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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
df894795652eade60afed50ad3263308f1c1165a | 618003631150032a5676f229d13a079ac875ff77 | /test/norm_cast_lemma_order.lean | f9b1cc8fe067ac9b47a45572e34992c254cf4b5a | [
"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 | 654 | lean | import data.nat.cast
import tactic.norm_cast
constant ℝ : Type
@[instance] constant real.add_monoid : add_monoid ℝ
@[instance] constant real.has_one : has_one ℝ
-- set_option trace.simplify.rewrite true
set_option pp.notation false
set_option pp.numerals false
-- should work
#eval norm_cast.numeral_to_coe `(0 : ℝ)
#... |
7b011d16fea79f5fd9fc233424cb4bc5e8460791 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/order/order_iso_nat.lean | e351387de049c666b7070c304933f00b7d06c092 | [
"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 | 8,381 | 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.equiv.denumerable
import order.preorder_hom
import order.conditionally_complete_lattice
namespace rel_embedding
variables {α : Type*} {r : α → α → Prop}... |
23cfa8f078539f9187adb275e8fde5a78623283f | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/default_auto.lean | 72654054254e28bde2b1c0d1a1536aae26392c6f | [] | 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 | 188 | lean | import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.group.default
import Mathlib.algebra.module.basic
import Mathlib.PostPort
namespace Mathlib
end Mathlib |
a9aa3cdb8a629959b7e5d132b4e10350b6d49c19 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/category_theory/preadditive/additive_functor.lean | fa8a760ce267e50229769f6407f7007430b531af | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 6,008 | lean | /-
Copyright (c) 2021 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz, Scott Morrison
-/
import category_theory.limits.preserves.shapes.biproducts
import category_theory.preadditive.functor_category
/-!
# Additive Functors
A functor between two ... |
b4649c05047c5ef1b97f6a27a9363803068c0d92 | 271e26e338b0c14544a889c31c30b39c989f2e0f | /src/Init/Control/EState.lean | dc389d07c7f0fa07d8a9ad2bd5fbde33cf30b917 | [
"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 | 5,613 | 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.Control.State
import Init.Control.Except
universes u v
namespace EStateM
inductive Result (ε σ α : Type u)
| ok {} : α → σ → Result... |
f4db9a51bc8e645b3831a5764ac438e98d229d9a | 71c05f289da9a856f1d16197a32b6a874eb1052e | /hlean/basics.hlean | b9cdbb7404026325aa146200b3f710535ed34e07 | [] | no_license | gbaz/works-in-progress | e7701b1c2f8d0cfb6bfb8d84fc4d21ffd9937521 | af7bacd7f68649106a3581c232548958aca79a08 | refs/heads/master | 1,661,485,946,844 | 1,659,018,408,000 | 1,659,018,408,000 | 32,045,948 | 14 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 12,898 | hlean | import types.int algebra.field hit.set_quotient hit.trunc
open eq sigma sigma.ops equiv is_equiv equiv.ops eq.ops int algebra nat set_quotient is_trunc trunc quotient
record prerat : Type := (num : ℤ) (denom : ℕ)
namespace prerat
inductive rat_rel : prerat → prerat → Type :=
| Rmk : Π (a b : prerat), int.mul (num ... |
707b95ff5d5585d07a25ff2eb93f1b1482f7f86c | b73bd2854495d87ad5ce4f247cfcd6faa7e71c7e | /src/game/world1/level4.lean | 1798696c24db5b6ae65110533de47b28fc74157b | [] | no_license | agusakov/category-theory-game | 20db0b26270e0c95a3d5605498570273d72f731d | 652dd7e90ae706643b2a597e2c938403653e167d | refs/heads/master | 1,669,201,216,310 | 1,595,740,057,000 | 1,595,740,057,000 | 280,895,295 | 12 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,154 | lean | import category_theory.category.default
universes v u -- The order in this declaration matters: v often needs to be explicitly specified while u often can be omitted
namespace category_theory
variables (C : Type u) [category.{v} C]
/-
# Category world
## Level 3: The `specialize` tactic
-/
/-So recall that, in t... |
796ae4645a0716ba3fb249fb843da76bd0eea400 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/data/nat/succ_pred.lean | b791d6026a764a3e737d8a562fd36b4e4c576457 | [
"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 | 1,597 | lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import order.succ_pred.basic
/-!
# Successors and predecessors of naturals
In this file, we show that `ℕ` is both an archimedean `succ_order` and an archimedean `pred_o... |
61f564c151fb57072a5e4bea1f8e384ed4e71f59 | 947b78d97130d56365ae2ec264df196ce769371a | /src/Lean/Compiler/IR/Borrow.lean | 30791da8a6456e1f429d39680ffcfe85a085177e | [
"Apache-2.0"
] | permissive | shyamalschandra/lean4 | 27044812be8698f0c79147615b1d5090b9f4b037 | 6e7a883b21eaf62831e8111b251dc9b18f40e604 | refs/heads/master | 1,671,417,126,371 | 1,601,859,995,000 | 1,601,860,020,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,013 | 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.ExportAttr
import Lean.Compiler.IR.CompilerM
import Lean.Compiler.IR.NormIds
namespace Lean
namespace IR
namespace Borrow
namespace O... |
3017c94e191efaf631b342df74c50f20f926e2a8 | dbf7a3e568ead66ea066e61c38691e95c8c9f42d | /src/instructor/lectures/lecture_2.lean | b28a766d35e30758eff6aa765664ee2fb9383282 | [] | no_license | Grodfey/cs2120f21 | 332cc4bc49b8e971d166b43bfb2bd5821236a282 | 3eaf07375bc30331e4080a12676e8a06e14ac80d | refs/heads/main | 1,690,228,439,304 | 1,630,542,337,000 | 1,630,542,337,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,612 | lean | /-
INFERENCE RULE #1/2: EQUALITY IS REFLEXIVE
Everything is equal to itself. A bit more formally,
if one is given a type, T, and a value, t, of this
type, then you may have a proof of t = t "for free."
-/
axiom eq_refl :
∀ (T : Type) -- if T is any type (of thing)
(t : T), -- and t is thing of that type, ... |
8d9a9ffef07c7829e5a7cb9a4e89be52ca986505 | 626e312b5c1cb2d88fca108f5933076012633192 | /src/topology/continuous_function/basic.lean | 8f45d4502805f15a127ad73e6161ae56818d3269 | [
"Apache-2.0"
] | permissive | Bioye97/mathlib | 9db2f9ee54418d29dd06996279ba9dc874fd6beb | 782a20a27ee83b523f801ff34efb1a9557085019 | refs/heads/master | 1,690,305,956,488 | 1,631,067,774,000 | 1,631,067,774,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,934 | lean | /-
Copyright © 2020 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri
-/
import topology.subset_properties
import topology.tactic
import topology.algebra.ordered.proj_Icc
/-!
# Continuous bundled map
In this file we define the type `c... |
7438326ba6a3d1a9ba37cf4cef98e8bb1b7bb6fc | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/mv_polynomial/supported.lean | 74a8397d4e531d89a55282d6a271ea4eb8d4d0d2 | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 4,130 | lean | /-
Copyright (c) 2021 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import data.mv_polynomial.variables
/-!
# Polynomials supported by a set of variables
This file contains the definition and lemmas about `mv_polynomial.supported`.
## ... |
6886f72f3f0f9c2a9647b9bba88a6833e6357fb1 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/analysis/normed_space/hahn_banach.lean | 05d7da98291a50cd9defe4c73fbbce6e3cca1c7a | [
"Apache-2.0"
] | permissive | dupuisf/mathlib | 62de4ec6544bf3b79086afd27b6529acfaf2c1bb | 8582b06b0a5d06c33ee07d0bdf7c646cae22cf36 | refs/heads/master | 1,669,494,854,016 | 1,595,692,409,000 | 1,595,692,409,000 | 272,046,630 | 0 | 0 | Apache-2.0 | 1,592,066,143,000 | 1,592,066,142,000 | null | UTF-8 | Lean | false | false | 5,689 | 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 analysis.normed_space.operator_norm
import analysis.normed_space.extend
import analysis.convex.cone
/-!
