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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
6386b574a3dc0ea95c78f08644d4448d77497dd5 | 1abd1ed12aa68b375cdef28959f39531c6e95b84 | /src/analysis/convex/combination.lean | f769e6849ab77a93e7fae7b74b205b166acd4faa | [
"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 | 18,034 | lean | /-
Copyright (c) 2019 Yury Kudriashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudriashov
-/
import algebra.big_operators.order
import analysis.convex.hull
import linear_algebra.affine_space.barycentric_coords
/-!
# Convex combinations
This file defines c... |
8357cbb97cd477492b31ed789d0d0c28e2abf622 | 3adda22358e3c0fbae44c6c35fdddbebf9358ef4 | /src/zero_point_seven_one.lean | 4f3b7e1a7d9627e7d4a965b27e10f4d91b1a6a55 | [
"Apache-2.0"
] | permissive | ImperialCollegeLondon/M1F-exam-may-2018 | 1539951b055cea5bac915bdb6fa1969e2f323402 | 8b5eca2037d4a14d6cfac3da1858b6c4119216d3 | refs/heads/master | 1,586,895,978,182 | 1,557,175,794,000 | 1,557,175,794,000 | 164,093,611 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,285 | lean | import for_mathlib.decimal_expansions
open decimal
noncomputable definition s : ℝ := (71/100 : ℝ)
theorem sQ : s = ((71/100:ℚ):ℝ) := by unfold s;norm_num
theorem floor_s : floor s = 0 :=
by rw [← floor_of_bounds, s, int.cast_zero]; norm_num
theorem floor_10s : floor (71/10 : ℝ) = 7 :=
begin
rw [← floor_of_bound... |
a2f455dfd4d0536e0cc7d7d4ea340c3260d44a17 | 3dc4623269159d02a444fe898d33e8c7e7e9461b | /.github/workflows/project_1_a_decrire/projet_A2/moprhisme.lean | c290c59cb99c8694f55aad43287b303ffcf2fc38 | [] | 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 | 2,376 | lean | import .X
import .action_Idem_X
import category_theory.natural_transformation
import category_theory.types
import data.quot
open CommRing
open X
open A2
open A2_disc
open idem_action_X
namespace π
variables (R : Type)[comm_ring R]
#check (A(R)).r
/--
## X := R ↦ { (x,y) ∈ A^2 ∣ (x-y)^2 inversible} we define π : ... |
d04c17a431c1bc96e855ae023d985b00fc993935 | 969dbdfed67fda40a6f5a2b4f8c4a3c7dc01e0fb | /src/linear_algebra/char_poly/coeff.lean | 84c6481f13efc7f35c00832ddcc4ebea6b61e3bb | [
"Apache-2.0"
] | permissive | SAAluthwela/mathlib | 62044349d72dd63983a8500214736aa7779634d3 | 83a4b8b990907291421de54a78988c024dc8a552 | refs/heads/master | 1,679,433,873,417 | 1,615,998,031,000 | 1,615,998,031,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,999 | lean | /-
Copyright (c) 2020 Aaron Anderson, Jalex Stark. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Aaron Anderson, Jalex Stark.
-/
import data.matrix.char_p
import linear_algebra.char_poly.basic
import linear_algebra.matrix
import ring_theory.polynomial.basic
import alg... |
295b7e8ab9e3d22c9d20fd6fad5310dd9982c3aa | 5749d8999a76f3a8fddceca1f6941981e33aaa96 | /src/topology/algebra/infinite_sum.lean | cf1c03ebefd5657b405d7d2737209e2b72889619 | [
"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 | 28,984 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
Infinite sum over a topological monoid
This sum is known as unconditionally convergent, as it sums to the same value under all possible
permutations. For Euclidean spa... |
ef73c8777607a0bab976bee903a9715298a1f656 | 947fa6c38e48771ae886239b4edce6db6e18d0fb | /src/data/int/modeq.lean | f9f9160004dd2098ccca78226d302eb411d0ec11 | [
"Apache-2.0"
] | permissive | ramonfmir/mathlib | c5dc8b33155473fab97c38bd3aa6723dc289beaa | 14c52e990c17f5a00c0cc9e09847af16fabbed25 | refs/heads/master | 1,661,979,343,526 | 1,660,830,384,000 | 1,660,830,384,000 | 182,072,989 | 0 | 0 | null | 1,555,585,876,000 | 1,555,585,876,000 | null | UTF-8 | Lean | false | false | 7,509 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import data.nat.modeq
import tactic.ring
/-!
# Congruences modulo an integer
This file defines the equivalence relation `a ≡ b [ZMOD n]` on the integers, similarly to ... |
ce6938bffd06401baa52f9ac389c57dee461d362 | 367134ba5a65885e863bdc4507601606690974c1 | /src/analysis/normed_space/inner_product.lean | 4faed77d18012bc47ee7b62cfc4a1b270cdffacd | [
"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 | 125,780 | lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Sébastien Gouëzel, Frédéric Dupuis, Heather Macbeth
-/
import linear_algebra.bilinear_form
import linear_algebra.sesquilinear_form
import topology.metric_space.pi_Lp
imp... |
195b511c495d97920a75fee4d2e0323bde24005d | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/mv_polynomial/funext_auto.lean | a5009b07a14885224e7a006997917de7ccb177c3 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,492 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.polynomial.ring_division
import Mathlib.data.mv_polynomial.rename
import Mathlib.ring_... |
5e7342597cc84c53c3c77c1256fd61f4e25ab53c | 4727251e0cd73359b15b664c3170e5d754078599 | /archive/imo/imo1969_q1.lean | a2ccb8cca33e618cb4407f81beb10883ff8ad5c3 | [
"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 | 2,981 | lean | /-
Copyright (c) 2020 Kevin Lacker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker
-/
import algebra.group_power.identities
import data.int.nat_prime
import tactic.linarith
import tactic.norm_cast
import data.set.finite
/-!
# IMO 1969 Q1
Prove that there ... |
bf929bca2c14c62d537c6c99e7f51a4599693767 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/monad/algebra_auto.lean | d9be7f76e27ab9c9acfee3b444f49dd906fcdc28 | [] | 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 | 13,883 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Bhavik Mehta
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.monad.basic
import Mathlib.category_theory.adjunction.basic
i... |
8d382aeb8d274eee9074e91f538d0b8130008f36 | fecda8e6b848337561d6467a1e30cf23176d6ad0 | /src/ring_theory/integral_domain.lean | a97e8641ef9cc360579724d5edff0777411d524e | [
"Apache-2.0"
] | permissive | spolu/mathlib | bacf18c3d2a561d00ecdc9413187729dd1f705ed | 480c92cdfe1cf3c2d083abded87e82162e8814f4 | refs/heads/master | 1,671,684,094,325 | 1,600,736,045,000 | 1,600,736,045,000 | 297,564,749 | 1 | 0 | null | 1,600,758,368,000 | 1,600,758,367,000 | null | UTF-8 | Lean | false | false | 6,916 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Chris Hughes
-/
import data.fintype.card
import data.polynomial.ring_division
import group_theory.order_of_element
import algebra.geom_sum
/-!
# Integral domains
Ass... |
ed8d4e8da3172a787f40e7ebc8e5559c4af25f37 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/analysis/normed_space/euclidean_dist.lean | db9daacf6614b65d1291acb8ac8a80d0ed0516e0 | [
"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 | 4,630 | lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import analysis.normed_space.inner_product
/-!
