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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
b6a8188d14d9c17329695c6787fffd74a18facec | 8d65764a9e5f0923a67fc435eb1a5a1d02fd80e3 | /src/data/finset/sort.lean | 46684f5b8c2a1f7152c23502ff07aa631b9ccbf1 | [
"Apache-2.0"
] | permissive | troyjlee/mathlib | e18d4b8026e32062ab9e89bc3b003a5d1cfec3f5 | 45e7eb8447555247246e3fe91c87066506c14875 | refs/heads/master | 1,689,248,035,046 | 1,629,470,528,000 | 1,629,470,528,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,798 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.fintype.basic
import data.multiset.sort
import data.list.nodup_equiv_fin
/-!
# Construct a sorted list from a finset.
-/
namespace finset
open multiset... |
0df1fc572269b7aa652a2cabacb3fdcc9a2dcad1 | cc060cf567f81c404a13ee79bf21f2e720fa6db0 | /lean/tactics-monad.lean | 51625f3696cf6eca4476cb1a74f910dda80c831c | [
"Apache-2.0"
] | permissive | semorrison/proof | cf0a8c6957153bdb206fd5d5a762a75958a82bca | 5ee398aa239a379a431190edbb6022b1a0aa2c70 | refs/heads/master | 1,610,414,502,842 | 1,518,696,851,000 | 1,518,696,851,000 | 78,375,937 | 2 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 110 | lean | open tactic
variables A B : Prop
example : A → B → A ∧ B :=
by do trace "Hi, Mom!",
trace_state
|
078e7883e98e49d663ac1d59d741b5bbaaf60edf | 8930e38ac0fae2e5e55c28d0577a8e44e2639a6d | /tests/tactics.lean | 65d3eeafcb8ecadb186aa911bf47398830732aa2 | [
"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 | 9,673 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import tactic data.set.lattice
section solve_by_elim
example {a b : Prop} (h₀ : a → b) (h₁ : a) : b :=
begin
apply_assumption,
apply_assumption,
end
example {a b : Pr... |
93b993d1fef54810ca5e079d0ae613a283f5927d | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/topology/metric_space/gromov_hausdorff_realized.lean | cc1860ca7f0283cc18501c62d25afc42099a9b8e | [
"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 | 27,426 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import topology.metric_space.gluing
import topology.metric_space.hausdorff_distance
import topology.continuous_function.bounded
/-!
# The Gromov-Hausdorff dist... |
f81e0c4e13f11aa88e0168d3bf9c034172f78d2a | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/number_theory/pythagorean_triples.lean | 125ef8ae9b4d667946e661d54950e2fdab06c863 | [
"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 | 25,921 | lean | /-
Copyright (c) 2020 Paul van Wamelen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul van Wamelen
-/
import algebra.field
import ring_theory.int.basic
import algebra.group_with_zero.power
import tactic.ring
import tactic.ring_exp
import tactic.field_simp
import d... |
d13f14486d14f01138de45295169e4445e1f583b | f618aea02cb4104ad34ecf3b9713065cc0d06103 | /src/data/rat.lean | 3f7cb76704712b6bc96bd2f8b21c854e0c820396 | [
"Apache-2.0"
] | permissive | joehendrix/mathlib | 84b6603f6be88a7e4d62f5b1b0cbb523bb82b9a5 | c15eab34ad754f9ecd738525cb8b5a870e834ddc | refs/heads/master | 1,589,606,591,630 | 1,555,946,393,000 | 1,555,946,393,000 | 182,813,854 | 0 | 0 | null | 1,555,946,309,000 | 1,555,946,308,000 | null | UTF-8 | Lean | false | false | 44,990 | 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
Introduces the rational numbers as discrete, linear ordered field.
-/
import
data.nat.gcd data.pnat data.int.sqrt data.equiv.encodable order.basic
... |
136d9bd4ca4d5b13f099e545b168ddd3b46e1a38 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/algebraic_geometry/projective_spectrum/scheme.lean | d99ce60d766e8010920b50a2e4a623cdc218c3fc | [
"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 | 14,993 | lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
import algebraic_geometry.projective_spectrum.structure_sheaf
import algebraic_geometry.Spec
/-!
# Proj as a scheme
This file is to prove that `Proj` is a scheme.
## N... |
3b3b671b7871ed9380bfb7ff91bdb58d546ea2e8 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/order/boolean_algebra.lean | bba1cd7a4266310a570f49a27dc5f3a8c4f19fb7 | [
"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 | 3,851 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Type class hierarchy for Boolean algebras.
-/
import order.bounded_lattice
set_option old_structure_cmd true
universes u v
variables {α : Type u} {w x y z : α}
/-- S... |
abf99ec9f26b25f3cd89d289a496fc96cfcfbbaf | c31182a012eec69da0a1f6c05f42b0f0717d212d | /src/facts/nnreal.lean | 7f39c879ed061d5121d384dcb22f4b4c5be6fdbd | [] | no_license | Ja1941/lean-liquid | fbec3ffc7fc67df1b5ca95b7ee225685ab9ffbdc | 8e80ed0cbdf5145d6814e833a674eaf05a1495c1 | refs/heads/master | 1,689,437,983,362 | 1,628,362,719,000 | 1,628,362,719,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,836 | lean | import data.real.nnreal
open_locale nnreal
namespace nnreal
variables (r r' k c c₁ c₂ c₃ : ℝ≥0)
instance fact_le_of_lt [h : fact (c₁ < c₂)] : fact (c₁ ≤ c₂) := ⟨h.1.le⟩
instance fact_pos_of_one_le [hk : fact (1 ≤ c)] : fact (0 < c) :=
⟨lt_of_lt_of_le zero_lt_one hk.1⟩
instance fact_le_mul_of_one_le_left [hk : fac... |
dfbb3fee5c2d74aeaf1551046002455eef783a3e | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /stage0/src/Lean/Elab/Tactic/Congr.lean | 72ed18527ae8a0540f0a613a5a24eb827914b937 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | EdAyers/lean4 | 57ac632d6b0789cb91fab2170e8c9e40441221bd | 37ba0df5841bde51dbc2329da81ac23d4f6a4de4 | refs/heads/master | 1,676,463,245,298 | 1,660,619,433,000 | 1,660,619,433,000 | 183,433,437 | 1 | 0 | Apache-2.0 | 1,657,612,672,000 | 1,556,196,574,000 | Lean | UTF-8 | Lean | false | false | 595 | 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.Tactic.Congr
import Lean.Elab.Tactic.Basic
namespace Lean.Elab.Tactic
namespace Lean.Elab.Tactic
@[builtinTactic Parser.Tactic.congr] def... |
24c1f68cce7550f36f10419979e2431fd7b63563 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/analysis/convex/exposed.lean | fe68eb7cfffb27a92a6098c8566293a0036141c6 | [
"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 | 9,336 | lean | /-
Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import analysis.convex.extreme
import analysis.convex.function
import analysis.normed_space.ordered
/-!
# Exposed sets
This file defines exp... |
ddb8f585b325630513e1cae81b9b8291601e1d80 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/ring_theory/norm.lean | 1a57f15de105abfe01901481f7081f04ed61c3ea | [
"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 | 6,035 | lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import linear_algebra.matrix.charpoly.coeff
import linear_algebra.determinant
import ring_theory.power_basis
/-!
