46d86642d7875b47c | refs/heads/master | 1,611,410,334,552 | 1,474,425,686,000 | 1,474,425,686,000 | 12,043,103 | 5 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 488 | lean | open nat
definition iter (f : nat → nat) (n : nat) : nat :=
nat.rec_on n
(f 1)
(λ (n₁ : nat) (r : nat), f r)
definition ack (m : nat) : nat → nat :=
nat.rec_on m
nat.succ
(λ (m₁ : nat) (r : nat → nat), iter r)
theorem ack_0_n (n : nat) : ack 0 n = n + 1 :=
rfl
theorem ack_m_0 (m : nat) : ack (m + 1) 0 = ack... |
537ce3db8fdcc479c2747bff62174c881750f0a4 | 6b2a480f27775cba4f3ae191b1c1387a29de586e | /group_rep1/morphism.lean | c37562e0f766639e351852e3fc8f51ea8c944935 | [] | no_license | Or7ando/group_representation | a681de2e19d1930a1e1be573d6735a2f0b8356cb | 9b576984f17764ebf26c8caa2a542d248f1b50d2 | refs/heads/master | 1,662,413,107,324 | 1,590,302,389,000 | 1,590,302,389,000 | 258,130,829 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 1,648 | lean | import .group_representation
universe variables u v w w' w'' w'''
open linear_map
variables {G : Type u} [group G] {R : Type v}[ring R]
namespace morphism
variables {M : Type w} [add_comm_group M] [module R M]
{M' : Type w'} [add_comm_group M'] [module R M']
/--
a morphism `f : ρ ⟶ π` between repr... |
c6b8ef4fbaf1c825223cc7f337286d14a48d8967 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebra/lie/cartan_subalgebra.lean | 296ff9f84ed19382a171e622b388dfab51c7b281 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 4,257 | lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import algebra.lie.nilpotent
import algebra.lie.centralizer
/-!
# Cartan subalgebras
Cartan subalgebras are one of the most important concepts in Lie theory. We define th... |
e966f4c9cb3fe15fe78b3712ad5a6ec03325e4c8 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/meta/expr.lean | 4cd94956870b845d8dc2e22731bcd2b729555fad | [
"Apache-2.0"
] | permissive | rmitta/mathlib | 8d90aee30b4db2b013e01f62c33f297d7e64a43d | 883d974b608845bad30ae19e27e33c285200bf84 | refs/heads/master | 1,585,776,832,544 | 1,576,874,096,000 | 1,576,874,096,000 | 153,663,165 | 0 | 2 | Apache-2.0 | 1,544,806,490,000 | 1,539,884,365,000 | Lean | UTF-8 | Lean | false | false | 25,483 | lean | /-
Copyright (c) 2019 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Simon Hudon, Scott Morrison, Keeley Hoek, Robert Y. Lewis
-/
import data.string.defs
/-!
# Additional operations on expr and related types
This file defines basic ope... |
93e832b7f738faf5cc5f0b8ab62470dcffc0abaa | 618003631150032a5676f229d13a079ac875ff77 | /src/category_theory/sparse.lean | 6a61d6cb5ad7a239eda449f0e31d71c419aeb91e | [
"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 | 828 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.category
/-!
A sparse category is a category with at most one morphism between each pair of objects.
Examples include posets, but many indexi... |
8a511fb9d78085ed8510524434c9eb3c8d222454 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/analysis/ODE/picard_lindelof.lean | 4e6b3f6ab62321f61396949cc98dacb9ad1a8786 | [
"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 | 15,026 | lean | /-
Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import analysis.special_functions.integrals
import topology.metric_space.contracting
/-!
# Picard-Lindelöf (Cauchy-Lipschitz) Theorem
In this file we prove ... |
e68316671e76503b9c7a499c2b404a4b48812331 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /stage0/src/Init/Data/Option/Instances.lean | a2eb044390c7f6e9acac1b3321086ff0ef9c7250 | [
"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 | 660 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import Init.Data.Option.Basic
universe u v
theorem Option.eq_of_eq_some {α : Type u} : ∀ {x y : Option α}, (∀z, x = some z ↔ y = some z) → x = y
... |
372014f9933ffb53b4c1606d7bd13a2ce6f06c7e | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/order/iterate.lean | 1dfdb3b58f77d3e6e5afef28f5fdb11d66121d0a | [
"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 | 9,077 | lean | /-
Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import logic.function.iterate
import order.monotone.basic
/-!