# Euclidean distance on a finite dimensional space
When we define a smooth bump function on a normed space, it is u... |
dda83c93a5457b1579d26889cf0a6906026a028d | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/group_theory/sylow.lean | 1560211d6a95cc240e88e8a2f645c29c4dbf75ef | [
"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 | 36,163 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Thomas Browning
-/
import data.nat.factorization.basic
import data.set_like.fintype
import group_theory.group_action.conj_act
import group_theory.p_group
import group_theo... |
5cf3c66a707ec11dee321b4c029564eb6f2e8eb6 | e6b8240a90527fd55d42d0ec6649253d5d0bd414 | /src/tactic/core.lean | bddb850660dcdf4c8a320e9e6b19ed739c3c37bc | [
"Apache-2.0"
] | permissive | mattearnshaw/mathlib | ac90f9fb8168aa642223bea3ffd0286b0cfde44f | d8dc1445cf8a8c74f8df60b9f7a1f5cf10946666 | refs/heads/master | 1,606,308,351,137 | 1,576,594,130,000 | 1,576,594,130,000 | 228,666,195 | 0 | 0 | Apache-2.0 | 1,576,603,094,000 | 1,576,603,093,000 | null | UTF-8 | Lean | false | false | 56,741 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Simon Hudon, Scott Morrison, Keeley Hoek
-/
import data.dlist.basic category.basic meta.expr meta.rb_map data.bool
namespace expr
open tactic
attribute [derive has_re... |
6c7575459018a2960894af938f18873406ab9f9f | 8cb37a089cdb4af3af9d8bf1002b417e407a8e9e | /library/init/meta/smt/smt_tactic.lean | da840e209282f79331620e8eaa4f123f239a9c68 | [
"Apache-2.0"
] | permissive | kbuzzard/lean | ae3c3db4bb462d750dbf7419b28bafb3ec983ef7 | ed1788fd674bb8991acffc8fca585ec746711928 | refs/heads/master | 1,620,983,366,617 | 1,618,937,600,000 | 1,618,937,600,000 | 359,886,396 | 1 | 0 | Apache-2.0 | 1,618,936,987,000 | 1,618,936,987,000 | null | UTF-8 | Lean | false | false | 15,125 | 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.control
import init.meta.simp_tactic
import init.meta.smt.congruence_closure
import init.meta.smt.ematch
universe u
run_cmd mk_simp_at... |
fb60bb707c70974717a3e1ce05ea3b0089bb630d | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/syntaxPrio.lean | 08adc4dcc1d3b43e143d7709bcde65585f1f9620 | [
"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 | 246 | lean | syntax "foo! " term:max : term
macro_rules
| `(foo! $x) => `($x + 1)
#eval foo! 2
theorem ex1 : foo! 2 = 3 :=
rfl
syntax (priority := high) "foo!" term:max : term
macro_rules
| `(foo! $x) => `($x * 2)
theorem ex2 : foo! 2 = 4 :=
rfl
|
98712e8303d4b3395b7ac2398d60d9071bff5ca7 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/measure_theory/haar_measure.lean | 3db2eb7edaa1db7496c139efc20d8f2d4d93c796 | [
"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 | 30,108 | lean | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import measure_theory.content
import measure_theory.group
/-!
# Haar measure
In this file we prove the existence of Haar measure for a locally compact Hausdorff ... |
30eefbd89bfac94fbbfc7bf4aef577f8539182ab | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/1675.lean | 4101e234461598fdfc85bdd28b71fe3a255b81b2 | [
"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 | 1,246 | lean | def foo (a b : nat) : Prop :=
a = 0 ∧ b = 0
attribute [simp] foo nat.zero_add
example (p : nat → Prop) (a b : nat) : foo a b → p (a + b) → p 0 :=
begin
intros h₁ h₂,
simp * at *,
end
example (a b : nat) (p : nat → Prop) (h₁ : a = b + 0) (h₂ : b = 0) (h₃ : p a) : p 0 ∧ a = 0 :=
by simp * at *
constant q : Prop
a... |
46c98c451fffa006e8619e79e421fa1af76f8441 | a4673261e60b025e2c8c825dfa4ab9108246c32e | /tests/lean/Format.lean | e3367b06a2f32203a73b14caaa979befd15a3b24 | [
"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 | 615 | lean | #lang lean4
import Lean.Data.Format
open Lean
open Lean.Format
def eval (w : Nat) (f : Format) : IO Unit := do
IO.println $ f.prettyAux w
-- hard line breaks should re-evaluate flattening behavior within group
#eval eval 5 $ fill (text "a" ++ line ++ text "b\nlooooooooong" ++ line ++ text "c") ++ line ++ text "d"
--... |
5e77283f44f7d5cebed5c9735700214ce0015dde | 9dd3f3912f7321eb58ee9aa8f21778ad6221f87c | /tests/lean/struct_class.lean | 3b9d0ca6527ce814d3640dd5599834fd174f0da6 | [
"Apache-2.0"
] | permissive | bre7k30/lean | de893411bcfa7b3c5572e61b9e1c52951b310aa4 | 5a924699d076dab1bd5af23a8f910b433e598d7a | refs/heads/master | 1,610,900,145,817 | 1,488,006,845,000 | 1,488,006,845,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 196 | lean | prelude
import init.core
structure [class] point (A : Type*) (B : Type*) :=
mk :: (x : A) (y : B)
print classes
structure point2 (A : Type*) (B : Type*) :=
mk :: (x : A) (y : B)
print classes
|
ba49ad4be84574caea4e53dbd0f2e5a0066f9e96 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/tactic.lean | 2836094187eb95ca7a3f59f30b036b669f7dd507 | [
"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 | 4,185 | lean | /-
Copyright (c) 2020 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton
-/
import tactic.auto_cases
import tactic.tidy
import tactic.with_local_reducibility
import tactic.show_term
import topology.basic
/-!
# Tactics for topology
> THIS FILE IS S... |
7e29e93bbbd42afa0bb1ef14f0016a3c28c643a4 | 26bff4ed296b8373c92b6b025f5d60cdf02104b9 | /tests/lean/run/parity.lean | fb4bd43b50416a85a02a5c8755d1443e723dd604 | [
"Apache-2.0"
] | permissive | guiquanz/lean | b8a878ea24f237b84b0e6f6be2f300e8bf028229 | 242f8ba0486860e53e257c443e965a82ee342db3 | refs/heads/master | 1,526,680,092,098 | 1,427,492,833,000 | 1,427,493,281,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 638 | lean | import data.nat
open nat
inductive Parity : nat → Type :=
| even : ∀ n : nat, Parity (2 * n)
| odd : ∀ n : nat, Parity (2 * n + 1)
open Parity
definition parity : Π (n : nat), Parity n
| parity 0 := even 0
| parity (n+1) :=
begin
have aux : Parity n, from parity n,
cases aux with (k, k),
begin
... |
c0ffb0235d71bba0d5d3d12d4a41ff17dd62157b | e9078bde91465351e1b354b353c9f9d8b8a9c8c2 | /snippets.hlean | d1c6f0928e4dccc6e3b7cb0159b1a42990560aba | [
"Apache-2.0"
] | permissive | EgbertRijke/leansnippets | 09fb7a9813477471532fbdd50c99be8d8fe3e6c4 | 1d9a7059784c92c0281fcc7ce66ac7b3619c8661 | refs/heads/master | 1,610,743,957,626 | 1,442,532,603,000 | 1,442,532,603,000 | 41,563,379 | 0 | 0 | null | 1,440,787,514,000 | 1,440,787,514,000 | null | UTF-8 | Lean | false | false | 6,546 | hlean | import hit.pushout types.nat.basic types.pointed
/---------------------------------------------------------------------------------------------------
Show that type quotient preserves equivalence.
Can this be done without univalence?
