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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
fb8e445bc5c018716066b2b749fc56bc5f4fb8de | 4727251e0cd73359b15b664c3170e5d754078599 | /src/algebra/hom/equiv.lean | 5b3369b11c96af271448fc4ade3eadbfd586240f | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 29,482 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Callum Sutton, Yury Kudryashov
-/
import algebra.group.type_tags
import algebra.group_with_zero.basic
import data.pi.algebra
/-!
# Multiplicative and additive equivs
... |
fc751f34d4a2a6a61ccf12634a3f4099048d159c | 87fd6b43d22688237c02b87c30d2a524f53bab24 | /src/game/sets/sqrt2NotRational.lean | 954a9df14656ae7447cf121d619936ee41281cb0 | [
"Apache-2.0"
] | permissive | grthomson/real-number-game | 66142fedf0987db90f66daed52f9c8b42b70f909 | 8ddc15fdddc241c246653f7bb341df36e4e880a8 | refs/heads/master | 1,668,059,330,605 | 1,592,873,454,000 | 1,592,873,454,000 | 262,025,764 | 0 | 0 | null | 1,588,849,107,000 | 1,588,849,106,000 | null | UTF-8 | Lean | false | false | 6,584 | lean | import tactic.ring
import tactic.linarith
import data.rat.basic
import data.rat.cast
/- Section
1.4 An Application
-/
/-
Prove that there is no rational number whose square is 2
using the techniques introduced earlier.
-/
def even (a : ℤ) := ∃ b : ℤ, a = 2 * b
def odd (a : ℤ) := ∃ b : ℤ, a = 2 * b + 1
lemma not_e... |
f3b39720b76bf81b0ec73f9ae25196955df1f4a6 | 5bf112cf7101c6c6303dc3fd0b3179c860e61e56 | /design/determine.lean | 2db09431ecc03345e895c4f9f7017864eb68bbfa | [
"Apache-2.0"
] | permissive | fredfeng/formal-encoding | 7ab645f49a553dfad2af03fcb4289e40fc679759 | 024efcf58672ac6b817caa10dfe8cd9708b07f1b | refs/heads/master | 1,597,236,551,123 | 1,568,832,149,000 | 1,568,832,149,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,541 | lean | /-
Design challenge: how to represent problems that require "determining" a set.
------------------------------------------------------------------------------
Consider the following problem:
"""
[IMO 2019, Problem 1]
Let ℤ be the set of integers. Determine all functions f : ℤ → ℤ such that, for all integers a and b,... |
72e1b1e4f957e9d46ddabc7daa233a2f823e6861 | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /src/Lean/Elab/Syntax.lean | eafc98916d0ccf680c587d93265757faef98cd8b | [
"Apache-2.0"
] | permissive | WojciechKarpiel/lean4 | 7f89706b8e3c1f942b83a2c91a3a00b05da0e65b | f6e1314fa08293dea66a329e05b6c196a0189163 | refs/heads/master | 1,686,633,402,214 | 1,625,821,189,000 | 1,625,821,258,000 | 384,640,886 | 0 | 0 | Apache-2.0 | 1,625,903,617,000 | 1,625,903,026,000 | null | UTF-8 | Lean | false | false | 15,267 | 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.Elab.Command
import Lean.Parser.Syntax
import Lean.Elab.Util
namespace Lean.Elab.Term
/-
Expand `optional «precedence»` where
«precedence» := ... |
efdd09474b4e1258c143bcb9f96fba1080724a8c | ee8cdbabf07f77e7be63a449b8483ce308d37218 | /lean/src/test/induction-12dvd4expnp1p20.lean | 1e717a83497b8604b5a804debef45f1b1f337ad1 | [
"MIT",
"Apache-2.0"
] | 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 | 229 | 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.basic
example (n : ℕ) : 12 ∣ 4^(n+1) + 20 :=
begin
sorry
end
|
5ecca6894656e08fa262272a21d2f4a590640086 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/measure_theory/simple_func_dense.lean | c49668cbe5a1138db72758680eff85badb95fa1b | [
"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 | 14,947 | 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.l1_space
/-!
# Density of simple functions
Show that each Borel measurable function can be approximated,
both pointwise and in `L¹` norm, by a ... |
ff12cd63950281cdd9629fe327a96716d0a0e735 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/analysis/inner_product_space/rayleigh.lean | 95fe87c85c53c547dce6b592413833f3736af245 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 12,447 | lean | /-
Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth, Frédéric Dupuis
-/
import analysis.inner_product_space.calculus
import analysis.inner_product_space.dual
import analysis.inner_product_space.adjoint
import analysis.c... |
15ff53fe919f8d4852e4fe0351ac95964d278ef0 | 586535ff9853f5b85dc5fdeb5b78f1ad2d573a6e | /src/well_foundedness.lean | f5e0b1a8b5d75e62e22d2f593662239a9b0b4700 | [
"Apache-2.0"
] | permissive | Kha/rc-correctness | fede4ae228c5f04985cf332e718a5a433230b150 | be5a521f1b0528ccbc685619b265cd11ea854edf | refs/heads/master | 1,595,967,325,275 | 1,568,889,756,000 | 1,568,889,756,000 | 209,523,947 | 0 | 0 | Apache-2.0 | 1,568,888,337,000 | 1,568,888,336,000 | null | UTF-8 | Lean | false | false | 3,237 | lean | import type_system
namespace rc_correctness
open rc_correctness.expr
open rc_correctness.fn_body
open rc_correctness.ob_lin_type
inductive fn_body_wf (β : const → var → ob_lin_type) (δ : const → fn) : finset var → finset var → fn_body → Prop
notation Γ `; ` Δ ` ⊢ `:1 F := fn_body_wf Γ Δ F
| ret {Γ Δ : finset var} {x... |
15b9cf3c9593749c7ce27815cbb05dec6f11593a | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/order/field/basic.lean | 049eff237f9b8e431d946699309500171ca0a203 | [
"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 | 31,907 | lean | /-
Copyright (c) 2014 Robert Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Lewis, Leonardo de Moura, Mario Carneiro, Floris van Doorn
-/
import order.bounds.order_iso
import algebra.field.basic
import algebra.order.field.defs
import algebra.group_power.o... |
2a974dae08c41fa28b1e4d185b190ccb9e21f0b5 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /stage0/src/Lean/Environment.lean | e4e4864ffb3b34e8c1f8e14831f905ed6342b9fe | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | cipher1024/lean4 | 6e1f98bb58e7a92b28f5364eb38a14c8d0aae393 | 69114d3b50806264ef35b57394391c3e738a9822 | refs/heads/master | 1,642,227,983,603 | 1,642,011,696,000 | 1,642,011,696,000 | 228,607,691 | 0 | 0 | Apache-2.0 | 1,576,584,269,000 | 1,576,584,268,000 | null | UTF-8 | Lean | false | false | 35,164 | 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 Std.Data.HashMap
import Lean.ImportingFlag
import Lean.Data.SMap
import Lean.Declaration
import Lean.LocalContext
import Lean.Util.Path
import Lean.U... |
67c75ebc29e35b634473fc84e9e7bf618b8a002e | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/topology/continuous_function/compact.lean | 9a8aee0c1dc53a15a6d4e8f273a2a87ec9ff3533 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 14,041 | 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 topology.continuous_function.bounded
import topology.uniform_space.compact_separated
import tactic.equiv_rw
/-!
# Continuous functions on a compact space
Con... |
3b428a754440fa106eff6aaac613b931e5bbda77 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/algebra/module/injective.lean | d16645b9f5f7611f2816ab0ebc76569e6bd52e85 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 16,529 | 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 algebra.category.Module.abelian
import category_theory.preadditive.injective
import ring_theory.ideal.basic
/-!