# Inequalities on iterates
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this fi... |
90663c06a25e78ca3da2ee29d83ac3cd2e9b5b6a | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/ring_theory/valuation/integral.lean | a92c3437d8f20ff206b488d3da483cf41698005d | [
"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 | 2,069 | 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 ring_theory.integrally_closed
import ring_theory.valuation.integers
/-!
# Integral elements over the ring of integers of a valution
The ring of integers is integrally... |
fb8048c51c836ccbe3b9c034dedc90e98147064e | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/data/rat/order.lean | eebc444d157a6fc5821e04751d61cddca6f77426 | [
"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 | 8,397 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import data.rat.basic
/-!
# Order for Rational Numbers
## Summary
We define the order on `ℚ`, prove that `ℚ` is a discrete, linearly ordered field,... |
0305ce9b52ea76e272b867f230d03e326025d287 | d436468d80b739ba7e06843c4d0d2070e43448e5 | /src/topology/algebra/ring.lean | c5c3b0100e52965d123dca4c0fcd5f7f30fe184b | [
"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 | 3,777 | 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 ring_theory.ideals
open classical set lattice filter topological_space
open_locale class... |
7ca6a8fa643d20bf564f104b21de4794d7538c50 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/geometry/manifold/partition_of_unity.lean | 76fec8fd69de3c58a3a18011427bf7a7348a0d32 | [
"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 | 18,920 | lean | /-
Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import geometry.manifold.algebra.structures
import geometry.manifold.bump_function
import topology.paracompact
import topology.partition_of_unity
import topol... |
d25de66ea85dc6140d99dea939939ae1a965e596 | 83c8119e3298c0bfc53fc195c41a6afb63d01513 | /library/init/data/int/order.lean | c27b969e86344c89c68f702af0217fa98304022b | [
"Apache-2.0"
] | permissive | anfelor/lean | 584b91c4e87a6d95f7630c2a93fb082a87319ed0 | 31cfc2b6bf7d674f3d0f73848b842c9c9869c9f1 | refs/heads/master | 1,610,067,141,310 | 1,585,992,232,000 | 1,585,992,232,000 | 251,683,543 | 0 | 0 | Apache-2.0 | 1,585,676,570,000 | 1,585,676,569,000 | null | UTF-8 | Lean | false | false | 11,814 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
The order relation on the integers.
-/
prelude
import init.data.int.basic init.data.ordering.basic
local attribute [simp] sub_eq_add_neg
namespace int
private def nonn... |
547f0c82c6a324dd6cd35eb8c3eedda80b9634ab | 3446e92e64a5de7ed1f2109cfb024f83cd904c34 | /src/game/world1/level1.lean | 896b7982ae5c4b19828780340af93e75f2325632 | [] | no_license | kckennylau/natural_number_game | 019f4a5f419c9681e65234ecd124c564f9a0a246 | ad8c0adaa725975be8a9f978c8494a39311029be | refs/heads/master | 1,598,784,137,722 | 1,571,905,156,000 | 1,571,905,156,000 | 218,354,686 | 0 | 0 | null | 1,572,373,319,000 | 1,572,373,318,000 | null | UTF-8 | Lean | false | false | 4,484 | lean | import mynat.definition -- Imports Peano's definition of the natural numbers.
namespace mynat -- hide
/-
# The Natural Number Game, version 1.0beta.
## By Kevin Buzzard and Mohammad Pedramfar.
Special thanks to Rob Lewis for tactic hackery, Sian Carey for power world (world 4),
and, last but not least, the 2019-20... |
e9d5da71f1f175faf9f6b8c03caba1105003e5d5 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/meta/expr.lean | 2b0df42f1b89f9ea18d1012ebd5243e7ab74da4d | [
"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 | 36,514 | lean | /-
Copyright (c) 2019 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Simon Hudon, Scott Morrison, Keeley Hoek, Robert Y. Lewis
-/
import data.string.defs
import tactic.derive_inhabited
/-!