---------------------------------------------------------------------------------... |
4477e503622daa763ad50483a8522fbd5a0bc1da | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/analysis/special_functions/pow.lean | 7e05493581f95397d1f9bea72c63fff6e0ca5b30 | [
"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 | 69,671 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Sébastien Gouëzel,
Rémy Degenne
-/
import analysis.special_functions.trigonometric
import analysis.calculus.extend_deriv
... |
4e6852fb591bfeb165a2d557d808092444ccd6a7 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/complex/is_R_or_C.lean | 96cd64257da9bcb75507246ee9390f9326f897d0 | [] | 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 | 29,469 | lean | /-
Copyright (c) 2020 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.real.sqrt
import Mathlib.field_theory.tower
import Mathlib.analysis.normed_space.fin... |
a6f5cecfd8c3caa31656f130a6fbb1a8f4891d53 | 1437b3495ef9020d5413178aa33c0a625f15f15f | /analysis/ennreal.lean | 96b29fbd82b99689102b38b1b14eb33859dfd8fc | [
"Apache-2.0"
] | permissive | jean002/mathlib | c66bbb2d9fdc9c03ae07f869acac7ddbfce67a30 | dc6c38a765799c99c4d9c8d5207d9e6c9e0e2cfd | refs/heads/master | 1,587,027,806,375 | 1,547,306,358,000 | 1,547,306,358,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 18,740 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
Extended non-negative reals
-/
import analysis.nnreal data.real.ennreal
noncomputable theory
open classical set lattice filter
local attribute [instance] prop_decidable
... |
69e05fd1efa1f329a85d2a3929bee27c6caf09af | e151e9053bfd6d71740066474fc500a087837323 | /src/hott/init/ua.lean | ad5fc6fb9763f693fb193f2d9e4d7d6076d5f3f1 | [
"Apache-2.0"
] | permissive | daniel-carranza/hott3 | 15bac2d90589dbb952ef15e74b2837722491963d | 913811e8a1371d3a5751d7d32ff9dec8aa6815d9 | refs/heads/master | 1,610,091,349,670 | 1,596,222,336,000 | 1,596,222,336,000 | 241,957,822 | 0 | 0 | Apache-2.0 | 1,582,222,839,000 | 1,582,222,838,000 | null | UTF-8 | Lean | false | false | 3,440 | lean | /-
Copyright (c) 2014 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer, Floris van Doorn
Ported from Coq HoTT
-/
import .equiv
universes u v w l
hott_theory
namespace hott
open eq equiv hott.is_equiv
axiom univalence (A B : Type u) ... |
2d6155ceb7736b258d3073876d98f91d013375ac | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Compiler/IR/CompilerM.lean | b104dbec08c2810eaee1a7922298118d47018520 | [
"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 | 4,972 | 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.Environment
import Lean.Compiler.IR.Basic
import Lean.Compiler.IR.Format
namespace Lean.IR
inductive LogEntry where
| step (cls : Name) (dec... |
a3faedcb9cd1e6f14d46a5525b5ab1f7cdbde96d | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /hott/init/hit.hlean | d96137396c4e45b0288f6b02af3dac167aa267e2 | [
"Apache-2.0"
] | permissive | soonhokong/lean-osx | 4a954262c780e404c1369d6c06516161d07fcb40 | 3670278342d2f4faa49d95b46d86642d7875b47c | refs/heads/master | 1,611,410,334,552 | 1,474,425,686,000 | 1,474,425,686,000 | 12,043,103 | 5 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 3,301 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
Declaration of the primitive hits in Lean
-/
prelude
import .trunc .pathover
open is_trunc eq
/-
We take two higher inductive types (hits) as primitive notion... |
a3a9b6203e8e43b36ce8ffc0cbacbf8f5c78cb19 | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/ring_theory/ideals.lean | 1f57a38cb78355ce64b8fe33c48d07fa86241a9c | [
"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 | 19,006 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Chris Hughes, Mario Carneiro
-/
import algebra.associated linear_algebra.basic order.zorn
universes u v
variables {α : Type u} {β : Type v} {a b : α}
open set function lattice
... |
13f0854fb5a8655628fa9df59e80b13e8869f5c0 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/data/nat/modeq.lean | 8edb26e35638d8b7d369b7b4b74ffbd1a886e629 | [
"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 | 20,914 | 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.gcd
import data.list.rotate
import tactic.abel
/-!
# Congruences modulo a natural number
This file defines the equivalence relation `a ≡ b [MOD n]` ... |
cb2d7f7aedc290f68fc5cbbb2c1fe11f899bc820 | 618003631150032a5676f229d13a079ac875ff77 | /src/data/zsqrtd/gaussian_int.lean | 13e3db28dededd2a23d8249e6f1d2a7cad25d3a1 | [
"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 | 12,654 | lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Chris Hughes
-/
import data.zsqrtd.basic
import data.complex.basic
import ring_theory.principal_ideal_domain
import number_theory.quadratic_reciprocity
/-!
# Gaussian integers
The Gaussi... |
9846dd0889db63aad6bb4753a8683484b40a64c1 | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/data/hash_map.lean | f0efb6f04039083922a24b194f78e08d2326e6ae | [
"Apache-2.0"
] | permissive | fpvandoorn/mathlib | b21ab4068db079cbb8590b58fda9cc4bc1f35df4 | b3433a51ea8bc07c4159c1073838fc0ee9b8f227 | refs/heads/master | 1,624,791,089,608 | 1,556,715,231,000 | 1,556,715,231,000 | 165,722,980 | 5 | 0 | Apache-2.0 | 1,552,657,455,000 | 1,547,494,646,000 | Lean | UTF-8 | Lean | false | false | 27,903 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Mario Carneiro
-/
import data.list.basic data.pnat data.array.lemmas
logic.basic algebra.group
data.list.defs data.nat.basic data.option.basic
data.b... |
6591f0a551c4ff2f2a3caaf6c12843de44756017 | 626e312b5c1cb2d88fca108f5933076012633192 | /src/measure_theory/measure/haar.lean | 10b96e20d8c55542668025ddd92a93c4b7ac3ea8 | [
"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 | 27,634 | lean | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import measure_theory.measure.content
import measure_theory.group.prod
/-!
# Haar measure
In this file we prove the existence of Haar measure for a locally comp... |
944b6b33ed9429a5394b399100e2a4a82b60ebd5 | 957a80ea22c5abb4f4670b250d55534d9db99108 | /tests/lean/run/reflected.lean | 1d929d4851401038a01ee800d2b21fc5e3e442e0 | [
"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 | 161 | lean | meta def eval_list (α : Type) [reflected α] (e : expr) : tactic (list α) :=
tactic.eval_expr (list α) e
run_cmd eval_list ℕ ↑`([1, 2]) >>= tactic.trace
|
f5cc1c6199fda19abda88b99a084ee1fd3fdfe51 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/data/ordmap/ordnode.lean | 74806eac4d7ff06babe4c123ae8ceecc14d4ac2c | [
"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 | 42,070 | 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.list.defs
import data.nat.psub
/-!
# Ordered sets
This file defines a data structure for ordered sets, supporting a
variety of useful operations includi... |
a7c41d8de18c2ffd5ce4c38bc423d515bb1dfe34 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Lean/Server/FileWorker/Utils.lean | 9e637a0482c9c8c1f4f9ead037d2a15747568cd8 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 2,484 | lean | /-
Copyright (c) 2020 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki, Marc Huisinga
-/
import Lean.Server.Utils
import Lean.Server.Snapshots
import Lean.Server.AsyncList
import Lean.Server.Rpc.Basic
namespace Lean.Server.FileWork... |
5caf90283060aa9d7d159dfb0f843f04c54bc034 | 7282d49021d38dacd06c4ce45a48d09627687fe0 | /tests/lean/simp10.lean | 482a6534e18c90114d592d35c999ac8c8eedab42 | [
"Apache-2.0"
] | permissive | steveluc/lean | 5a0b4431acefaf77f15b25bbb49294c2449923ad | 92ba4e8b2d040a799eda7deb8d2a7cdd3e69c496 | refs/heads/master | 1,611,332,256,930 | 1,391,013,244,000 | 1,391,013,244,000 | 16,361,079 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 289 | lean | variable f : Nat → Nat
variable g : Nat → Nat
variable a : Nat
axiom fid (x : Nat) : g x ≠ 0 → f x = x
add_rewrite fid
axiom gcnst (x : Nat) : g x = 1
add_rewrite gcnst
(*
local t = parse_lean("f a")
local r, pr = simplify(t)
print(r)
print(pr)
get_environment():type_check(pr)
*) |
7f5c12eeb58430f6a25471ea27594b1103a37513 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/category_theory/functor/basic.lean | 9385d84f3bf378ee28cffe0eb46b2b60f8d158cf | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 4,014 | 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
-/
import tactic.reassoc_axiom
import category_theory.category.basic
/-!