# Norm for (finite) ring extensions
Suppose we have an `... |
fd1b2cf7db030f9e7bcfa8abe29ee5ea048f4c90 | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/analysis/analytic/linear.lean | 7c6dcec3c3f063999f3cb760cd3202bef09dc439 | [
"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 | 1,925 | lean | /-
Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Yury G. Kudryashov
-/
import analysis.analytic.basic
/-!
# Linear functions are analytic
In this file we prove that a `continuous_linear_map` defines an analytic function with
the... |
7703b90467929d3533142e78bdaaf83abb537898 | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/topology/compacts.lean | 1d31302587df07a45a334a338a8743c866bb8f10 | [
"Apache-2.0"
] | permissive | ayush1801/mathlib | 78949b9f789f488148142221606bf15c02b960d2 | ce164e28f262acbb3de6281b3b03660a9f744e3c | refs/heads/master | 1,692,886,907,941 | 1,635,270,866,000 | 1,635,270,866,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,184 | 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
-/
import topology.homeomorph
/-!
# Compact sets
## Summary
We define the subtype of compact sets in a topological space.
## Main Definitions
- `closeds α` is th... |
be55c84e26513e2848caec74759543ce7235fa95 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/measure_theory/measure_space.lean | 64a4840ff2d2e3125dde98ddf9a7f6afc3430a57 | [
"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 | 35,657 | 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.lattice data.set.finite
import topology.instances.ennreal
measure_theory.outer_measure
/-!
# Measure spaces
Measures are rest... |
506f20c404e2df85de3402542eb19f6cecf9b55d | 969dbdfed67fda40a6f5a2b4f8c4a3c7dc01e0fb | /src/linear_algebra/finite_dimensional.lean | f45665f59398d272a028999cac9cdd86535f63b6 | [
"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 | 57,256 | 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 linear_algebra.dimension
import ring_theory.principal_ideal_domain
import algebra.algebra.subalgebra
/-!
# Finite dimensional vector spaces
Definition and basic ... |
0736907eede25cdab23caa7bdef82ecbb4056c17 | 38bf3fd2bb651ab70511408fcf70e2029e2ba310 | /src/category_theory/yoneda.lean | 3cce67c690e0313ad497b8806bda955e1a82284f | [
"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 | 7,518 | 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 category_theory.opposites
import category_theory.hom_functor
/-!
# The Yoneda embedding
The Yoneda embedding as a functor `yoneda : C ⥤ (Cᵒᵖ ⥤ Type v₁)`,
alo... |
e56b72e132ed4c55e7085069e4963a7cde605bbb | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/data/set/equinumerosity.lean | 93a64198cc3281380cbfc1fa7176f765427c9ee3 | [
"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 | 8,911 | lean | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
Two sets are equinumerous, or equipollent, if there is a bijection between them. It is sometimes
said that two such sets "have the same cardinality."
-/
import .classical_... |
879682f9c825678257a0347f796d7d63723af66e | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/ring_theory/noetherian.lean | a63c5282785fa846146c53f1d6b4686f9ae41d43 | [
"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 | 39,174 | lean | /-
Copyright (c) 2018 Mario Carneiro, Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kevin Buzzard
-/
import group_theory.finiteness
import data.multiset.finset_ops
import algebra.algebra.tower
import order.order_iso_nat
import ring_theor... |
628c04173d2da353011675bb8fcd349fcb48f7fd | d642a6b1261b2cbe691e53561ac777b924751b63 | /src/analysis/normed_space/banach.lean | 1838ef8062ebeb7d9cff5695d8cf11049c7edf0f | [
"Apache-2.0"
] | permissive | cipher1024/mathlib | fee56b9954e969721715e45fea8bcb95f9dc03fe | d077887141000fefa5a264e30fa57520e9f03522 | refs/heads/master | 1,651,806,490,504 | 1,573,508,694,000 | 1,573,508,694,000 | 107,216,176 | 0 | 0 | Apache-2.0 | 1,647,363,136,000 | 1,508,213,014,000 | Lean | UTF-8 | Lean | false | false | 10,503 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
Banach spaces, i.e., complete vector spaces.
This file contains the Banach open mapping theorem, i.e., the fact that a bijective
bounded linear map between Banac... |
e84e2cd3ef1cde711a36d85b56493b6acf608129 | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/linear_algebra/determinant.lean | 90cc855d5481cbce6f39d759fd1a02fc891ce787 | [
"Apache-2.0"
] | permissive | mcncm/mathlib | 8d25099344d9d2bee62822cb9ed43aa3e09fa05e | fde3d78cadeec5ef827b16ae55664ef115e66f57 | refs/heads/master | 1,672,743,316,277 | 1,602,618,514,000 | 1,602,618,514,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,469 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Chris Hughes, Tim Baanen
-/
import data.matrix.pequiv
import data.fintype.card
import group_theory.perm.sign
import algebra.algebra.basic
import tactic.ring
universes u v w z
op... |
e772c371e69aa533cedc909d525eb430d4192e71 | 618003631150032a5676f229d13a079ac875ff77 | /src/data/nat/parity.lean | 7b0b2ac36ed8953784048a83bca8f4f1bedd7075 | [
"Apache-2.0"
] | permissive | awainverse/mathlib | 939b68c8486df66cfda64d327ad3d9165248c777 | ea76bd8f3ca0a8bf0a166a06a475b10663dec44a | refs/heads/master | 1,659,592,962,036 | 1,590,987,592,000 | 1,590,987,592,000 | 268,436,019 | 1 | 0 | Apache-2.0 | 1,590,990,500,000 | 1,590,990,500,000 | null | UTF-8 | Lean | false | false | 3,693 | lean | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
The `even` predicate on the natural numbers.
-/
import data.nat.modeq
namespace nat
@[simp] theorem mod_two_ne_one {n : nat} : ¬ n % 2 = 1 ↔ n % 2 = 0 :=
by cases mod_t... |
91e653c9f707ad7a68c2eb8a46bac557d83c8706 | 3ef5255cebe505e5ab251615d9fbf31a132f461d | /lean/old/test2.lean | a4991eb04c06f94727fd42b0a3225b9dccf4f330 | [] | no_license | avigad/scratch | 42441a2ea94918049391e44d7adab304d3adea51 | 3fb9cef15bc5581c9602561427a7f295917990a2 | refs/heads/master | 1,608,917,412,424 | 1,473,078,921,000 | 1,473,078,921,000 | 17,224,172 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,640 | lean | import path_new
open path
inductive category [class] (ob : Type) [fob : fibrant ob] : Type :=
mk : Π (hom : ob → ob → Type) [fhom : Πa b : ob, fibrant (hom a b)]
(comp : Π⦃a b c : ob⦄, hom b c → hom a b → hom a c)
(id : Π {a : ob}, hom a a),
(Π ⦃a b c d : ob⦄ {h : hom c d} {g : hom b c} {f : hom ... |
5c7679a5b06ddad8c6078ba8b1e888499b9e735b | aa5a655c05e5359a70646b7154e7cac59f0b4132 | /stage0/src/Lean/Elab/Quotation.lean | 78879886714fd271625f0ca87eeaf539bd5170e0 | [
"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 | 23,566 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich
Elaboration of syntax quotations as terms and patterns (in `match_syntax`). See also `./Hygiene.lean` for the basic
hygiene workings and data types.
-/
import... |
c06081856c721fec7295c20c8745e3340925bcfd | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/algebra/big_operators/order.lean | 23ae1ab25e660ab4fdb5858c7124719ddd63c426 | [
"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 | 12,072 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import algebra.big_operators.basic
/-!