# Additional operations on expr and related typ... |
78725d92e8f6f26b06d3a6443ffc7c91eb7564d1 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/list/default_auto.lean | 1a342b7ab43a1c28daf89997f0bc0ee505ddbd69 | [] | 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 | 1,016 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.list.alist
import Mathlib.data.list.bag_inter
import Mathlib.data.list.basic
impo... |
6a7f5bcd08ed7f19d22d40e8d1ee6aedcca23ab5 | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/category_theory/instances/Top/limits.lean | 52e5b899be9c98f591afee3fad47a9986ab866eb | [
"Apache-2.0"
] | permissive | fpvandoorn/mathlib | b21ab4068db079cbb8590b58fda9cc4bc1f35df4 | b3433a51ea8bc07c4159c1073838fc0ee9b8f227 | refs/heads/master | 1,624,791,089,608 | 1,556,715,231,000 | 1,556,715,231,000 | 165,722,980 | 5 | 0 | Apache-2.0 | 1,552,657,455,000 | 1,547,494,646,000 | Lean | UTF-8 | Lean | false | false | 2,811 | lean | -- Copyright (c) 2017 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Patrick Massot, Scott Morrison, Mario Carneiro
import category_theory.instances.Top.basic
import category_theory.limits.types
import category_theory.limits.preserves
open categ... |
3484a0d790ba6f8b0b3853ff0338a1149804c40a | 4727251e0cd73359b15b664c3170e5d754078599 | /src/analysis/normed_space/mazur_ulam.lean | 862b9eb6145189be2e46d7e2217c793b0012782c | [
"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 | 6,828 | 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 topology.instances.real_vector_space
import analysis.normed_space.affine_isometry
import linear_algebra.affine_space.midpoint
/-!
# Mazur-Ulam Theorem
Mazu... |
6d757c3d022cedd48a358c1ad2c699af881b4c76 | 9cba98daa30c0804090f963f9024147a50292fa0 | /old/metrology/measurement.lean | 09e3a45d9a73dfa4425aeee75326786964d72105 | [] | no_license | kevinsullivan/phys | dcb192f7b3033797541b980f0b4a7e75d84cea1a | ebc2df3779d3605ff7a9b47eeda25c2a551e011f | refs/heads/master | 1,637,490,575,500 | 1,629,899,064,000 | 1,629,899,064,000 | 168,012,884 | 0 | 3 | null | 1,629,644,436,000 | 1,548,699,832,000 | Lean | UTF-8 | Lean | false | false | 888 | lean | import .dimensions
import .unit
namespace measurementSystem
/-
We define a measurement system to be a 7-tuple
of units: one for length, one for mass, etc.
-/
structure MeasurementSystem : Type :=
mk ::
(length : unit.length)
(mass : unit.mass)
(time : unit.time)
(current : unit.current)
(temperature : unit.temperatur... |
ee79f4ebaa7ed461f7df1e2a36a1d92f16826d30 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/inner_product_space/adjoint.lean | 768e5627ed4a4421e0e02d40e8907396e14f999f | [
"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 | 19,107 | lean | /-
Copyright (c) 2021 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis, Heather Macbeth
-/
import analysis.inner_product_space.dual
import analysis.inner_product_space.pi_L2
/-!