# Functors
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> https://g... |
bc4eb68add95b5f90545017e5f85bca739766368 | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /library/init/trace.lean | 9519ec16e69f3a7b453b44e654837fafd006832b | [
"Apache-2.0"
] | permissive | soonhokong/lean-osx | 4a954262c780e404c1369d6c06516161d07fcb40 | 3670278342d2f4faa49d95b46d86642d7875b47c | refs/heads/master | 1,611,410,334,552 | 1,474,425,686,000 | 1,474,425,686,000 | 12,043,103 | 5 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 373 | lean | -- Copyright (c) 2016 Microsoft Corporation. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Author: Leonardo de Moura
prelude
import init.string
/- This function has a native implementation that displays the given string in the regular output stream. -/
definition trace ... |
56e05953bba55516f7da37c930f551b8958accad | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/order/filter/ultrafilter_auto.lean | 97826138b576bfdf1dbe4f2864843e076ae31e83 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 12,392 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.order.filter.cofinite
import Mathlib.PostPort
universes u_... |
0628c86cbd4f00d067a3ac3a4469d170e986bb85 | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/measure_theory/l1_space.lean | 94f895c645e43d9a3a8745bc1f4a79e18049f78d | [
"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 | 33,281 | lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
-/
import measure_theory.lp_space
/-!
# Integrable functions and `L¹` space
In the first part of this file, the predicate `integrable` is defined and basic properties o... |
b4659c603b862d2a5a0afe3a56d0f36df2c367dc | 57fdc8de88f5ea3bfde4325e6ecd13f93a274ab5 | /logic/function.lean | 37185700850efa86a49cf34ad4a2398507b81dfa | [
"Apache-2.0"
] | permissive | louisanu/mathlib | 11f56f2d40dc792bc05ee2f78ea37d73e98ecbfe | 2bd5e2159d20a8f20d04fc4d382e65eea775ed39 | refs/heads/master | 1,617,706,993,439 | 1,523,163,654,000 | 1,523,163,654,000 | 124,519,997 | 0 | 0 | Apache-2.0 | 1,520,588,283,000 | 1,520,588,283,000 | null | UTF-8 | Lean | false | false | 7,318 | lean | /-
Copyright (c) 2016 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
Miscellaneous function constructions and lemmas.
-/
import logic.basic data.option
universes u v w
namespace function
section
variables {α : Sort u} ... |
2698ed488fb2541a0bde84f3ccc8414bcd8a45f5 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/category_theory/bicategory/locally_discrete.lean | f9c0b443bb47edcb5c31991e9c112959b747b2c7 | [
"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 | 2,839 | lean | /-
Copyright (c) 2022 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
import category_theory.discrete_category
import category_theory.bicategory.functor
import category_theory.bicategory.strict
/-!
# Locally discrete bicategories
A category... |
b1bb9538c12fb93c68888646241308ccba927a40 | 06be757c84c5c318d56b5d07f1dff4eb19b949d8 | /src/for_mathlib/adic_topology.lean | 57cc0ab78b1b9c75982de6ed13d6d3701cc0fee7 | [
"Apache-2.0"
] | permissive | mr-infty/perfectoid-spaces | ea3e5d161072f6de646b660cc55217838d3ceded | 1a49b3897ec3c7b871d8c970926c00f727a4e2a6 | refs/heads/master | 1,587,252,317,856 | 1,547,326,614,000 | 1,547,326,614,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,829 | lean | /-
This file defines the I-adic topology on a commutative ring R with ideal I.
The ring is wrapped in `adic_ring I := R`, which then receive all relevant type classes.
The end-product is `instance : topological_ring (adic_ring I)`.
-/
import tactic.ring
import data.pnat
import ring_theory.ideal_operations
import anal... |
06a87c65b4705c7b683e51df2727d3ac48d9d8f9 | 359199d7253811b032ab92108191da7336eba86e | /src/mywork/jacqueline-chao_homeworks.lean | 088e0569b6a318b479a871029f1248d20d34d162 | [] | no_license | arte-et-marte/my_cs2120f21 | 0bc6215cb5018a3b7c90d9d399a173233f587064 | 91609c3609ad81fda895bee8b97cc76813241e17 | refs/heads/main | 1,693,298,928,348 | 1,634,931,202,000 | 1,634,931,202,000 | 399,946,705 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 518 | lean | /-
#1
By the equality theorem of symmetry, we are able to rewrite w = z to z = w. The equality theorem of symmetry is proven
by the axiom of substitutability of equals and the axiom of reflexivity.
-/
/-
#2
-/
def prop_1 : Prop :=
∀ (T : Type) (x y z w : T) (p1 : x = y) (p2 : y = z) (p3 : w = z), z = w
/-
#4
Assume... |
af40c05ab2cee612e0e1fef15f35e48d5b3b9f0b | 5d166a16ae129621cb54ca9dde86c275d7d2b483 | /tests/lean/elab12.lean | 39b7bd1087c612d56c33fc5386ca5a6f876d9661 | [
"Apache-2.0"
] | permissive | jcarlson23/lean | b00098763291397e0ac76b37a2dd96bc013bd247 | 8de88701247f54d325edd46c0eed57aeacb64baf | refs/heads/master | 1,611,571,813,719 | 1,497,020,963,000 | 1,497,021,515,000 | 93,882,536 | 1 | 0 | null | 1,497,029,896,000 | 1,497,029,896,000 | null | UTF-8 | Lean | false | false | 393 | lean | #check (take a : nat, have H : 0, from rfl a,
(H a a) : ∀ a : nat, a = a)
#check (take a : nat, have H : a = a, from rfl a,
(H a a) : ∀ a : nat, a = a)
#check (take a : nat, have H : a = a, from a + 0,
(H a a) : ∀ a : nat, a = a)
#check (take a : nat, have H : a = a, from rfl,
(H a) : ∀ a : nat, a = a)
#check (... |
4c11f0d7f4c5f5ee91de87f9b95067b7bdae90c9 | 3dc4623269159d02a444fe898d33e8c7e7e9461b | /.github/workflows/project_1_a_decrire/foncteur/Untitled-1.lean | 36894f5b0797a1a1fa42f062f0e34a2966dd3a92 | [] | 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 | 7,056 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.opposites
import category_theory.hom_functor
/-!
# The Yoneda embedding
The Yoneda embedding as a functor `yoneda : C ⥤ (Cᵒᵖ ⥤ Type v₁)`,
alo... |
a79d7e1ef802ea8cd0bca5a4bdb350480e127094 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/category_theory/linear/yoneda.lean | 0c9f6a68d62d3d747075b8634010cb1a12ef3696 | [
"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 | 2,792 | 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.category.Module.basic
import category_theory.linear
import category_theory.preadditive.additive_functor
import category_theory.preadditive.yoneda
/-!
