chars int64 40 24k | content_type stringclasses 9
values | id stringlengths 13 64 | source stringclasses 5
values | subset stringclasses 31
values | text stringlengths 40 24k |
|---|---|---|---|---|---|
2,155 | lean_file_chunk | 3dd430c8425a26d5b6ccd1d0f98f358c56ead35f9e69157a5da837daa96a5472 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
-/
module
public import Mathlib.Algebra.BigOperators.Group.Finset.Defs
/-! # Lemmas about coprimality with big products.
These lemmas are kept separa... |
1,147 | lean_file_chunk | 0223096e695fc204ee30b1211c1975aa7cf2928ae2453fa74ebb36bd2172de2d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yongshun Ye. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yongshun Ye
-/
module
public import Mathlib.Data.Nat.GCD.Basic
public import Mathlib.Data.Nat.Prime.Defs
/-!
# Lemmas related to `Nat.Prime` and `lcm`
This file contains lemmas related... |
2,450 | lean_file_chunk | a884d33df451dd23be6ed91fa34005248d45bae089f608822201dcedc0ae9dce | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Shing Tak Lam, Mario Carneiro
-/
module
public import Mathlib.Data.List.Palindrome
public import Mathlib.Data.Nat.Digits.Lemmas
/-!
# Divisibility tests for natural numbe... |
22,234 | lean_file_chunk | f791a542a615b45bf4850d919a3e512da54055059a708341b2da6f1591a1a23a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Shing Tak Lam, Mario Carneiro
-/
module
public import Mathlib.Algebra.BigOperators.Intervals
public import Mathlib.Algebra.BigOperators.Ring.List
public import Mathlib.Dat... |
21,031 | lean_file_chunk | 4419a887ea8a5b450b09ca7f8360facc9c25ac2e1052bb76ac43a74105de4eac | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Shing Tak Lam, Mario Carneiro
-/
module
public import Mathlib.Tactic.NormNum
public import Mathlib.Tactic.Ring
public import Mathlib.Tactic.Linarith
public import Mathlib.... |
9,200 | lean_file_chunk | 030daeae1679330480a9b689695427dc997a170e56fbfa767ec4e3449bda5e39 | lean_source_file | pkg_mathlib_source_file_chunks | /-
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
-/
module
public import Mathlib.Data.Finset.NatAntidiagonal
public import Mathlib.Data.Nat.GCD.Basic
public import Mathlib.Data.Nat.Bin... |
7,818 | lean_file_chunk | 1135bbddb632c140d79715146e1e04eabc483acbee97871e0087237237f5ab13 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Data.Nat.Fib.Basic
/-!
# Zeckendorf's Theorem
This file proves Zeckendorf's theorem: Every natural number can be written uniquely as a sum... |
731 | lean_file_chunk | 49b1fb61c53f56cc66cd05d641c4d6846f0440b97b8a1497f448a2ebe2e5269f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Ralf Stephan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ralf Stephan
-/
module
public import Mathlib.Data.Nat.Prime.Defs
public import Mathlib.Data.Nat.Nth
/-!
# The Nth primes
-/
public section
namespace Nat
@[simp]
theorem nth_prime_ze... |
944 | lean_file_chunk | f3db16c1c59fd078e05476bf813b331c5da8740a4142e904d58a906d1257651b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
module
public import Mathlib.Data.Nat.Prime.Basic
/-!