# Hahn-Banach theorem
In this file ... |
762c5f8eae77bfe791be519c320d558373e29bd3 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/category_theory/epi_mono.lean | 8ddac9bf1b11344579bdc6c838eddd378e491c49 | [
"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 | 7,152 | lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Scott Morrison
Facts about epimorphisms and monomorphisms.
The definitions of `epi` and `mono` are in `category_theory.category`,
since they are used by some lemmas for `is... |
a59f28f3d5bc685f3c8bee5ad5c7ae037c3a7293 | 69cc382047d7d9c97af93f321d222357eaa44574 | /xenalib/real_experiments.lean | 898bb972ccdd498e4619b09eb3cd60a16afaf083 | [] | no_license | semorrison/xena | 368c31585912e6d36484ba5e53c9d238fb52073e | 3f5f660d5a9073f107cb5310c987322eb87cc760 | refs/heads/master | 1,625,661,998,437 | 1,507,044,754,000 | 1,507,044,754,000 | 105,729,983 | 0 | 0 | null | 1,507,089,611,000 | 1,507,089,611,000 | null | UTF-8 | Lean | false | false | 1,635 | lean | /- Fake real numbers.
There are technical difficulties in accessing real numbers
in the online version of Lean. Anyone who is using Lean online but
wants real numbers can just cut and paste the below code.
This gives us a class "real", which is a fake version of the
real numbers. See if you can spot any differences!
-/... |
6becf813d283c1dbd07267b25ac2d63bffc3850a | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/topology/sheaves/sheaf_of_functions.lean | 2809f219c3f631e3c7b0c1360d285bb2103f36a9 | [
"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 | 4,018 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Scott Morrison
-/
import topology.sheaves.presheaf_of_functions
import topology.sheaves.sheaf_condition.unique_gluing
import category_theory.limits.shapes.types
import ... |
54ecf4a9bfc1a09d8a878c2dfdaf86aa62d4706f | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/sigma/interval.lean | 0c70e2cc3b00fc60ead5b0aaf527f785c20a080e | [
"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 | 3,064 | lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import data.sigma.order
import order.locally_finite
/-!
# Finite intervals in a sigma type
This file provides the `locally_finite_order` instance for the disjoint sum o... |
5033e98320ba379d33b2e5057b25e189b115ef0b | 618003631150032a5676f229d13a079ac875ff77 | /src/data/buffer/basic.lean | ba3d88acb1c88e868ffef3dc18f2b93a36f21c51 | [
"Apache-2.0"
] | permissive | awainverse/mathlib | 939b68c8486df66cfda64d327ad3d9165248c777 | ea76bd8f3ca0a8bf0a166a06a475b10663dec44a | refs/heads/master | 1,659,592,962,036 | 1,590,987,592,000 | 1,590,987,592,000 | 268,436,019 | 1 | 0 | Apache-2.0 | 1,590,990,500,000 | 1,590,990,500,000 | null | UTF-8 | Lean | false | false | 1,871 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
Traversable instance for buffers.
-/
import data.buffer
import data.array.lemmas
import control.traversable.instances
namespace buffer
open function
variables {α : Type*} ... |
f118508562952f4bb8f3e222bae7f7f8ef9a29ec | 4727251e0cd73359b15b664c3170e5d754078599 | /src/number_theory/sum_two_squares.lean | 098a5058731c605b9959b08e2e2ceda8435e4787 | [
"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 | 981 | 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 number_theory.zsqrtd.gaussian_int
/-!
# Sums of two squares
Proof of Fermat's theorem on the sum of two squares. Every prime congruent to 1 mod 4 is the sum
of ... |
733881e9d6e25b2b6151e47b3d8ae43c0d5d77b4 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/simp_rfl_proof_issue.lean | 0b283611d1f464bf8de21c25fd5f48d648946976 | [
"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 | 290 | lean | @[irreducible] def f : nat → nat
| 0 := 1
| (n+1) := 2 * f n
lemma ex1 (n : nat) : f (n+1) = 2 * f n :=
begin
fail_if_success {refl},
simp only [f]
end
lemma ex2 (n : nat) (h : f (n+1) = 0) : 2 * f n = 0 :=
begin
fail_if_success {exact h},
simp only [f] at h,
exact h
end
|
0b4ff1f3834554a8be74b0b53a9950425e2a25db | 7b66d83f3b69dae0a3dfb684d7ebe5e9e3f3c913 | /src/hints/thursday/afternoon/category_theory/exercise1/hint2.lean | b9f677aabea0b71bd894d47771d95631c8a7a90d | [] | permissive | dpochekutov/lftcm2020 | 58a09e10f0e638075b97884d3c2612eb90296adb | cdfbf1ac089f21058e523db73f2476c9c98ed16a | refs/heads/master | 1,669,226,265,076 | 1,594,629,725,000 | 1,594,629,725,000 | 279,213,346 | 1 | 0 | MIT | 1,594,622,757,000 | 1,594,615,843,000 | null | UTF-8 | Lean | false | false | 805 | lean | import algebra.category.CommRing
import category_theory.yoneda
noncomputable theory
open category_theory
open opposite
/-!
Let's give the forward map first, not worrying about naturality.
-/
def CommRing_forget_representable : Σ (R : CommRing), (forget CommRing) ≅ coyoneda.obj (op R) :=
⟨CommRing.of (polynomial ℤ),
... |
c121b8a0e954c900afe7800b246e33f8fd453ed1 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/algebra/punit_instances.lean | 1f736e393ea2675de9a6b48e6a20c80acc1d1062 | [
"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 | 2,778 | lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import algebra.module.basic
/-!
# Instances on punit
This file collects facts about algebraic structures on the one-element type, e.g. that it is a
commutative ring.
-/
uni... |
0b936ed1e24d9dd4b4f3583f587bbfa44b01b3f4 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/letBRecOnIssue.lean | f3fe5a5b2f42614b60ca9d6586e1609341dae9e3 | [
"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 | 1,302 | lean | import Lean
section events
universe u v
-- | Polymorphic to and sum.
def pto (E: Type → Type u) (F: Type → Type v) :=
∀ T, E T → F T
def psum (E: Type → Type u) (F: Type → Type v) :=
fun T => E T ⊕ F T
inductive PVoid: Type -> Type u
infixr:40 " ~> " => pto
infixr:60 " +' " => psum
end events
/- finite interac... |
7a95bafeeae5a653e223a050dd97fce91bcc6169 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/ring_theory/chain_of_divisors.lean | 9c69310477c7f0d1345b52727c8d2fc93885f6e1 | [
"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 | 22,290 | lean | /-
Copyright (c) 2021 Paul Lezeau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Paul Lezeau
-/
import algebra.is_prime_pow
import algebra.squarefree
import order.hom.bounded
import algebra.gcd_monoid.basic
/-!