... |
177187b0e7867e8621737e7c97aa7cbe207b48a6 | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/measure_theory/borel_space.lean | 8af37ddbc36f18f0ab53d25cf13a1c7fb1976bd5 | [
"Apache-2.0"
] | permissive | hamdysalah1/mathlib | b915f86b2503feeae268de369f1b16932321f097 | 95454452f6b3569bf967d35aab8d852b1ddf8017 | refs/heads/master | 1,677,154,116,545 | 1,611,797,994,000 | 1,611,797,994,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 64,371 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov
-/
import measure_theory.measure_space
import measure_theory.ae_measurable_sequence
import analysis.complex.basic
import analysis.normed_space.finite_di... |
9077de50f658aeb406052169e88be870e2b731c6 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/algebra/group/to_additive.lean | 526c049f14a110aff6ec59c3ec85e5712b882320 | [
"Apache-2.0"
] | permissive | hikari0108/mathlib | b7ea2b7350497ab1a0b87a09d093ecc025a50dfa | a9e7d333b0cfd45f13a20f7b96b7d52e19fa2901 | refs/heads/master | 1,690,483,608,260 | 1,631,541,580,000 | 1,631,541,580,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 21,431 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Yury Kudryashov, Floris van Doorn
-/
import tactic.transform_decl
import tactic.algebra
/-!
# Transport multiplicative to additive
This file defines an attribute `to_... |
4b328c9b9c389ce8da834441f7c157cad5d8f86f | 626e312b5c1cb2d88fca108f5933076012633192 | /src/measure_theory/measure/measure_space_def.lean | 32770ee001d8cb6738a29d49768291f3c186e81d | [
"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 | 18,433 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import measure_theory.measure.outer_measure
import order.filter.countable_Inter
import data.set.accumulate
/-!
# Measure spaces
This file defines me... |
696bfe5cc6b63e0f3061cd71bd0152cfce19933d | 01ae0d022f2e2fefdaaa898938c1ac1fbce3b3ab | /categories/currying/currying_3.lean | d78e88f0840a3bedfb21f3abb0f9cba54881be50 | [] | no_license | PatrickMassot/lean-category-theory | 0f56a83464396a253c28a42dece16c93baf8ad74 | ef239978e91f2e1c3b8e88b6e9c64c155dc56c99 | refs/heads/master | 1,629,739,187,316 | 1,512,422,659,000 | 1,512,422,659,000 | 113,098,786 | 0 | 0 | null | 1,512,424,022,000 | 1,512,424,022,000 | null | UTF-8 | Lean | false | false | 1,181 | lean | -- Copyright (c) 2017 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Scott Morrison
-- import .currying_2
-- open categories
-- open categories.isomorphism
-- open categories.functor
-- open categories.equivalence
-- open categories.functor_cate... |
fc72d07f61fc4a5f4211677f1da16103da8a9705 | 3f1a1d97c03bb24b55a1b9969bb4b3c619491d5a | /library/data/stream.lean | 102a6d493b50b408e274453e28b950a0c3c601ad | [
"Apache-2.0"
] | permissive | praveenmunagapati/lean | 00c3b4496cef8e758396005013b9776bb82c4f56 | fc760f57d20e0a486d14bc8a08d89147b60f530c | refs/heads/master | 1,630,692,342,183 | 1,515,626,222,000 | 1,515,626,222,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 21,672 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
open nat function option
universes u v w
def stream (α : Type u) := nat → α
namespace stream
variables {α : Type u} {β : Type v} {δ : Type w}
def cons (a ... |
74f5c6e20882ff17ffaac8f00b7e588014dfda3b | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/category_theory/functor/currying.lean | a0c3fa5094f044f40c9cbf4ffc55ce36036d4e88 | [
"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 | 4,128 | lean | /-
Copyright (c) 2017 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.products.bifunctor
/-!
# Curry and uncurry, as functors.
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corr... |
64aaa3e37fe53980dcac670dc421f13294c2685d | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/finsupp/fin.lean | eafd0136429cb7e2b5658d72b6ce96160da75e0a | [
"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 | 2,507 | lean | /-
Copyright (c) 2021 Ivan Sadofschi Costa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ivan Sadofschi Costa
-/
import data.finsupp.defs
/-!
# `cons` and `tail` for maps `fin n →₀ M`
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a c... |
5f96e178a02d41fa1e97e60ee524db72579c8506 | 4b846d8dabdc64e7ea03552bad8f7fa74763fc67 | /library/init/category/monad.lean | 63403fc6cbdd764ded228e47177c024173e1b0ee | [
"Apache-2.0"
] | permissive | pacchiano/lean | 9324b33f3ac3b5c5647285160f9f6ea8d0d767dc | fdadada3a970377a6df8afcd629a6f2eab6e84e8 | refs/heads/master | 1,611,357,380,399 | 1,489,870,101,000 | 1,489,870,101,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,188 | lean | /-
Copyright (c) Luke Nelson and Jared Roesch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Luke Nelson, Jared Roesch, Sebastian Ullrich
-/
prelude
import init.category.applicative
universes u v
class has_bind (m : Type u → Type v) :=
(bind : Π {α... |
293546f9705d61b9cd5be3fe0daafb80cf822ec7 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /src/Lean/Meta/Constructions.lean | 5c99f73bcb1588f656166a765b3d5409fd273ffa | [
"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 | 5,793 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.AuxRecursor
import Lean.Meta.AppBuilder
namespace Lean
@[extern "lean_mk_cases_on"] opaque mkCasesOnImp (env : Environment) (declName : @& Nam... |
73a78171ab3e60dc3ea88be2472bb3aaccdf5a37 | 66a6486e19b71391cc438afee5f081a4257564ec | /algebra/ses.hlean | 89f0eea69866af90e1404052c40f6bfef12c0251 | [
"Apache-2.0"
] | permissive | spiceghello/Spectral | c8ccd1e32d4b6a9132ccee20fcba44b477cd0331 | 20023aa3de27c22ab9f9b4a177f5a1efdec2b19f | refs/heads/master | 1,611,263,374,078 | 1,523,349,717,000 | 1,523,349,717,000 | 92,312,239 | 0 | 0 | null | 1,495,642,470,000 | 1,495,642,470,000 | null | UTF-8 | Lean | false | false | 10,434 | hlean | /-
Copyright (c) 2017 Egbert Rijke. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Egbert Rijke
Basic facts about short exact sequences.
At the moment, it only covers short exact sequences of abelian groups, but this should be extended to short exact sequences in any... |
4cf2af1a3146f5ccabb10a2250c2a4e9a53eac52 | e030b0259b777fedcdf73dd966f3f1556d392178 | /library/init/cc_lemmas.lean | 71cb72532b367c0399e55e38a9a5a037edd18ff8 | [
"Apache-2.0"
] | permissive | fgdorais/lean | 17b46a095b70b21fa0790ce74876658dc5faca06 | c3b7c54d7cca7aaa25328f0a5660b6b75fe26055 | refs/heads/master | 1,611,523,590,686 | 1,484,412,902,000 | 1,484,412,902,000 | 38,489,734 | 0 | 0 | null | 1,435,923,380,000 | 1,435,923,379,000 | null | UTF-8 | Lean | false | false | 4,684 | lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.propext init.classical
/- Lemmas use by the congruence closure module -/
lemma iff_eq_of_eq_true_left {a b : Prop} (h : a = true) : (a... |
79bbb3edfe4af7a545178aec2b2f9102a5af25bb | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/topology/compact_open.lean | 78fd62cddd93dc772be64a3cbd145a03f1c183cd | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 19,326 | lean | /-
Copyright (c) 2018 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton
-/
import tactic.tidy
import topology.continuous_function.basic
import topology.homeomorph
import topology.subset_properties
import topology.maps
/-!
# The compact-open topol... |
383a72a09047be074eb3935e1edf1e7971498637 | e00ea76a720126cf9f6d732ad6216b5b824d20a7 | /src/topology/separation.lean | 1ade7ed0eaa8d457efbae0d2ab215338b1911464 | [
"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 | 16,724 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
Separation properties of topological spaces.
-/
import topology.subset_properties
open set filter
open_locale topological_space
local attribute [insta... |
d738eeabb6b68b3d5eb4e615cf5c68cb8c34a727 | 95dcf8dea2baf2b4b0a60d438f27c35ae3dd3990 | /src/data/fin.lean | 0612c9d2e8a5680c4665b8dd4aeff430f66b101e | [
"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 | 7,029 | lean | /-
Copyright (c) 2017 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Robert Y. Lewis
More about finite numbers.
