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class | length_bytes int64 3 6.4M | extension stringclasses 4
values | content stringlengths 3 6.12M |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
62bc8f1a817baf32320b592e9a7090dc66503f3a | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/real/cau_seq_completion.lean | c71b1028d0bfbfbf782f8144482e2a449c74ae07 | [
"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 | 12,459 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Robert Y. Lewis
-/
import data.real.cau_seq
/-!
# Cauchy completion
This file generalizes the Cauchy completion of `(ℚ, abs)` to the completion of a ring
with absolut... |
af1ab41925fd7d73e20f45725536ab4c3984dad9 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/combinatorics/young/semistandard_tableau.lean | 4c1261a411e9debb67bdd0dc3da3a96a2c3b8f49 | [
"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 | 4,905 | lean | /-
Copyright (c) 2022 Jake Levinson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jake Levinson
-/
import combinatorics.young.young_diagram
/-!
# Semistandard Young tableaux
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a correspondi... |
7ce646e8a8deda074e5b5ca8b473edccdeae091b | f10d66a159ce037d07005bd6021cee6bbd6d5ff0 | /to_finsupp.lean | a40bbcdaa127f42a39f7500eb6a8c88b91cbe564 | [] | no_license | johoelzl/mason-stother | 0c78bca183eb729d7f0f93e87ce073bc8cd8808d | 573ecfaada288176462c03c87b80ad05bdab4644 | refs/heads/master | 1,631,751,973,492 | 1,528,923,934,000 | 1,528,923,934,000 | 109,133,224 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 8,002 | lean | import data.finsupp
universes u v w
open finset
lemma finset.sum_ite_general'' {α : Type u} {β : Type v} [decidable_eq α] [add_comm_monoid β] {f g : α → β} (s : finset α)
(p : α → Prop) [decidable_pred p] :
s.sum (λ z, if p z then f z else g z) = (s.filter p).sum f + (s.filter $ λx, ¬ p x).sum g :=
begin
have h1 ... |
07113febf94c3dbbe301bd8bc1e1e2fbbd2d260c | d5bef83c55d40cb88f9a01b755c882a93348a847 | /library/init/logic.lean | 1a1e510daf4b97520b7649a40eb47064bc38846f | [
"Apache-2.0"
] | permissive | urkud/lean | 587d78216e1f0c7f651566e9e92cf8ade285d58d | 3526539070ea6268df5dd373deeb3ac8b9621952 | refs/heads/master | 1,660,171,634,921 | 1,657,873,466,000 | 1,657,873,466,000 | 249,789,456 | 0 | 0 | Apache-2.0 | 1,585,075,263,000 | 1,585,075,263,000 | null | UTF-8 | Lean | false | false | 38,878 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Floris van Doorn
-/
prelude
import init.core
universes u v w
@[simp] lemma opt_param_eq (α : Sort u) (default : α) : opt_param α default = α ... |
8fe371161b824c775c5667a559f5965d553fac1d | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /src/Lean/Elab/Tactic/BuiltinTactic.lean | ef2111354ba43272a5a46a8c8177d2d963ef7e94 | [
"Apache-2.0"
] | permissive | WojciechKarpiel/lean4 | 7f89706b8e3c1f942b83a2c91a3a00b05da0e65b | f6e1314fa08293dea66a329e05b6c196a0189163 | refs/heads/master | 1,686,633,402,214 | 1,625,821,189,000 | 1,625,821,258,000 | 384,640,886 | 0 | 0 | Apache-2.0 | 1,625,903,617,000 | 1,625,903,026,000 | null | UTF-8 | Lean | false | false | 9,912 | 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.Tactic.Basic
namespace Lean.Elab.Tactic
open Meta
@[builtinTactic Lean.Parser.Tactic.«done»] def evalDone : Tactic := fun _ =>
done
@[... |
e5bd8600f807babc267f5355aade54a284cacb33 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /library/data/fintype/basic.lean | ba0305769b5fe48e71e75118bc02f2cb4a374ad0 | [
"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 | 9,146 | lean | /-
Copyright (c) 2015 Leonardo de Moura. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
Finite type (type class).
-/
import data.list.perm data.list.as_type data.bool data.equiv
open list bool unit decidable option function
structure fintype [class]... |
c36cf45be52a1bdb7eaee6042259bc3a73f8904f | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/algebra/opposites.lean | f6481c810de7e289722bf7a118ab1e6fbbfc41e3 | [
"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 | 10,991 | 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... |
eace4030d02c3eee56dc5e0290f32faa3538ccb2 | 0cdd90d2d613d48e567989a6bb0c5808ed4ad727 | /src/padovan_sequence.lean | d1033fc161dc0291a14e4b86076036492742f773 | [
"MIT"
] | permissive | SnobbyDragon/happynumbers | e749077a6aed5b6158f168293466130c729ddbcc | e71d1c05d461a27db7dfbaa34561ad7c1e141836 | refs/heads/master | 1,669,489,237,904 | 1,596,426,948,000 | 1,596,426,948,000 | 275,297,492 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,352 | lean | import data.stream.basic
import tactic
namespace padovan
private def padovan_aux_step : (ℕ × ℕ × ℕ) → (ℕ × ℕ × ℕ) := λ t, ⟨t.2.1, t.2.2, t.1 + t.2.1⟩
private def padovan_aux_stream : stream (ℕ × ℕ × ℕ) := stream.iterate padovan_aux_step ⟨1, 1, 1⟩
def padovan (n : ℕ) : ℕ := (padovan_aux_stream n).1
@[simp] lemma pa... |
810074d73bbf280b1224ef8b8db4a40b48460d74 | a25cc44b447f2fbde61e4b848318762eb892f2bf | /src/upper.lean | c537093514445da8f21550f711a69b0821d3e70d | [] | no_license | NeilStrickland/itloc | 20f9b9bcaa4d5840f7f32e84108174b294d84b1a | 5b13b5b418766d10926b983eb3dd2ac42abf63d8 | refs/heads/master | 1,592,747,030,159 | 1,578,138,004,000 | 1,578,138,004,000 | 197,470,135 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,403 | lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Neil Strickland
Given a finite poset `P`, we define `upper P` to be the set of
subsets `U ⊆ P` that are closed upwards. We order this by
*reverse* inclusion, to ensure that the map... |
2c6359c0877566e3db2e58e9cc48e576835a1c6d | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /src/Lean/Compiler/IR/ElimDeadBranches.lean | 84749f19a76397e11a5a7ce0a21f1dfac29d0e1e | [
"Apache-2.0"
] | permissive | dupuisf/lean4 | d082d13b01243e1de29ae680eefb476961221eef | 6a39c65bd28eb0e28c3870188f348c8914502718 | refs/heads/master | 1,676,948,755,391 | 1,610,665,114,000 | 1,610,665,114,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,549 | 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.Compiler.IR.Format
import Lean.Compiler.IR.Basic
import Lean.Compiler.IR.CompilerM
namespace Lean.IR.UnreachableBranches
/-- Value used in the... |
2a5c6167ee91ec546a0d0f189afa2b20441ded33 | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/algebra/direct_sum/basic.lean | 7e79c3d2a6c9fd74c6b6317a2f1ab7589a5a6d8e | [
"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 | 7,366 | 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 data.dfinsupp
import group_theory.submonoid.operations
import group_theory.subgroup.basic
/-!
# Direct sum
This file defines the direct sum of abelian groups, indexed ... |
60e8a17a9c93096f08a8f2c393bc430ec2416b81 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/tactic/lift.lean | c6d761db900212e2a916377d410a6529f1a0c4bc | [
"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 | 9,470 | 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... |
c70e5f61d0b6c10dcb04421a62fd0b7514c2cf39 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/tactic/ext.lean | 4bbc9171ddd3d2f61937a2a6f50e224025fffb38 | [
"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 | 11,728 | 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.rcases data.list.defs data.sum
universes u₁ u₂
open interactive interactive.types
open lean.parser nat tactic
/--
`derive_struct_ext_lemma n` generates two ... |
452be4e40dabf6e680f9b97e9808a137e4f45b4e | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/algebra/char_p/basic.lean | 47f7376d3777663b4b67ef7133b052399b284374 | [
"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 | 15,080 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Joey van Langen, Casper Putz
-/
import data.nat.choose
import data.int.modeq
import algebra.iterate_hom
import group_theory.order_of_element
/-!