# Injective modules
## Main definitions
* `modu... |
8adcb930a1d26a40b987e711fd0d165d8ff88133 | 8f83e52da30f74edd26b394c8cbbaa68b2ac41aa | /06-formalizacija-dokazov/vaje-imp-za-zamudnike.lean | 70cccd88e73e5b48347f707b68bf075808ce3340 | [] | no_license | petrapodlogar/teorija-programskih-jezikov | ec790e2a6cd293d54b6c1bdd48cbb8bd7e2b2421 | def21623d0b6bf1090e5d05e7c1d391aacdc70f2 | refs/heads/master | 1,599,611,534,895 | 1,574,856,756,000 | 1,574,856,756,000 | 221,290,046 | 0 | 0 | null | 1,573,585,033,000 | 1,573,585,033,000 | null | UTF-8 | Lean | false | false | 7,404 | lean | -- ==================== Syntax ====================
def loc := string
inductive aexp : Type
| Lookup : loc -> aexp
| Int : int -> aexp
| Plus : aexp -> aexp -> aexp
| Minus : aexp -> aexp -> aexp
| Times : aexp -> aexp -> aexp
inductive bexp : Type
| Bool : bool -> bexp
| Equal : aexp -> aexp -> bexp
| Less : aexp... |
ce3b09cf5cfacbe494ad27c2b70ac35238e30ece | 6b10c15e653d49d146378acda9f3692e9b5b1950 | /examples/basic_skills/unnamed_626.lean | 3f8b83d511ee33b47789deeabe4c2cc30798006e | [] | 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 | 227 | lean | namespace my_ring
variables {R : Type*} [ring R]
-- BEGIN
theorem add_left_cancel {a b c : R} (h : a + b = a + c) : b = c :=
sorry
theorem add_right_cancel {a b c : R} (h : a + b = c + b) : a = c :=
sorry
-- END
end my_ring |
107c1d243c3f21326172e83151adf5b8cf1ebf62 | 968e2f50b755d3048175f176376eff7139e9df70 | /examples/prop_logic_theory/unnamed_622.lean | e5a88eb21a6a66e78c3e4a4e74f5232805317e50 | [] | no_license | gihanmarasingha/mth1001_sphinx | 190a003269ba5e54717b448302a27ca26e31d491 | 05126586cbf5786e521be1ea2ef5b4ba3c44e74a | refs/heads/master | 1,672,913,933,677 | 1,604,516,583,000 | 1,604,516,583,000 | 309,245,750 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 287 | lean | variables p q r : Prop
-- BEGIN
example (h₁ : p → q) (h₂ : q → r) (h₃ : p) : r :=
begin
apply h₂, -- By implication elimination on `h₂`, it suffices to prove `q`.
show q, from h₁ h₃ -- We show `q` by implication elimination on `h₁` and `h₃`.
end
-- END |
f6dc72bc2fd66e0c89b0da9d9a1fc335e797d3b6 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/equiv/mul_add.lean | d99cd66b6ed77a581c9fa092318c7afc104e2a27 | [] | 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 | 18,717 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Callum Sutton, Yury Kudryashov
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.algebra.group.hom
import Mathlib.algebra.group.type_tags
im... |
191c6572b2db875c90dc1e7324ff96a0a07aba6b | a9d0fb7b0e4f802bd3857b803e6c5c23d87fef91 | /hott/init/util.hlean | cf5c8d203cbaca858cf45b0b8b52d505280d95cc | [
"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 | 517 | hlean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
Auxiliary definitions used by automation
-/
prelude
import init.trunc
open is_trunc
definition eq_rec_eq.{l₁ l₂} {A : Type.{l₁}} {B : A → Type.{l₂}} [h : is... |
253a83556cef2fb72a5cefc0756ee24959997dd0 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/ring_theory/rees_algebra.lean | 527905271083a19d4266b6a5407c0268dedf1015 | [
"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 | 4,083 | 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 ring_theory.finiteness
import ring_theory.ideal.local_ring
import ring_theory.nakayama
/-!
# Rees algebra
The Rees algebra of an ideal `I` is the subalgebra `R[I... |
c75500b9252de6dc6f5cc4fe41235f278a564b96 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/topology/stone_cech.lean | f4991763d0076c7c8a870d2741e5a65a3f07880f | [
"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 | 11,611 | 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 topology.bases
import topology.dense_embedding
/-! # Stone-Čech compactification
Construction of the Stone-Čech compactification using ultrafilters.
Parts of the ... |
75bc467fce235b03c8c59ff1fc96b7a90031ee5d | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/order/ideal.lean | 29610eac3191b568029573d48c601fea37cb3898 | [
"Apache-2.0"
] | permissive | Lix0120/mathlib | 0020745240315ed0e517cbf32e738d8f9811dd80 | e14c37827456fc6707f31b4d1d16f1f3a3205e91 | refs/heads/master | 1,673,102,855,024 | 1,604,151,044,000 | 1,604,151,044,000 | 308,930,245 | 0 | 0 | Apache-2.0 | 1,604,164,710,000 | 1,604,163,547,000 | null | UTF-8 | Lean | false | false | 4,943 | lean | /-
Copyright (c) 2020 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
import order.basic
import data.equiv.encodable.basic
/-!
# Order ideals, cofinal sets, and the Rasiowa–Sikorski lemma
## Main definitions
We work with a preorder `P` throu... |
ecac80f890be818c620267329fa21c4430d1125d | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/data/fintype.lean | 8cfcf6f8ec8fc3f704b489773f6af0c28f1c07e2 | [
"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 | 29,895 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Mario Carneiro
Finite types.
-/
import data.finset algebra.big_operators data.array.lemmas
universes u v
variables {α : Type*} {β : Type*} {γ : Type*}
/-- `fintype α` means that `α` ... |
3061634be47f194d1919930930fabff42fbb78fe | ff5230333a701471f46c57e8c115a073ebaaa448 | /tests/lean/run/eq_cases_on.lean | 1cfa9a4dc40409b4ae4b40ed82c6bd26b5485135 | [
"Apache-2.0"
] | permissive | stanford-cs242/lean | f81721d2b5d00bc175f2e58c57b710d465e6c858 | 7bd861261f4a37326dcf8d7a17f1f1f330e4548c | refs/heads/master | 1,600,957,431,849 | 1,576,465,093,000 | 1,576,465,093,000 | 225,779,423 | 0 | 3 | Apache-2.0 | 1,575,433,936,000 | 1,575,433,935,000 | null | UTF-8 | Lean | false | false | 240 | lean | def g {n m : nat} (v : array (n + m) nat) : array (m + n) nat :=
eq.rec_on (add_comm n m) v -- Worked before
def f {n m : nat} (v : array (n + m) nat) : array (m + n) nat :=
eq.cases_on (add_comm n m) v -- eq.cases_on was not being erased
|
bcc51b5ce76bbfbcddacec6760b59d670643c56a | 367134ba5a65885e863bdc4507601606690974c1 | /src/geometry/manifold/basic_smooth_bundle.lean | c8e88273746252512e3b413e5b188641b00d1785 | [
"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 | 31,911 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import topology.topological_fiber_bundle
import geometry.manifold.smooth_manifold_with_corners
/-!
# Basic smooth bundles
In general, a smooth bundle is a bun... |
a366b830435af6cd7b577ca07ad7b0d9861efd7e | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/ring_theory/witt_vector/domain.lean | 2e00ed154519515f664015f4f9e222ca9753be13 | [
"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 | 3,812 | lean | /-
Copyright (c) 2022 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
-/
import ring_theory.witt_vector.identities
/-!