# Chains of divisors
> THIS FILE IS SYNCH... |
0021288f1087f0b3686cdc9cc283bb7b2f441e36 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/analysis/calculus/deriv.lean | a4995f17716f45dcf65fe2a7facaa0b846caa0d2 | [] | 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 | 108,071 | lean | /-
Copyright (c) 2019 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner, Sébastien Gouëzel
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.analysis.calculus.fderiv
import Mathlib.data.polynomial.derivative
import ... |
e01e98220b4d23dd4e0ac1bded399e9e0fb23413 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/1007.lean | 4f8775000ab071d3b668abdc68d604aeb0f91b03 | [
"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 | 1,877 | lean | class Vec (X : Type u)
class IsLin {X Y} [Vec X] [Vec Y] (f : X → Y)
structure ℝ where
value : Float
instance instFoo1 {X : Type u} {Y : Type v} [Vec X] [Vec Y] : Vec (X × Y) := sorry
instance instProblem {α : Type u} {X : Type v} [Vec X] : Vec (α → X) := sorry
instance (priority := default+1) instFoo2 : Vec ℝ :=... |
610f5962a5e12eabef19bd0cca17a38e1556faed | 4919181312c130f03eed71db8c80aa1cbd140256 | /src/to_mathlib.lean | e24db64bb56cb41b19a2f957309654979f39a3d8 | [] | no_license | williamdemeo/flypitch | 62143800b790f0a0ffcd338c82b6bf3cd401552b | f73127c3ad36e6c2f074a26518dc333f07c1ab85 | refs/heads/master | 1,587,042,220,139 | 1,547,238,998,000 | 1,547,238,998,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 20,094 | lean | /- theorems which we should (maybe) backport to mathlib -/
import data.finset algebra.ordered_group tactic.squeeze
universe variables u v w
namespace tactic
namespace interactive
/- maybe we should use congr' 1 instead? -/
meta def congr1 : tactic unit :=
do focus1 (congr_core >> all_goals (try reflexivity >> try ... |
f761b87d7266022fed98d2e3ccc15e6efb05bc4c | eb9357a70318e50e095b58730bebfe0cffee457f | /lean/love12_basic_mathematical_structures_exercise_sheet.lean | 982287929e810432b9ec7aae0259988d3c94c763 | [] | no_license | Vierkantor/logical_verification_2021 | 7485dd916953131d501760f023d5b30fbb74d36a | 9500b9c194e22a9ab4067321cfed7a1f445afcfc | refs/heads/main | 1,692,560,845,086 | 1,624,721,275,000 | 1,624,721,275,000 | 416,354,079 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,700 | lean | import .love12_basic_mathematical_structures_demo
/-! # LoVe Exercise 12: Basic Mathematical Structures -/
set_option pp.beta true
set_option pp.generalized_field_notation false
namespace LoVe
/-! ## Question 1: Type Classes
Recall the inductive type `btree` we introduced earlier: -/
#check btree
/-! The foll... |
5f6e93a8878c331b5b5c95fb87969ff897377fa1 | ebf7140a9ea507409ff4c994124fa36e79b4ae35 | /src/solutions/friday/topology.lean | d791c38fbae5a6336b8748ec6a8ee99de4b55709 | [] | no_license | fundou/lftcm2020 | 3e88d58a92755ea5dd49f19c36239c35286ecf5e | 99d11bf3bcd71ffeaef0250caa08ecc46e69b55b | refs/heads/master | 1,685,610,799,304 | 1,624,070,416,000 | 1,624,070,416,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 15,744 | lean | import topology.metric_space.basic
open_locale classical filter topological_space
namespace lftcm
open filter set
/-!
# Filters
## Definition of filters
-/
def principal {α : Type*} (s : set α) : filter α :=
{ sets := {t | s ⊆ t},
univ_sets := begin
-- sorry
tauto,
-- sorry
end,
sets_of_superset ... |
4738cd96ce0a340be1cb3bae2bba6f7cd1e2f515 | 556aeb81a103e9e0ac4e1fe0ce1bc6e6161c3c5e | /src/starkware/cairo/lean/semantics/soundness/prelude.lean | c05a8a6f29668789a52afefbc86e375b239bfa3f | [
"Apache-2.0"
] | permissive | starkware-libs/formal-proofs | d6b731604461bf99e6ba820e68acca62a21709e8 | f5fa4ba6a471357fd171175183203d0b437f6527 | refs/heads/master | 1,691,085,444,753 | 1,690,507,386,000 | 1,690,507,386,000 | 410,476,629 | 32 | 9 | Apache-2.0 | 1,690,506,773,000 | 1,632,639,790,000 | Lean | UTF-8 | Lean | false | false | 4,796 | lean | /-
These are properties that depend on the specific choice of the prime field characteristic in Cairo, as well as the fact that the range check bound
`rc_bound` is less than or equal to 2^128. (In practice, they are equal.)
-/
import starkware.cairo.lean.semantics.soundness.hoare
def PRIME := 3618502788666131213697322... |
add3c13f991f738fa2d987c7f4d33ed278023618 | bbecf0f1968d1fba4124103e4f6b55251d08e9c4 | /src/topology/metric_space/contracting.lean | 5e7a3829c90c7ad6d51f119cc91b36fd85b06522 | [
"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 | 15,808 | lean | /-
Copyright (c) 2019 Rohan Mitta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rohan Mitta, Kevin Buzzard, Alistair Tucker, Johannes Hölzl, Yury Kudryashov
-/
import analysis.specific_limits
import data.setoid.basic
import dynamics.fixed_points.topology
/-!
# Contr... |
96686f27fbc3e76264151265f9108e927f9332e0 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/typevec.lean | e6b852c6bae1253e51361fa5bcfa1e9c33a7c8e0 | [
"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 | 24,492 | lean | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Mario Carneiro, Simon Hudon
-/
import data.fin2
import logic.function.basic
import tactic.basic
/-!
# Tuples of types, and their categorical structure.
## Features
* ... |
aede42f8c19eb0983c98cfcc8eea4971ade44434 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebraic_topology/dold_kan/homotopies.lean | 631f3cb9fe164913b33a4ade8a76d5bbc9dac1c6 | [
"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 | 7,878 | lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import algebra.homology.homotopy
import algebraic_topology.dold_kan.notations
/-!
# Construction of homotopies for the Dold-Kan correspondence
TODO (@joelriou) continue add... |
02a98f0044ab1b7aac93e91c82d7685073e1e142 | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /tests/lean/run/new_frontend2.lean | 42479407f1d5bf77a06823985d27bb358b9c0d3d | [
"Apache-2.0"
] | permissive | williamdemeo/lean4 | 72161c58fe65c3ad955d6a3050bb7d37c04c0d54 | 6d00fcf1d6d873e195f9220c668ef9c58e9c4a35 | refs/heads/master | 1,678,305,356,877 | 1,614,708,995,000 | 1,614,708,995,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 741 | lean |
declare_syntax_cat foo
variable {m : Type → Type}
variable [s : Functor m]
#check @Nat.rec
#check s.map
/-
The following doesn't work because
```
variable [r : Monad m]
#check r.map
```
because `Monad.to* methods have bad binder annotations
-/
theorem aux (a b c : Nat) (h₁ : a = b) (h₂ : c = b) : a = c := by
let... |
5827f0b55dce1e52f42a9286b2c9665818a9afc9 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/normed/group/SemiNormedGroup/kernels.lean | b1822fbc5011c53765ec63a7c1dd6e0d52339c2a | [
"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 | 13,358 | lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca, Johan Commelin, Scott Morrison
-/
import analysis.normed.group.SemiNormedGroup
import analysis.normed.group.quotient
import category_theory.limits.shapes.kernels
/-!