# Characteristic of semirings
-/... |
908b43b22f1652bdbb74d22b5613a537cdb3d434 | a4673261e60b025e2c8c825dfa4ab9108246c32e | /tests/lean/run/doNotation1.lean | be0877b7e4afd3991dba704a1c0a479ff8fc06b7 | [
"Apache-2.0"
] | permissive | jcommelin/lean4 | c02dec0cc32c4bccab009285475f265f17d73228 | 2909313475588cc20ac0436e55548a4502050d0a | refs/heads/master | 1,674,129,550,893 | 1,606,415,348,000 | 1,606,415,348,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,057 | lean | open Lean
def f : IO Nat :=
pure 0
def g (x : Nat) : IO Nat :=
pure (x + 1)
def g1 {α : Type} (x : α) : IO (α × α) :=
pure (x, x)
def g2 (p : Nat × Nat) : Nat :=
p.1
-- set_option trace.Elab.definition true
def h (x : Nat) : StateT Nat IO Nat := do
let s ← get
let a ← f -- liftM inserted here
let b ← g1 1 ... |
cd2eb7b882b829110c76ede0bd38fdc149f72c80 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/deprecated/subgroup.lean | 2cd64ba456c5d5f1dfe549da9b0f501037c99f47 | [
"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 | 25,257 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mitchell Rowett, Scott Morrison, Johan Commelin, Mario Carneiro,
Michael Howes
-/
import group_theory.subgroup.basic
import deprecated.submonoid
/-!
# Unbundled subg... |
3617881ba7cca0a0ccd3933647527bafcca3fbaa | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/data/real/irrational.lean | 17cdfc7d2b96f7bda37e2e1328fb3749b5acb080 | [
"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 | 4,747 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne.
Irrationality of real numbers.
-/
import data.real.basic data.padics.padic_norm
open rat real multiplicity
def irrati... |
4378c5ae283b508f818f1fd0758a93697929b614 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/analysis/inner_product_space/spectrum.lean | 525c6e21e8b0f68a7ab3a2a4cb6c5a9126bddde5 | [
"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 | 12,367 | lean | /-
Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import analysis.inner_product_space.rayleigh
import analysis.inner_product_space.pi_L2
/-! # Spectral theory of self-adjoint operators
This file covers the spectr... |
cd34871acec2301b69848fc921458faf5dc67c8c | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/linear_algebra/dual.lean | cd44bcc83191c14edbe354f63553f28d37b89cba | [
"Apache-2.0"
] | permissive | ChrisHughes24/mathlib | 98322577c460bc6b1fe5c21f42ce33ad1c3e5558 | a2a867e827c2a6702beb9efc2b9282bd801d5f9a | refs/heads/master | 1,583,848,251,477 | 1,565,164,247,000 | 1,565,164,247,000 | 129,409,993 | 0 | 1 | Apache-2.0 | 1,565,164,817,000 | 1,523,628,059,000 | Lean | UTF-8 | Lean | false | false | 6,599 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Fabian Glöckle
Dual vector spaces, the spaces of linear functionals to the base field, including the dual basis
isomorphism and evaluation isomorphism in the finite-di... |
c6c986bf56d07e378ba016bba6c1199ec8c5c993 | 618003631150032a5676f229d13a079ac875ff77 | /src/field_theory/finite.lean | fc4ededfe19b8199c93b8ee14c4d2032dd4d0850 | [
"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 | 10,176 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Joey van Langen, Casper Putz
-/
import data.equiv.ring
import data.zmod.basic
import linear_algebra.basis
import ring_theory.integral_domain
/-!
# Finite fields
This fil... |
a97099eac3570e0e86e7e075ebfa4149691bf08c | 41ebf3cb010344adfa84907b3304db00e02db0a6 | /uexp/src/uexp/meta/canonize.lean | 6bb6ffcebb85523adbab351f4b23862a454e52a3 | [
"BSD-2-Clause"
] | permissive | ReinierKoops/Cosette | e061b2ba58b26f4eddf4cd052dcf7abd16dfe8fb | eb8dadd06ee05fe7b6b99de431dd7c4faef5cb29 | refs/heads/master | 1,686,483,953,198 | 1,624,293,498,000 | 1,624,293,498,000 | 378,997,885 | 0 | 0 | BSD-2-Clause | 1,624,293,485,000 | 1,624,293,484,000 | null | UTF-8 | Lean | false | false | 4,441 | lean | import .cosette_tactics .TDP
open tactic
section canonize
meta inductive canonize_term_repr : Type
| sig : expr → list name → canonize_term_repr
| prod : list expr → canonize_term_repr
meta def expr_to_canonize_term_repr (ex : expr)
: tactic canonize_term_repr :=
match sigma_expr_to_sigma_repr ex with
| ⟨[], ... |
f5f14a524db130aa82328c3b8dbb6e9a852567ca | 12dabd587ce2621d9a4eff9f16e354d02e206c8e | /world05/level06.lean | beba877a8ebe13670944f67321590a7949736f56 | [] | no_license | abdelq/natural-number-game | a1b5b8f1d52625a7addcefc97c966d3f06a48263 | bbddadc6d2e78ece2e9acd40fa7702ecc2db75c2 | refs/heads/master | 1,668,606,478,691 | 1,594,175,058,000 | 1,594,175,058,000 | 278,673,209 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 139 | lean | example (P Q R : Type) : (P → (Q → R)) → ((P → Q) → (P → R)) :=
begin
intro f,
intro h,
intro p,
apply (f p),
apply (h p),
end
|
cc0d3cf52836d0405aff7167f8134e5637ba3b1a | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/field_theory/minpoly.lean | 80106643f08f258d7b2c4b6a445f438e9768778e | [
"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 | 18,023 | lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johan Commelin
-/
import data.polynomial.field_division
import ring_theory.integral_closure
import ring_theory.polynomial.gauss_lemma
/-!
# Minimal polynomials
This file ... |
ce16ba53ddbdd7f036c9eab0544b9f58c82b5cac | ad0c7d243dc1bd563419e2767ed42fb323d7beea | /algebra/field_power.lean | e117ca99c94e20c4b739b1e921ab9e76047d7bcc | [
"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 | 3,260 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
Integer power operation on fields.
-/
import algebra.group_power tactic.wlog
universe u
section field_power
open int nat
variables {α : Type u} [division_ring α]
... |
35f43812f2bd9cccdc8bee308e20889d4eabd807 | 367134ba5a65885e863bdc4507601606690974c1 | /src/category_theory/limits/functor_category.lean | ef18c2dfe044d50b6e9d55163652e6fd719c3705 | [
"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 | 10,671 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.limits.preserves.limits
open category_theory category_theory.category
namespace category_theory.limits
universes v v₂ u -- declare the `v`'s... |
7c4dd4a8873d2a92406591a88687c402f8e8aba6 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/field_theory/splitting_field.lean | 395ec472898d5e57b1d3a944d6603b60a85ab02f | [
"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 | 31,229 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
Definition of splitting fields, and definition of homomorphism into any field that splits
-/
import ring_theory.adjoin_root
import ring_theory.algebra_tower
import ring_the... |
8ae99ea68b164df089ef2304161a52a161f097f4 | 367134ba5a65885e863bdc4507601606690974c1 | /src/ring_theory/coprime.lean | b985e82d0034455b375e83a02c65b56aa3fb3f0f | [
"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 | 11,824 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Ken Lee, Chris Hughes
-/
import tactic.ring
import algebra.big_operators.basic
import data.fintype.basic
import data.int.gcd
import data.set.disjointed
/-!