-/
import data.nat.basic
open fin nat
/-- `fin 0` is empty -/
def fin_zero_elim {C : Sort*} : fin 0 → C :=
λ x, false.elim $ nat.not_lt_ze... |
b11b01463ee4658204c55062ee1141d3157cd012 | 70f065bb7bcce71301a0b7f8542ed0157358a740 | /lean/mobiles.lean | e62ad9e45ec4e605dc58427a9a6ce36a636e105c | [
"Apache-2.0",
"BSD-2-Clause",
"LicenseRef-scancode-unknown-license-reference"
] | permissive | lambdageek/coda | 0ff93e32d477be834e997955f04787d116bc0b0e | 6cca584fca7af1a3d20df2eacf26ee3e7e34d0c7 | refs/heads/master | 1,586,044,462,939 | 1,540,629,980,000 | 1,540,629,980,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,460 | lean | import .invertible
open function
-- mostly just experimenting with more complicated symmetries, etc.
section mobiles
inductive rose : Type
| leaf : rose
| node : (ℕ -> rose) -> rose
-- mobile equivalence
inductive mobile : rose -> rose -> Prop
| leaf : mobile rose.leaf rose.leaf
| node : Π {f g : ℕ -> ... |
4270ce33540289b87aefc1ecfa698ceeecbfb0c3 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/topology/uniform_space/cauchy.lean | b189faf156d877287c39720dbaa2d10b35cd2e43 | [
"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 | 28,912 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import topology.uniform_space.basic
import topology.bases
import data.set.intervals
/-!
# Theory of Cauchy filters in uniform spaces. Complete uniform... |
530122b1afb7f25b0e5d293a371e2bd5a8325064 | ee8cdbabf07f77e7be63a449b8483ce308d37218 | /lean/src/test/mathd-algebra-17.lean | 7bc14accc1859f366af937552c8013121fe9d0d6 | [
"Apache-2.0",
"MIT"
] | permissive | zeta1999/miniF2F | 6d66c75d1c18152e224d07d5eed57624f731d4b7 | c1ba9629559c5273c92ec226894baa0c1ce27861 | refs/heads/main | 1,681,897,460,642 | 1,620,646,361,000 | 1,620,646,361,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 331 | lean | /-
Copyright (c) 2021 OpenAI. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kunhao Zheng
-/
import data.real.sqrt
import data.real.basic
example (a : ℝ) (h₀ : real.sqrt ( 4 + real.sqrt (16 + 16 * a) ) + real.sqrt ( 1 + real.sqrt (1 + a) ) = 6 ) : a = 8 :=
begin
sor... |
3d9f3942b3cda6e1dded4b1e8d0eda73d63418dc | a721fe7446524f18ba361625fc01033d9c8b7a78 | /elaborate/mul_comm.stripped.lean | d83f2b0717540e1cec6e06432955e5dd77a09360 | [] | 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 | 16,749 | lean | λ (m n : mynat), mynat.rec (eq.rec true.intro (eq.rec (eq.refl (zero = mul zero m)) (eq.rec (eq.rec (eq.refl (zero = mul zero m)) (eq.rec (eq.refl (mul zero m)) (mynat.rec (eq.refl zero) (λ (m_n : mynat) (m_ih : mul zero m_n = zero), eq.rec m_ih (eq.rec (eq.refl (add zero (mul zero m_n) = zero)) (eq.rec (eq.refl (add z... |
fff268c3c94c9f1d3b7bb3ce13cf416cf94646f4 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/algebra/module/graded_module.lean | 085b9dbb85c0d191ff4e9ada1ceda22b1936c3f7 | [
"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 | 9,041 | lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
import ring_theory.graded_algebra.basic
import algebra.graded_mul_action
import algebra.direct_sum.decomposition
import algebra.module.big_operators
/-!
# Graded Module... |
73a979e501c8acc0f96589b92588e2a2905dce9f | 22e97a5d648fc451e25a06c668dc03ac7ed7bc25 | /src/analysis/normed_space/bounded_linear_maps.lean | 0d513937ac5a528b82ca66f782b74b3ef34ad5f1 | [
"Apache-2.0"
] | permissive | keeferrowan/mathlib | f2818da875dbc7780830d09bd4c526b0764a4e50 | aad2dfc40e8e6a7e258287a7c1580318e865817e | refs/heads/master | 1,661,736,426,952 | 1,590,438,032,000 | 1,590,438,032,000 | 266,892,663 | 0 | 0 | Apache-2.0 | 1,590,445,835,000 | 1,590,445,835,000 | null | UTF-8 | Lean | false | false | 19,370 | 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
Continuous linear functions -- functions between normed vector spaces which are bounded and linear.
-/
import analysis.normed_space.multilinear
noncomp... |
f9b4e6f83626f613fdd893a832466ce2887da722 | bdb33f8b7ea65f7705fc342a178508e2722eb851 | /data/real/basic.lean | 24bf2a8bf48d29b00aebefcdc0bf6ef93fabd091 | [
"Apache-2.0"
] | permissive | rwbarton/mathlib | 939ae09bf8d6eb1331fc2f7e067d39567e10e33d | c13c5ea701bb1eec057e0a242d9f480a079105e9 | refs/heads/master | 1,584,015,335,862 | 1,524,142,167,000 | 1,524,142,167,000 | 130,614,171 | 0 | 0 | Apache-2.0 | 1,548,902,667,000 | 1,524,437,371,000 | Lean | UTF-8 | Lean | false | false | 24,425 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
The (classical) real numbers ℝ. This is a direct construction
from Cauchy sequences.
-/
import order.conditionally_complete_lattice data.real.cau_seq algebra.big_operat... |
f85d11479e5fe7dbcd380e7f653f44d6a4815f41 | 9b9a16fa2cb737daee6b2785474678b6fa91d6d4 | /src/data/equiv/denumerable.lean | 43baa9b6b217cd292aaf190fa69aa9933c07cdaf | [
"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 | 3,779 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
Denumerable (countably infinite) types, as a typeclass extending
encodable. This is used to provide explicit encode/decode functions
from nat, where the functions are kn... |
22ba9c4636ba67431f0fdb1cca0a5c8d44947c3c | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/associated.lean | 15c01059922c3d945959f7bde0e1b5fa18e16540 | [] | 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 | 22,111 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.multiset.basic
import Mathlib.algebra.divisibility
import Mathlib.Post... |
b28f9cde9ffdd9be8eea8a5588ab6556eaddd60e | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/652.lean | 35c79846d98d0742a1ea26b87080abf4ab1d45b0 | [
"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 | 363 | lean | section
parameters {b c : bool}
definition R : Prop := (b = c)
parameters (b c)
definition R2 := R
parameter (c)
parameter (b)
definition R3 := R
parameter {c}
parameter (b)
definition R4 := R
parameters {c b}
definition R5 := R
parameters (c)
definition R6 := R
end
#check @R
#check @R2
#... |
07197896a75e27a6688e1c59fb7da0c0ac7da75c | 43390109ab88557e6090f3245c47479c123ee500 | /src/category_theory/Problems/1_2.lean | fcec35f823c127bb9367de53ead61b6456748ccc | [
"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 | 2,320 | lean | import categories.CatGroups
import categories.tactics
import categories.functor
import categories.natural_transformation
open categories
open categories.isomorphism
open categories.functor
open categories.CatGroup
open categories.natural_transformation
--delaration of universes and variables
universes u v u₀ v₀ u₁ v₁ ... |
cf08a1717cf52d55289377e19b58c34555639330 | c45b34bfd44d8607a2e8762c926e3cfaa7436201 | /uexp/src/uexp/cosette_lemmas.lean | 03c4642e841c5d057813c0e654789d1e7d13c707 | [
"BSD-2-Clause"
] | permissive | Shamrock-Frost/Cosette | b477c442c07e45082348a145f19ebb35a7f29392 | 24cbc4adebf627f13f5eac878f04ffa20d1209af | refs/heads/master | 1,619,721,304,969 | 1,526,082,841,000 | 1,526,082,841,000 | 121,695,605 | 1 | 0 | null | 1,518,737,210,000 | 1,518,737,210,000 | null | UTF-8 | Lean | false | false | 4,128 | lean | import .u_semiring
import .extra_constants
/- lemmas used in congruence of u-semirings -/
section
variables {s: Schema} {t₁ t₂ t₃ t₄: Tuple s} {a b c d e f: usr} {R: Tuple s → usr}
private meta def simp_solve :=
`[intros h, rewrite ← h, try {simp <|> ac_refl}]
lemma ueq_symm: a = b → b = a :=
begin
intros, r... |
725d9fb7abefc44b392e5161ba62de34a70bb3f9 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebraic_geometry/projective_spectrum/structure_sheaf.lean | 9003dcd0fa7d16c93077e0502ada30c8f629a6c2 | [
"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 | 17,899 | lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
import algebraic_geometry.projective_spectrum.topology
import topology.sheaves.local_predicate
import ring_theory.graded_algebra.homogeneous_localization
import algebraic... |
e36f6d69e8d199b17a24bbdeae548864c3a328bd | c777c32c8e484e195053731103c5e52af26a25d1 | /src/analysis/calculus/lagrange_multipliers.lean | 98273ea1853e9b0252d638132e070f20f2709514 | [
"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 | 8,101 | lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import analysis.calculus.inverse
import linear_algebra.dual
/-!