# Witt vectors over a domain
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corre... |
37d143a5f2b811b097bf3b987c45db13bd0a1d6f | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/category_theory/closed/ideal.lean | 7d8c309392d38ec454c3b2d06a60db0b5e01172e | [
"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 | 11,903 | lean | /-
Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import category_theory.limits.preserves.shapes.binary_products
import category_theory.limits.constructions.finite_products_of_binary_products
import category_theory.monad... |
9115a4d5ec5f48593cd66f6bfc92c269698a03c7 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/algebraic_geometry/presheafed_space/has_colimits.lean | 5d9bac6f2dba552c8cf06c452be46a50bde44414 | [
"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 | 10,218 | 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 algebraic_geometry.presheafed_space
import topology.category.Top.limits
import topology.sheaves.limits
import category_theory.limits.concrete_category
/-!
# `... |
4f5452a4c15ce9aca1bc10a92982edfcaa206a8d | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebraic_topology/topological_simplex.lean | 552095a9fa08754d397ea7cb0547c3aac0b8f606 | [
"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 | 3,366 | lean | /-
Copyright (c) 2021 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Adam Topaz
-/
import algebraic_topology.simplex_category
import topology.category.Top.basic
import topology.instances.nnreal
/-!
# Topological simplices
> THIS FILE IS SY... |
6bc25fea7acbd2a3809682ce5929a1f32d23cee4 | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/data/quaternion.lean | 0e8c5bfcfb27d1a9f8780c7b9426701331b1d46d | [
"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 | 21,223 | lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import tactic.ring_exp
import algebra.algebra.basic
import algebra.opposites
import data.equiv.ring
/-!
# Quaternions
In this file we define quaternions `ℍ[R]` ov... |
aa53f1773cc174712ed3f80300d9e1f54bf630ba | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /stage0/src/Init/Lean/Meta/DiscrTreeTypes.lean | e028f62735da280a7066ea2261e34160aabea005 | [
"Apache-2.0"
] | permissive | mhuisi/lean4 | 28d35a4febc2e251c7f05492e13f3b05d6f9b7af | dda44bc47f3e5d024508060dac2bcb59fd12e4c0 | refs/heads/master | 1,621,225,489,283 | 1,585,142,689,000 | 1,585,142,689,000 | 250,590,438 | 0 | 2 | Apache-2.0 | 1,602,443,220,000 | 1,585,327,814,000 | C | UTF-8 | Lean | false | false | 1,460 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import Init.Lean.Expr
namespace Lean
namespace Meta
/- See file `DiscrTree.lean` for the actual implementation and documentation. -/
namespace Di... |
d11512dde27b182b534570bb730e9a150302ec1a | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /src/Lean/Elab/PreDefinition/Structural.lean | 87897a85f61ffb7d8768910f6289f96e14fce601 | [
"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 | 22,907 | 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.Util.ForEachExpr
import Lean.Meta.ForEachExpr
import Lean.Meta.RecursorInfo
import Lean.Meta.Match.Match
import Lean.Elab.PreDefinition.Basic
na... |
f2fe00b09da93f6da884756e78385e817be387dc | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/data/string/defs.lean | 7c3ec28747ddf01a9d8911b0cba6721c97f97c7d | [
"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 | 270 | lean |
namespace string
def map_tokens (c : char) (f : list string → list string) : string → string :=
intercalate (singleton c) ∘ f ∘ split (= c)
def over_list (f : list char → list char) : string → string :=
list.as_string ∘ f ∘ string.to_list
end string
|
656cb04ec6639bf7d72818287e1c314446c769e7 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/measure_theory/integral/set_to_l1.lean | bf85324211a74a272bcc4b0d3a57e88665cdaf20 | [
"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 | 87,250 | lean | /-
Copyright (c) 2021 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne
-/
import measure_theory.function.simple_func_dense_lp
/-!
# Extension of a linear function from indicators to L1
Let `T... |
b1f0a6ef75138ba386eeb1f8013691e569ad7f95 | 2a70b774d16dbdf5a533432ee0ebab6838df0948 | /_target/deps/mathlib/src/ring_theory/dedekind_domain.lean | 2a08829060045229472bbafcca7181a809d5fcb4 | [
"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 | 10,139 | lean | /-
Copyright (c) 2020 Kenji Nakagawa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenji Nakagawa, Anne Baanen, Filippo A. E. Nuccio
-/
import ring_theory.discrete_valuation_ring
import ring_theory.fractional_ideal
import ring_theory.ideal.over
/-!
# Dedekind domain... |
598507ada563b77125b50d80465bde11abe11bed | 6b2a480f27775cba4f3ae191b1c1387a29de586e | /group_rep_2/Tools/tools.lean | a2eb386c9fda342b21c6ee15c51664ca440bdffb | [] | no_license | Or7ando/group_representation | a681de2e19d1930a1e1be573d6735a2f0b8356cb | 9b576984f17764ebf26c8caa2a542d248f1b50d2 | refs/heads/master | 1,662,413,107,324 | 1,590,302,389,000 | 1,590,302,389,000 | 258,130,829 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 127 | lean | import Tools.bilinear_over_comm_ring
import Tools.diagonal_sum
import Tools.function_space
import Tools.matrix Tools.projector |
45e4ced878185c88443793c8487203012321cba7 | 618003631150032a5676f229d13a079ac875ff77 | /src/tactic/show_term.lean | e4e2ed39206d25edd9f35ae24bdf924d71c26112 | [
"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 | 1,201 | 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 tactic.doc_commands
open tactic
namespace tactic.interactive
/--
`show_term { tac }` runs the tactic `tac`,
and then prints the term that was constructed.
... |
c038b900404df644fddba003855ee7579c61aa1a | b9a81ebb9de684db509231c4469a7d2c88915808 | /src/super/equality.lean | d6feadbe3ba02d2a83ed7d2958abdc62e126b1d2 | [] | 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 | 1,255 | 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 .prover_state .utils
open tactic monad expr list
namespace super
meta def try_unify_eq_l (c : clause) (i : nat) : tactic clause := do
guard $ clause.li... |
b66d068410324f993d61f46eaa5011f910e54235 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/algebra/group_ring_action.lean | 17fc0bda39f5e505038c85b99a5eac10b0dc20da | [
"Apache-2.0"
] | permissive | stjordanis/mathlib | 51e286d19140e3788ef2c470bc7b953e4991f0c9 | 2568d41bca08f5d6bf39d915434c8447e21f42ee | refs/heads/master | 1,631,748,053,501 | 1,627,938,886,000 | 1,627,938,886,000 | 228,728,358 | 0 | 0 | Apache-2.0 | 1,576,630,588,000 | 1,576,630,587,000 | null | UTF-8 | Lean | false | false | 5,385 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import group_theory.group_action.group
import data.equiv.ring
import ring_theory.subring
/-!
# Group action on rings
This file defines the typeclass of monoid acting on semi... |
d189ff8f661dd52ccaa01d43d190a22b05c0f327 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/analysis/special_functions/non_integrable.lean | d3ae8b75964d55eea70b925fcb8edecf4e5eb43f | [
"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 | 9,537 | 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.special_functions.integrals
/-!
# Non integrable functions
In this file we prove that the derivative of a function that tends to infinity is not i... |
a97f83cda504eab79378eddcaf935b2660fbebaa | ce89339993655da64b6ccb555c837ce6c10f9ef4 | /bluejam/chap5_exercise4.5.lean | ed96b9f63cbd51502eb641b8da410564350a2caf | [] | 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 | 3,466 | lean |
open classical
variables (α : Type) (p q : α → Prop)
variable a : α
variable r : Prop
-- This is required to add a to tactics
include a
example : (∃ x : α, r) → r :=
begin
intros h,
cases h,
assumption
end
example : r → (∃ x : α, r) :=
begin
intros,
apply exists.intro,
repeat { assumption }
end
exam... |
49449222360275f69610261ea180bf76f1cf04c3 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/field_theory/separable.lean | a1dd56957cd6b96404862fa3c37704b43d734284 | [
"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 | 21,379 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import algebra.polynomial.big_operators
import algebra.squarefree
import field_theory.minpoly
import field_theory.splitting_field
import data.polynomial.expand
/-!