# Coprime elements of... |
f231b222a24faf6807dcdf0a4e74b42f0203d087 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/hott/614.hlean | 075fb966adc87515b854254c68a04ba945fae1e7 | [
"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 | 593 | hlean | import homotopy.circle
open circle eq int pi
attribute circle.rec [recursor]
protected definition my_decode {x : circle} (c : circle.code x) : base = x :=
begin
induction x,
{ revert c, exact power loop },
{ apply arrow_pathover_left, intro b, apply concato_eq, apply pathover_eq_r,
rewrite [power_con,trans... |
59a81f7ee95ba51bfdf15e0786c3f596feb686eb | 07c6143268cfb72beccd1cc35735d424ebcb187b | /src/data/mv_polynomial.lean | 65b46d353e9b56134abdf6bc09b8559924e4bb75 | [
"Apache-2.0"
] | permissive | khoek/mathlib | bc49a842910af13a3c372748310e86467d1dc766 | aa55f8b50354b3e11ba64792dcb06cccb2d8ee28 | refs/heads/master | 1,588,232,063,837 | 1,587,304,803,000 | 1,587,304,803,000 | 176,688,517 | 0 | 0 | Apache-2.0 | 1,553,070,585,000 | 1,553,070,585,000 | null | UTF-8 | Lean | false | false | 56,743 | 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, Shing Tak Lam
-/
import algebra.ring
import data.finsupp data.polynomial data.equiv.ring data.equiv.fin
import tactic.omega
/-!
# Mult... |
cd8258c6ae1c92f9889848889500f5dec2c4b285 | 8d65764a9e5f0923a67fc435eb1a5a1d02fd80e3 | /src/tactic/transform_decl.lean | 67c7e7830bbdb31f2942ba5f67f86b4c635d5213 | [
"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 | 5,283 | lean | /-
Copyright (c) 2017 Mario Carneiro All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Floris van Doorn
-/
import tactic.core
namespace tactic
open expr
/-- Auxilliary function for `additive_test`. The bool argument *only* matters when applied
to exactly... |
0f9187b5bfcc3f6653d63708d9919f14597b1021 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/analysis/calculus/inverse.lean | 782b5ef686d90d466a0b0ac05c3a517c52dbcdc5 | [] | 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 | 34,560 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Heather Macbeth.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.analysis.calculus.times_cont_diff
import Mathlib.topology.local_homeomo... |
7837573de6b3e1e689c9e0c1303b778e462a83a7 | e61a235b8468b03aee0120bf26ec615c045005d2 | /stage0/src/Init/Lean/Scopes.lean | 1dcb04f3b691da1a531e587add54c37048526973 | [
"Apache-2.0"
] | permissive | SCKelemen/lean4 | 140dc63a80539f7c61c8e43e1c174d8500ec3230 | e10507e6615ddbef73d67b0b6c7f1e4cecdd82bc | refs/heads/master | 1,660,973,595,917 | 1,590,278,033,000 | 1,590,278,033,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,719 | 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
-/
prelude
import Init.Lean.Environment
namespace Lean
/- Scope management
TODO: delete after we delete parser implemented in C++.
We have decided to store ... |
09043feea529e3eea6b50ff01403382ad949c278 | ad0c7d243dc1bd563419e2767ed42fb323d7beea | /category_theory/examples/topological_spaces.lean | a8c8f929aa887381af03310429eb520952e6c4a0 | [
"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 | 2,535 | 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.full_subcategory
import category_theory.functor_category
import category_theory.natural_isomorphism
import ... |
f0f401479124c3a3e108f0e2bd38b75233d4bcc1 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/category_theory/abelian/ext.lean | e3a47ba8fcfcdfa191e1602b5b64bd28c12a5f76 | [
"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 | 2,679 | lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Adam Topaz
-/
import algebra.category.Group.basic
import algebra.category.Module.abelian
import category_theory.functor.left_derived
import category_theory.linear.yoned... |
3eadc0db907c242a32a88985546b46ec2ae945ec | 08bd4ba4ca87dba1f09d2c96a26f5d65da81f4b4 | /tests/lean/formatTerm.lean | 1500e469b4eca6a610983e0a242508434ac351f3 | [
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"Apache-2.0",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | gebner/lean4 | d51c4922640a52a6f7426536ea669ef18a1d9af5 | 8cd9ce06843c9d42d6d6dc43d3e81e3b49dfc20f | refs/heads/master | 1,685,732,780,391 | 1,672,962,627,000 | 1,673,459,398,000 | 373,307,283 | 0 | 0 | Apache-2.0 | 1,691,316,730,000 | 1,622,669,271,000 | Lean | UTF-8 | Lean | false | false | 1,121 | lean | import Lean
open Lean PrettyPrinter
def fmt (stx : CoreM Syntax) : CoreM Format := do PrettyPrinter.ppTerm ⟨← stx⟩
#eval fmt `(if c then do t else e)
#eval fmt `(if c then do t; t else e)
#eval fmt `(if c then do t else do e)
#eval fmt `(if let x := c then do t else do e)
#eval fmt `(if c then do t else if c then do ... |
6f43e2899b98256bc401c4fc77b82da66cc938ab | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /tests/lean/run/synthPending1.lean | d7231a21c0d356938eb03961d9c925a548925558 | [
"Apache-2.0"
] | permissive | WojciechKarpiel/lean4 | 7f89706b8e3c1f942b83a2c91a3a00b05da0e65b | f6e1314fa08293dea66a329e05b6c196a0189163 | refs/heads/master | 1,686,633,402,214 | 1,625,821,189,000 | 1,625,821,258,000 | 384,640,886 | 0 | 0 | Apache-2.0 | 1,625,903,617,000 | 1,625,903,026,000 | null | UTF-8 | Lean | false | false | 50 | lean |
theorem ex : Not (1 = 2) :=
ofDecideEqFalse rfl
|
3ebe581d56541324a12dcb77a0010b4b86bae8f9 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/measure_theory/covering/vitali.lean | c3ab69ef80710e7d07abccaa8a7eb76d6f51a548 | [
"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 | 29,556 | lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import topology.metric_space.basic
import measure_theory.constructions.borel_space
import measure_theory.covering.vitali_family
/-!
# Vitali covering theorems
... |
bdabc6b972b6ede02ae7b49865edc2cb6080b6bc | 95dcf8dea2baf2b4b0a60d438f27c35ae3dd3990 | /src/algebra/module.lean | d1a96e1fcbbd9f980f15493b9f2607dc713275ee | [
"Apache-2.0"
] | permissive | uniformity1/mathlib | 829341bad9dfa6d6be9adaacb8086a8a492e85a4 | dd0e9bd8f2e5ec267f68e72336f6973311909105 | refs/heads/master | 1,588,592,015,670 | 1,554,219,842,000 | 1,554,219,842,000 | 179,110,702 | 0 | 0 | Apache-2.0 | 1,554,220,076,000 | 1,554,220,076,000 | null | UTF-8 | Lean | false | false | 13,287 | lean | /-
Copyright (c) 2015 Nathaniel Thomas. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nathaniel Thomas, Jeremy Avigad, Johannes Hölzl, Mario Carneiro
Modules over a ring.
-/
import algebra.ring algebra.big_operators group_theory.subgroup group_theory.group_action
op... |
1c3e069c8a1f1a43da6c2aec3fe1c57ef1e325f9 | e39f04f6ff425fe3b3f5e26a8998b817d1dba80f | /category_theory/limits/types.lean | 052922f07ce022522791d9f6bf250c596f925e3d | [
"Apache-2.0"
] | permissive | kristychoi/mathlib | c504b5e8f84e272ea1d8966693c42de7523bf0ec | 257fd84fe98927ff4a5ffe044f68c4e9d235cc75 | refs/heads/master | 1,586,520,722,896 | 1,544,030,145,000 | 1,544,031,933,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,587 | lean | -- Copyright (c) 2018 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Scott Morrison, Reid Barton
import category_theory.limits.limits
universes u v
open category_theory
open category_theory.limits
namespace category_theory.limits.types
variab... |
500e25b55ef8d78b3c2dcf753d7bbe2bb95f4cc1 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/ring_theory/localization/integer.lean | a5fdd511ce77b18170fc9f011fdedfcb0766da2c | [
"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 | 5,365 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen
-/
import ring_theory.localization.basic
/-!