# Lagrange multipliers
In this file we formalize the
[Lagrange multipliers](https://en.wikipedia.o... |
757a182d49e28df249c7d20996f17e578b859e61 | 77cc0c0aa84a25574cde49a43e1ea911e4992d9b | /Lean Proof DES Sequence.lean | 7367b7a333b977de873e195b76e48ce885846dd0 | [] | no_license | GGFSilva/LeanCryptographyProof | 41ed2cb4d67949f2e2dc6eba63d82c786aa179d3 | bea98d6201546f1e38a08fd3eb7be494e589b006 | refs/heads/master | 1,621,411,996,962 | 1,585,665,794,000 | 1,585,665,794,000 | 251,599,965 | 2 | 2 | null | null | null | null | UTF-8 | Lean | false | false | 1,596 | lean | variable L (n : nat) : data
variable R (n : nat) : data
variable Ld (n : nat) : data
variable Rd (n : nat) : data
premise BaseLeft : Ld 0 = R 16
premise BaseRight : Rd 0 = L 16
premise StepLeft : ∀ i : nat, Ld i = R (16 - i) → Ld (i + 1) = R (16 - (i + 1))
premise StepRight : ∀ i : nat, Rd i = L (16 - i) →... |
394b6d8659e58ed11baced584ffb63df1b743903 | de91c42b87530c3bdcc2b138ef1a3c3d9bee0d41 | /old/override/axisOrientationOverride.lean | ad429d26eb87386c0a456f2f6aedf0ee52b2bc73 | [] | no_license | kevinsullivan/lang | d3e526ba363dc1ddf5ff1c2f36607d7f891806a7 | e9d869bff94fb13ad9262222a6f3c4aafba82d5e | refs/heads/master | 1,687,840,064,795 | 1,628,047,969,000 | 1,628,047,969,000 | 282,210,749 | 0 | 1 | null | 1,608,153,830,000 | 1,595,592,637,000 | Lean | UTF-8 | Lean | false | false | 380 | lean | import ..imperative_DSL.environment
import ..eval.axisOrientationEval
open lang.axisOrientation
def assignAxisOrientation : environment.env → orientationVar → orientationExpr → environment.env
| i v e :=
{
ax := ⟨(λ r,
if (orientationVarEq v r)
then (axisOrientationEval e i... |
715066591c63c3b0f190f204e732ca42d544d510 | 947b78d97130d56365ae2ec264df196ce769371a | /tests/lean/run/float_cases_bug.lean | 4a3cf3476cbd2e6df1c6d860adced45e092bfdd6 | [
"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 | 84 | lean | new_frontend
def foo (xs : List Nat) :=
xs.span (fun n => oldCoe (decide (n = 1)))
|
e7e00ec5bcbbb7db3cf1e4c668ccddc1fdaed724 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/data/nat/pairing.lean | 587cec20814766aeeb7111f0317712584c3aaf14 | [
"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 | 3,600 | 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, Mario Carneiro
Elegant pairing function.
-/
import data.nat.sqrt
open prod decidable
namespace nat
/-- Pairing function for the natural numbers. -/
def mkp... |
52b0a1da8f7941b4797f9d85316c8492c6e830e6 | ad0c7d243dc1bd563419e2767ed42fb323d7beea | /group_theory/submonoid.lean | 4dcb9c0cfb5564244a74a566d0fccde0686b1d8f | [
"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 | 5,957 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro
-/
import algebra.group_power
import tactic.subtype_instance
variables {α : Type*} [monoid α] {s : set α}
variables {β : Type... |
c81d5bafe60084866a1c1fbc8db47f7cb3f36264 | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/category_theory/subobject/factor_thru.lean | 5af424e7fb513a485323e5389bec8497d9ea6adb | [
"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 | 9,101 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Scott Morrison
-/
import category_theory.subobject.basic
/-!
# Factoring through subobjects
The predicate `h : P.factors f`, for `P : subobject Y` and `f : X ⟶ Y`
asser... |
1e56aa7502cbaa75e7d3044a00dbb49b8a4c75c5 | 4fa161becb8ce7378a709f5992a594764699e268 | /src/tactic/ring_exp.lean | be5e885bad625dd6339bafd27aebfc85f4be2a3f | [
"Apache-2.0"
] | permissive | laughinggas/mathlib | e4aa4565ae34e46e834434284cb26bd9d67bc373 | 86dcd5cda7a5017c8b3c8876c89a510a19d49aad | refs/heads/master | 1,669,496,232,688 | 1,592,831,995,000 | 1,592,831,995,000 | 274,155,979 | 0 | 0 | Apache-2.0 | 1,592,835,190,000 | 1,592,835,189,000 | null | UTF-8 | Lean | false | false | 56,232 | lean | /-
Copyright (c) 2019 Tim Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Tim Baanen.
Solve equations in commutative (semi)rings with exponents.
-/
import tactic.norm_num
/-!
# `ring_exp` tactic
A tactic for solving equations in commutative (semi)rings,
where ... |
346b85c4fb9f9fb1c5506722f21af3d35ce46f90 | 627a10913304584f8f0a507f57ba7d8ce98067fd | /src/constructible.lean | 5dc073c4c754d06997d594744d7bb88ede7a4dac | [] | no_license | shingtaklam1324/constructible-nums | 0762314244b3aff1c8fef1d398e9f939d86f1796 | 3d0d382643c757c64f2bbcb8416fa3acabb4d68c | refs/heads/master | 1,680,408,834,461 | 1,617,676,007,000 | 1,617,676,007,000 | 355,247,914 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,689 | lean | import data.real.sqrt
inductive constructible : ℝ → Prop
| one : constructible 1
| add : ∀ ⦃x y⦄, constructible x → constructible y → constructible (x + y)
| neg : ∀ ⦃x⦄, constructible x → constructible (-x)
| mul : ∀ ⦃x y⦄, constructible x → constructible y → constructible (x * y)
| inv : ∀ ⦃x⦄, constructible x → con... |
228a24e50e6eda571df43fffb03a5a88d00dabeb | 43390109ab88557e6090f3245c47479c123ee500 | /src/chris_hughes_various/fermat_sum_two_squares.lean | 66b9681bd5aa4bc07d18d0294aee84f14b158538 | [
"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 | 14,733 | lean | import data.int.basic data.fintype data.nat.modeq data.set.finite data.nat.prime tactic.ring
universe u
local attribute [instance, priority 0] classical.prop_decidable
local attribute [instance] set_fintype
open fintype finset
noncomputable lemma fintype_of_injective {α β : Type*} {f : α → β} [fintype β]
(hf : fu... |
a9115c54bda012a4bbba0561fd5a531aa6d786e4 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/measure_theory/integral/torus_integral.lean | 57bd43db674a7627dae7357ad61830a196211e16 | [
"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 | 12,449 | lean | /-
Copyright (c) 2022 Cuma Kökmen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Cuma Kökmen, Yury Kudryashov
-/
import measure_theory.constructions.prod.integral
import measure_theory.integral.circle_integral
/-!