... |
1cf0861893fee37a562b7fb7de2fe6e04d94bab4 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/category_theory/abelian/non_preadditive.lean | 6d6abb27a611a873a5748d395623262f4e53756e | [
"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 | 32,028 | 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 category_theory.limits.shapes.finite_products
import category_theory.limits.shapes.kernels
import category_theory.limits.shapes.normal_mono
import category_theor... |
6b232745f5c6e7e506defa5df43179f78797abd8 | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /06_Inductive_Types.org.38.lean | e11f59a937c85e1a98a45468454e900f9b35b18c | [] | no_license | cjmazey/lean-tutorial | ba559a49f82aa6c5848b9bf17b7389bf7f4ba645 | 381f61c9fcac56d01d959ae0fa6e376f2c4e3b34 | refs/heads/master | 1,610,286,098,832 | 1,447,124,923,000 | 1,447,124,923,000 | 43,082,433 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 281 | lean | /- page 90 -/
import standard
import data.nat
open nat
inductive cbtree :=
| leaf : cbtree
| sup : (ℕ → cbtree) → cbtree
namespace cbtree
definition succ (t : cbtree) : cbtree :=
sup (λ n, t)
definition omega : cbtree :=
sup (nat.rec leaf (λ n t, succ t))
end cbtree
|
a1cdc2981044554c2f08224e0338c43cfb2ff975 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/data/seq/seq.lean | c53724acbca2cfb7368ea07e44d8a7e2fbb8a250 | [
"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 | 28,404 | 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 tactic.basic
import data.list.basic data.stream data.lazy_list data.seq.computation logic.basic
universes u v w
/-
coinductive seq (α : Type u) : Type u
| nil... |
5222bbc6e8e49f3c3a705609c4374c9d626e208c | ebf7140a9ea507409ff4c994124fa36e79b4ae35 | /src/solutions/thursday/linear_algebra.lean | e0ce969f1bd0157fd851a5b66f76d434c0fea013 | [] | no_license | fundou/lftcm2020 | 3e88d58a92755ea5dd49f19c36239c35286ecf5e | 99d11bf3bcd71ffeaef0250caa08ecc46e69b55b | refs/heads/master | 1,685,610,799,304 | 1,624,070,416,000 | 1,624,070,416,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,456 | lean | import analysis.normed_space.inner_product
import data.matrix.notation
import linear_algebra.bilinear_form
import linear_algebra.matrix
import tactic
universes u v
noncomputable theory
namespace lftcm
section exercise1
namespace module
open module
variables (R M : Type*) [comm_semiring R] [add_comm_monoid M] [mod... |
eebfc48a1cf2f287f9b3686c2db1035f826d0602 | 02005f45e00c7ecf2c8ca5db60251bd1e9c860b5 | /src/data/finset/lattice.lean | 011e065a449030d7d5affa340c2c0e5af2c07a44 | [
"Apache-2.0"
] | permissive | anthony2698/mathlib | 03cd69fe5c280b0916f6df2d07c614c8e1efe890 | 407615e05814e98b24b2ff322b14e8e3eb5e5d67 | refs/heads/master | 1,678,792,774,873 | 1,614,371,563,000 | 1,614,371,563,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 29,462 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
-/
import data.finset.fold
import data.multiset.lattice
import order.order_dual
import order.complete_lattice
/-!
# Lattice operations on finsets
-/
variables {α β γ : ... |
a2df9dd266edd4e8c764e4fcc6db026b8afa83d4 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/topology/algebra/module.lean | afad80c9c3fe158f876450550367da43602bfe1f | [
"Apache-2.0"
] | permissive | abentkamp/mathlib | d9a75d291ec09f4637b0f30cc3880ffb07549ee5 | 5360e476391508e092b5a1e5210bd0ed22dc0755 | refs/heads/master | 1,682,382,954,948 | 1,622,106,077,000 | 1,622,106,077,000 | 149,285,665 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 57,233 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo, Yury Kudryashov
-/
import topology.algebra.ring
import topology.algebra.mul_action
import topology.uniform_space.uniform_embedding
imp... |
f7120e90101a5d43b6dbf540007cf2ece9c2f4e1 | 1901b51268d21ec7361af7d3534abd9a8fa5cf52 | /scratch/cr.lean | 176539fbc4b84538101d5fb61df6fbcee2e31867 | [] | no_license | vbeffara/lean | b9ea4107deeaca6f4da98e5de029b62e4861ab40 | 0004b1d502ac3f4ccd213dbd23589d4c4f9fece8 | refs/heads/main | 1,652,050,034,756 | 1,651,610,858,000 | 1,651,610,858,000 | 225,244,535 | 6 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 1,221 | lean | import analysis.complex.basic -- pour travailler sur ℂ
import analysis.calculus.deriv -- pour utiliser la dérivation déjà créée de façon générale
noncomputable theory
def C_to_R2 : ℂ →L[ℝ] ℝ × ℝ := complex.equiv_real_prodₗ
def R2_to_C : ℝ × ℝ →L[ℝ] ℂ := complex.equiv_real_prodₗ.symm
def realify (f : ℂ → ℂ) : ℝ × ℝ →... |
b7f72fd9de7e16bd7a58bcbef5723463a7f0a9a6 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/user_notation.lean | b88cf6f9ba94e5e3893b4e53d262973d62a496ce | [
"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 | 1,077 | lean | open lean (parser)
open lean.parser
open interactive
open tactic
reserve prefix `unquote! `:100
reserve prefix `unquote2! `:100
@[user_notation]
meta def unquote_macro (_ : parse $ tk "unquote!") (e : parse lean.parser.pexpr) : parser pexpr :=
↑(to_expr e >>= eval_expr pexpr)
#eval unquote! ``(1 + 1)
@[user_notation... |
b3b230813adc80628a203c413913fc3ada18b994 | 6fbf10071e62af7238f2de8f9aa83d55d8763907 | /examples/biimplication_properties.lean | 492b5cdb6c85c09f6ab8ee519336897c86656ff3 | [] | no_license | HasanMukati/uva-cs-dm-s19 | ee5aad4568a3ca330c2738ed579c30e1308b03b0 | 3e7177682acdb56a2d16914e0344c10335583dcf | refs/heads/master | 1,596,946,213,130 | 1,568,221,949,000 | 1,568,221,949,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,270 | lean | -- Reflexive
-- Does A ↔ A?
example: ∀(A: Prop), A ↔ A :=
begin
assume A,
split,
assume pf_A,
assumption,
assume pf_A,
assumption,
end
-- Symmetric (exercise)
-- Does (A ↔ B) → (B ↔ A)?
example: ∀(A B: Prop),
(A ↔ B) → (B ↔ A) :=
begin
assume A B,
assume pf_A_iff_B,
have pf_A_to_B := (iff.e... |
51dfe881d214c8189dde754c044d33823ab8bf87 | 35960c5b117752aca7e3e7767c0b393e4dbd72a7 | /src/typing/default.lean | 588c7807777acaf38efccccbae6dd5e3e7b97956 | [
"Apache-2.0"
] | permissive | spl/tts | 461dc76b83df8db47e4660d0941dc97e6d4fd7d1 | b65298fea68ce47c8ed3ba3dbce71c1a20dd3481 | refs/heads/master | 1,541,049,198,347 | 1,537,967,023,000 | 1,537,967,029,000 | 119,653,145 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14 | lean | import .props
|
23d9371f755bba6082609e696b08c7cd59d7d043 | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /stage0/src/Lean/Data/KVMap.lean | 3c2b0514d203c52fabf778ce787561619d75c671 | [
"Apache-2.0"
] | permissive | walterhu1015/lean4 | b2c71b688975177402758924eaa513475ed6ce72 | 2214d81e84646a905d0b20b032c89caf89c737ad | refs/heads/master | 1,671,342,096,906 | 1,599,695,985,000 | 1,599,695,985,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,745 | 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
-/
import Lean.Data.Name
namespace Lean
inductive DataValue
| ofString (v : String)
| ofBool (v : Bool)
| ofName (v : Name)
| ofNat (v : Nat)
| ofInt ... |
d3fc31682d12f26e5dca9cf3218a6f68ba8c398b | e8d53a7b78545d183a23dd7bd921bc7ff312989f | /test.hlean | 830c9e6091f095f0c436fd6cf05acf17543d3318 | [] | no_license | Sumit0730/Impredicative | 857007626592440a27cf4440aa9a226d0ede7f3e | a75cb9989a684133d31d4889a746ee4fa7b66cea | refs/heads/master | 1,631,994,804,745 | 1,531,980,761,000 | 1,531,980,761,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,305 | hlean |
open funext eq trunc is_trunc prod sum
attribute trunc.rec [recursor]
definition my.inv (A : Type)(x y : A)(p : x=y) : y = x :=
eq.rec (eq.refl x) p
-- check ℕ
-- check Π(X : Type.{0}), ℕ
definition Or (A B : Prop.{0}) : Type.{0} :=
Π(X : Prop.{0}), (A → X) → ((B → X) → X)
definition Or_is_prop (A B : Prop.{0... |
6c869b871167e9af95146d2b5700a2d0a10cd278 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/algebraic_geometry/gluing.lean | 8e7a89c701c99ad91fcab4883c8d13453b800ec5 | [
"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 | 17,337 | lean | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import algebraic_geometry.presheafed_space.gluing
/-!
# Gluing Schemes
Given a family of gluing data of schemes, we may glue them together.