# Integer elements of a localization
## Main definitions
* `is_loc... |
0529900999c9ec7838cf1c9eaa7ea423453d94c7 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/differential_object.lean | 96de5d3b8a33deee920fc8d917559669bd3b93ba | [
"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 | 8,871 | 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 data.int.basic
import category_theory.shift
import category_theory.concrete_category.basic
/-!
# Differential objects in a category.
A differential object in... |
69a217d84e0d7844674801ea2310c923908bb43f | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/linear_algebra/pi_tensor_product.lean | 551441a21b78ea801f86d0530eca3b57a6c1b953 | [
"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 | 21,385 | lean | /-
Copyright (c) 2020 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis, Eric Wieser
-/
import group_theory.congruence
import linear_algebra.multilinear
/-!
# Tensor product of an indexed family of semimodules over commutative semirings
... |
b84ed9f7f0aa6366f88926595fd6ca9195bd1fe3 | 0c6b99c0daded009943e570c13367c8cc7d3bcae | /chapter4.lean | eb2616b606365eaa494c32bb5d95b7d6ad75ffed | [] | no_license | TateKennington/logic-and-proof-exercises | e3c5c5b12b6238b47b0c5acf8717923bd471a535 | acca8882026e7b643453eb096d3021cd043005bd | refs/heads/main | 1,687,638,489,616 | 1,626,858,474,000 | 1,626,858,474,000 | 371,871,374 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,293 | lean | variables A B C D: Prop
example : A ∧ (A → B) → B :=
assume h,
have A, from and.left h,
have A → B, from and.right h,
‹A → B› ‹A›
example : A → ¬ (¬ A ∧ B) :=
assume :A,
show ¬ (¬ A ∧ B), from
assume h,
have nA: ¬A, from and.left h,
nA ‹A›
example : ¬ (A ∧ B) → (A → ¬ B) :=
assume h₁,
assu... |
fc445118c47e1b2c66af8f7060a31fce8bf81124 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/indicator_function.lean | 2762a65b1b36bdb5659d730becf25db23946c007 | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 24,625 | lean | /-
Copyright (c) 2020 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
-/
import algebra.support
/-!
# Indicator function
- `indicator (s : set α) (f : α → β) (a : α)` is `f a` if `a ∈ s` and is `0` otherwise.
- `mul_indicator (s : set α) (... |
4e32beca58b8aa6f368e0a98144aa72f513ea1e6 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/data/zmod/defs.lean | 320127f005773b35ffe743a0907f5b4d0adc8c3f | [
"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 | 6,732 | lean | /-
Copyright (c) 2022 Eric Rodriguez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Rodriguez
-/
import data.int.modeq
/-!
# Definition of `zmod n` + basic results.
This file provides the basic details of `zmod n`, including its commutative ring structure.
##... |
18f41385364ef7be99b128121e9edc3cb658fdac | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/run/335.lean | e2515ac48b53686a9ec6f2d66f993d79f14255ea | [
"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 | 617 | lean | constant foo : {x : Nat} → Type
constant bar : {T : Type} → ({x : T} → Type) → Type
structure Baz where
baz : {x : Nat} → Type
#check bar foo
#check fun (b : Baz) => bar b.baz
structure Ty where
ctx : Type
ty : ctx → Type
structure Tm where
ty : Ty
tm : ∀ {Γ}, ty.ty Γ
#check fun (Γ : Type)
(A : Ty)
(Actx ... |
487b5edd0e596765a1a1f51bdf8e21ee07edf118 | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /stage0/src/Std/Data/HashMap.lean | 5b3c0bc1ed624e28fa546c08cc0d985dbcd5d7ee | [
"Apache-2.0"
] | permissive | WojciechKarpiel/lean4 | 7f89706b8e3c1f942b83a2c91a3a00b05da0e65b | f6e1314fa08293dea66a329e05b6c196a0189163 | refs/heads/master | 1,686,633,402,214 | 1,625,821,189,000 | 1,625,821,258,000 | 384,640,886 | 0 | 0 | Apache-2.0 | 1,625,903,617,000 | 1,625,903,026,000 | null | UTF-8 | Lean | false | false | 7,719 | lean | /-
Copyright (c) 2018 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
import Std.Data.AssocList
namespace Std
universe u v w
def HashMapBucket (α : Type u) (β : Type v) :=
{ b : Array (AssocList α β) // b.size > 0 }
def Has... |
5141f604b6ea781d5c73a4ce15fbdcdcbc0a5664 | 592ee40978ac7604005a4e0d35bbc4b467389241 | /Library/generated/mathscheme-lean/CommutativeMonoid1.lean | 2ce8082bac3ed2e270f4c9796d8a75a5259198b5 | [] | no_license | ysharoda/Deriving-Definitions | 3e149e6641fae440badd35ac110a0bd705a49ad2 | dfecb27572022de3d4aa702cae8db19957523a59 | refs/heads/master | 1,679,127,857,700 | 1,615,939,007,000 | 1,615,939,007,000 | 229,785,731 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,903 | lean | import init.data.nat.basic
import init.data.fin.basic
import data.vector
import .Prelude
open Staged
open nat
open fin
open vector
section CommutativeMonoid1
structure CommutativeMonoid1 (A : Type) : Type :=
(op : (A → (A → A)))
(one : A)
(lunit_one : (∀ {x : A} , (op one x) = x))
(ru... |
eb80275cfee98c6cd7090aaddd9708e0a1393262 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/geometry/manifold/algebra/lie_group.lean | 90009628761f93b527d6697c990f47279327f8df | [
"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 | 8,538 | lean | /-
Copyright © 2020 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri
-/
import geometry.manifold.algebra.monoid
/-!
# Lie groups
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to math... |
a05812d395c71b9b6b184b8bb7845809bf4303f5 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/set/intervals/disjoint.lean | a361c5dede68cb0d673906c4a1f72affbb370c50 | [
"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 | 3,400 | 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, Yury Kudryashov
-/
import data.set.lattice
/-!
# Extra lemmas about intervals
This file contains lemmas about intervals that cannot be included into `data.set.int... |
e9e7199fe420bd242a1abf81afdc55e89c7dc2e3 | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/geometry/manifold/basic_smooth_bundle.lean | 8b4a3a302e6691ce332ae9f3b90dc9b946e8512e | [
"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 | 31,758 | 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.topological_fiber_bundle
import geometry.manifold.smooth_manifold_with_corners
/-!