# Results about big operators with values in an ordered algebraic structure.
Mostly monotonicity results for the `∑` operati... |
6bada7b2ddb855b2cd0985148a76f54e91e3a146 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/set1.lean | a0d5d681d17720669fcaa2a807115319748e7355 | [
"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 | 237 | lean | variables A : Type
instance : has_subset (set A) := ⟨λ s t, ∀ ⦃x⦄, x ∈ s → x ∈ t⟩
example (s₁ s₂ s₃ : set A) : s₁ ⊆ s₂ → s₂ ⊆ s₃ → s₁ ⊆ s₃ :=
assume h₁ h₂ a ains₁,
h₂ (h₁ ains₁)
|
77e7ea26818a36ed7b66e2522a72f515d2c0eb10 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/data/rbtree/basic.lean | 2e95df9fa44fb2f21f8bb6fd54b304c080ba7bd2 | [] | 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 | 5,374 | 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
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
universes u
namespace Mathlib
namespace rbnode
inductive is_node_of {α : Type u} : rbnod... |
1e8ad314a8bc16d366796aa342865d4116005225 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/topology/homeomorph.lean | eaf7605b21f74c829545e3832beb807406be7d85 | [
"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 | 20,187 | lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Sébastien Gouëzel, Zhouhang Zhou, Reid Barton
-/
import logic.equiv.fin
import topology.dense_embedding
import topology.support
/-!
# Homeomorphisms
This... |
8ed80d0a903c03714fb3281b6c894b672d9f92fc | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/seclvl.lean | d0e6df26f690e90c3d3206aae6723e178d43671f | [
"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 | 312 | lean | section
variables (A B C : Type)
definition foo := A → B
#check foo A B
#check foo B C
#check foo A A
end
constants A B C : Type
#check foo A B
#check foo B C
#check foo A A
section
variables (A B C : Type)
definition foo2 := A → B
#check foo2 A B
#check foo2 B C
#check foo2 A A
end
|
66a48e808fffbe3e99ea742780db6d66b32a727b | 367134ba5a65885e863bdc4507601606690974c1 | /src/ring_theory/principal_ideal_domain.lean | e3442407cb171041c0bb45625b3d522fd993bdce | [
"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 | 9,013 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Chris Hughes, Morenikeji Neri
-/
import ring_theory.noetherian
import ring_theory.unique_factorization_domain
/-!
# Principal ideal rings and principal ideal domains
A principal ideal ri... |
5c37ff38b5c3f0a3fcead4a0bdb63f10a4d9f83a | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/eq18.lean | c0b963742a8f3e24ffd890c9988542175a40efc2 | [
"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 | 342 | lean | import data.examples.vector
open nat vector
definition last {A : Type} : Π {n}, vector A (succ n) → A
| last (a :: nil) := a
| last (a :: v) := last v
theorem last_cons_nil {A : Type} {n : nat} (a : A) : last (a :: nil) = a :=
rfl
theorem last_cons {A : Type} {n : nat} (a : A) (v : vector A (succ n)) : last (a :: ... |
139f3bf8e0cff196a3726a8e2f392ae30f320f8e | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /test/delta_instance.lean | 32a1bb7538793185f1e3595d50140814d859abe1 | [
"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 | 961 | lean | /-
Copyright (c) 2019 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
-/
import data.set.basic
import algebra.category.Mon.basic
def X : Type := set ℕ
instance : has_coe_to_sort X Type := set.has_coe_to_sort
@[derive ring] def T := ℤ
... |
a9152cddec8aa90632e615c049a7619fd07fc996 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/def1.lean | 83156af66cc793500a6aba8fe2b269553a3d8a39 | [
"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 | 160 | lean | universe variable u
variable {A : Type u}
lemma foo (f : A → A → A) (a b c : A) (H₁ : a = b) (H₂ : c = b) : f a = f c :=
H₂ ▸ eq.symm H₁ ▸ rfl
|
c49dcf2c05bf579d038f3e1d0c44ad7339757656 | 618003631150032a5676f229d13a079ac875ff77 | /src/tactic/lift.lean | 11f363f242388dc26bd5982b697529330f5a0989 | [
"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 | 8,858 | lean | /-
Copyright (c) 2019 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import tactic.rcases
/-!
# lift tactic
This file defines the lift tactic, allowing the user to lift elements from one type to another
under a specified condition... |
ab7f40d12c732b5843a8eeb58e8ecb329dfa7fea | b1e80085f6d9158c0b431ffc4fa9d0d53cbac8e4 | /src/free.lean | 9b2934875eb0b160aa487fd398d15654fbeaae76 | [] | no_license | dwarn/nielsen-schreier-2 | d73c20e4d2a8ae537fe4f8063272d0b72c58276a | e51a8c6511d374dc584698c7fa236a5be47e7dbe | refs/heads/master | 1,679,911,740,113 | 1,615,656,058,000 | 1,615,656,058,000 | 344,111,212 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,503 | lean | import category_theory.single_obj
category_theory.functor
category_theory.elements
category_theory.action
group_theory.free_group
quiver
misc
open category_theory
universes u v
class is_free_group (G) [group.{u} G] :=
(gp_gens : Type u)
(gp_emb : gp_gens → G)
(gp_lift {X} [gr... |
da7f79ac228af417b6749fae80025f0cc28290ef | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Util/CollectMVars.lean | fd71d68baf57c1c4280585aaf702724b9218a579 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 1,152 | 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.Expr
namespace Lean
namespace CollectMVars
structure State where
visitedExpr : ExprSet := {}
result : Array MVarId := #[]
in... |
63ae96c1d32c33f5e95f3da5b446557e6ca11034 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/topology/continuous_function/bounded.lean | 90d13d7137b47eab75fa38304645479f684436a3 | [
"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 | 35,542 | lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Mario Carneiro, Yury Kudryashov, Heather Macbeth
-/
import analysis.normed_space.basic
import topology.continuous_function.algebra
/-!
# Bounded continuous funct... |
d13b903eb056dc236a488278a6ef407914aa17f7 | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /src/Lean/Attributes.lean | 0b60c2355387183c55bcc420b3224f31d7d9f6d9 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | tobiasgrosser/lean4 | ce0fd9cca0feba1100656679bf41f0bffdbabb71 | ebdbdc10436a4d9d6b66acf78aae7a23f5bd073f | refs/heads/master | 1,673,103,412,948 | 1,664,930,501,000 | 1,664,930,501,000 | 186,870,185 | 0 | 0 | Apache-2.0 | 1,665,129,237,000 | 1,557,939,901,000 | Lean | UTF-8 | Lean | false | false | 20,516 | 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.CoreM
import Lean.MonadEnv
namespace Lean
inductive AttributeApplicationTime where
| afterTypeChecking | afterCompilation | beforeElaboratio... |
9062125bbb1169b02930d8195e38e25b695cd0ca | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/data/multiset/antidiagonal.lean | 819ad5fb53b8ef1461971eec578bcbdc7ebf3a16 | [
"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 | 2,976 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
-/
import data.multiset.powerset
/-!