# Separab... |
9da486ee35b46330177fdf63887d31faa31c65c6 | 0e175f34f8dca5ea099671777e8d7446d7d74227 | /library/init/meta/interactive.lean | 384f67ac5785a46222480f7a1669a2b0742f1b06 | [
"Apache-2.0"
] | permissive | utensil-contrib/lean | b31266738071c654d96dac8b35d9ccffc8172fda | a28b9c8f78d982a4e82b1e4f7ce7988d87183ae8 | refs/heads/master | 1,670,045,564,075 | 1,597,397,599,000 | 1,597,397,599,000 | 287,528,503 | 0 | 0 | Apache-2.0 | 1,597,408,338,000 | 1,597,408,337,000 | null | UTF-8 | Lean | false | false | 71,222 | 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, Jannis Limperg
-/
prelude
import init.meta.tactic init.meta.rewrite_tactic init.meta.simp_tactic
import init.meta.smt.congruence_closure init.control.combinat... |
ee8eb9def98c60678095066834951530ff49b894 | 4fa161becb8ce7378a709f5992a594764699e268 | /src/topology/metric_space/basic.lean | 6162c6253b345f207f18d7370b383551aea8b6af | [
"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 | 74,800 | lean | /-
Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Metric spaces.
Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
Many definitions and theorems expected on metric spaces are already introduced o... |
cf6b6954e07abdb6d1d3346da7346bf09e8caf04 | 2a70b774d16dbdf5a533432ee0ebab6838df0948 | /_target/deps/mathlib/src/data/equiv/basic.lean | 81a9f4149443f8f7d7cd2088710bb57645d7c3e3 | [
"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 | 86,459 | 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
-/
import data.set.function
/-!
# Equivalence between types
In this file we define two types:
* `equiv α β` a.k.a. `α ≃ β`: a bijective map ... |
190e496879f1cce8f04f345eac30b47a7f69e53b | 626e312b5c1cb2d88fca108f5933076012633192 | /src/analysis/calculus/local_extr.lean | f81806979a87889459ec7fdc08e7f6632a00a10a | [
"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 | 18,173 | lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import analysis.calculus.deriv
import topology.algebra.ordered.extend_from
import topology.algebra.polynomial
import topology.local_extr
/-!
# Local extrema of smo... |
6142ddf09ff0dd8e2a6d570f0007db70f82f07eb | 842b7df4a999c5c50bbd215b8617dd705e43c2e1 | /lean_test/src/test.lean | fc65eb92ebfc9bf661cfb8766a1fd5f3c3476650 | [] | no_license | Samyak-Surti/LeanCode | 1c245631f74b00057d20483c8ac75916e8643b14 | 944eac3e5f43e2614ed246083b97fbdf24181d83 | refs/heads/master | 1,669,023,730,828 | 1,595,534,784,000 | 1,595,534,784,000 | 282,037,186 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 294 | lean | variables P Q R : Prop
theorem basic_logic : (P → Q) ∧ (Q → R) → (P → R) :=
begin
intro H, -- H is "P implies Q and Q implies R"
intro HP, -- we want P -> R so let's assume P.
have HQ : Q,
exact H.left HP, -- apply P->Q to P to get Q.
-- now we can get the goal
exact H.right HQ
end |
b231d22021c57b8163f009ab6bb28659e08f81b1 | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/complex/module.lean | b0ffdbbff8b7f11ce2e975092fbf769f410170ce | [
"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 | 6,890 | lean | /-
Copyright (c) 2020 Alexander Bentkamp, Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, Sébastien Gouëzel
-/
import data.complex.basic
import algebra.algebra.ordered
import data.matrix.notation
import field_theory.tower
import li... |
671da52e47af5bd7bdc30b53de4c33f56057a422 | 367134ba5a65885e863bdc4507601606690974c1 | /src/analysis/special_functions/arsinh.lean | 7931a62432d4fd7a0ff5196f140c1e03446d9c49 | [
"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 | 2,989 | lean | /-
Copyright (c) 2020 James Arthur. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: James Arthur, Chris Hughes, Shing Tak Lam
-/
import analysis.special_functions.trigonometric
/-!
# Inverse of the sinh function
In this file we prove that sinh is bijective and hence h... |
ba1968048c80b3331749e17ebccc37436e9f5216 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/probability/kernel/cond_distrib.lean | d1a141b01b8e496b5285525ba844efdc7652b883 | [
"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 | 17,180 | lean | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import probability.kernel.disintegration
import probability.notation
/-!
# Regular conditional probability distribution
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any... |
b29c00f3adc1f0e54189b53f82f52247b3a9db3c | 82b86ba2ae0d5aed0f01f49c46db5afec0eb2bd7 | /stage0/src/Init/Data/ToString/Basic.lean | f6d464d233f52c264d9d6c3a08af56c110923ba7 | [
"Apache-2.0"
] | permissive | banksonian/lean4 | 3a2e6b0f1eb63aa56ff95b8d07b2f851072d54dc | 78da6b3aa2840693eea354a41e89fc5b212a5011 | refs/heads/master | 1,673,703,624,165 | 1,605,123,551,000 | 1,605,123,551,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,304 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import Init.Data.String.Basic
import Init.Data.UInt
import Init.Data.Nat.Div
import Init.Data.Repr
import Init.Control.Id
open Sum Subtype Nat
unive... |
d63bcd3d33d81d51a32fac243366265d2417c62f | 6fbf10071e62af7238f2de8f9aa83d55d8763907 | /src/2.4_logic_functions.lean | 3c27baa1f2abc03ca1938bc994c28a929c3c54b2 | [] | 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 | 2,757 | lean | /-
Copyright 2019 Kevin Sullivan and Ben Hocking.
-/
namespace Functions.ex0
axioms S T : Type
def single_valued := ∀ f : S → T,
∀ x : S, ∀ y z : T,
f x = y ∧ f x = z → y = z
end Functions.ex0
namespace Functions.ex1
axioms S T : Type
def total := ∀ f : S → T,
∀ x : S, ∃ y : T, f x = y
end Function... |
e8827b3e7e93c6827af1040c428d12503281bf8b | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /tests/lean/interactive/foldingRange.lean | 8ace1baca7ff72855b72e7629d825fcfe579cd3a | [
"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 | 416 | lean | --^ textDocument/foldingRange
import Lean
import Lean.Data
open Lean
namespace Foo
open Std
open Lean
section Bar
/-!
A module-level doc comment
-/
/--
Some documentation comment
-/
@[inline]
def add (x y : Nat) :=
x + y
inductive InductiveTy
| a
|
/--
Another doc comment. This one is not folded.
-... |
fe9cd7187d058e06ba2054c03cb4f936a633eff3 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/data/nat/fib.lean | acf6505001d9e18c08881fcd469e739be647e81e | [
"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 | 12,979 | lean | /-
Copyright (c) 2019 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann, Kyle Miller, Mario Carneiro
-/
import data.nat.gcd
import logic.function.iterate
import data.finset.nat_antidiagonal
import algebra.big_operators.basic
import tacti... |
012cbb9fe091e3a186acaf074ece5a1c84f55e89 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/algebra/group_ring_action/subobjects.lean | 638436b5ccd3c39031c20b733a9d2f3cd431bf30 | [
"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 | 1,160 | lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import algebra.group_ring_action.basic
import group_theory.subgroup.basic
/-!