# Prime numbers
This file develops the theory of prime numbers: natu... |
2,302 | lean_file_chunk | 91c946b21177d5887b28721d479b05adca50d4b0001ddade7f2dfa198ff8cb35 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
module
public import Mathlib.Algebra.Ring.Int.Defs
public import Mathlib.Data.Nat.Prime.Basic
public import Mathlib.Algebra.... |
11,163 | lean_file_chunk | 387596bc9f23f8144e01bc1d6b9a61a6d266217cce6d174299b2d6c99f7e7a0e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
module
public import Mathlib.Algebra.GroupWithZero.Associated
public import Mathlib.Algebra.Ring.Parity
public import Mathli... |
16,109 | lean_file_chunk | 896f1cf900f9320e7cdcc099f6f48d0f3123126a8d481bb00b89bfa878315668 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
module
public import Mathlib.Algebra.Group.Nat.Units
public import Mathlib.Algebra.GroupWithZero.Nat
public import Mathlib.A... |
1,490 | lean_file_chunk | dc41896e87e24f42b51219c58eac4bf21a0f5b1f81d29dbf8d29a33c26c81111 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
module
public import Mathlib.Data.Nat.Factorial.Basic
public import Mathlib.Data.Nat.Prime.Defs
public import Mathlib.Order.... |
1,644 | lean_file_chunk | 01a72a235f5fafcbd6ecdec62ab321deae6a5e48d47bc43acd38bf3bda5244f8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
module
public import Mathlib.Data.Nat.Factorial.Basic
public import Mathlib.Data.Nat.Prime.Basic
/-!
# Prime natural numbers... |
4,595 | lean_file_chunk | 60e0a4b061e0591f50ee9852f4b1d8dfa712987c3b13312733a973bdd5c98fe5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
public import Mathlib.Algebra.Order.Group.Unbundled.Abs
public import Mathlib.Algebra.Order.Ring.Nat
public import Mathlib.Algebra.Order.Sub.Basic
public impo... |
4,814 | lean_file_chunk | 315e8ce35a4df1990b531a7ba387a22b5a2bbf16f76a78b143981676c002d547 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
public import Mathlib.Algebra.Order.Monoid.Unbundled.Basic
public import Mathlib.Algebra.Order.ZeroLEOne
public import Mathlib.Data.Nat.Cast.Basic
public impo... |
2,411 | lean_file_chunk | 47c33dbeb0940cd419f05c77d7e92505bdb5ac1280370c01eff8fc363be096e2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Yaël Dillies, Patrick Stevens
-/
module
public import Mathlib.Algebra.Order.Field.Basic
/-!
# Cast of naturals into ordered fields
This file concerns the canonical h... |
2,880 | lean_file_chunk | ba866c6f206e55a2253ae7564d9dd566268b2955a245e55d0722966dd6818e54 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
module
public import Mathlib.Algebra.BigOperators.Finprod
public import Mathlib.Data.Set.Card
public import Mathlib.Data.Setoid.Partition
/-! # Cardin... |
3,317 | lean_file_chunk | b2093a6665e5b2a9f125c0b8532483a1b533a9f10366848373380546f3e8774b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
module
public import Mathlib.Algebra.Order.Nonneg.Field
public import Mathlib.Data.Rat.Cast.Defs
public import Mathlib.Tactic.Positivity.Basic
/-!
#... |
9,816 | lean_file_chunk | 218e1425bb0fc2532ce048ac1aebee6d11b8b81c3532942acb042bc1b7f33c31 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
module
public import Mathlib.Algebra.Order.Field.Rat
public import Mathlib.Data.Rat.Cast.CharZero
public import Mathlib.Tactic.Positivity.Core
/-!
#... |
826 | lean_file_chunk | b8ddefc4c095c47eee81188499ca95e3c0a0bc4bdb856b376022d94028543ddf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Data.Rat.Cast.CharZero
public import Mathlib.Data.Rat.Cast.Lemmas
/-!
The `OfScientific` instance for any characteristic zero field
is wel... |
10,659 | lean_file_chunk | 6d3eb0162ab2bfb7eb1c34137c40843db579751dff4d8378d18b354caa5ffe7f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
module
public import Mathlib.Algebra.Field.Basic
public import Mathlib.Algebra.Field.Rat
public import Mathlib.Algebra.Group.Commute.Basic
public imp... |
4,289 | lean_file_chunk | 60e9909b07fcfe4855cdac27d81f748e9796aa5631927a69eefdc0da808bf765 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
module
public import Mathlib.Algebra.GroupWithZero.Units.Lemmas
public import Mathlib.Data.Rat.Cast.Defs
/-!