# Adjoint of operators on Hilbert spaces
> THIS FILE IS S... |
9b1546dd0e3f5afc5b90ddc81cfeac3a6d9d0016 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/ring_theory/subring/pointwise.lean | f4893695db3f51d17b175ccd7cce155a56230a2e | [
"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 | 4,479 | lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import ring_theory.subsemiring.pointwise
import group_theory.subgroup.pointwise
import ring_theory.subring.basic
/-! # Pointwise instances on `subring`s
This file provide... |
c7376e4baf5e6239ee20635243401aba26b172cc | 471bedbd023d35c9d078c2f936dd577ace7f5813 | /library/init/meta/simp_tactic.lean | 3dfe7eb6422762e0b4cdfc8488b1b6952c4b81be | [
"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 | 28,072 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.meta.tactic init.meta.attribute init.meta.constructor_tactic
import init.meta.relation_tactics init.meta.occurrences
import init.data.op... |
a351317a29015873f7132d66a9669f1682e5dc22 | 22e97a5d648fc451e25a06c668dc03ac7ed7bc25 | /src/data/matrix/basic.lean | aa0fed9ddca7d16582c9823216485fcfac7501f7 | [
"Apache-2.0"
] | permissive | keeferrowan/mathlib | f2818da875dbc7780830d09bd4c526b0764a4e50 | aad2dfc40e8e6a7e258287a7c1580318e865817e | refs/heads/master | 1,661,736,426,952 | 1,590,438,032,000 | 1,590,438,032,000 | 266,892,663 | 0 | 0 | Apache-2.0 | 1,590,445,835,000 | 1,590,445,835,000 | null | UTF-8 | Lean | false | false | 19,140 | lean | /-
Copyright (c) 2018 Ellen Arlt. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ellen Arlt, Blair Shi, Sean Leather, Mario Carneiro, Johan Commelin
-/
import algebra.pi_instances
/-!
# Matrices
-/
universes u v w
open_locale big_operators
@[nolint unused_arguments]
... |
6f08be30883d4c44b8db2ab42d9a19be3b3cf2ce | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/analysis/inner_product_space/dual.lean | 588dfa1ec932872371f5bc882d1c3f1975952c44 | [
"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 | 6,607 | lean | /-
Copyright (c) 2020 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import analysis.inner_product_space.projection
import analysis.normed_space.dual
import analysis.normed_space.star.basic
/-!
# The Fréchet-Riesz representation the... |
15e5273e9a07434099f95e43b162d0b36fb70a05 | 874a8d2247ab9a4516052498f80da2e32d0e3a48 | /ramsey_lb.lean | 73122bd9164d9216715c50935463a91e7456626b | [] | no_license | AlexKontorovich/Spring2020Math492 | 378b36c643ee029f5ab91c1677889baa591f5e85 | 659108c5d864ff5c75b9b3b13b847aa5cff4348a | refs/heads/master | 1,610,780,595,457 | 1,588,174,859,000 | 1,588,174,859,000 | 243,017,788 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 2,815 | lean | import data.nat.basic
import data.int.basic
import data.rat.basic
import algebra.field_power
import tactic
import data.finset
import algebra.big_operators
import data.real.basic
import data.set.lattice
open finset
open nat
local notation `edges_of `X := powerset_len 2 X
universe u
variables {α : Type u} (K : fins... |
12bf82a9cba3aa1e70f8293c995a75d653f25c95 | a81826cfd4fd71c797ea79b8e827b03ccb332c17 | /src/p_laplacian/basic.lean | 1903fda607e378b98e8a3e4778d1e45b24bffc26 | [
"Apache-2.0"
] | permissive | jamesa9283/Generalised-Trigonometric-Functions-for-Lean | 0a0f4774363c3708be466526935c6d07f4b970f0 | 33775fb8286eacfc17397fe41af9d446cbdd78f3 | refs/heads/master | 1,669,337,232,958 | 1,597,061,947,000 | 1,597,061,947,000 | 276,104,804 | 0 | 0 | null | 1,593,540,795,000 | 1,593,523,262,000 | Lean | UTF-8 | Lean | false | false | 4,647 | lean | import tactic
import data.real.basic
import data.complex.exponential
import analysis.special_functions.pow
noncomputable theory
open_locale classical
open real
notation `|`x`|` := abs x
variables (a : ℝ) (b : ℝ)
/-!