# Instances of `mul_semiring_action` for subobjects
> THIS FILE IS SYNCHRONIZED WITH MATHLIB... |
43e2fcf48065d55e6a6ed2f44b76ab5116221045 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/analysis/normed_space/euclidean_dist.lean | 243699b0e5eef19bdd2761814381f66177cbcf28 | [
"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 | 4,622 | 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.pi_Lp
/-!
# Euclidean distance on a finite dimensional space
When we define a smooth bump function on a normed space, it is useful to... |
699ddfc2b91ee8440cc058fc66f691aa8c5f09cf | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /stage0/src/Lean/Elab/Term.lean | d657541f04a05f7189fbfece0e510999a18f61de | [
"Apache-2.0"
] | permissive | dupuisf/lean4 | d082d13b01243e1de29ae680eefb476961221eef | 6a39c65bd28eb0e28c3870188f348c8914502718 | refs/heads/master | 1,676,948,755,391 | 1,610,665,114,000 | 1,610,665,114,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 59,999 | 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.ResolveName
import Lean.Util.Sorry
import Lean.Structure
import Lean.Meta.ExprDefEq
import Lean.Meta.AppBuilder
import Lean.Meta.SynthInstance
i... |
d9817101f8522f0668904ac7e5970a9ba42bb589 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/real/pi/leibniz.lean | adb643d477827bbd8290fd850e431c0f8814fe2c | [
"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 | 7,680 | lean | /-
Copyright (c) 2020 Benjamin Davidson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Benjamin Davidson
-/
import analysis.special_functions.trigonometric.arctan_deriv
/-! ### Leibniz's Series for Pi -/
namespace real
open filter set
open_locale classical big_oper... |
3470aca9e4368a19955d5838ff22835d28cfdbbc | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/logic/equiv/list.lean | 6c73ce175a80efceb0efe8a0282144b2c477c8d5 | [
"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 | 14,388 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.finset.sort
import logic.denumerable
/-!
# Equivalences involving `list`-like types
This file defines some additional constructive equivalences using `e... |
f38273d67b6d71cb3c3888d2807427d2a225c76f | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/extra/tree_list_rec.lean | 46c053f4aaa8d3b39b20e1232a4a093d41249ba9 | [
"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 | 931 | lean | open nat
inductive tree (A : Type*) :=
leaf : A → tree A,
node : tree_list A → tree A
with tree_list :=
nil : tree_list A,
cons : tree A → tree_list A → tree_list A
namespace tree
open tree_list
definition size {A : Type*} : tree A → nat
with size_l : tree_list A → nat,
size (leaf a) := 1,
size (... |
90ad74f5bcf8219237c42bac43df9e0e2fc4844b | c45b34bfd44d8607a2e8762c926e3cfaa7436201 | /uexp/src/uexp/ucongr_test.lean | 26a2cef227e80225461853d51006e8d28444ae7c | [
"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 | 2,054 | lean | import .ucongr
set_option profiler true
lemma congr_trans_ex1 {s: Schema} (a b c d e f: Tuple s):
(a ≃ c) * ((a ≃ b) * (e ≃ f)) = (a ≃ c) * ((a ≃ b) * (f ≃ e)) :=
begin
ucongr,
end
lemma congr_trans_ex2 {s: Schema} (a b c d e f: Tuple s):
(a ≃ c) * ((b ≃ a) * (e ≃ f)) = (a ≃ c) * ((a ≃ b) * (f ≃ e)) :=
b... |
603ffb2faa9cd5ac62f96179524e497c9f0e5765 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/data/padics/padic_norm.lean | 9c79627ff2e20b275d96fd8e7fb00db71dea8847 | [
"Apache-2.0"
] | permissive | lacker/mathlib | f2439c743c4f8eb413ec589430c82d0f73b2d539 | ddf7563ac69d42cfa4a1bfe41db1fed521bd795f | refs/heads/master | 1,671,948,326,773 | 1,601,479,268,000 | 1,601,479,268,000 | 298,686,743 | 0 | 0 | Apache-2.0 | 1,601,070,794,000 | 1,601,070,794,000 | null | UTF-8 | Lean | false | false | 25,156 | 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
-/
import algebra.gcd_monoid
import algebra.field_power
import ring_theory.multiplicity
import data.real.cau_seq
import tactic.ring_exp
import tactic.basic
/-!
# p-ad... |
7f411b5b12430841f766ac8c86cc0d2029672182 | 94096349332b0a0e223a22a3917c8f253cd39235 | /src/game/world3/level5.lean | efd47061b51e08222fb65cd89276300f56edee85 | [] | no_license | robertylewis/natural_number_game | 26156e10ef7b45248549915cc4d1ab3d8c3afc85 | b210c05cd627242f791db1ee3f365ee7829674c9 | refs/heads/master | 1,598,964,725,038 | 1,572,602,236,000 | 1,572,602,236,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,353 | lean | import game.world3.level4 -- hide
import mynat.mul -- hide
namespace mynat -- hide
/-
# Multiplication World
## Level 5: `mul_assoc`
Currently our tools for multiplication include the
following:
* `mul_zero m : m * 0 = 0`
* `zero_mul m : 0 * m = 0`
* `mul_succ a b : a * succ b = a * b + a`
* `mul_add t a b : t * ... |
b3fd5e401183aa362cb070a1589c3586ae917f84 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /stage0/src/Init/Lean/Compiler/IR/FreeVars.lean | 98c88940582a2f6a54718c4eb233b634a0ac1b50 | [
"Apache-2.0"
] | permissive | mhuisi/lean4 | 28d35a4febc2e251c7f05492e13f3b05d6f9b7af | dda44bc47f3e5d024508060dac2bcb59fd12e4c0 | refs/heads/master | 1,621,225,489,283 | 1,585,142,689,000 | 1,585,142,689,000 | 250,590,438 | 0 | 2 | Apache-2.0 | 1,602,443,220,000 | 1,585,327,814,000 | C | UTF-8 | Lean | false | false | 9,344 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import Init.Lean.Compiler.IR.Basic
namespace Lean
namespace IR
namespace MaxIndex
/- Compute the maximum index `M` used in a declaration.
We `M... |
ec2df0f6eb70cf99af2717d670a95d7f609908f3 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/topology/category/Top/opens.lean | b467ad061bda30e7f6913dbfea761c73a8a8de4a | [
"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 | 3,945 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import topology.category.Top.basic
import category_theory.natural_isomorphism
import category_theory.opposites
import category_theory.eq_to_hom
import topology.opens
... |
23cb8b30cbe76fbcadb5f09a61ad4d35a2df41a7 | e4850d3690538c747274f940d23178380b465a23 | /LeanNixStatic1/Extern.lean | ead09f6a670930d1beb9187300c3bc5a7bff2448 | [] | no_license | zygi/leannixstatic1 | 5d81973a69c98e6f29e9283c245d10f81303155c | b10ce543ec1d990186295bfd33bc84d3a69a6fd7 | refs/heads/master | 1,678,438,994,937 | 1,614,394,028,000 | 1,614,394,028,000 | 342,754,763 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 76 | lean | @[extern "add_magic_constant"]
constant addMagicConstant (x: UInt64): UInt64 |
d054afdf56460b26c6c4c349d1f73e83b52485c2 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/control/traversable/instances.lean | 4045ce39d57855b439f793f21797d6b58cf5472f | [
"Apache-2.0"
] | permissive | AntoineChambert-Loir/mathlib | 64aabb896129885f12296a799818061bc90da1ff | 07be904260ab6e36a5769680b6012f03a4727134 | refs/heads/master | 1,693,187,631,771 | 1,636,719,886,000 | 1,636,719,886,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,488 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import control.traversable.lemmas
import data.list.forall2
import data.set.lattice
/-!