# The antidiagonal on a multiset.
The antidiagonal of a multiset `s` consists of all pairs `(t₁, t₂)`
such that `t₁ + t₂ = s`. Thes... |
88cadabb89144c3acf3fc0955894cb29102a48e0 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/bad_end_error_pos.lean | cf4c7a84cf788387ccf7b7ff1df6fb885df53380 | [
"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 | 312 | lean | example (a b : nat) (f : nat → nat) : f (a + b) = f (b + a) :=
by rw nat.add_comm
example (a b : nat) (f : nat → nat) : f (a * b) = f (b * a) :=
by rw nat.mul_comm
end
example (a b c : nat) (f : nat → nat → nat) : f (b * c) (a * b * c) = f (c * b) (a * (b * c)) :=
by rw [nat.mul_assoc, nat.mul_comm]
|
470736faa9a49fe454643f137a4ddaf2e0899f8c | ff5230333a701471f46c57e8c115a073ebaaa448 | /library/init/data/int/order.lean | b3f566eff37686178bb52a322f21643545cb95a8 | [
"Apache-2.0"
] | permissive | stanford-cs242/lean | f81721d2b5d00bc175f2e58c57b710d465e6c858 | 7bd861261f4a37326dcf8d7a17f1f1f330e4548c | refs/heads/master | 1,600,957,431,849 | 1,576,465,093,000 | 1,576,465,093,000 | 225,779,423 | 0 | 3 | Apache-2.0 | 1,575,433,936,000 | 1,575,433,935,000 | null | UTF-8 | Lean | false | false | 11,821 | 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
namespace int
private def nonneg (a : ℤ) : Prop := int.cases_on a (as... |
6a433da4dd677303629710f6077226fe3787e8d1 | 271e26e338b0c14544a889c31c30b39c989f2e0f | /stage0/src/Init/Data/String/Basic.lean | 6a6635d263d0b0390f767408a9781bc24449e2c2 | [
"Apache-2.0"
] | permissive | dgorokho/lean4 | 805f99b0b60c545b64ac34ab8237a8504f89d7d4 | e949a052bad59b1c7b54a82d24d516a656487d8a | refs/heads/master | 1,607,061,363,851 | 1,578,006,086,000 | 1,578,006,086,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 15,169 | 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.List.Basic
import Init.Data.Char.Basic
import Init.Data.Option.Basic
universes u
structure String :=
(data : List Char)
abbrev Str... |
e307c60cc09e8ce58eecc3fbcc1f5aa5d3c81d3c | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/order.lean | e0822efd52e253aa8b56abe04e367a81ed920641 | [] | 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 | 17,422 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.tactic.alias
import Mathlib.tactic.lint.default
import Mathlib.PostPort
universes u u_1
... |
df5e7156e74b09ac6b1386df3da6a2dfa9547bcd | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/measure_theory/integral/interval_integral.lean | 24c0a6899878bf03e7181ab11f0203a0414d75a1 | [
"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 | 130,884 | 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, Patrick Massot, Sébastien Gouëzel
-/
import analysis.normed_space.dual
import data.set.intervals.disjoint
import measure_theory.measure.haar_lebesgue
import ana... |
1c1a1b0a0d82955122737dc67f274d49beda1973 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /test/tauto.lean | 30d9919b2470713e1e4b8113a6f6b856aa9e9f67 | [
"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 | 2,498 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import tactic.tauto
section tauto₀
variables p q r : Prop
variables h : p ∧ q ∨ p ∧ r
include h
example : p ∧ p :=
by tauto
end tauto₀
section tauto₁
variables α : Type
... |
7bbb53c722d1b48b11690acf43ac94e722d7de5a | 54d7e71c3616d331b2ec3845d31deb08f3ff1dea | /library/init/wf.lean | 5a6aae1e4b2fee5d13243c0cf3b3e06c0cf85aea | [
"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 | 6,440 | 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
inductive acc {α : Type u} (r : α → α → Prop) : α → Prop
| intro : ∀ x, (∀ y, r y x → acc y... |
9e0802578e0267798bbcee379372d10a8808fe75 | 43390109ab88557e6090f3245c47479c123ee500 | /src/finite_dimensional_vector_spaces/tmp.lean | e7be17664291badd7dcc9db537cdab9671bede6c | [
"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 | 3,052 | lean | import finite_dimensional_vector_spaces.ring_n_is_module
universes u
namespace fin_vector_space
variables (R : Type u) [h : field R] (n : ℕ)
-- structure fin_dim_ring extends module R (vector R n)
include h
def elemental_vector (i : fin n) : vector R n :=
match n, i with
| 0, _ := vector.nil
| (n+1), ⟨0, _⟩ := v... |
86bcd7a69c442895e7d5bb35cb498e94081104fc | 05b503addd423dd68145d68b8cde5cd595d74365 | /src/order/complete_lattice.lean | 8fb2af63cb409412fada5ba1b0a2ea0f9897acb3 | [
"Apache-2.0"
] | permissive | aestriplex/mathlib | 77513ff2b176d74a3bec114f33b519069788811d | e2fa8b2b1b732d7c25119229e3cdfba8370cb00f | refs/heads/master | 1,621,969,960,692 | 1,586,279,279,000 | 1,586,279,279,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 33,547 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Theory of complete lattices.
-/
import order.bounded_lattice order.bounds data.set.basic tactic.pi_instances tactic.alias
set_option old_structure_cmd true
open set
u... |
d9086e04630709201ef877032ffdf565939d07f2 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /src/Lean/Elab/ElabRules.lean | 4eb04b48708831f6760d504c8de4ec7bd78a8c96 | [
"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 | 4,921 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Elab.MacroArgUtil
import Lean.Elab.AuxDef
namespace Lean.Elab.Command
open Lean.Syntax
open Lean.Parser.Term hiding macroArg
def withExpectedT... |
d08eca77ae75a6de39a72ed95e1f8ed2ba5256e9 | fe25de614feb5587799621c41487aaee0d083b08 | /src/Lean/Elab/Declaration.lean | dbf4060d291372ded4c27fad4c9066ac8bd081e4 | [
"Apache-2.0"
] | permissive | pollend/lean4 | e8469c2f5fb8779b773618c3267883cf21fb9fac | c913886938c4b3b83238a3f99673c6c5a9cec270 | refs/heads/master | 1,687,973,251,481 | 1,628,039,739,000 | 1,628,039,739,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 12,980 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
import Lean.Util.CollectLevelParams
import Lean.Elab.DeclUtil
import Lean.Elab.DefView
import Lean.Elab.Inductive
import Lean.Elab.Struct... |
c0006df1669b11187366fbbc843aa42cb4834646 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/algebra/category/Module/kernels.lean | 6c48b46f78f0f9da40f9f088693775b310908edf | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 4,169 | lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import algebra.category.Module.epi_mono
/-!
# The concrete (co)kernels in the category of modules are (co)kernels in the categorical sense.
-/
open category_theory
op... |
2e94ec611d5c7e5af1ee8ce2251cad467d4d1efb | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/category_theory/currying.lean | 3df0f37ed015586343284d49ae33bb462ce2d859 | [
"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 | 3,918 | 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 category_theory.products.bifunctor
/-!
# Curry and uncurry, as functors.
We define `curry : ((C × D) ⥤ E) ⥤ (C ⥤ (D ⥤ E))` and `uncurry : (C ⥤ (D ⥤ E)) ⥤ ((C... |
c6ec84f728af3e6b98a6096e39b1496ac0c709fc | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /archive/100-theorems-list/9_area_of_a_circle.lean | 23d77b6715d7ad4569d8e5f4ab4ce8b864c30f7e | [
"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 | 6,420 | lean | /-
Copyright (c) 2021 James Arthur, Benjamin Davidson, Andrew Souther. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: James Arthur, Benjamin Davidson, Andrew Souther
-/
import measure_theory.interval_integral
import analysis.special_functions.sqrt
/-!