## Main definitions
* `algeb... |
a23fd3936e35340e2b214c4a68f83abd2d4624c5 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Compiler/LCNF/PullFunDecls.lean | 3a0be7b8c8daaaf0c476983eb090fcff18791e1b | [
"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 | 5,569 | 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.Compiler.LCNF.CompilerM
import Lean.Compiler.LCNF.DependsOn
import Lean.Compiler.LCNF.PassManager
namespace Lean.Compiler.LCNF
namespace PullFu... |
f972a7f6ae668f09f72c2a550a2bebb1f68953c3 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/ulift.lean | 5384eb374deed25fdb079deb88df7173b1da27b0 | [
"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 | 2,789 | lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import logic.equiv.basic
/-!
# Extra lemmas about `ulift` and `plift`
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a correspondin... |
47819c93d8f68fe363e50030acca75c2986c51c6 | cc060cf567f81c404a13ee79bf21f2e720fa6db0 | /lean/20170321-types-and-sorts.lean | 4b7c6a1b0c19a703e7862e5d2a0e690cb517c18a | [
"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 | 1,316 | lean | universe variables u v
structure Category :=
(Obj : Sort u)
(Hom : Obj → Obj → Sort v)
(identity : Π X : Obj, Hom X X)
(compose : Π { X Y Z : Obj }, Hom X Y → Hom Y Z → Hom X Z)
-- (left_identity : ∀ { X Y : Obj } (f : Hom X Y), compose (identity X) f = f)
-- (right_identity : ∀ { X Y : Obj } (f : Hom X ... |
658b0c04470597805652a799923f8cd11eff53a3 | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /src/Lean/Server/AsyncList.lean | 188c5d779375e7d70663ec1ed87a4fb5aa2e7a2a | [
"Apache-2.0"
] | permissive | williamdemeo/lean4 | 72161c58fe65c3ad955d6a3050bb7d37c04c0d54 | 6d00fcf1d6d873e195f9220c668ef9c58e9c4a35 | refs/heads/master | 1,678,305,356,877 | 1,614,708,995,000 | 1,614,708,995,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,957 | lean | /-
Copyright (c) 2020 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki
-/
import Init.System.IO
namespace IO
universes u v
/-- An async IO list is like a lazy list but instead of being *unevaluated* `Thunk`s,
lazy tails are `Task`... |
6d8a0dd822a27f8988eb9f4111be3bf8e0ea793b | fc8450d786b31f87c7f0f41b251d4cdb0ce5b395 | /static/linguist.lean | 2895f727c78f78d326505367181d9dec2a23d332 | [
"CC-BY-4.0"
] | permissive | utensil/lean-cheatsheet | ffd40997e8624b8aad5342c204f02fdc1528b68e | 05cbd991b85bb45ab87f28cf85f2c13aacb31d14 | refs/heads/master | 1,669,024,676,471 | 1,595,667,401,000 | 1,595,667,401,000 | 272,878,080 | 1 | 0 | null | 1,592,413,010,000 | 1,592,368,310,000 | Lean | UTF-8 | Lean | false | false | 95 | lean | //
// This file only exists to trick Github Linguist into showing this as a Lean project :)
//
|
a7b7076232a4726c51d5106e832b97e98eba2801 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /test/delta_instance.lean | 411e55bd7a52368addb61325ac4116289f677959 | [
"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 | 923 | 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
import algebra.category.Mon.basic
@[derive has_coe_to_sort] def X : Type := set ℕ
@[derive ring] def T := ℤ
class binclass (T1 T2 : Type)
instan... |
4af191b5c62da4507aa06a054519d6497d0435a0 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/zmod/parity_auto.lean | 673df1c0cc0ea3c8144de423eac4186b3e52cd39 | [] | 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 | 779 | lean | /-
Copyright (c) 2020 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Kyle Miller
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.nat.parity
import Mathlib.data.zmod.basic
import Mathlib.PostPort
namespace Mathlib
/-!
# R... |
221c649591b89c57c14444618ae05d821e986c95 | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /hott/init/datatypes.hlean | 68b8e521ef82d7043095b0cad0089192028ea2b1 | [
"Apache-2.0"
] | permissive | tjiaqi/lean | 4634d729795c164664d10d093f3545287c76628f | d0ce4cf62f4246b0600c07e074d86e51f2195e30 | refs/heads/master | 1,622,323,796,480 | 1,422,643,069,000 | 1,422,643,069,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,880 | hlean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jakob von Raumer
Basic datatypes
-/
prelude
notation [parsing-only] `Type'` := Type.{_+1}
notation [parsing-only] `Type₊` := Type.{_+1}
notation `Type₀` := ... |
87d406cd71b5d9f4421b62d819dd05194ae293ab | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/group_theory/subgroup.lean | b03010561674bb78e6eca6931e0e50889bc7e41d | [
"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 | 29,165 | 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.submonoid
open set function
variables {G : Type*} {H : Type*} {... |
4522cbc009bb343659939f2819d96084e4570a4e | b2c4bd81ed12cc14c20704365f094339d4c894a2 | /src/graph_theory/graph_induction.lean | 11909bea3b5bcc3d82c66d2cfabb0b4e49836092 | [] | no_license | agusakov/graph_theory_2020 | 711639d9d9b25fd83899620da11ae1753d11d48b | 83a8afc31aa28dbec39a768d6042d3cb515f7a16 | refs/heads/master | 1,669,901,277,114 | 1,596,931,643,000 | 1,596,931,643,000 | 285,154,458 | 5 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,037 | lean | import .subgraph
noncomputable theory
open_locale classical
universes u
variables {V : Type u}
namespace simple_graph
variables (G : simple_graph V)
include G
variables [fintype V]
-- want a lemma that 2 * card_edges equals the card of a specific finset.
-- lemma 2 * G.card_edges = finset.card G.E_finset
@[... |
fca9fd19e2e5305a450646131d369fa18c6830cf | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/order/monoid/defs.lean | d4052dac4ecbcf5d3d6fc8e88a7f2dd553c2f262 | [
"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 | 4,569 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl
-/
import algebra.order.monoid.lemmas
import order.bounded_order
/-!
# Ordered monoids
> THIS FILE IS SYNCHRONIZED WIT... |
453c43db1ba61678fd97ae0ba19a8882b022a15b | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/archimedean_auto.lean | 25b4a8759b6b1d1189852d08daae15b21f6b3144 | [] | 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 | 8,021 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
Archimedean groups and fields.
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.field_power
import Mathlib.data.rat.default
import ... |
1fc4cdab4017fbe930768975ebe5d8f34cdbdf38 | 5e3548e65f2c037cb94cd5524c90c623fbd6d46a | /src_icannos_totilas/applications_lineaires/cpge_applin_8_a.lean | 1e8818769066b13cbcdcc7ea6ba5157bf7149d24 | [] | no_license | ahayat16/lean_exos | d4f08c30adb601a06511a71b5ffb4d22d12ef77f | 682f2552d5b04a8c8eb9e4ab15f875a91b03845c | refs/heads/main | 1,693,101,073,585 | 1,636,479,336,000 | 1,636,479,336,000 | 415,000,441 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 272 | lean | import algebra.module.linear_map
import linear_algebra.basic
import data.real.basic
theorem cpge_applin_8_a
(R : Type*) (E : Type*) (F : Type*)
[field R]
[add_comm_group E] [module R E]
(u : linear_map R E E) (F : submodule R E):
u ⁻¹' (u '' F) = F + u.ker
:= sorry |
ac4266ba23e0f5d7a21f2bbc56220c4cd932039e | 3dd1b66af77106badae6edb1c4dea91a146ead30 | /tests/lean/run/e8.lean | cf7ab93c4761f68db2c0c29ea2729e126fc4a9ad | [
"Apache-2.0"
] | permissive | silky/lean | 79c20c15c93feef47bb659a2cc139b26f3614642 | df8b88dca2f8da1a422cb618cd476ef5be730546 | refs/heads/master | 1,610,737,587,697 | 1,406,574,534,000 | 1,406,574,534,000 | 22,362,176 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 834 | lean | precedence `+`:65
namespace nat
variable nat : Type.{1}
variable add : nat → nat → nat
infixl + := add
end
namespace int
using nat (nat)
variable int : Type.{1}
variable add : int → int → int
infixl + := add
variable of_nat : nat → int
coercion of_nat
end
-- Using "only" the notation and declaratio... |
4fb03e3fd15f375a3d827903d08d3a0f1d77e8f4 | 2eab05920d6eeb06665e1a6df77b3157354316ad | /src/measure_theory/measure/regular.lean | 60c7cb66ffc3489eb7d21c52e1806bfdb8e2507b | [
"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 | 33,912 | lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris Van Doorn, Yury Kudryashov
-/
import measure_theory.constructions.borel_space
/-!