# Traversable instances
This file provides instances of `traversable` for types fro... |
6f607658fb9e23213fd9d2e5b3989cf658a0611f | 8b9f17008684d796c8022dab552e42f0cb6fb347 | /library/init/datatypes.lean | 00f7dbf12a28e4125f44d2f53a92028110407156 | [
"Apache-2.0"
] | permissive | chubbymaggie/lean | 0d06ae25f9dd396306fb02190e89422ea94afd7b | d2c7b5c31928c98f545b16420d37842c43b4ae9a | refs/heads/master | 1,611,313,622,901 | 1,430,266,839,000 | 1,430,267,083,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,854 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.datatypes
Authors: Leonardo de Moura
Basic datatypes
-/
prelude
notation `Prop` := Type.{0}
notation [parsing-only] `Type'` := Type.{_+1}
notation [parsing-only] `Type₊` ... |
28bf35431435869eeb2bea75fbc20c08dbbc5f30 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/category_theory/subobject/lattice.lean | 359d0877b0f9e43bd296cfcb2672acefd8716a4d | [
"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 | 22,580 | 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.factor_thru
import category_theory.subobject.well_powered
/-!
# The lattice of subobjects
We provide the `semilattice... |
1bda6263100ec41b687dcfed81ab6b9d0e358773 | c777c32c8e484e195053731103c5e52af26a25d1 | /src/combinatorics/additive/behrend.lean | 857a123b6c14edc9e76654d1f2860038e57af4e4 | [
"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 | 22,418 | lean | /-
Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import analysis.inner_product_space.pi_L2
import combinatorics.additive.salem_spencer
import combinatorics.pigeonhole
import data.complex.expo... |
08080d062d453647d36cf18a3d4bdadfc3e449ad | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/list/zip.lean | 9045ca2f512626af9ca992be5a98df3f97155d95 | [] | 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 | 9,806 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kenny Lau
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.list.basic
import Mathlib.PostPort
universes u v w z u_1 u_2 u_3
namespa... |
fc84902db24ce475546448c8fd91e1c2bcff93b7 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/topology/algebra/module.lean | 07fd916d6be1af25fdc799ea695731f29aaa0acb | [
"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 | 74,311 | 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, Frédéric Dupuis,
Heather Macbeth
-/
import topology.algebra.ring
import topology.algebra.mul_action
import topology... |
aa82604e3391d1aa65bb6b716a0317eaa9092a66 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/algebra/euclidean_domain.lean | 18e231fc665b227148be4987c3c6b8233ed2acf1 | [
"Apache-2.0"
] | permissive | agjftucker/mathlib | d634cd0d5256b6325e3c55bb7fb2403548371707 | 87fe50de17b00af533f72a102d0adefe4a2285e8 | refs/heads/master | 1,625,378,131,941 | 1,599,166,526,000 | 1,599,166,526,000 | 160,748,509 | 0 | 0 | Apache-2.0 | 1,544,141,789,000 | 1,544,141,789,000 | null | UTF-8 | Lean | false | false | 14,744 | lean | /-
Copyright (c) 2018 Louis Carlin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Louis Carlin, Mario Carneiro
Euclidean domains and Euclidean algorithm (extended to come)
A lot is based on pre-existing code in mathlib for natural number gcds
-/
import data.int.basic... |
248d5f36ef350dabc258fe61205d117643120a11 | 271e26e338b0c14544a889c31c30b39c989f2e0f | /tests/lean/mvar3.lean | c8ddc49c4bd2cf38f95f8646f7e1ec800ec25e8a | [
"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 | 2,837 | lean | import Init.Lean.MetavarContext
open Lean
def mkLambdaTest (mctx : MetavarContext) (ngen : NameGenerator) (lctx : LocalContext) (xs : Array Expr) (e : Expr)
: Except MetavarContext.MkBinding.Exception (MetavarContext × NameGenerator × Expr) :=
match MetavarContext.mkLambda xs e lctx { mctx := mctx, ngen := ngen } ... |
adf6ebe4d85c1649ad95b0ea4464ebcee99d1d03 | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/category_theory/functor.lean | 7fc51ea01a82f4807b34bc089a9fd1ced07d3f47 | [
"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 | 3,478 | 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
Defines a functor between categories.
(As it is a 'bundled' object rather than the `is_functorial` typeclass parametrised
by the underlyin... |
b83a3f1cde6c93fbcdc6e5bb2ce6e493af5ef715 | 8e2026ac8a0660b5a490dfb895599fb445bb77a0 | /tests/lean/run/pred_using_structure_cmd.lean | cca05317789eef4b1b21f58520d4f281abccb286 | [
"Apache-2.0"
] | permissive | pcmoritz/lean | 6a8575115a724af933678d829b4f791a0cb55beb | 35eba0107e4cc8a52778259bb5392300267bfc29 | refs/heads/master | 1,607,896,326,092 | 1,490,752,175,000 | 1,490,752,175,000 | 86,612,290 | 0 | 0 | null | 1,490,809,641,000 | 1,490,809,641,000 | null | UTF-8 | Lean | false | false | 345 | lean | variable {A : Type}
structure has_refl (R : A → A → Prop) : Prop :=
(refl : ∀ a, R a a)
structure is_equiv (R : A → A → Prop) extends has_refl R : Prop :=
(symm : ∀ a b, R a b → R b a)
(trans : ∀ a b c, R a b → R b c → R a c)
#check @is_equiv.refl
#check @is_equiv.symm
#check @is_equiv.trans
#check @is_equiv.to_has_... |
f92e6a6810c943370291d66593ff8cfc04601dd8 | 491068d2ad28831e7dade8d6dff871c3e49d9431 | /library/algebra/field.lean | a8cb2a2e0359966b478e7be198c8c6c72aa56ff1 | [
"Apache-2.0"
] | permissive | davidmueller13/lean | 65a3ed141b4088cd0a268e4de80eb6778b21a0e9 | c626e2e3c6f3771e07c32e82ee5b9e030de5b050 | refs/heads/master | 1,611,278,313,401 | 1,444,021,177,000 | 1,444,021,177,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 19,646 | lean | /-
Copyright (c) 2014 Robert Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Lewis
Structures with multiplicative and additive components, including division rings and fields.
The development is modeled after Isabelle's library.
-/
import logic.eq logic.c... |
4e11e4c7e63f8f793bea81f4336031af3569d470 | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/subtype.lean | a33d49b6c76c2723e2c46dfb8d2fb8f7224773ba | [
"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 | 5,998 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl
-/
import tactic.lint
import tactic.ext
import tactic.simps
open function
namespace subtype
variables {α : Sort*} {β : Sort*} {γ : Sort*} {p : α → Prop} {q : α → Prop}
... |
7bd994dab9bcbb5604d2f4cd983089f1ba3f0b94 | a7eef317ddec01b9fc6cfbb876fe7ac00f205ac7 | /src/algebra/group_with_zero.lean | abdceb5f85b3cde2fedec9e34f284ebc4c456cb0 | [
"Apache-2.0"
] | permissive | kmill/mathlib | ea5a007b67ae4e9e18dd50d31d8aa60f650425ee | 1a419a9fea7b959317eddd556e1bb9639f4dcc05 | refs/heads/master | 1,668,578,197,719 | 1,593,629,163,000 | 1,593,629,163,000 | 276,482,939 | 0 | 0 | null | 1,593,637,960,000 | 1,593,637,959,000 | null | UTF-8 | Lean | false | false | 25,746 | 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 algebra.group.commute
import tactic.alias
import tactic.push_neg
/-!