# Freek № 9: The... |
8fa62c0d4f545cfc67d89f58013445d643924402 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/category_theory/category/Quiv.lean | 69a43a4ec20f0c55e2744aaae0333257a830c22a | [
"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 | 3,138 | lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.path_category
import category_theory.category.Cat
/-!
# The category of quivers
The category of (bundled) quivers, and the free/forgetful adj... |
ab6ecb521a0345568f73a3ddcc0cdcb6933f4adf | 2c096fdfecf64e46ea7bc6ce5521f142b5926864 | /src/Lean/Meta/Tactic/Util.lean | 278cbf4381d691e333d290390cfacc27c7fa978a | [
"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 | 6,321 | 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.ForEachExpr
import Lean.Meta.Basic
import Lean.Meta.AppBuilder
import Lean.Meta.PPGoal
namespace Lean.Meta
/-- Get the user name of the g... |
5ddeb887cac09a70a5bb2770b9606951f4e06c86 | bb31430994044506fa42fd667e2d556327e18dfe | /src/topology/metric_space/emetric_space.lean | 1146f5df46403e9117c7c3651b3d0ac81b6c4dc5 | [
"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 | 51,221 | lean | /-
Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
-/
import data.nat.interval
import data.real.ennreal
import topology.uniform_space.pi
import topo... |
cd0de3b636e1805bfbeb54105958b6535b6be248 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/category_theory/monoidal/opposite.lean | 39b647f35172684ff2a92808c98aba5e5734a4d7 | [
"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 | 5,625 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.monoidal.category
/-!
# Monoidal opposites
We write `Cᵐᵒᵖ` for the monoidal opposite of a monoidal category `C`.
-/
universes v₁ v₂ u₁ u₂
... |
66140f5642ddbd8fe64c029f3f8550eb6de0fd0e | f00cc9c04d77f9621aa57d1406d35c522c3ff82c | /library/init/data/list/lemmas.lean | 54ba0abb9766d2f20d189165fac23adfff775245 | [
"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 | 10,457 | lean | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn
-/
prelude
import init.data.list.basic init.function init.meta init.data.nat.lemmas
import init.meta.interactive i... |
101fee627bc96f88e6e4a58ddd662af02a4fbbe6 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/414.lean | c9269557b90e609e9fcb715031e1adcc21bc3c3e | [
"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 | 169 | lean | macro_rules (kind := num)
| `($n:num) => `("world")
#check 2
macro_rules
| `($n:num) => `("hello")
#check 2
macro_rules (kind := num)
| n => `("boo")
#check 2
|
bc67869723f21967e82432a228517bcc9dc1c29a | c777c32c8e484e195053731103c5e52af26a25d1 | /src/geometry/euclidean/sphere/power.lean | ad14d1991684f15dfcf392e68b52e45283dd238c | [
"Apache-2.0"
] | permissive | kbuzzard/mathlib | 2ff9e85dfe2a46f4b291927f983afec17e946eb8 | 58537299e922f9c77df76cb613910914a479c1f7 | refs/heads/master | 1,685,313,702,744 | 1,683,974,212,000 | 1,683,974,212,000 | 128,185,277 | 1 | 0 | null | 1,522,920,600,000 | 1,522,920,600,000 | null | UTF-8 | Lean | false | false | 5,761 | lean | /-
Copyright (c) 2021 Manuel Candales. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Manuel Candales, Benjamin Davidson
-/
import geometry.euclidean.angle.unoriented.affine
import geometry.euclidean.sphere.basic
/-!
# Power of a point (intersecting chords and secants... |
c38271f911685a2192b1aac45034e8927c4b8aab | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/finset/sort.lean | e8e20dd8b84a5adb5cdadaac48398b566ddea833 | [
"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 | 10,659 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.fintype.basic
import data.multiset.sort
import data.list.nodup_equiv_fin
/-!
# Construct a sorted list from a finset.
-/
namespace finset
open multiset... |
5dbb6ae6b9375b382c39c6912b25e9f6fa779ccf | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/set_theory/ordinal/arithmetic.lean | daeab4abbea76962afd7175b5b0eb872163196e5 | [
"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 | 84,799 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Floris van Doorn, Violeta Hernández Palacios
-/
import set_theory.ordinal.basic
import tactic.by_contra
/-!
# Ordinal arithmetic
> THIS FILE IS SYNCHRONIZED WITH MATH... |
c449cdad25c1998fe2f94003bb103c5a7d251251 | 82b86ba2ae0d5aed0f01f49c46db5afec0eb2bd7 | /stage0/src/Lean/Data/FormatMacro.lean | 177281b50b852360132a50313ad19b4e67e2af2d | [
"Apache-2.0"
] | permissive | banksonian/lean4 | 3a2e6b0f1eb63aa56ff95b8d07b2f851072d54dc | 78da6b3aa2840693eea354a41e89fc5b212a5011 | refs/heads/master | 1,673,703,624,165 | 1,605,123,551,000 | 1,605,123,551,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 464 | 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.Data.Format
namespace Lean
syntax:max "f!" (interpolatedStr term) : term
macro_rules
| `(f! $interpStr) => do
let chunks := interpStr.ge... |
8d2199d87a2fd313b20048a5f41baa15a2f56703 | c465bc191b95d7a9e7544551279b09708d373f58 | /real_sense_failure.lean | 181c72c4819f212c840062cd2e650c6fef3f8c7e | [] | no_license | kevinsullivan/physvm_develop | b7a4149c72a10b3a87894c5db5af9b2ce5885c80 | a57e9c87d4d3fb7548dc6dfae3b932a51fc25b67 | refs/heads/main | 1,692,010,146,359 | 1,633,989,164,000 | 1,633,989,164,000 | 397,360,532 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 17,473 | lean | import .phys.time.time
import .phys.time_series.geom3d
import .standards.time_std
noncomputable theory
/-
This sensor-streaming application runs in an assumed
world with 3-d geometry and time as physical dimensions.
We import and will build from phys.geom and phys.time.
These modules provide a 3d geometric affine sp... |
3c40efce95a89be931272090682e14d0a95d3017 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /test/library_search/nat.lean | 2f88dfda03f360972531ac7b84221c66ba32c3a7 | [
"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 | 2,467 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import tactic.suggest
import data.nat.basic
namespace test.library_search
/- Turn off trace messages so they don't pollute the test build: -/
set_option trace.silen... |
49631c0fd4afe0df604afc28bcdf13b2729bcacf | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/data/real/nnreal.lean | e00bd3c2478bda624c61ea0e6f633643358333b6 | [
"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 | 24,883 | 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 data.real.basic order.lattice algebra.field
noncomputable theory
open_locale classical
/-- Nonnegative real numbers. -/
def nnre... |
daa3d33710cc5076d15ce34d93a3e8280f480b99 | 4bcaca5dc83d49803f72b7b5920b75b6e7d9de2d | /src/Lean/Util/Recognizers.lean | 9447e91aa87e872aeb91638d39a47e1dfb929ec1 | [
"Apache-2.0"
] | permissive | subfish-zhou/leanprover-zh_CN.github.io | 30b9fba9bd790720bd95764e61ae796697d2f603 | 8b2985d4a3d458ceda9361ac454c28168d920d3f | refs/heads/master | 1,689,709,967,820 | 1,632,503,056,000 | 1,632,503,056,000 | 409,962,097 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,031 | 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.Environment
namespace Lean
namespace Expr
@[inline] def const? (e : Expr) : Option (Name × List Level) :=
match e with
| Expr.const n us _... |
d8d3531256eb589796409dcd319b2ac52de55422 | 8eeb99d0fdf8125f5d39a0ce8631653f588ee817 | /src/topology/sheaves/sheaf_condition/pairwise_intersections.lean | 6b7f1e1bb5d78b2e2556f57cf867fbbb5de0512d | [
"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 | 12,070 | 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 topology.sheaves.sheaf
import category_theory.limits.preserves.basic
import category_theory.category.pairwise
/-!