# Regular measures
A measure is `outer_regular` if the measure of any measurable set `A` ... |
76ea5f13984585bdcd6a41821ff4797d42753c55 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/ring_theory/ideal/prod.lean | 081fdbb7af8fb0d73f596f14e554c4510b8017b2 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 6,020 | 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 ring_theory.ideal.operations
/-!
# Ideals in product rings
For commutative rings `R` and `S` and ideals `I ≤ R`, `J ≤ S`, we define `ideal.prod I J` as the
pro... |
bba7ac8a99bdf2c25f16c1e9ca5ca7dd27100c32 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/inner_product_space/gram_schmidt_ortho.lean | ad0ae5dd303c551fa04988a54d0f43dc259fac89 | [
"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 | 17,671 | lean | /-
Copyright (c) 2022 Jiale Miao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jiale Miao, Kevin Buzzard, Alexander Bentkamp
-/
import analysis.inner_product_space.pi_L2
import linear_algebra.matrix.block
/-!
# Gram-Schmidt Orthogonalization and Orthonormalization
... |
1e0e595564f3a0ac3c50b636919cb57c64288e78 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /hott/algebra/default.hlean | ab1f32887c569f01f0c27d2ebc245efe44aaea6c | [
"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 | 197 | hlean | /-
Copyright (c) 2016 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import .homotopy_group .ordered_field
|
30e7ae502883b8e58ae0f5606e1eca07bda5c39c | 75db7e3219bba2fbf41bf5b905f34fcb3c6ca3f2 | /tests/lean/ppbug.lean | 0c95330f2ad4e69e398861e556a703eba1f9eff7 | [
"Apache-2.0"
] | permissive | jroesch/lean | 30ef0860fa905d35b9ad6f76de1a4f65c9af6871 | 3de4ec1a6ce9a960feb2a48eeea8b53246fa34f2 | refs/heads/master | 1,586,090,835,348 | 1,455,142,203,000 | 1,455,142,277,000 | 51,536,958 | 1 | 0 | null | 1,455,215,811,000 | 1,455,215,811,000 | null | UTF-8 | Lean | false | false | 18 | lean | check char.rec_on
|
df8c9615d78a94b0eff79590b4a9a6da29a5504e | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/data/nat/digits.lean | 5eb28b8ac4a92a0819a9e00f33b938099e9f3d1f | [
"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 | 21,747 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Shing Tak Lam, Mario Carneiro
-/
import data.int.modeq
import data.list.indexes
import tactic.interval_cases
import tactic.linarith
/-!
# Digits of a natural number
T... |
6cd603108e938a625c0dd96b889d7ea65d44eaed | bb31430994044506fa42fd667e2d556327e18dfe | /src/data/matrix/dmatrix.lean | 2fe70c3422ed09dac18528f3444eebfe9036ecf5 | [
"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 | 5,470 | 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 algebra.group.pi
import data.fintype.basic
/-!
# Matrices
-/
universes u u' v w z
/-- `dmatrix m n` is the type of dependently typed matrices
whose rows are ... |
281f9a749abfec81728ef16d862cd14e77f4cbf9 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/order/category/omega_complete_partial_order.lean | 7e2df466c1d7cc8b6e11700fd5c6aa99bb69f06f | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 4,120 | lean | /-
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import order.omega_complete_partial_order
import order.category.Preorder
import category_theory.limits.shapes.products
import category_theory.limits.shapes.equalizers
impo... |
9a49ae23e95775bc8c555c471277fda9a4b32ebc | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/rfl_simp_thm.lean | 5f84fab634a4ca38ea14faf17bf598a0e6efe389 | [
"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 | 187 | lean | def inc (x : Nat) := x + 1
@[simp] theorem inc_eq : inc x = x + 1 := rfl
theorem ex (a b : Fin (inc n)) (h : a = b) : b = a := by
simp only [inc_eq] at a
trace_state
exact h.symm
|
671f31e1aa6871acd864c95fed44d844cec8636a | 54ce0561cebde424526f41d45f490ed56be2bd0c | /scratch/alternative.lean | a15d250ebb0d4985ce0de21844193b4c609aed1f | [] | no_license | melembroucarlitos/Tao_Analysis-LEAN | cf7b3298d317891a09e4bf21cfe7c7ffcb57b9a9 | 3f4fc7e090d96b6cef64896492fba4bef124794b | refs/heads/master | 1,692,952,385,694 | 1,636,287,522,000 | 1,636,287,522,000 | 400,630,166 | 3 | 0 | null | 1,635,910,807,000 | 1,630,096,823,000 | Lean | UTF-8 | Lean | false | false | 3,709 | lean | namespace hidden
-- In order for this to be the axiom of infinity, we would need to put instead
-- axiom myNat : Set
-- and make it work by rewriting the below axioms
axiom myNat : Type
axiom zero : myNat
axiom succ : myNat -> myNat
axiom zero_not_succ : ∀ (n : myNat), succ n ≠ zero
axiom succ_injective : ∀ (n m ... |
a6d66c5dbf39d238c81439f4372a64e8db1af5dd | dd0f5513e11c52db157d2fcc8456d9401a6cd9da | /08_Building_Theories_and_Proofs.org.4.lean | b6376142f2905f979c11cae6789d9313449e374a | [] | no_license | cjmazey/lean-tutorial | ba559a49f82aa6c5848b9bf17b7389bf7f4ba645 | 381f61c9fcac56d01d959ae0fa6e376f2c4e3b34 | refs/heads/master | 1,610,286,098,832 | 1,447,124,923,000 | 1,447,124,923,000 | 43,082,433 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 396 | lean | import standard
structure Semigroup : Type :=
(carrier : Type)
(mul : carrier → carrier → carrier)
(mul_assoc : ∀ a b c : carrier, mul (mul a b) c = mul a (mul b c))
notation a `*` b := Semigroup.mul _ a b
attribute Semigroup.carrier [coercion]
-- BEGIN
structure morphism (S1 S2 : Semigroup) : Type :=
(mor : S1 → S2... |
5496e1e19184749d22a5a492969c73f4c3ff951d | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/finset/finsupp.lean | 9bed84e1c066996a775e8831c0eda765313f7c50 | [
"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 | 3,352 | lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import algebra.big_operators.finsupp
import data.finset.pointwise
import data.finsupp.indicator
import data.fintype.big_operators
/-!
# Finitely supported product of fin... |
15f1720a2c7f732578bc1a7e98c8d872d0421233 | 2a70b774d16dbdf5a533432ee0ebab6838df0948 | /_target/deps/mathlib/src/analysis/normed_space/basic.lean | 3ebca9e8983163f49ef1d1078b3c10bd4fd17e70 | [
"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 | 56,190 | 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
-/
import topology.instances.nnreal
import topology.algebra.module
import topology.metric_space.antilipschitz
/-!