# Groups with an adjoined zero element
This file describes structures that are not usual... |
0d5f405ece23fe1595cb6d566c93f71db5c5201e | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /tests/lean/run/smartUnfoldingBug.lean | bf9d90e768f56232b212eee5485c9e09a9d65cd4 | [
"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 | 6,310 | lean | import Lean.Elab
open Nat
structure ProvedSkip(n m: Nat) where
result : Nat
lt : m < n → result = m
ge : n ≤ m → result = m + 1
def provedSkip (n m : Nat) : ProvedSkip n m :=
if c : m < n then
⟨m, fun _ => rfl, fun hyp => False.elim (Nat.lt_irrefl m (Nat.lt_of_lt_of_le c hyp))⟩
else
⟨m + 1, fun hyp ... |
e72b174e4a071f3f53f48ed60cda2e8a2b2e2307 | 1e561612e7479c100cd9302e3fe08cbd2914aa25 | /mathlib4_experiments/Data/Multiset/nodup.lean | 371cad5d95da985d61f5551c231af47952b3083a | [
"Apache-2.0"
] | permissive | kbuzzard/mathlib4_experiments | 8de8ed7193f70748a7529e05d831203a7c64eedb | 87cb879b4d602c8ecfd9283b7c0b06015abdbab1 | refs/heads/master | 1,687,971,389,316 | 1,620,336,942,000 | 1,620,336,942,000 | 353,994,588 | 7 | 4 | Apache-2.0 | 1,622,410,748,000 | 1,617,361,732,000 | Lean | UTF-8 | Lean | false | false | 10,074 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
--import data.multiset.powerset
--import data.multiset.range
import mathlib4_experiments.Data.Multiset.Basic
import mathlib4_experiments.Data.List.Defs
/-!
# ... |
c3e92dec878f648fdcc47f6a0dc8909433583715 | d29d82a0af640c937e499f6be79fc552eae0aa13 | /src/measure_theory/set_integral.lean | 7dc003b9eb52778312c6ad5984c7a6dec4e5cd6e | [
"Apache-2.0"
] | permissive | AbdulMajeedkhurasani/mathlib | 835f8a5c5cf3075b250b3737172043ab4fa1edf6 | 79bc7323b164aebd000524ebafd198eb0e17f956 | refs/heads/master | 1,688,003,895,660 | 1,627,788,521,000 | 1,627,788,521,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 36,799 | lean | /-
Copyright (c) 2020 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Yury Kudryashov
-/
import measure_theory.integrable_on
import measure_theory.bochner_integration
/-!
# Set integral
In this file we prove some properties of `∫ x in s, ... |
e851e0c7a1682459620f88c3dacae5c13deb54d8 | 40ad357bbd0d327dd1e3e7f7beb868bd4e5b0a9d | /src/temporal_logic/lemmas.lean | 0e49ba81035d69402d1fa214be0e2cf0d5f16b20 | [] | no_license | unitb/temporal-logic | 9966424f015976d5997a9ffa30cbd77cc3a9cb1c | accec04d1b09ca841be065511c9e206b725b16e9 | refs/heads/master | 1,633,868,382,769 | 1,541,072,223,000 | 1,541,072,223,000 | 114,790,987 | 5 | 3 | null | null | null | null | UTF-8 | Lean | false | false | 18,198 | lean |
import data.stream
import util.meta.tactic
import util.logic
import util.classical
import util.predicate
import util.meta.tactic.propositional
import tactic
import temporal_logic.tactic
universe variables u u₀ u₁ u₂
variables {α : Sort u₀} {β : Type u₁} {γ : Sort u₂}
namespace temporal
open predicate stream
att... |
ff4d6a58206545f1bcfcf2ed1036cd1e9a3e4999 | 80cc5bf14c8ea85ff340d1d747a127dcadeb966f | /src/category_theory/monoidal/of_has_finite_products.lean | f9272ed1fca9f6bc7930b2b37ae6ce39cc9b9f47 | [
"Apache-2.0"
] | permissive | lacker/mathlib | f2439c743c4f8eb413ec589430c82d0f73b2d539 | ddf7563ac69d42cfa4a1bfe41db1fed521bd795f | refs/heads/master | 1,671,948,326,773 | 1,601,479,268,000 | 1,601,479,268,000 | 298,686,743 | 0 | 0 | Apache-2.0 | 1,601,070,794,000 | 1,601,070,794,000 | null | UTF-8 | Lean | false | false | 12,041 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Simon Hudon
-/
import category_theory.monoidal.braided
import category_theory.limits.shapes.binary_products
import category_theory.limits.shapes.terminal
/-!
# The nat... |
9797b6f6211b1cd75f83db3fb9f2dae9bcccc3ce | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/data/qpf/multivariate/constructions/fix.lean | 5a6d73d0146e88b8f924ae1900344a4e9e29b377 | [
"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 | 12,880 | lean | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad, Simon Hudon
-/
import data.pfunctor.multivariate.W
import data.qpf.multivariate.basic
universes u v
/-!
# The initial algebra of a multivariate qpf is again a qpf.
For a... |
6e8b54e08f7ea37b7d58171c1b2c0353c4b8c9e8 | acc85b4be2c618b11fc7cb3005521ae6858a8d07 | /data/encodable.lean | 500d94530805fc563e7c8df71ea01d5547b73fcd | [
"Apache-2.0"
] | permissive | linpingchuan/mathlib | d49990b236574df2a45d9919ba43c923f693d341 | 5ad8020f67eb13896a41cc7691d072c9331b1f76 | refs/heads/master | 1,626,019,377,808 | 1,508,048,784,000 | 1,508,048,784,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 8,765 | 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, Mario Carneiro
Type class for encodable Types.
Note that every encodable Type is countable.
-/
import data.finset data.list data.list.perm data.list.sort
... |
a24e38a93b8c7d2ac2dbdaa2285e824a3e274b54 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/category_theory/fully_faithful.lean | 21c4b2a4b272d576c447160ddcd2444702d3a951 | [
"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 | 9,163 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.natural_isomorphism
import data.equiv.basic
/-!
# Full and faithful functors
We define typeclasses `full` and `faithful`, decorating functors... |
45151d50d07c58caaa55be70b22c2e9e2620c7c7 | 42c01158c2730cc6ac3e058c1339c18cb90366e2 | /M1F/2017-18/Example_Sheet_01/Question_05/solution_5.lean | 1e7c7255a50c08a7975f782ca36dd0f38814bf25 | [] | no_license | ChrisHughes24/xena | c80d94355d0c2ae8deddda9d01e6d31bc21c30ae | 337a0d7c9f0e255e08d6d0a383e303c080c6ec0c | refs/heads/master | 1,631,059,898,392 | 1,511,200,551,000 | 1,511,200,551,000 | 111,468,589 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,109 | lean | inductive zfc : Type
| empty : zfc
| insert : zfc → zfc → zfc
instance : has_emptyc zfc := ⟨zfc.empty⟩
instance : has_insert zfc zfc := ⟨zfc.insert⟩
instance : has_zero zfc := ⟨{}⟩
instance : has_one zfc := ⟨{0}⟩
def succ (a : zfc) : zfc := has_insert.insert a a
def zfc_add : zfc → zfc → zfc
| m 0 := m
| m (zfc.in... |
5f25592098e84236c2131caa609e852544d0c2d3 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/measure_theory/decomposition/radon_nikodym.lean | 3de23f002f72e832f92136fcf5bdb9e9c61be230 | [
"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 | 4,915 | lean | /-
Copyright (c) 2021 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import measure_theory.decomposition.lebesgue
/-!