## p-GTFs
This is my speciality but it _needs_ integration, so this won't be able to be
filled i... |
1c1773b0395e3f68eba01a8a70cebccff215cc3c | d7189ea2ef694124821b033e533f18905b5e87ef | /galois/list/mem.lean | a6a0dbf04cff50d01689e7c1b6a7ab3b7bb2d965 | [
"Apache-2.0"
] | permissive | digama0/lean-protocol-support | eaa7e6f8b8e0d5bbfff1f7f52bfb79a3b11b0f59 | cabfa3abedbdd6fdca6e2da6fbbf91a13ed48dda | refs/heads/master | 1,625,421,450,627 | 1,506,035,462,000 | 1,506,035,462,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,659 | lean | import galois.tactic
universes u
namespace list
def mem_induction {A : Type u}
(P : A → list A → Prop)
(Phere : ∀ x xs, P x (x :: xs))
(Pthere : ∀ x y ys, P x ys → P x (y :: ys))
(x : A) (xs : list A) (H : x ∈ xs)
: P x xs
:= begin
induction xs, cases H,
dsimp [has_mem.mem, list.mem] at H,
induction H, subs... |
26bb86b30be3a14b91ae67d084a97479c1570514 | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/topology/uniform_space/complete_separated.lean | 5364e04cb70554b8f5e59891ffaae76606427279 | [
"Apache-2.0"
] | permissive | fpvandoorn/mathlib | b21ab4068db079cbb8590b58fda9cc4bc1f35df4 | b3433a51ea8bc07c4159c1073838fc0ee9b8f227 | refs/heads/master | 1,624,791,089,608 | 1,556,715,231,000 | 1,556,715,231,000 | 165,722,980 | 5 | 0 | Apache-2.0 | 1,552,657,455,000 | 1,547,494,646,000 | Lean | UTF-8 | Lean | false | false | 852 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
Theory of complete separated uniform spaces.
This file is for elementary lemmas that depend on both Cauchy filters and separation.
-/
import topology.uniform_spa... |
8183b4c21333c01c35abe786ab5073d0a5eacd9b | a537b538f2bea3181e24409d8a52590603d1ddd9 | /examples/knot_isotopy.lean | 7e8bb22b3cc0ff2673ce6da3af162f6348a3a27e | [] | no_license | rwbarton/lean-tidy | 6134813ded72b275d19d4d32514dba80c21708e3 | fe1125d32adb60decda7a77d0f679614ba9f6fbb | refs/heads/master | 1,585,549,718,705 | 1,538,120,619,000 | 1,538,120,624,000 | 150,864,330 | 0 | 0 | null | 1,538,225,790,000 | 1,538,225,790,000 | null | UTF-8 | Lean | false | false | 6,386 | lean | import tidy.tidy
inductive slice
| pos : ℕ → slice
| neg : ℕ → slice
| cup : ℕ → slice
| cap : ℕ → slice
open slice
inductive diagram
| nil
| cons : slice → diagram → diagram
infixr ` ~~ `:80 := diagram.cons
notation `t[` l:(foldr `, ` (h t, diagram.cons h t) diagram.nil `]`) := l
namespace isotopy
variable (d :... |
1b1b8ed1946818127d9e315a5276e556f3928dd4 | 3aad12fe82645d2d3173fbedc2e5c2ba945a4d75 | /src/data/equiv/nursery.lean | ef7559d0ebad09f274e37f559df660d5efe76884 | [] | no_license | seanpm2001/LeanProver-Community_MathLIB-Nursery | 4f88d539cb18d73a94af983092896b851e6640b5 | 0479b31fa5b4d39f41e89b8584c9f5bf5271e8ec | refs/heads/master | 1,688,730,786,645 | 1,572,070,026,000 | 1,572,070,026,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 232 | lean |
import data.equiv.basic
lemma equiv.forall_iff_forall {α β} {p : α → Prop} (f : α ≃ β) :
(∀ x, p x) ↔ (∀ x, p $ f.symm x) :=
iff.intro
(assume h x, h _)
(assume h x, by { specialize h (f x), revert h, simp })
|
b7cea61dbe90acdc4b930ef7debac55a683b89e5 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/order/lattice.lean | 1022d57cd1387a175cfe71920e24b7bba006bc01 | [
"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 | 42,104 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import order.monotone
import order.rel_classes
import tactic.simps
import tactic.pi_instances
/-!