# Normed spaces
-/
variables {α : Typ... |
bc8fbd07fc6bbf23b9ad4e1826559cfdcd3e7040 | a721fe7446524f18ba361625fc01033d9c8b7a78 | /src/principia/mynat/fta.lean | ef236c73a384bb772d3670102580dfaa14957ec1 | [] | 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 | 2,364 | lean | import .hcf
import ..myint.dvd
import ..logic
namespace hidden
open myint
namespace mynat
theorem coprime_imp_either_nzero {m n : mynat} (h : coprime m n) :
m ≠ 0 ∨ n ≠ 0 :=
begin
by_contradiction h0,
rw [not_or_distrib, not_not, not_not] at h0,
cases h0 with hm hn,
subst hm, subst hn,
unfold coprime at h... |
01977b470dcedc4807ed761b68da1f9f7d7a76d3 | 471bedbd023d35c9d078c2f936dd577ace7f5813 | /library/init/core.lean | 132cb4f4e3848ab6e4e3968befa9f735c52c41ca | [
"Apache-2.0"
] | permissive | lambdaxymox/lean | e06f0fa503666df827edd9867d7f49ca017aae64 | fc13c8c72a15dab71a2c2b31410c2cadc3526bd7 | refs/heads/master | 1,666,785,407,985 | 1,666,153,673,000 | 1,666,153,673,000 | 310,165,986 | 0 | 0 | Apache-2.0 | 1,604,542,096,000 | 1,604,542,095,000 | null | UTF-8 | Lean | false | false | 18,729 | 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... |
92d4e90329e4ce828c26d66821de72a359101954 | 9c2e8d73b5c5932ceb1333265f17febc6a2f0a39 | /src/S4/rules.lean | 888c99f3fd9193be5033651e47060df3d4a10733 | [
"MIT"
] | permissive | minchaowu/ModalTab | 2150392108dfdcaffc620ff280a8b55fe13c187f | 9bb0bf17faf0554d907ef7bdd639648742889178 | refs/heads/master | 1,626,266,863,244 | 1,592,056,874,000 | 1,592,056,874,000 | 153,314,364 | 12 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 23,635 | lean | import .semantics
open nnf subtype list
inductive node (Γ : sseqt) : Type
| closed : unsatisfiable (Γ.m ++ Γ.b) → node
| open_ : {x : model // (minfo x.1).id = Γ} → node
open node
def contra_rule_seqt {Δ : sseqt} {n} (h : var n ∈ Δ.m ∧ neg n ∈ Δ.m) : node Δ :=
begin
left,
{exact unsat_contra_seqt h.1 h.2}
end
... |
5f8e5c7fd6a0f237c711f183f673fe3e8829bf25 | ec5a7ae10c533e1b1f4b0bc7713e91ecf829a3eb | /ijcar16/examples/cc8.lean | 76489dd55557f5d1ecbc2a4c238b9247e9a9361e | [
"MIT"
] | permissive | leanprover/leanprover.github.io | cf248934af7c7e9aeff17cf8df3c12c5e7e73f1a | 071a20d2e059a2c3733e004c681d3949cac3c07a | refs/heads/master | 1,692,621,047,417 | 1,691,396,994,000 | 1,691,396,994,000 | 19,366,263 | 18 | 27 | MIT | 1,693,989,071,000 | 1,399,006,345,000 | Lean | UTF-8 | Lean | false | false | 2,277 | lean | /-
Example/test file for the congruence closure procedure described in the paper:
"Congruence Closure for Intensional Type Theory"
Daniel Selsam and Leonardo de Moura
The tactic `by blast` has been configured in this file to use just
the congruence closure procedure using the command
set_option blast.strategy... |
8960cbe89639359c72059bd3834b6c63b6ba2894 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/algebra/homology/differential_object.lean | 7b68f14c679666d1689f2e8ca00ff06f70a49185 | [
"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 | 3,677 | 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 algebra.homology.homological_complex
import category_theory.differential_object
import category_theory.graded_object
/-!
# Homological complexes are different... |
c1eb735b442ef577b5442943a9ef24739ec2637c | 08a8ee10652ba4f8592710ceb654b37e951d9082 | /src/hott/types/nat/basic.lean | b7537758f8b58f17f0f2eccedaa6a3bbc848e60d | [
"Apache-2.0"
] | permissive | felixwellen/hott3 | e9f299c84d30a782a741c40d38741ec024d391fb | 8ac87a2699ab94c23ea7984b4a5fbd5a7052575c | refs/heads/master | 1,619,972,899,098 | 1,509,047,351,000 | 1,518,040,986,000 | 120,676,559 | 0 | 0 | null | 1,518,040,503,000 | 1,518,040,503,000 | null | UTF-8 | Lean | false | false | 10,118 | lean | /-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
(Ported from standard library)
Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad
Basic operations on the natural numbers.
-/
import hott.algebra.ring
universes u v w
hott_theory
na... |
50177bdbdd90f30b8cab1bfd1b9903c21bdcd8ff | 947b78d97130d56365ae2ec264df196ce769371a | /src/Lean/Compiler/IR/Format.lean | 7c91651aeb9ca0f5bea6b46d02de159a8924874b | [
"Apache-2.0"
] | permissive | shyamalschandra/lean4 | 27044812be8698f0c79147615b1d5090b9f4b037 | 6e7a883b21eaf62831e8111b251dc9b18f40e604 | refs/heads/master | 1,671,417,126,371 | 1,601,859,995,000 | 1,601,860,020,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,060 | 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.Data.Format
import Lean.Compiler.IR.Basic
namespace Lean
namespace IR
private def formatArg : Arg → Format
| Arg.var id => format id
| Arg... |
dd31abed09c2ee2df1b15efa07253c7ff81f7488 | 5749d8999a76f3a8fddceca1f6941981e33aaa96 | /src/data/polynomial.lean | 78f93afee49727aefe58dfc7f61267ba177a584c | [
"Apache-2.0"
] | permissive | jdsalchow/mathlib | 13ab43ef0d0515a17e550b16d09bd14b76125276 | 497e692b946d93906900bb33a51fd243e7649406 | refs/heads/master | 1,585,819,143,348 | 1,580,072,892,000 | 1,580,072,892,000 | 154,287,128 | 0 | 0 | Apache-2.0 | 1,540,281,610,000 | 1,540,281,609,000 | null | UTF-8 | Lean | false | false | 103,289 | 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, Jens Wagemaker
Theory of univariate polynomials, represented as `ℕ →₀ α`, where α is a commutative semiring.
-/
import data.finsupp algebra.gcd_domain ring... |
76a44a5da5b239dee14b97e7af74827401f89a68 | b9a81ebb9de684db509231c4469a7d2c88915808 | /src/super/clause_ops.lean | e83097d6bf2195849e67c4d2480acb3d0d503103 | [] | no_license | leanprover/super | 3dd81ce8d9ac3cba20bce55e84833fadb2f5716e | 47b107b4cec8f3b41d72daba9cbda2f9d54025de | refs/heads/master | 1,678,482,996,979 | 1,676,526,367,000 | 1,676,526,367,000 | 92,215,900 | 12 | 6 | null | 1,513,327,539,000 | 1,495,570,640,000 | Lean | UTF-8 | Lean | false | false | 3,379 | lean | /-
Copyright (c) 2017 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner
-/
import .clause
open monad tactic expr
namespace super
local attribute [instance] has_monad_lift_to_has_coe
meta def on_left_at {m} [monad m] (c : clause) (i : ℕ)
... |
a0e849c3371c1b7647eff69dec15ed03d9fb1bec | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Elab/PreDefinition/Structural/Preprocess.lean | 1b67a1c62b2589f27780c61426f806bbac536e26 | [
"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 | 869 | 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.Meta.Transform
namespace Lean.Elab.Structural
open Meta
private def shouldBetaReduce (e : Expr) (recFnName : Name) : Bool :=
if e.isHeadBeta... |
013a6c9dafde482b704ee6daed908414086233b0 | ce89339993655da64b6ccb555c837ce6c10f9ef4 | /bluejam/topprover/03.lean | d9666ee0f9348c38f9a7c3cb06689206bb5c6c78 | [] | no_license | zeptometer/LearnLean | ef32dc36a22119f18d843f548d0bb42f907bff5d | bb84d5dbe521127ba134d4dbf9559b294a80b9f7 | refs/heads/master | 1,625,710,824,322 | 1,601,382,570,000 | 1,601,382,570,000 | 195,228,870 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 38 | lean | example : 1 + 1 = 2 :=
by simp * at *
|
2384d4ae9f60bfb4a079361c99b5436e41fd8255 | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/data/zsqrtd/basic.lean | 59c8a4949596d6f0562d8b3050565bba9712473f | [
"Apache-2.0"
] | permissive | vaibhavkarve/mathlib | a574aaf68c0a431a47fa82ce0637f0f769826bfe | 17f8340912468f49bdc30acdb9a9fa02eeb0473a | refs/heads/master | 1,621,263,802,637 | 1,585,399,588,000 | 1,585,399,588,000 | 250,833,447 | 0 | 0 | Apache-2.0 | 1,585,410,341,000 | 1,585,410,341,000 | null | UTF-8 | Lean | false | false | 27,111 | 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 algebra.associated data.nat.gcd tactic.ring
/-- The ring of integers adjoined with a square root of `d`.