# Equivalent formulations of the sheaf cond... |
d87546045265c38a97f25f8641d245773bcac91d | cbcb0199842f03e7606d4e43666573fc15dd07a5 | /src/topology/metric_space/basic.lean | 6ca34d759a3a0ce4fcaf228e0ea7b1749dda6ae9 | [
"Apache-2.0"
] | permissive | truonghoangle/mathlib | a6a7c14b3767ec71156239d8ea97f6921fe79627 | 673bae584febcd830c2c9256eb7e7a81e27ed303 | refs/heads/master | 1,590,347,998,944 | 1,559,728,860,000 | 1,559,728,860,000 | 187,431,971 | 0 | 0 | null | 1,558,238,525,000 | 1,558,238,525,000 | null | UTF-8 | Lean | false | false | 56,228 | lean | /-
Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Metric spaces.
Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
Many definitions and theorems expected on metric spaces are already introduced o... |
827bea7de65be384c5b585b864da52fa2c1ce2a8 | 13d50f9487a2afddb5e1ae1bbe68f7870f70e79a | /OldRecursor.lean | fd67cd3bf7890d244c743ca09f3bc300bd877129 | [] | no_license | gebner/lean4-mathlib-import | 09a09d9cc30738bcc253e919ab3485e13b8f992d | 719c0558dfa9c4ec201aa40f4786d5f1c1e4bd1e | refs/heads/master | 1,649,553,984,859 | 1,584,121,837,000 | 1,584,121,837,000 | 238,557,672 | 4 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 3,263 | lean | import Init.Lean
-- import Import.ExportParser
open Lean Lean.Meta
namespace Array
def take {α} (xs : Array α) (i : Nat) : Array α :=
(xs.toList.take i).toArray
def splitAt {α} (xs : Array α) (i : Nat) : Array α × Array α :=
((xs.toList.take i).toArray, (xs.toList.drop i).toArray)
end Array
namespace Lean
-- #pr... |
41c896d38bdbac5d23d0e687e6db2e07a32a1a0d | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/lake/Lake/Config/LeanExe.lean | 565861f35687c3ffae05399b20f9fe05157704ec | [
"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 | 2,994 | lean | /-
Copyright (c) 2022 Mac Malone. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mac Malone
-/
import Lake.Config.Module
namespace Lake
open Lean System
/-- A Lean executable -- its package plus its configuration. -/
structure LeanExe where
/-- The package the exec... |
d14cda2c9455c7ef7633056621a3ccad5087fc6d | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebraic_geometry/Spec.lean | 05e1db2032b9528b6814badd35d0ec99b80b4ddb | [
"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 | 10,917 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Justus Springer
-/
import algebraic_geometry.locally_ringed_space
import algebraic_geometry.structure_sheaf
import logic.equiv.transfer_instance
import ring_theory.loca... |
1e47356e7f1b7c16be8be003104c9facff70807d | 5883d9218e6f144e20eee6ca1dab8529fa1a97c0 | /src/vrel/update.lean | b5c2958734610b9eefcc0c8748ccae79cea36c85 | [] | no_license | spl/alpha-conversion-is-easy | 0d035bc570e52a6345d4890e4d0c9e3f9b8126c1 | ed937fe85d8495daffd9412a5524c77b9fcda094 | refs/heads/master | 1,607,649,280,020 | 1,517,380,240,000 | 1,517,380,240,000 | 52,174,747 | 4 | 0 | null | 1,456,052,226,000 | 1,456,001,163,000 | Lean | UTF-8 | Lean | false | false | 3,590 | lean | /-
This file contains the `vrel` `update` operation and its properties.
-/
import .type
import data.fresh
import data.sigma.extra
namespace acie -----------------------------------------------------------------
namespace vrel -----------------------------------------------------------------
variables {V : Type} [d... |
51766a18dc11b2c4701384fb7c3eb45e778406ec | 77c5b91fae1b966ddd1db969ba37b6f0e4901e88 | /src/algebra/opposites.lean | 29f2b43ef923ea532d87fe0ae838670cb47953a7 | [
"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 | 21,941 | 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.opposite
import algebra.field
import algebra.group.commute
import group_theory.group_action.defs
import data.equiv.mul_add
/-!
# Algebraic operations on `αᵒᵖ`
Thi... |
e1fc0a7238d8a731dc8512cd5b41bd25bd5c766b | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/topology/path_connected.lean | 8847f32208b6f4fbb2143aba37e49605bb47a794 | [
"Apache-2.0"
] | permissive | ayush1801/mathlib | 78949b9f789f488148142221606bf15c02b960d2 | ce164e28f262acbb3de6281b3b03660a9f744e3c | refs/heads/master | 1,692,886,907,941 | 1,635,270,866,000 | 1,635,270,866,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 36,591 | lean | /-
Copyright (c) 2020 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import topology.unit_interval
import topology.algebra.ordered.proj_Icc
import topology.continuous_function.basic
/-!
# Path connectedness
## Main definitions
In th... |
bf753bf14dbce4381c5b1f9e526df5cc03f2497b | 54deab7025df5d2df4573383df7e1e5497b7a2c2 | /data/seq/parallel.lean | 4e2a56f85e98c5bcac6dd8122c0d6905b17faec5 | [
"Apache-2.0"
] | permissive | HGldJ1966/mathlib | f8daac93a5b4ae805cfb0ecebac21a9ce9469009 | c5c5b504b918a6c5e91e372ee29ed754b0513e85 | refs/heads/master | 1,611,340,395,683 | 1,503,040,489,000 | 1,503,040,489,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 12,248 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
Parallel computation of a computable sequence of computations by
a diagonal enumeration.
The important theorems of this operation are proven as
terminates_paralle... |
4d28025347e88ae91277cd801edace80991c0c23 | 8d65764a9e5f0923a67fc435eb1a5a1d02fd80e3 | /src/linear_algebra/matrix/trace.lean | 1d4ee1067a146fbfb2cdf0161841b3587f0e6163 | [
"Apache-2.0"
] | permissive | troyjlee/mathlib | e18d4b8026e32062ab9e89bc3b003a5d1cfec3f5 | 45e7eb8447555247246e3fe91c87066506c14875 | refs/heads/master | 1,689,248,035,046 | 1,629,470,528,000 | 1,629,470,528,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,338 | lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-/
import data.matrix.basic
/-!