# Basic smooth bundles
In general, a smooth bundle is a bun... |
a89fe6f7a01d4d7e60b9fd88d3d886e2b60376b0 | 3f7026ea8bef0825ca0339a275c03b911baef64d | /src/category_theory/functor_category.lean | 7f531f56533e791b62dc904a8b165f5282118952 | [
"Apache-2.0"
] | permissive | rspencer01/mathlib | b1e3afa5c121362ef0881012cc116513ab09f18c | c7d36292c6b9234dc40143c16288932ae38fdc12 | refs/heads/master | 1,595,010,346,708 | 1,567,511,503,000 | 1,567,511,503,000 | 206,071,681 | 0 | 0 | Apache-2.0 | 1,567,513,643,000 | 1,567,513,643,000 | null | UTF-8 | Lean | false | false | 3,935 | 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.natural_transformation
namespace category_theory
universes v₁ v₂ v₃ u₁ u₂ u₃ -- declare the `v... |
3fb11f2bc28149b2f9113834a36bdd02e0531696 | fcf3ffa92a3847189ca669cb18b34ef6b2ec2859 | /src/world2/level6.lean | e836fb047282cda527a21e768f1c9b314e2505f5 | [
"Apache-2.0"
] | permissive | nomoid/lean-proofs | 4a80a97888699dee42b092b7b959b22d9aa0c066 | b9f03a24623d1a1d111d6c2bbf53c617e2596d6a | refs/heads/master | 1,674,955,317,080 | 1,607,475,706,000 | 1,607,475,706,000 | 314,104,281 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 265 | lean | import mynat.definition
import mynat.add
import world2.level2
import world2.level4
namespace mynat
lemma add_right_comm (a b c: mynat) : a + b + c = a + c + b :=
begin [nat_num_game]
rw add_assoc,
rw add_comm b,
rw add_assoc,
refl,
end
end mynat
|
847865f7b97f145e38b508d600a349116f5c2b83 | a8ca99e8fae20e1383a6a786312b9f44f7dfdb42 | /coq/2.2 types as objects.lean | 537be997183f49792aa4744a65688c9dcb299420 | [
"MIT"
] | permissive | nolmeunion/learn | b715a4e9560101275c9c418d191cc198c905d189 | 482f4b8a5de81375e5663ea0b065d25f2f7da4b6 | refs/heads/master | 1,671,751,332,943 | 1,601,261,285,000 | 1,601,261,285,000 | 287,418,011 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 474 | lean | #check nat
#check bool
#check nat → bool
#check nat × nat → nat
#check nat → (nat → nat)
#check (nat → nat) → nat
constants α β : Type
constant F : Type → Type
#check F
#check prod α β
#check list α
#check list nat
#check Type
-- Type is a set
-- Type == Type 0
-- type of Type 0 is Type 1
-- type... |
48099e12c7c9a68b3f4c33bb4bab7083fe4fc0b1 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/category_theory/limits/preserves/shapes/kernels.lean | 3c9751734eae023fa6a7f72198e61f83512551c7 | [
"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 | 7,565 | lean | /-
Copyright (c) 2022 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.limits.shapes.kernels
import category_theory.limits.preserves.shapes.equalizers
import category_theory.limits.preserves.shapes.zero
/-!
# Pres... |
4f25eadce85c33f8910e3207bd82087ca8963764 | 0c9c1ff8e5013c525bf1d72338b62db639374733 | /library/init/core.lean | c510ee535b339d33019fedf006fe5a7418dacfb4 | [
"Apache-2.0"
] | permissive | semorrison/lean | 1f2bb450c3400098666ff6e43aa29b8e1e3cdc3a | 85dcb385d5219f2fca8c73b2ebca270fe81337e0 | refs/heads/master | 1,638,526,143,586 | 1,634,825,588,000 | 1,634,825,588,000 | 258,650,844 | 0 | 0 | Apache-2.0 | 1,587,772,955,000 | 1,587,772,954,000 | null | UTF-8 | Lean | false | false | 18,592 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
notation, basic datatypes and type classes
-/
prelude
notation `Prop` := Sort 0
notation f ` $ `:1 a:0 := f a
universes u v w
/--
The kernel definitional e... |
315dda9e5ecf777d8f367524276c4254731dd9ef | a44280b79dc85615010e3fbda46abf82c6730fa3 | /library/init/lean/compiler/ir.lean | f02ec0090876cda3445d6e5915482a93ac045546 | [
"Apache-2.0"
] | permissive | kodyvajjha/lean4 | 8e1c613248b531d47367ca6e8d97ee1046645aa1 | c8a045d69fac152fd5e3a577f718615cecb9c53d | refs/heads/master | 1,589,684,450,102 | 1,555,200,447,000 | 1,556,139,945,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 16,258 | 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.name init.lean.kvmap
prelude
/-
Implements (extended) λPure and λRc proposed in the article
"Counting Immutable Beans", Sebastian Ullrich ... |
531615c7b86fcd2a57685d161fe50b077a760c78 | a721fe7446524f18ba361625fc01033d9c8b7a78 | /elaborate/mul_cancel_induction.stripped.lean | 654426fcc3e3d6a7235b9e1b98e0c366d66e5fcf | [] | no_license | Sterrs/leaning | 8fd80d1f0a6117a220bb2e57ece639b9a63deadc | 3901cc953694b33adda86cb88ca30ba99594db31 | refs/heads/master | 1,627,023,822,744 | 1,616,515,221,000 | 1,616,515,221,000 | 245,512,190 | 2 | 0 | null | 1,616,429,050,000 | 1,583,527,118,000 | Lean | UTF-8 | Lean | false | false | 18,680 | lean | mynat.rec (λ {m k : mynat} (hmn0 : m = zero → false) (hmk0 : zero = mul m k), eq.rec (eq.refl k) (mynat.rec (eq.rec true.intro (eq.rec (eq.refl ((m = zero → false) → zero = zero → zero = zero)) (eq.rec (propext {mp := λ (hab : (m = zero → false) → zero = zero → zero = zero) (hc : m = zero → false), (eq.rec {mp := λ (h ... |
896140e43941115d8226064d6665e830abbcca4b | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/measure_theory/probability_mass_function.lean | 0109981417717d88f8448c25c486986bcd313394 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 13,254 | 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.ennreal
/-!
# Probability mass functions
This file is about probability mass functions or discrete probability measures:
a function `α → ℝ... |
1e4d8a593a46fb54b944fe309ae6ad7f4f1ea69b | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /src/Lean/Elab/MacroArgUtil.lean | 16e84d9dbc8180e3b30365ce096a33a3951e80d2 | [
"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 | 4,251 | 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.Syntax
namespace Lean.Elab.Command
open Lean.Syntax
open Lean.Parser.Term hiding macroArg
open Lean.Parser.Command
/-- Convert `macro` ar... |
5792419f1b7f77164760c453d124b469312d22d5 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/booltst.lean | b0359ead0cb2940e42f96c649e35c89cd72066e0 | [
"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 | 37 | lean | import data.bool
open bool
check ff
|
e7ac7ffb513327f261cfd9ff1377c3375fe94de7 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /stage0/src/Lean/Parser/Tactic.lean | 33a3086d2e085ccb415c9ac0acc8ce5f9cda4cc3 | [
"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 | 1,244 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
import Lean.Parser.Term
namespace Lean
namespace Parser
namespace Tactic
builtin_initialize
register_parser_alias tacticSeq
@[builti... |
8e7a7baaaf3b117d9f88102cf25d5e5e446f9c58 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/algebra/ring/idempotents.lean | d6d32cfbe379fbc934e81075ac0acce141b65f83 | [
"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 | 3,873 | lean | /-
Copyright (c) 2022 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin
-/
import algebra.ring.basic
import algebra.group_power.basic
import tactic.nth_rewrite.default
/-!
# Idempotents
This file defines idempotents for an arbitary... |
0fc5ee7d0b3b8b6fe3acb16304a5a639ad38c055 | 6fca17f8d5025f89be1b2d9d15c9e0c4b4900cbf | /src/game/world10/level16.lean | 15ac4dab1631019cb22c066477a83b6478093630 | [
"Apache-2.0"
] | permissive | arolihas/natural_number_game | 4f0c93feefec93b8824b2b96adff8b702b8b43ce | 8e4f7b4b42888a3b77429f90cce16292bd288138 | refs/heads/master | 1,621,872,426,808 | 1,586,270,467,000 | 1,586,270,467,000 | 253,648,466 | 0 | 0 | null | 1,586,219,694,000 | 1,586,219,694,000 | null | UTF-8 | Lean | false | false | 436 | lean | import game.world10.level15 -- hide
namespace mynat -- hide
/-
# Inequality world.
## Level 16: equivalence of two definitions of `<`
Now let's go the other way.
-/
/- Lemma :
For all naturals $a$ and $b$,
$$
\operatorname{succ}(a)\le b
\implies
a\le b\land\lnot(b\le a).$$
-/
lemma lt_aux_two (a b : mynat) : su... |
bd7b151122e9ea7c396d3bcad12a1c5909c2cab9 | 682dc1c167e5900ba3168b89700ae1cf501cfa29 | /src/del/semantics/consistencyDEL.lean | 40e39c12731a745317a9d7bcbc3c20ed4a7ed69b | [] | no_license | paulaneeley/modal | 834558c87f55cdd6d8a29bb46c12f4d1de3239bc | ee5d149d4ecb337005b850bddf4453e56a5daf04 | refs/heads/master | 1,675,911,819,093 | 1,609,785,144,000 | 1,609,785,144,000 | 270,388,715 | 13 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 18,055 | lean | /-
Copyright (c) 2021 Paula Neeley. All rights reserved.