# Radon-Nikodym theorem
This file proves the Radon-Nikodym theorem. The Radon-Nikodym theorem states that, given measures... |
ec7a4eff7c70b44b1bc68eeee64f601ea237e6bc | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/data/equiv/functor.lean | fefa6dfe696f899ffd07e065eac7cf2a78807550 | [] | 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 | 2,785 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Simon Hudon, Scott Morrison
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.data.equiv.basic
import Mathlib.control.bifunctor
import Mathl... |
4e75b5cef006bbb4ae353a1267ac54fd421107ac | 302c785c90d40ad3d6be43d33bc6a558354cc2cf | /src/analysis/normed_space/basic.lean | ee39eeb815b6b5dbfc95fb0014df51ccf25173dd | [
"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 | 71,605 | 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.algebra.algebra
import topology.metric_space.antilipschitz
/-!
# Norm... |
307b903340cf958a3eb7238ecf441d7872eaa591 | 83c8119e3298c0bfc53fc195c41a6afb63d01513 | /library/init/category/monad_fail.lean | f73742e35c41e2071a7391307196c62750cc9d43 | [
"Apache-2.0"
] | permissive | anfelor/lean | 584b91c4e87a6d95f7630c2a93fb082a87319ed0 | 31cfc2b6bf7d674f3d0f73848b842c9c9869c9f1 | refs/heads/master | 1,610,067,141,310 | 1,585,992,232,000 | 1,585,992,232,000 | 251,683,543 | 0 | 0 | Apache-2.0 | 1,585,676,570,000 | 1,585,676,569,000 | null | UTF-8 | Lean | false | false | 603 | 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.category.lift init.data.string.basic
universes u v
class monad_fail (m : Type u → Type v) :=
(fail {} : Π {a}, string → m a)
def matc... |
6a8638623226e8174c1b9507ed157d253b72631a | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/interactive/hole1.lean | 81a18fb02aa90ee643600c47659816fe8451e224 | [
"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 | 85 | lean | def x : nat → nat :=
λ a, {! a + a !}
--^ "command": "hole", "action": "Use"
|
b255914b7ff6a857aec8d5a375e5b00e3b307d01 | 432d948a4d3d242fdfb44b81c9e1b1baacd58617 | /src/algebra/continued_fractions/computation/approximation_corollaries.lean | 7787c0242ed6f5e5b44c55a1390fca7fe0f03af6 | [
"Apache-2.0"
] | permissive | JLimperg/aesop3 | 306cc6570c556568897ed2e508c8869667252e8a | a4a116f650cc7403428e72bd2e2c4cda300fe03f | refs/heads/master | 1,682,884,916,368 | 1,620,320,033,000 | 1,620,320,033,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,584 | lean | /-
Copyright (c) 2021 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import algebra.continued_fractions.computation.approximations
import algebra.continued_fractions.convergents_equiv
import topology.algebra.ordered
/-!
# Corollari... |
84b8e2c4f119304e038a5c72739d213eb0d0c4f3 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/linear_algebra/quotient.lean | e76a86d7e1d913f9eec7e6995e98c5597b4d0f3d | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 21,368 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov
-/
import group_theory.quotient_group
import linear_algebra.span
/-!
# Quotients by submodules
> THIS FILE IS SYNCHRONI... |
ba9f4560b8c74054a2f26a43cfed5bfb1bf99db8 | 437dc96105f48409c3981d46fb48e57c9ac3a3e4 | /src/topology/metric_space/emetric_space.lean | b025a644cc593bc910ab950832409e07f295b63b | [
"Apache-2.0"
] | permissive | dan-c-k/mathlib | 08efec79bd7481ee6da9cc44c24a653bff4fbe0d | 96efc220f6225bc7a5ed8349900391a33a38cc56 | refs/heads/master | 1,658,082,847,093 | 1,589,013,201,000 | 1,589,013,201,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 40,247 | lean | /-
Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
-/
import data.real.ennreal
import topology.uniform_space.uniform_embedding
import topology.unifo... |
b0596796770e0c649d4ea160c8ff3c16f976acc3 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/quot.lean | 6f32e7c9e1e52f62a2b41635dcce1ca176782fc2 | [
"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 | 27,597 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import logic.relator
/-!
# Quotient types
This module extends the core library's treatment of quotient types (`init.data.quot`).
## Tags
quotient
-/
variables {α... |
b3186aeb7440a65143a566c04d3ef720f15370b1 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/number_theory/padics/padic_norm.lean | 848016d6de9f955a31520ba8df65fd326cc23aa2 | [
"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 | 9,929 | 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
-/
import number_theory.padics.padic_val
/-!
# p-adic norm
This file defines the p-adic norm on ℚ.
The p-adic valuation on ℚ is the difference of the multiplicities... |
bf3c4dadc4f682fcd29baba4efb82eef2e51e044 | 0c6b99c0daded009943e570c13367c8cc7d3bcae | /chapter5.lean | 157d480149ce22f2a8575a7cdba765eff334068e | [] | no_license | TateKennington/logic-and-proof-exercises | e3c5c5b12b6238b47b0c5acf8717923bd471a535 | acca8882026e7b643453eb096d3021cd043005bd | refs/heads/main | 1,687,638,489,616 | 1,626,858,474,000 | 1,626,858,474,000 | 371,871,374 | 4 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,864 | lean | section
variable A: Prop
variable h: A ∨ ¬A
example: (¬A → false) → A :=
assume hna,
have h₁: A → A, from assume :A, this,
have h₂: ¬A → A, from assume :¬A, false.elim (hna this),
or.elim h h₁ h₂
end
section
variables A B: Prop
variable h: ¬A ∨ ¬B
example: ¬(A ∧ B) :=
assume h₁,
h... |
acc1d1c46134922c20f33f2fc62cfb744f70b177 | e0f9ba56b7fedc16ef8697f6caeef5898b435143 | /src/data/list/sigma.lean | 32a0e9ab9caf7e42312bef2a0701f82ca25d0606 | [
"Apache-2.0"
] | permissive | anrddh/mathlib | 6a374da53c7e3a35cb0298b0cd67824efef362b4 | a4266a01d2dcb10de19369307c986d038c7bb6a6 | refs/heads/master | 1,656,710,827,909 | 1,589,560,456,000 | 1,589,560,456,000 | 264,271,800 | 0 | 0 | Apache-2.0 | 1,589,568,062,000 | 1,589,568,061,000 | null | UTF-8 | Lean | false | false | 24,093 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Sean Leather
Functions on lists of sigma types.
-/
import data.list.perm
import data.list.range
import data.sigma
universes u v
namespace list
variables {α : Type u}... |
663af5bbe812ddb11777363e8724fb3b0d2b26be | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/analysis/normed_space/M_structure.lean | 83daa7c1b1d291a8318fea3baebbed517ae7332e | [
"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 | 13,587 | lean | /-
Copyright (c) 2022 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin
-/
import analysis.normed_space.basic
import algebra.ring.idempotents
import tactic.noncomm_ring
/-!
# M-structure
A projection P on a normed space X is said t... |
abed4b138b5cc81c09fdcc70e88bfd02c9347285 | 5df84495ec6c281df6d26411cc20aac5c941e745 | /src/formal_ml/real_random_variable.lean | 5e382a8e716ea677045f8dcebeefcec270d7a77e | [
"Apache-2.0"
] | permissive | eric-wieser/formal-ml | e278df5a8df78aa3947bc8376650419e1b2b0a14 | 630011d19fdd9539c8d6493a69fe70af5d193590 | refs/heads/master | 1,681,491,589,256 | 1,612,642,743,000 | 1,612,642,743,000 | 360,114,136 | 0 | 0 | Apache-2.0 | 1,618,998,189,000 | 1,618,998,188,000 | null | UTF-8 | Lean | false | false | 102,609 | lean | /-
Copyright 2020 Google LLC
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
di... |
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