# (Semi-)lattices
Semilattices are partially ordered sets with joi... |
455292ecb80db677706cd12efb610640ab477b71 | e030b0259b777fedcdf73dd966f3f1556d392178 | /tests/lean/run/pack_unpack1.lean | b552e302b57aba4005ccddce8e7d63644d1252d8 | [
"Apache-2.0"
] | permissive | fgdorais/lean | 17b46a095b70b21fa0790ce74876658dc5faca06 | c3b7c54d7cca7aaa25328f0a5660b6b75fe26055 | refs/heads/master | 1,611,523,590,686 | 1,484,412,902,000 | 1,484,412,902,000 | 38,489,734 | 0 | 0 | null | 1,435,923,380,000 | 1,435,923,379,000 | null | UTF-8 | Lean | false | false | 2,273 | lean | inductive tree_core (A : Type*) : bool → Type*
| leaf' : A → tree_core ff
| node' : tree_core tt → tree_core ff
| nil' {} : tree_core tt
| cons' : tree_core ff → tree_core tt → tree_core tt
attribute [reducible]
definition tree (A : Type*) := tree_core A ff
attribute [reducible]
definition tree_list (A : Ty... |
5ca40b7251929e7cf9e076ed14c16caacc5bee27 | 342425037bb9207ebcc87b62ab094d311b0787bb | /src/exercises/07_first_negations.lean | 294c5880d39ccc94da42669fa3d71575554d5826 | [
"Apache-2.0"
] | permissive | Denglihua/tutorials | 6d4c219784f34acaa0bfcdfc388e980fd04b0cc2 | 6449169303de57d5f1799c25ac2a51af7062931d | refs/heads/master | 1,673,009,657,280 | 1,604,880,270,000 | 1,604,880,270,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,794 | lean | import tuto_lib
import data.int.parity
/-
Negations, proof by contradiction and contraposition.
This file introduces the logical rules and tactics related to negation:
exfalso, by_contradiction, contrapose, by_cases and push_neg.
There is a special statement denoted by `false` which, by definition,
has no proof.
So ... |
277c912b4e7078d3ccc31ace3ee785c2580d5dbb | 302b541ac2e998a523ae04da7673fd0932ded126 | /tests/bench/treemap.lean | d63789a5fc1380608f9d9d2485c3ca6e11bb4bf7 | [] | no_license | mattweingarten/lambdapure | 4aeff69e8e3b8e78ea3c0a2b9b61770ef5a689b1 | f920a4ad78e6b1e3651f30bf8445c9105dfa03a8 | refs/heads/master | 1,680,665,168,790 | 1,618,420,180,000 | 1,618,420,180,000 | 310,816,264 | 2 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 330 | lean | set_option trace.compiler.ir.init true
inductive Tree
| Nil : Tree
| Node : Nat -> Tree -> Tree -> Tree
open Tree
partial def make : Nat -> Tree
| 0 => Leaf
| n => Node n (make (n-1)) (make (n-1))
def mapTree : (Nat -> Nat) -> Tree -> Tree
| _, Nil => Nil
| f, Node n l r => Node (f n) (mapTree f l) (mapT... |
d5bc59bb5637f6744ab1a12b900f1738b39b1def | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/measure_theory/measurable_space.lean | 1eaa86b0ad7c0ecd7bc5dfe0cfb227e385e68bcf | [] | 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 | 62,510 | 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.data.set.disjointed
import Mathlib.data.set.countable
import Mathlib.data.i... |
42671ec1cf8cab137bf340368df5dd1134625313 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/finset/mul_antidiagonal.lean | 154fbc72e8a2490937a28d73b4cffff664b6c09c | [
"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 | 3,824 | lean | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Yaël Dillies
-/
import data.set.pointwise.basic
import data.set.mul_antidiagonal
/-! # Multiplication antidiagonal as a `finset`.