Author: Paula Neeley
Following the textbook "Dynamic Epistemic Logic" by
Hans van Ditmarsch, Wiebe van der Hoek, and Barteld Kooi
-/
import del.languageDEL del.syntax.syntaxDEL
import del.semantics.semanticsDEL del.syntax.syntaxlemmasDEL
import del.syntax.soun... |
a6193b8aec5fae7be5ea6b1b5f70542d1bb5dbe5 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/1606.lean | f01e8acbce4c055992b8ca7f96166a24bbe122ef | [
"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 | 551 | lean | example : True := by
skip
skip --< should complain about misleading indentation
trivial
macro "frobnicate" : tactic => `(tactic| skip)
example : True := by
conv =>
skip
frobnicate --< should not parse frobnicate as a tactic
trivial
-- check error message without default handler for conv tactics
d... |
27b5bdc52343f36c214c4e3ade0b9f70c9a41705 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/calcBug.lean | a6e4ccbdbd0793c7d8b07207d6ab111fb50afd1e | [
"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 | 304 | lean | namespace Hidden
open Nat
theorem zero_add (n : Nat) : 0 + n = n :=
Nat.recOn (motive := fun x => 0 + x = x)
n
rfl
(fun (n : Nat) (ih : 0 + n = n) =>
show 0 + succ n = succ n from
calc
0 + succ n = succ (0 + n) := rfl
_ = succ n := by rw [ih])
end Hidden
|
ca9ac67a3a4247c839cf24b4268de2e65bf83bca | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/data/pfun.lean | 071550fef62c904bf1fdf83c0f4b49561dd4f288 | [
"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 | 13,682 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Jeremy Avigad, Simon Hudon
-/
import data.part
import data.rel
/-!
# Partial functions
This file defines partial functions. Partial functions are like functions, exce... |
f47bd516dfaa8daca344cd0ffb89a2d4a79dd7fa | b19a1b7dc79c802247fdce4c04708e070863b4d2 | /namespaces.lean | e5b795398852aa07b0a0039824746c71655f4b88 | [] | no_license | utanapishtim/promethazine | 99a1e80311fb20251a54ba78a534b23852b88c40 | 08a6f9bd6dd08feb3df8d4697e19ffc8d333b249 | refs/heads/master | 1,653,595,504,487 | 1,480,129,933,000 | 1,480,129,933,000 | 74,801,596 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 293 | lean | namespace foo
constant A : Type
constant a : A
constant f : A → A
definition fa : A := f a
namespace bar
definition ffa : A := f (f a)
check fa
check ffa
end bar
check fa
check bar.ffa
end foo
check foo.fa
check foo.bar.ffa
open foo
check fa
check bar.ffa
|
dec5b4ef968e1aab2adc77dcc87c2910f5a037ed | 76df16d6c3760cb415f1294caee997cc4736e09b | /rosette-benchmarks-4/jitterbug/jitterbug/lean/src/bv/helper.lean | db7a4eeac9a15934aac467bde2be09dd7c2a69da | [
"MIT"
] | permissive | uw-unsat/leanette-popl22-artifact | 70409d9cbd8921d794d27b7992bf1d9a4087e9fe | 80fea2519e61b45a283fbf7903acdf6d5528dbe7 | refs/heads/master | 1,681,592,449,670 | 1,637,037,431,000 | 1,637,037,431,000 | 414,331,908 | 6 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 711 | lean | import data.int.modeq
import tactic.basic
import tactic.linarith.frontend
import tactic.ring_exp
namespace bv.helper
open nat
lemma pow2_succ (n : ℕ) : 2^(succ n) = 2 * 2^n :=
by simp [pow_succ, mul_comm]
lemma two_pos : 2 > 0 :=
dec_trivial
lemma pow2_pos (n : ℕ) : 2^n > 0 :=
pow_pos two_pos n
@[simp]
lemma bit_d... |
0834c38aec3e352e60ce792115456b3219a015bf | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/order/filter/ultrafilter.lean | b2f2b93c935aac3da1a133dd25b358190e9279a9 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 16,696 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jeremy Avigad, Yury Kudryashov
-/
import order.filter.cofinite
import order.zorn
/-!
# Ultrafilters
An ultrafilter is a minimal (maximal in the set order) proper filt... |
401cca9e58e0282b4a5f1f7d6dcd15733df23649 | 4950bf76e5ae40ba9f8491647d0b6f228ddce173 | /src/ring_theory/derivation.lean | f22eec16816560172029492887ca27c1ae56bf67 | [
"Apache-2.0"
] | permissive | ntzwq/mathlib | ca50b21079b0a7c6781c34b62199a396dd00cee2 | 36eec1a98f22df82eaccd354a758ef8576af2a7f | refs/heads/master | 1,675,193,391,478 | 1,607,822,996,000 | 1,607,822,996,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,122 | lean | /-
Copyright © 2020 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Nicolò Cavalleri.
-/
import algebra.lie.basic
import ring_theory.algebra_tower
/-!
# Derivations
This file defines derivation. A derivation `D` from the `R`-algebra `A` to the `A`-mo... |
07244313961397e9af5831134d291ceee6458ac0 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /test/examples.lean | 54ab934a9e02ffcb0c2b77a125fbb4f7482e1c9a | [
"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 | 2,160 | lean | import data.finset.basic
/-!
## Miscellaneous examples
Please don't add further content to this file;
it too easily becomes a grab bag of forgotten arcana.
Tactics should have their own file in the `test/` directory.
Examples verifying correct behaviour of simp sets or instances
belong in `src/` near the definition... |
df7413ff8da4876acc0547beae0e21ff0ce39db5 | 02fbe05a45fda5abde7583464416db4366eedfbf | /library/init/algebra/order.lean | 76371309670ccb01da161467118afb16521cf4f9 | [
"Apache-2.0"
] | permissive | jasonrute/lean | cc12807e11f9ac6b01b8951a8bfb9c2eb35a0154 | 4be962c167ca442a0ec5e84472d7ff9f5302788f | refs/heads/master | 1,672,036,664,637 | 1,601,642,826,000 | 1,601,642,826,000 | 260,777,966 | 0 | 0 | Apache-2.0 | 1,588,454,819,000 | 1,588,454,818,000 | null | UTF-8 | Lean | false | false | 11,505 | 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.logic init.classical init.meta.name init.algebra.classes
/- Make sure instances defined in this file have lower priority than the ones
... |
875d74309a41c50ed470a1b4874beb20cbc374de | c09f5945267fd905e23a77be83d9a78580e04a4a | /src/topology/separation.lean | dc1789f164e03e76b5327b3f2058643cf2c9da40 | [
"Apache-2.0"
] | permissive | OHIHIYA20/mathlib | 023a6df35355b5b6eb931c404f7dd7535dccfa89 | 1ec0a1f49db97d45e8666a3bf33217ff79ca1d87 | refs/heads/master | 1,587,964,529,965 | 1,551,819,319,000 | 1,551,819,319,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 12,435 | 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.order
open set filter lattice
local attribute [instance] classical.prop_decidable
uni... |
80fb3a35adc3bfc6eed6886a80dfe23bfbd36169 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/logic/relator.lean | e2d4251b193b51ca4d93a4c3fc7154bb7179fcd7 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 3,583 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import logic.basic
/-!