# Trace of a matrix
This file defines the trace of a matrix, the linear map
sending a matrix ... |
221c250d8e19dad05288fc3fe5f111931737126f | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/simp26.lean | 1bb309a90e1619f9ac81e6e0dfb7c595664fec01 | [
"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 | 472 | lean | rewrite_set simple
add_rewrite eq_id imp_truel imp_truer Nat::add_zeror : simple
variables a b : Nat
variable f : (Nat → Nat) → Nat
(*
local t = parse_lean('λ x, a + 0 = 1 → x > f (λ y, y + a)')
local t2, pr = simplify(t, "simple")
print(t2)
print(pr)
get_environment():type_check(pr)
*)
(*
local t = parse_lean('λ x, ... |
3782ecf5d311221f212708bfc7130f5453b229e6 | 5d166a16ae129621cb54ca9dde86c275d7d2b483 | /tests/lean/run/have4.lean | 9d3d899316f575e54f20842a889bcb6d179cf03a | [
"Apache-2.0"
] | permissive | jcarlson23/lean | b00098763291397e0ac76b37a2dd96bc013bd247 | 8de88701247f54d325edd46c0eed57aeacb64baf | refs/heads/master | 1,611,571,813,719 | 1,497,020,963,000 | 1,497,021,515,000 | 93,882,536 | 1 | 0 | null | 1,497,029,896,000 | 1,497,029,896,000 | null | UTF-8 | Lean | false | false | 241 | lean | prelude
definition Prop : Type.{1} := Type.{0}
constants a b c : Prop
axiom Ha : a
axiom Hb : b
axiom Hc : c
#check have H1 : a, from Ha,
then have H2 : a, from H1,
have H3 : a, from H2,
then have H4 : a, from H3,
H4
|
130a96245c0019a312b364d10a8c5dae89b5d4ad | 8e31b9e0d8cec76b5aa1e60a240bbd557d01047c | /src/simplex2.lean | 438875b719625e1b39b3d5d77c1edc5c2f12e9e0 | [] | no_license | ChrisHughes24/LP | 7bdd62cb648461c67246457f3ddcb9518226dd49 | e3ed64c2d1f642696104584e74ae7226d8e916de | refs/heads/master | 1,685,642,642,858 | 1,578,070,602,000 | 1,578,070,602,000 | 195,268,102 | 4 | 3 | null | 1,569,229,518,000 | 1,562,255,287,000 | Lean | UTF-8 | Lean | false | false | 44,302 | lean | import tableau order.lexicographic
open matrix fintype finset function pequiv partition
variables {m n : ℕ}
local notation `rvec`:2000 n := matrix (fin 1) (fin n) ℚ
local notation `cvec`:2000 m := matrix (fin m) (fin 1) ℚ
local infix ` ⬝ `:70 := matrix.mul
local postfix `ᵀ` : 1500 := transpose
namespace tableau
def... |
0c9903868800f64b2f0840d4a46446541ce7f3de | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/hom/equiv/units/group_with_zero.lean | e0144e693d766d4b6c9dca3e2855f0ed6d40804b | [
"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 | 1,336 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Callum Sutton, Yury Kudryashov
-/
import algebra.hom.equiv.units.basic
import algebra.group_with_zero.units.basic
/-!
# Multiplication by a nonzero element in a `group... |
e50c7ba9883e58d064209ca503ee531b7760fed9 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/ring/order_synonym.lean | a10d6672f5c8090aee569dcef221069415f4a907 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 2,983 | lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Yaël Dillies
-/
import algebra.ring.defs
import algebra.group.order_synonym
/-!
# Ring structure on the order type synonyms
> THIS FILE IS SYNCHRONIZED WITH MATHLIB... |
d57aeea114b6c4236c8fac171864b29331b1a70d | c777c32c8e484e195053731103c5e52af26a25d1 | /src/data/mv_polynomial/basic.lean | 269d6e815638762f11a00e76ff825dfe9034c9d7 | [
"Apache-2.0"
] | permissive | kbuzzard/mathlib | 2ff9e85dfe2a46f4b291927f983afec17e946eb8 | 58537299e922f9c77df76cb613910914a479c1f7 | refs/heads/master | 1,685,313,702,744 | 1,683,974,212,000 | 1,683,974,212,000 | 128,185,277 | 1 | 0 | null | 1,522,920,600,000 | 1,522,920,600,000 | null | UTF-8 | Lean | false | false | 52,662 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
-/
import algebra.algebra.tower
import algebra.monoid_algebra.support
import data.finsupp.antidiagonal
import order.symm_diff
import rin... |
9c8dd254c5d63375a07716ce0ec3d68d582b4655 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/algebra/module/pid.lean | fe80596510b4af0b422a79b88203826387c119d2 | [
"Apache-2.0"
] | permissive | kbuzzard/mathlib | 2ff9e85dfe2a46f4b291927f983afec17e946eb8 | 58537299e922f9c77df76cb613910914a479c1f7 | refs/heads/master | 1,685,313,702,744 | 1,683,974,212,000 | 1,683,974,212,000 | 128,185,277 | 1 | 0 | null | 1,522,920,600,000 | 1,522,920,600,000 | null | UTF-8 | Lean | false | false | 13,723 | lean | /-
Copyright (c) 2022 Pierre-Alexandre Bazin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pierre-Alexandre Bazin
-/
import algebra.module.dedekind_domain
import linear_algebra.free_module.pid
import algebra.module.projective
import algebra.category.Module.biproducts... |
a9ee028d07bd7c56dce7c7a9cd4903720dded2b6 | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/category_theory/sites/pretopology.lean | 267b5b235b547a5232093c7e99c6ac0084d72a81 | [
"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 | 7,267 | 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.sites.grothendieck
/-!
# Grothendieck pretopologies
Definition and lemmas about Grothendieck pretopologies.
A Grothendieck pretopology for a cat... |
766b1e9a8e592f5d2cfe14bd206f5c1f51769eb0 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /library/init/category/transformers.lean | 842d9cd55302457c4cd5f1aa5cafbc975ff05813 | [
"Apache-2.0"
] | permissive | GaloisInc/lean | aa1e64d604051e602fcf4610061314b9a37ab8cd | f1ec117a24459b59c6ff9e56a1d09d9e9e60a6c0 | refs/heads/master | 1,592,202,909,807 | 1,504,624,387,000 | 1,504,624,387,000 | 75,319,626 | 2 | 1 | Apache-2.0 | 1,539,290,164,000 | 1,480,616,104,000 | C++ | UTF-8 | Lean | false | false | 1,620 | lean | /-
Copyright (c) 2016 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner
-/
prelude
import init.category.state init.function init.coe
namespace monad
class monad_transformer (transformer : ∀m [monad m], Type → Type) :=
(is_monad : ∀m [monad m]... |
34f35255d6a3bb2e16c022f6da414c0c80e20cf6 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/algebra/ring/opposite.lean | 7363824c72da6ae50549436e355402467a91aa8e | [
"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 | 11,454 | 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 algebra.group.opposite
import algebra.hom.ring
/-!
# Ring structures on the multiplicative opposite
-/
universes u v
variables (α : Type u)
namespace mul_opposite
ins... |
9b305dc86fab2c01fb0daffef9e73c57401ba70a | 1446f520c1db37e157b631385707cc28a17a595e | /stage0/src/Init/Lean/Data/Position.lean | f0d0746d0f7af291f4cce972fa43e9af2c36966e | [
"Apache-2.0"
] | permissive | bdbabiak/lean4 | cab06b8a2606d99a168dd279efdd404edb4e825a | 3f4d0d78b2ce3ef541cb643bbe21496bd6b057ac | refs/heads/master | 1,615,045,275,530 | 1,583,793,696,000 | 1,583,793,696,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,762 | 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, Sebastian Ullrich
-/
prelude
import Init.Data.Nat
import Init.Data.RBMap
import Init.Lean.Data.Format
namespace Lean
structure Position :=
(line : Nat)
(c... |
00c7cc71d7f8d225a23d417e820cd75a788a0ef9 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/data/int/cast.lean | dd553a423cb9f75ad4101419cfee22870a0e6b83 | [
"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 | 9,930 | 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
import data.nat.cast
import tactic.pi_instances
import data.sum.basic
/-!