# Integral over a torus in `ℂⁿ`
> THIS FILE IS SYNCH... |
ad09055c7eb5e0bafa55e97b752ac21938b89cf3 | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/data/real/golden_ratio.lean | e33854b7364c80ccdb438718ecc13e4cbacf3993 | [
"Apache-2.0"
] | permissive | hamdysalah1/mathlib | b915f86b2503feeae268de369f1b16932321f097 | 95454452f6b3569bf967d35aab8d852b1ddf8017 | refs/heads/master | 1,677,154,116,545 | 1,611,797,994,000 | 1,611,797,994,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,590 | lean | /-
Copyright (c) 2020 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker, Alexey Soloyev, Junyan Xu
-/
import data.real.irrational
import data.nat.fib
import data.matrix.notation
import tactic.ring_exp
import algebra.linear_recurrence
/-... |
8e86383f514601c370e0ff38b6dbed11125ec7d6 | d1774029fbd8268ede99d7d27f259681cf192af7 | /src/fstar/prims.lean | d1bc696d19c6e3b4d1d9136ac5376cabe2795e4e | [] | no_license | jroesch/fstar-prims | a37e4d8bb512b11f9960133a134288a0c8f5b280 | fe164fd4e9d84a5a4a411c26764e905e87292021 | refs/heads/master | 1,611,366,029,928 | 1,496,184,935,000 | 1,496,184,935,000 | 92,883,062 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,176 | lean | namespace fstar
def pure_pre := Prop
def pure_post (A : Type) := A -> Prop
-- For the VC generation
constant FStar.Tactics.Effect.Tac (A : Type) : Prop
def Prims.unit := unit
constant lean : unit -> FStar.Tactics.Effect.Tac unit
@[reducible] def pos := { x : nat // 0 < x }
@[reducible] def pos.mk (n : nat) (prf : 0 ... |
b6ac3cc2ff0837790237d0e004915e6ca95c06cf | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/bench/rbmap3.lean | 57d15b2007107b4427419d687c10f2303825f211 | [
"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 | 8,992 | lean | prelude
import init.core init.system.io init.data.ordering
universe u v w
inductive Rbcolor
| red | black
inductive Rbnode (α : Type u) (β : α → Type v)
| leaf {} : Rbnode
| Node (c : Rbcolor) (lchild : Rbnode) (key : α) (val : β key) (rchild :... |
3d19e3d50ab6f1dd3a0a65f9ef1b8cb0540b0d71 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/category/CommRing/adjunctions_auto.lean | 52bb8f65e2b4615ba0bbe94a7b1cceba484e821c | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,427 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Johannes Hölzl
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.category.CommRing.basic
import Mathlib.data.mv_polynomial.default
i... |
ef0297f17bba48a32064c250bc01e0fcb077438f | 957a80ea22c5abb4f4670b250d55534d9db99108 | /library/init/data/default.lean | d6b0d3eb851293eef4239dab0c5570ae8485ddea | [
"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 | 396 | 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.data.basic init.data.sigma init.data.nat init.data.char init.data.string
import init.data.list init.data.sum init.data.subtype init.data... |
211aa7e9183b415015fe68047a4a152a4f174137 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/category_theory/functor/epi_mono.lean | 363bd3e4d8602c4c2fdce7ef1e3c627c54645535 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 11,733 | lean | /-
Copyright (c) 2022 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import category_theory.epi_mono
import category_theory.limits.shapes.strong_epi
import category_theory.lifting_properties.adjunction
/-!
# Preservation and reflection ... |
0088a446a62ad8044a481fe67004464378a958de | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/algebra/field_power_auto.lean | 4542bef4f710f954c3581440f9d7c8370a4cdd9e | [] | 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 | 4,542 | 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 Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.group_with_zero.power
import Mathlib.tactic.l... |
faa65dc63cc168e911d8fd76a7904545e4e63212 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/calculus/deriv/basic.lean | f80d23c7f919e9d6411e86b34a770648c9cfc666 | [
"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 | 25,654 | 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 analysis.calculus.fderiv.basic
/-!
# One-dimensional derivatives
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file requ... |
27f2fc1d4c86e34a28ce1fdb68ee3d02b956bbc2 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/ring_theory/polynomial_algebra.lean | e0af32d136d9e48fcd3c3658e587c9c966152c1b | [
"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 | 10,872 | 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 ring_theory.matrix_algebra
import data.polynomial.algebra_map
import data.matrix.basis
import data.matrix.dmatrix
/-!
# Algebra isomorphism between matrices o... |
6b2c8141e1815ebaa420dcb2de5073e27698ea8b | 97f752b44fd85ec3f635078a2dd125ddae7a82b6 | /hott/algebra/category/functor/equivalence.hlean | ecfb179e3c565667cc5890869091d2a08398e838 | [
"Apache-2.0"
] | permissive | tectronics/lean | ab977ba6be0fcd46047ddbb3c8e16e7c26710701 | f38af35e0616f89c6e9d7e3eb1d48e47ee666efe | refs/heads/master | 1,532,358,526,384 | 1,456,276,623,000 | 1,456,276,623,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 16,004 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
Functors which are equivalences or isomorphisms
-/
import .adjoint
open eq functor iso prod nat_trans is_equiv equiv is_trunc
namespace category
variables {C D... |
29488496d4d098d2c1d09d6acc3b291ccb6924e3 | 6b10c15e653d49d146378acda9f3692e9b5b1950 | /examples/basic_skills/unnamed_564.lean | 503a3af1bb6fc0fc7dbae54c2ac3fd1951031e19 | [] | no_license | gebner/mathematics_in_lean | 3cf7f18767208ea6c3307ec3a67c7ac266d8514d | 6d1462bba46d66a9b948fc1aef2714fd265cde0b | refs/heads/master | 1,655,301,945,565 | 1,588,697,505,000 | 1,588,697,505,000 | 261,523,603 | 0 | 0 | null | 1,588,695,611,000 | 1,588,695,610,000 | null | UTF-8 | Lean | false | false | 251 | lean | namespace my_ring
variables {R : Type*} [ring R]
theorem add_zero (a : R) : a + 0 = a :=
by rw [add_comm, zero_add]
theorem add_right_neg (a : R) : a + -a = 0 :=
by rw [add_comm, add_left_neg]
end my_ring
#check @my_ring.add_zero
#check @add_zero |
43cfcf2ea06e87a39284752068eb2ec76616f8e9 | 947b78d97130d56365ae2ec264df196ce769371a | /src/Init/Data/Float.lean | 77bb3294d3e11d0a03a8eb69cdf8657b405f2680 | [
"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 | 4,160 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import Init.Core
import Init.Data.ToString
structure FloatSpec :=
(float : Type)
(val : float)
(lt : float → float → Prop)
(le : float → fl... |
05d792787609b934f400ea2cdf754261f4226cad | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /src/Lean/Compiler/CSE.lean | f8bdfd8df2dbba56abc7f42ed23116df7d04fcff | [
"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 | 1,765 | 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.CompilerM
import Lean.Compiler.Decl
namespace Lean.Compiler
/-! Common Sub-expression Elimination -/
namespace CSE
structure State ... |
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