# Relator for functions, pairs, sums, and lists.
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a correspondi... |
771db84c55d0731c9d32bd06b7c5b036e9f8dd5f | 3dc4623269159d02a444fe898d33e8c7e7e9461b | /.github/workflows/project_1_a_decrire/lean-scheme-submission/src/sheaves/presheaf_of_rings.lean | 05ece16e587cb6cf539d3afbbc14265c14c775db | [] | no_license | Or7ando/lean | cc003e6c41048eae7c34aa6bada51c9e9add9e66 | d41169cf4e416a0d42092fb6bdc14131cee9dd15 | refs/heads/master | 1,650,600,589,722 | 1,587,262,906,000 | 1,587,262,906,000 | 255,387,160 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,684 | lean | /-
Presheaf of rings.
https://stacks.math.columbia.edu/tag/006N
-/
import data.equiv.algebra
import topology.opens
import sheaves.presheaf
open topological_space
universes u v
-- Definition of a presheaf of rings.
structure presheaf_of_rings (α : Type u) [topological_space α]
extends presheaf α :=
(Fring ... |
93a5260199f2bd6e3b63d3f7ab281c639fe33401 | aa5a655c05e5359a70646b7154e7cac59f0b4132 | /tests/lean/run/subst.lean | 9ef6b778a554372991fbad54723e539fa6d70ab3 | [
"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 | 2,262 | lean |
universes u
def f1 (n m : Nat) (x : Fin n) (h : n = m) : Fin m :=
h ▸ x
def f2 (n m : Nat) (x : Fin n) (h : m = n) : Fin m :=
h ▸ x
theorem ex1 {α : Sort u} {a b c : α} (h₁ : a = b) (h₂ : b = c) : a = c :=
h₂ ▸ h₁
theorem ex2 {α : Sort u} {a b : α} (h : a = b) : b = a :=
h ▸ rfl
theorem ex3 {α : Sort u} {a b c : ... |
9291ad3672a47c441a177c83f264c0acd9c1fb0f | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/group_theory/free_group.lean | 4bfc175984254f4433d0e4f48864e79aa3bae602 | [
"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 | 32,603 | 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.fintype.basic
import group_theory.subgroup
/-!
# Free groups
This file defines free groups over a type. Furthermore, it is shown that the free group construction
... |
59c72a05514c12bb1a44d7e1e8b7c7ba6eeef488 | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /tests/lean/run/CommandExtOverlap.lean | 4c3f604ace3fe8fbcf15e1f3160656b1a0a69856 | [
"Apache-2.0"
] | permissive | WojciechKarpiel/lean4 | 7f89706b8e3c1f942b83a2c91a3a00b05da0e65b | f6e1314fa08293dea66a329e05b6c196a0189163 | refs/heads/master | 1,686,633,402,214 | 1,625,821,189,000 | 1,625,821,258,000 | 384,640,886 | 0 | 0 | Apache-2.0 | 1,625,903,617,000 | 1,625,903,026,000 | null | UTF-8 | Lean | false | false | 324 | lean | syntax (name := mycheck) "#check" sepBy(term, ",") : command
open Lean
macro_rules (kind := mycheck)
| `(#check $es,*) =>
let cmds := es.getElems.map $ fun e => Syntax.node `Lean.Parser.Command.check #[mkAtom "#check", e]
pure $ mkNullNode cmds
#check true
#check true, true
#check true, 1, 3, fun (x : Nat) => x ... |
fecf82dfcdb860dd6abc01b8bf456cfce61de926 | 9b9a16fa2cb737daee6b2785474678b6fa91d6d4 | /src/category_theory/discrete_category.lean | 5c6840370bade4f8231840a6b5ce17a6d4db9753 | [
"Apache-2.0"
] | permissive | johoelzl/mathlib | 253f46daa30b644d011e8e119025b01ad69735c4 | 592e3c7a2dfbd5826919b4605559d35d4d75938f | refs/heads/master | 1,625,657,216,488 | 1,551,374,946,000 | 1,551,374,946,000 | 98,915,829 | 0 | 0 | Apache-2.0 | 1,522,917,267,000 | 1,501,524,499,000 | Lean | UTF-8 | Lean | false | false | 1,637 | lean | -- Copyright (c) 2017 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Stephen Morgan, Scott Morrison
import data.ulift
import category_theory.natural_transformation
import category_theory.isomorphism
import category_theory.functor_category
namesp... |
77b9c93b6ef7d800b4bf8a709275e0211e80e8e1 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/single_obj.lean | 43eaf45676791d3001609cd310de4c2953d56b61 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 6,570 | lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import category_theory.endomorphism
import category_theory.category.Cat
import algebra.category.Mon.basic
import combinatorics.quiver.single_obj
/-!
# Single-objec... |
e33fe238382062d45d9e4eb002c30fd74c90d18e | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/field_theory/tower.lean | 487fdc65e7a4121ae21d8d40ac3a60480badb366 | [
"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 | 5,120 | 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.algebra_tower
import linear_algebra.matrix.finite_dimensional
import linear_algebra.matrix.to_lin
/-!
# Tower of field extensions
In this file we prove th... |
b8262d9a3983047fe3bba5239202a4490855412e | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/data/polynomial/basic.lean | 3517ef332e4859b6bdf5da802b01eedcc9236301 | [
"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 | 32,752 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker
-/
import algebra.monoid_algebra.basic
/-!
# Theory of univariate polynomials
This file defines `polynomial R`, the type of... |
220f369a62f751728101304e158e862600342093 | 5412d79aa1dc0b521605c38bef9f0d4557b5a29d | /src/Lean/Meta/FunInfo.lean | 16004ad2b10727be9f416a13cb4ffccfe71d32a4 | [
"Apache-2.0"
] | permissive | smunix/lean4 | a450ec0927dc1c74816a1bf2818bf8600c9fc9bf | 3407202436c141e3243eafbecb4b8720599b970a | refs/heads/master | 1,676,334,875,188 | 1,610,128,510,000 | 1,610,128,521,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,092 | 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.Meta.Basic
import Lean.Meta.InferType
namespace Lean.Meta
@[inline] private def checkFunInfoCache (fn : Expr) (maxArgs? : Option Nat) (k : Met... |
38af759bf9898bc78a2c17e62dc34b7484e7643b | 3f48345ac9bbaa421714efc9872a0409379bb4ae | /src/set_category/colimits/Coequalizer.lean | 8a77f93125bbf9f2801abd080b88cbcdd8e53035 | [] | no_license | QaisHamarneh/Coalgebra-in-Lean | b4318ee6d83780e5c734eb78fed98b1fe8016f7e | bd0452df98bc64b608e5dfd7babc42c301bb6a46 | refs/heads/master | 1,663,371,200,241 | 1,661,004,695,000 | 1,661,004,695,000 | 209,798,828 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,246 | lean | import tactic.tidy
import set_category.diagram_lemmas
import help_functions
import category_theory.category
namespace Coequalizer
open set
diagram_lemmas
classical
function
help_functions
category_theory
universe u
local notation f ` ⊚ `:80 g:80 := category_struct.comp g f
def is_co... |
3a1d8ce0f99bc3fa71d63a178124051498b7b678 | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/algebraic_geometry/presheafed_space.lean | f84b929f8c8fe292d1ecd65e3dfe8fa82e2b1d85 | [
"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 | 10,942 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import topology.sheaves.presheaf
/-!
# Presheafed spaces
Introduces the category of topological spaces equipped with a presheaf (taking values in an
arbitrary targe... |
93ff32c84818db9a9eb2ee29201487b58e6d93f2 | 82b86ba2ae0d5aed0f01f49c46db5afec0eb2bd7 | /stage0/src/Lean/Parser/Level.lean | e584d5f6a884d967d71c8ebb9d17e8135849ce8a | [
"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 | 1,093 | 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, Sebastian Ullrich
-/
import Lean.Parser.Extra
-- necessary for auto-generation
import Lean.PrettyPrinter.Parenthesizer
import Lean.PrettyPrinter.Formatter
n... |
2971b1c107bf9b037391577c6514b7bd160701b8 | 22e97a5d648fc451e25a06c668dc03ac7ed7bc25 | /src/number_theory/dioph.lean | 71c5261b96fa53f04d645c4f6fe0172e104739be | [
"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 | 36,863 | 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 number_theory.pell
import data.pfun
universe u
open nat function
namespace int
lemma eq_nat_abs_iff_mul (x n) : nat_abs x = n ↔ (x - n) * (x + n) = 0 :=
be... |
b59fc8c5e1406156b951168739dfc7a6905af797 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/category_theory/limits/shapes/products.lean | f39b4dc560a8655f1fa3df31c93a74068726115b | [
"Apache-2.0"
] | permissive | Lix0120/mathlib | 0020745240315ed0e517cbf32e738d8f9811dd80 | e14c37827456fc6707f31b4d1d16f1f3a3205e91 | refs/heads/master | 1,673,102,855,024 | 1,604,151,044,000 | 1,604,151,044,000 | 308,930,245 | 0 | 0 | Apache-2.0 | 1,604,164,710,000 | 1,604,163,547,000 | null | UTF-8 | Lean | false | false | 4,949 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.limits.limits
import category_theory.discrete_category
noncomputable theory
universes v u
open category_theory
namespace category_theory.li... |
0b954092806fdeb476765040d5659dc89fb36bc7 | 968e2f50b755d3048175f176376eff7139e9df70 | /examples/prop_logic_theory/unnamed_786.lean | fb8dfe44361d81bbdf3b3e623cf2c63ebe5b167c | [] | no_license | gihanmarasingha/mth1001_sphinx | 190a003269ba5e54717b448302a27ca26e31d491 | 05126586cbf5786e521be1ea2ef5b4ba3c44e74a | refs/heads/master | 1,672,913,933,677 | 1,604,516,583,000 | 1,604,516,583,000 | 309,245,750 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 425 | lean | variables p q : Prop
-- BEGIN
theorem and_of_and : p ∧ q → q ∧ p :=
begin
intro h, -- Assume `h : p ∧ q`. It suffices to prove `q ∧ p`.