These have the form `a + b √d` where... |
c3c8537a61819bb86e32b60672b8aaca194dd40b | 64874bd1010548c7f5a6e3e8902efa63baaff785 | /library/algebra/relation.lean | b8412353e383babd75d48e631402136203ab0611 | [
"Apache-2.0"
] | permissive | tjiaqi/lean | 4634d729795c164664d10d093f3545287c76628f | d0ce4cf62f4246b0600c07e074d86e51f2195e30 | refs/heads/master | 1,622,323,796,480 | 1,422,643,069,000 | 1,422,643,069,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,451 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.relation
Author: Jeremy Avigad
General properties of relations, and classes for equivalence relations and congruences.
-/
namespace relation
/- properties of binary r... |
913d6fd1c9c235a23e8272fa9e94e033f14ddbd2 | b66669ef1ec06ddbd9526fe3afe0a68566dfbad3 | /src/cell_automaton.lean | 0a6a7d3566b301fc748b0275fc84440b25031216 | [
"MIT"
] | permissive | FerdoSil/LatticesAndCellularAutomata | 40185a9099bb3cf1371c85f1ca33a17c2e26fecb | 2a69d2e74a231addf0e446dca86ef90d50d60218 | refs/heads/master | 1,587,683,992,072 | 1,586,018,471,000 | 1,586,018,471,000 | 171,533,028 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,895 | lean | -- Formalization of cellular automata defined over two-dimensional orthogonal geometric lattices.
-- The structure 'cell_automaton' represents a cellular automaton.
-- The function 'step_n a n' represents the 'n'th generation of the CA 'a'.
-- The function 'make_canonical' computes the canonical form of an automaton.... |
e73713846fcce8b2d38fa732b3f7f8253d959344 | 271e26e338b0c14544a889c31c30b39c989f2e0f | /stage0/src/Init/Lean/Elab/ResolveName.lean | bfea04e4138d2ae359376ef86ed7ea7bc1ea23fd | [
"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 | 4,841 | 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
-/
prelude
import Init.Lean.Modifiers
import Init.Lean.Elab.Alias
namespace Lean
namespace Elab
inductive OpenDecl
| simple (ns : Name) ... |
145bb18613bc363dfdd02845e211db161add8739 | 43390109ab88557e6090f3245c47479c123ee500 | /src/Geometry/tarski_2.lean | 6eea44cd9cab1e44eb1d1256f3ffc77f6f24df84 | [
"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 | 22,327 | lean | import geometry.tarski_1
open classical set
namespace Euclidean_plane
variables {point : Type} [Euclidean_plane point]
local attribute [instance, priority 0] prop_decidable
theorem six9 {a b p : point} : b ∈ ray p a → ray p a = ray p b :=
begin
intro h,
ext,
split,
intro h1,
cases h with h h2,
cases h2 with h2 ... |
c04a456fc74a02abd8bbf86341454a7e2436f9b2 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/data/finset/pi_induction.lean | be3fa94749c91f03ee57589f0d725ebdd675d1e0 | [
"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 | 5,065 | lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import data.fintype.basic
/-!
# Induction principles for `Π i, finset (α i)`
In this file we prove a few induction principles for functions `Π i : ι, finset (α i)... |
0384260feb9cebbb1dc3350b95693c25939cb1c4 | 9d2e3d5a2e2342a283affd97eead310c3b528a24 | /src/hints/thursday/afternoon/category_theory/exercise3/hint4.lean | 7ab27295ce3718e9119c533800458cf34d4c4ae2 | [] | permissive | Vtec234/lftcm2020 | ad2610ab614beefe44acc5622bb4a7fff9a5ea46 | bbbd4c8162f8c2ef602300ab8fdeca231886375d | refs/heads/master | 1,668,808,098,623 | 1,594,989,081,000 | 1,594,990,079,000 | 280,423,039 | 0 | 0 | MIT | 1,594,990,209,000 | 1,594,990,209,000 | null | UTF-8 | Lean | false | false | 518 | lean | import for_mathlib.category_theory -- This imports some simp lemmas that I realised belong in mathlib while writing this exercise.
open category_theory
variables {C : Type*} [category C]
variables {D : Type*} [category D]
lemma equiv_reflects_mono {X Y : C} (f : X ⟶ Y) (e : C ≌ D)
(hef : mono (e.functor.map f)) : ... |
d9423132de5bd0a2ebded0b03104c2354c7f4b2b | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/category/Module/tannaka.lean | 03dec3c757f8de3734bc4e736a6ae13b9ab5bfe3 | [
"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 | 1,466 | 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 algebra.category.Module.basic
import linear_algebra.span
/-!
# Tannaka duality for rings
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this fil... |
462c09a403ef05dceda550f63d248d492e552e46 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/algebra/group/pi.lean | d35ed4a1e66e08455bf880c7f8aadcd6870880d1 | [
"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 | 11,248 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot
-/
import data.pi
import data.set.function
import tactic.pi_instances
import algebra.group.hom_instances
/-!
# Pi instances for groups and monoids
This file ... |
0fd67408688f5e4a288f4bceba88ed6517f4446f | c777c32c8e484e195053731103c5e52af26a25d1 | /src/ring_theory/mv_polynomial/symmetric.lean | d0ab30e3b717603cdfdeede9bf73a602e82f7be0 | [
"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 | 7,940 | lean | /-
Copyright (c) 2020 Hanting Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Hanting Zhang, Johan Commelin
-/
import data.mv_polynomial.rename
import data.mv_polynomial.comm_ring
import algebra.algebra.subalgebra.basic
/-!
# Symmetric Polynomials and Elementary... |
075ab9633efec1d641b380648605374e8d62e0cf | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/run/auto_quote1.lean | 1600871c3e692cca22493e626935dc33faa6a7aa | [
"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 | 2,044 | lean | example (a b c : nat) : a = b → b = c → c = a :=
by {
intros,
apply eq.symm,
apply eq.trans,
assumption,
assumption
}
example (a b c : nat) : a = b → b = c → c = a :=
by intros; apply eq.symm; apply eq.trans; repeat {assumption}
example (p q r : Prop) : p → q → r → p ∧ q ∧ r ∧ p ∧ q :=
by intros; repeat {as... |
a268ca04281150d466dcabc869be80595ee02e51 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/nat/prime.lean | 6d43382089a8279b284fb3dded8944167a3831ab | [] | 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 | 14,392 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.nat.sqrt
import Mathlib.data.nat.gcd
import ... |
07e6f175e4d29db4249b4f3d892a3546cc49672e | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/run/intros_defeq_canonizer_bug.lean | fd05d03606e5ac9f3f517275c9827a5db7548251 | [
"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 | 268 | lean | constant {u} f {α : Type u} : α → α → α → α
axiom {u} fax {α : Type u} [ring α] (a b : α) : f a b a = 0
attribute [ematch] fax
universe variables u
lemma ex {α : Type u} [field α] (x y : α) : f (x + y) (y + x) (x + y) = 0 :=
begin [smt] ematch end
|
a303abeb071f300269a1b61ac59870d1c5f3bb06 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/def1.lean | 1eb4a18323bfc98f279374c1313ba5e34dae8c17 | [
"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 | 431 | lean |
inductive BV : Nat → Type
| nil : BV 0
| cons : (n : Nat) → (hd : Bool) → (tl : BV n) → BV (Nat.succ n)
open BV
def h : {n : Nat} → BV n.succ.succ → Bool
| _, cons (Nat.succ (Nat.succ m)) b v => b
| _, cons (Nat.succ Nat.zero) b v => not b
theorem ex1 (m : Nat) (b : Bool) (v : BV m.succ.succ) : h (cons m.succ... |
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