# Cast of integers (additional theorems)
This file proves additional... |
155b524c258d2102a48d83f8657f1871faf1862a | 8c9f90127b78cbeb5bb17fd6b5db1db2ffa3cbc4 | /∧.lean | 87fc494b242cbff9879f739c206d91c5d08c7b63 | [] | no_license | picrin/lean | 420f4d08bb3796b911d56d0938e4410e1da0e072 | 3d10c509c79704aa3a88ebfb24d08b30ce1137cc | refs/heads/master | 1,611,166,610,726 | 1,536,671,438,000 | 1,536,671,438,000 | 60,029,899 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 482 | lean | import data.prod
namespace hide
open prod
constant and : Prop → Prop → Prop
constant Proof : Prop → Type
constant and_intro : Π (p q : Prop), (Proof p) -> (Proof q) -> (Proof (and p q))
constant and_break : Π (p q : Prop), (Proof (and p q)) -> (Proof p) × (Proof q)
constants a b : Prop
constant anb : Proof (and a... |
5bb26570773c00d4a8f0914dadae9a92e9e16784 | f5f7e6fae601a5fe3cac7cc3ed353ed781d62419 | /test/ring.lean | 25541abac7cdffe0750a1eb7e6347043a83c984c | [
"Apache-2.0"
] | permissive | EdAyers/mathlib | 9ecfb2f14bd6caad748b64c9c131befbff0fb4e0 | ca5d4c1f16f9c451cf7170b10105d0051db79e1b | refs/heads/master | 1,626,189,395,845 | 1,555,284,396,000 | 1,555,284,396,000 | 144,004,030 | 0 | 0 | Apache-2.0 | 1,533,727,664,000 | 1,533,727,663,000 | null | UTF-8 | Lean | false | false | 542 | lean | import tactic.ring data.real.basic
example (x y : ℕ) : x + y = y + x := by ring
example (x y : ℕ) : x + y + y = 2 * y + x := by ring
example {α} [comm_ring α] (x y : α) : x + y + y - x = 2 * y := by ring
example (x y : ℚ) : x / 2 + x / 2 = x := by ring
example (x y : ℚ) : (x + y) ^ 3 = x ^ 3 + y ^ 3 + 3 * (x * y ^ 2 +... |
1c2d9b71f0d462e972404216aff0fef67ddc5eb9 | 618003631150032a5676f229d13a079ac875ff77 | /src/order/liminf_limsup.lean | 995b4a1325de6c75d3048693e1f37af58f69b04c | [
"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 | 19,851 | lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Johannes Hölzl
-/
import order.filter
/-!
# liminfs and limsups of functions and filters
Defines the Liminf/Limsup of a function taking values in a conditionall... |
0f25c9259110183e9cfb5e694f708dabc265bb50 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/lcnf4.lean | 49bee19ffab0a5c63b11756249cda71eab51793a | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 1,521 | lean | import Lean
partial def foo (n : Nat) : Nat := Id.run do
if n == 10 then return 0
foo (n+1)
partial def bar (n : Nat) : Nat := Id.run do
if n == 10 then 0 else
bar (n+1)
#print foo._unsafe_rec
#eval Lean.Compiler.compile #[``foo]
def xyz : BaseIO UInt32 := do
let ref ← IO.mkRef 42
ref.set 10
ref.get... |
26729005caf3f31f4d90aeea601877e7238c0b3e | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/ring_theory/polynomial/content.lean | d9e0d16cc5aa6bce228b289a46478a6ffb799187 | [
"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 | 16,783 | 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.gcd
import data.polynomial
import data.polynomial.erase_lead
import data.polynomial.cancel_leads
/-!
# GCD structures on polynomials
Definitions ... |
a66e869cd5c422679e1b5eb17287072eaea66750 | 076f5040b63237c6dd928c6401329ed5adcb0e44 | /answers/hw5_higher_order_functions.lean | 2dfccb6047d39ad470ca27192ddc201d26c1954d | [] | no_license | kevinsullivan/uva-cs-dm-f19 | 0f123689cf6cb078f263950b18382a7086bf30be | 09a950752884bd7ade4be33e9e89a2c4b1927167 | refs/heads/master | 1,594,771,841,541 | 1,575,853,850,000 | 1,575,853,850,000 | 205,433,890 | 4 | 9 | null | 1,571,592,121,000 | 1,567,188,539,000 | Lean | UTF-8 | Lean | false | false | 8,643 | lean | open list
/-
#1. You are to implement a function
that takes a "predicate" function and a
list and that returns a new list: namely
a list that contains all and only those
elements of the first list for which the
given predicate function returns true.
We start by giving you two predicate
functions. Each takes an argum... |
f600b46d2d29da14d7b1f99462495d7cc09cce20 | 9ee042bf34eebe0464f0f80c0db14ceb048dab10 | /stage0/src/Lean/Elab/PreDefinition/WF/PackDomain.lean | 234df1e8323768704dc43bd786d45997dab88281 | [
"Apache-2.0"
] | permissive | dexmagic/lean4 | 7507e7b07dc9f49db45df5ebd011886367dc2a6c | 48764b60d5bac337eaff4bf8a3d63a216e1d9e03 | refs/heads/master | 1,692,156,265,016 | 1,633,276,980,000 | 1,633,339,480,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,976 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Elab.PreDefinition.Basic
namespace Lean.Elab.WF
open Meta
/--
Given a (dependent) tuple `t` (using `PSigma`) of the given arity.
Return an... |
149a43809fe02cff4c88ae6e7affc9c2e8185cda | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/meta/expr.lean | bba75bd21608587f684c4e4447fbcde52e3afc4b | [
"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 | 46,452 | 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, Floris van Doorn
-/
import data.string.defs
import meta.rb_map
import tactic.derive_inhabited
/-!
# Addition... |
fb39b0fcef9f9de372cf5f54f84665eb3b5f77ca | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /src/Init/Lean/Meta/AppBuilder.lean | cb78230245ec1513f5ec4eaad113d01b993fe8b4 | [
"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 | 8,568 | 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 Init.Lean.Util.Recognizers
import Init.Lean.Meta.SynthInstance
namespace Lean
namespace Meta
/-- Given `e` s.t. `inferType e` is definitionally equ... |
4321f214603fdfde439cde7bf90d4df9ed9b98c3 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/univs.lean | 40abfdb08fded8c2a9d2934906810f7aad028e1f | [
"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 | 215 | lean | import algebra.category.basic
set_option pp.universes true
section
universes l₁ l₂ l₃ l₄
parameter C : Category.{l₁ l₂}
parameter f : Category.{l₁ l₂} → Category.{l₃ l₄}
check f C
end
|
cd0cccef9783a92fbc77967be363516c6ce2cf80 | 367134ba5a65885e863bdc4507601606690974c1 | /src/topology/algebra/uniform_ring.lean | e8d3524daabb9218471a4108586a664f597301f0 | [
"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 | 7,690 | 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 with uniform structure.
-/
import topology.algebra.group_completion
import topology.algebra.ring
open classical set filter ... |
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