split, -- By `∧` intro., it suffices to prove both `q` and `p`.
{ show q, from h.right, }, -- We show `q` from right `∧` elimination on `h`.... |
34d3e9d08eb6f1d61505453998c78040d43e582c | f02b05b665ad2d2cd970e93758a98d57f310a822 | /src/tactic/tcache/io.lean | 62bb91231e2ddb926235c77ebc65b40b1ccd92c9 | [] | no_license | khoek/leancache | b0ed5d2a9a2e87f58d4ad27343d957a9cd49ce5f | 5c8329f7b647b8d82966ab180c4473b20d1f249c | refs/heads/master | 1,585,344,140,717 | 1,549,094,327,000 | 1,549,094,327,000 | 147,138,187 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,138 | lean | import system.io
open io io.proc
namespace tcache
def CACHE_DIR := ".cache"
def exec_cmd (args : io.process.spawn_args) : io unit :=
spawn args >> return ()
def mk_cache_dir : io unit :=
exec_cmd {cmd := "mkdir", args := ["-p", CACHE_DIR], stdout := io.process.stdio.null, stderr := io.process.stdio.null}
def rm... |
2468a2da474a98c41f8c0d90d9139d50f5becae6 | ebbdcbd7ddc89a9ef7c3b397b301d5f5272a918f | /qp/p1_categories/c1_basic/s3_nattrans.lean | 327b0d3d70c2dc84dedfceb63929353cd17bd76a | [] | no_license | intoverflow/qvr | 34b9ef23604738381ca20b7d622fd0399d88f2dd | 0cfcd33fe4bf8d93851a00cec5bfd21e77105d74 | refs/heads/master | 1,616,591,570,371 | 1,492,575,772,000 | 1,492,575,772,000 | 80,061,627 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 28,042 | lean | /- -----------------------------------------------------------------------
Natural transformations.
----------------------------------------------------------------------- -/
import .s2_functors
namespace qp
open stdaux
universe variables ℓobj₁ ℓhom₁ ℓobj₂ ℓhom₂ ℓobj₃ ℓhom₃ ℓobj₄ ℓhom₄
/-! #brief A natural transfo... |
92c99e34c05a3a2ed77f4b0f6e54ebe2661a1a1c | 1f6fe2f89976b14a4567ab298c35792b21f2e50b | /homotopy/smash.hlean | 137b92a09463b574ba39b59f3b05bf67f479f4cf | [
"Apache-2.0"
] | permissive | jonas-frey/Spectral | e5c1c2f7bcac26aa55f7b1e041a81272a146198d | 72d521091525a4bc9a31cac859840efe9461cf66 | refs/heads/master | 1,610,235,743,345 | 1,505,417,795,000 | 1,505,417,795,000 | 102,653,342 | 0 | 0 | null | 1,504,728,483,000 | 1,504,728,483,000 | null | UTF-8 | Lean | false | false | 43,963 | hlean | -- Authors: Floris van Doorn
import homotopy.smash types.pointed2 .pushout homotopy.red_susp
open bool pointed eq equiv is_equiv sum bool prod unit circle cofiber prod.ops wedge is_trunc
function red_susp unit
/- To prove: Σ(X × Y) ≃ ΣX ∨ ΣY ∨ Σ(X ∧ Y) (notation means suspension, wedge, smash) -/
/- To pro... |
9d7102b1e9069bcdb17d7d6bad26681edc935496 | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /library/algebra/category/yoneda.lean | 72176d657419bfd7fd0ba45c724bf23034b3ae5e | [
"Apache-2.0"
] | permissive | codyroux/lean | 7f8dff750722c5382bdd0a9a9275dc4bb2c58dd3 | 0cca265db19f7296531e339192e9b9bae4a31f8b | refs/heads/master | 1,610,909,964,159 | 1,407,084,399,000 | 1,416,857,075,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 306 | lean | -- Copyright (c) 2014 Floris van Doorn. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Author: Floris van Doorn
import .constructions
open eq eq.ops category functor category.ops prod
namespace yoneda
--representable functor
section
end
end yoneda
|
e07850e40c0e6eb5d8dbd1997cc9100ba522521f | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/tactic/simps.lean | f4c64207c27f4de4966c86c8d4f5f959cdbaded3 | [
"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 | 25,532 | 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.core
/-!
# simps attribute
This file defines the `@[simps]` attribute, to automatically generate simp-lemmas
reducing a definition when projections... |
fbfedbe708ccbfc4b8849ce3236625c1155d3cb6 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/instances/rat_lemmas.lean | b20d5f7e8d5a2fed42b0ef1a2e92286fa83a2a5a | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 3,388 | lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import topology.instances.irrational
import topology.instances.rat
import topology.alexandroff
/-!
# Additional lemmas about the topology on rational numbers
> TH... |
c4db1fae70720e3c1595a865d2ec12f9b7b6e51d | 2a70b774d16dbdf5a533432ee0ebab6838df0948 | /_target/deps/mathlib/src/data/option/defs.lean | 7cc5f348c3736577e8c0c8467841396f79fddcb7 | [
"Apache-2.0"
] | permissive | hjvromen/lewis | 40b035973df7c77ebf927afab7878c76d05ff758 | 105b675f73630f028ad5d890897a51b3c1146fb0 | refs/heads/master | 1,677,944,636,343 | 1,676,555,301,000 | 1,676,555,301,000 | 327,553,599 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,899 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
Extra definitions on option.
-/
namespace option
variables {α : Type*} {β : Type*}
attribute [inline] option.is_some option.is_none
/-- An elimination principle for ... |
1aa09743d94b10a0a405fbc3b936957f231c6ed9 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebraic_geometry/presheafed_space/has_colimits.lean | 0f8b2c04e610f8ed8c58de08912f9872f3c37944 | [] | 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 | 10,134 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebraic_geometry.presheafed_space
import Mathlib.topology.category.Top.limits
import Math... |
a7bc6853bdf8f90512dcd95fb836b31c882a4db5 | fd3506535396cef3d1bdcf4ae5b87c8ed9ff2c2e | /group_theory/action.lean | 0dd68d60ab51c948610d4ad533521d81111f7c3b | [
"Apache-2.0"
] | permissive | williamdemeo/leanproved | 77933dbcb8bfbae61a753ae31fa669b3ed8cda9d | d8c2e2ca0002b252fce049c4ff9be0e9e83a6374 | refs/heads/master | 1,598,674,802,432 | 1,437,528,488,000 | 1,437,528,488,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 22,964 | lean | /-
Copyright (c) 2015 Haitao Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author : Haitao Zhang
-/
import algebra.group data .hom .perm .finsubg
namespace group
open finset algebra function
local attribute perm.f [coercion]
private lemma and_left_true {a b : Prop} ... |
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