We construct the `finset` of all... |
2bf681f00167956b0147926efb5c72b8bbffb69b | bb31430994044506fa42fd667e2d556327e18dfe | /src/linear_algebra/prod.lean | 98b279f10df23d1a4cdbb2f474c893ed5aff5ae3 | [
"Apache-2.0"
] | permissive | sgouezel/mathlib | 0cb4e5335a2ba189fa7af96d83a377f83270e503 | 00638177efd1b2534fc5269363ebf42a7871df9a | refs/heads/master | 1,674,527,483,042 | 1,673,665,568,000 | 1,673,665,568,000 | 119,598,202 | 0 | 0 | null | 1,517,348,647,000 | 1,517,348,646,000 | null | UTF-8 | Lean | false | false | 31,296 | 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, Kevin Buzzard, Yury Kudryashov, Eric Wieser
-/
import linear_algebra.span
import order.partial_sups
import algebra.algebra.prod
/-! ### Products of mod... |
5641c121a8da59ced2868aad807a40450e45d15e | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /tests/compiler/phashmap2.lean | feda9d19d04962042328b497802bca71d7a26ed6 | [
"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 | 1,571 | lean | import Std.Data.PersistentHashMap
import Lean.Data.Format
open Lean Std Std.PersistentHashMap
abbrev Map := PersistentHashMap Nat Nat
partial def formatMap : Node Nat Nat → Format
| Node.collision keys vals _ => Format.sbracket $
keys.size.fold
(fun i fmt =>
let k := keys.get! i;
let v := vals.get... |
86e93b01576c7af824d79ff1110042166669945a | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/linear_algebra/projective_space/basic.lean | 20cab642407c3e39056c50e3b72db771fdb9f06b | [
"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 | 8,053 | lean | /-
Copyright (c) 2022 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import linear_algebra.finite_dimensional
/-!
# Projective Spaces
This file contains the definition of the projectivization of a vector space over a field,
as well as the b... |
51b87395176311a5e5b84a728f4979e844d950e4 | de8d0cdc3dc15aa390280472764229d0e14e734c | /src/quotient.lean | d6bf9d64469dd5c1f7d6eb1685f2502a33eeb562 | [] | no_license | amesnard0/lean-topology | 94720ccf0af34961b24b52b96bcfb19df5c8f544 | e8f6a720c435cb59d098579a26f6eb70ea05f91a | refs/heads/main | 1,682,525,569,376 | 1,622,116,766,000 | 1,622,116,766,000 | 358,047,823 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,542 | lean | import tactic
import data.set.finite
import data.real.basic
import topological_spaces
import neighbourhoods
import topological_spaces2
import metric_spaces
open set
open topological_space
open metric_space
lemma Q_dense : dense {(q : ℝ) | (q : ℚ)} :=
begin
apply subset.antisymm,
simp,
intros x hx,
have clef... |
d99b4a10505ab302b839b9275f1862de3890c85c | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/number_theory/lucas_lehmer.lean | 84e00fda916c8a53bd1daf6e19986a8b6d5e31da | [
"Apache-2.0"
] | permissive | lacker/mathlib | f2439c743c4f8eb413ec589430c82d0f73b2d539 | ddf7563ac69d42cfa4a1bfe41db1fed521bd795f | refs/heads/master | 1,671,948,326,773 | 1,601,479,268,000 | 1,601,479,268,000 | 298,686,743 | 0 | 0 | Apache-2.0 | 1,601,070,794,000 | 1,601,070,794,000 | null | UTF-8 | Lean | false | false | 17,083 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro, Scott Morrison, Ainsley Pahljina
-/
import tactic.ring_exp
import tactic.interval_cases
import data.nat.parity
import data.zmod.basic
import group_theory.order_of_elemen... |
b9b41eb9f9a327f08e617b8879da55be8414d01f | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/ring_theory/localization/module.lean | 68953652dc66a00949d82e14278047b165435fc3 | [
"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 | 3,013 | lean | /-
Copyright (c) 2022 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu, Anne Baanen
-/
import linear_algebra.basis
import ring_theory.localization.fraction_ring
import ring_theory.localization.integer
/-!
# Modules / vector spaces over localizatio... |
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