# Casts of rational numbers into charac... |
1,275 | lean_file_chunk | 5c9922b9834e306e34dcaf12861be0166129ae6cdc58be7e5abff5d5fcf0cc44 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Tactic.Positivity
public import Mathlib.Algebra.Order.Field.Basic
/-!
Rational approximation of the square root of a natural number.
See ... |
1,879 | lean_file_chunk | 5458030996a1845c8ecdd6ed446920d59f52e57b97fdaf028b727b593398ac34 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Data.Rat.NatSqrt.Defs
public import Mathlib.Data.Real.Sqrt
/-!
Comparisons between rational approximations to the square root of a natural... |
1,512 | lean_file_chunk | 9d66a11c0a228d2154cf76d65953e476ea4a5c453e794e2acf1533c5a57936a5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
module
public import Mathlib.Algebra.Order.Ring.Abs
/-!
# Further lemmas about the integers
The distinction between this file and `Mathlib/Data/Int/Order/Basic.lean`... |
2,088 | lean_file_chunk | c509f4cf24d1fc85f09f5b619340245781a3abcc56645aa0f01d62cd82880f07 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
module
public import Mathlib.Data.Int.Notation
public import Mathlib.Data.Nat.Notation
public import Mathlib.Order.Defs.LinearOrder
public import Mathlib.Tactic.ByCase... |
1,891 | lean_file_chunk | f1e44d34f8274e82e46c99893174ac25e401c6819b5300f7f1272e8234ce3cd6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
module
public import Mathlib.Algebra.Order.Ring.Abs
/-!
# Lemmas about units in `ℤ`, which interact with the order structure.
-/
public section
namespace Int
theo... |
11,300 | lean_file_chunk | c18716ca498871c35927d7823332d96172d38c3f2c780cd9f797ed42fa82a805 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
public import Mathlib.Algebra.Group.TypeTags.Hom
public import Mathlib.Algebra.Ring.Int.Defs
public import Mathlib.Algebra.Ring.Parity
/-!
# Cast of integers... |
766 | lean_file_chunk | ea56a936f20dc77eceede9c6193ece24e12be911442886deab52cbe318882f24 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
public import Mathlib.Data.Int.Cast.Basic
public import Mathlib.Data.Nat.Cast.Prod
/-!
# The product of two `AddGroupWithOne`s.
-/
@[expose] public section
... |
987 | lean_file_chunk | ea6b4e3801426f1f810f31f339081a6ace148df681761ee29fc35df094c3fe86 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
public import Mathlib.Data.Int.Notation
public import Mathlib.Tactic.Push.Attr
/-!
# Cast of integers to function types
This file provides a (pointwise) cas... |
3,983 | lean_file_chunk | 5c33fb24ee012d1223681f65d91cd3b075d5d48c1812229e950ab3e4e829fa25 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Gabriel Ebner
-/
module
public import Mathlib.Data.Int.Cast.Defs
public import Mathlib.Algebra.Group.Basic
public import Mathlib.Data.Nat.Basic
/-!
# Cast of integers... |
1,805 | lean_file_chunk | 0b2c8b0dae452c57658602e67ba1fa6cda3e8f52d7bf040019a13c7abaf68007 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Gabriel Ebner
-/
module
public import Mathlib.Data.Nat.Cast.Defs
/-!
# Cast of integers
This file defines the *canonical* homomorphism from the integers into an
addi... |
1,125 | lean_file_chunk | c6a16383c598f9b409228a1c48be4f6b1ce5610fcef8bad51862c8e6254e0325 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
module
public import Mathlib.Algebra.Field.Defs
public import Mathlib.Algebra.Ring.Int.Defs
/-!
# Cast of integers into fields
This file concerns the canonical homom... |
2,072 | lean_file_chunk | dc1e865ea7649f47f8f294bdac12ae672589646745d3df4aa2d4cb70c139cdc9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
module
public import Mathlib.Data.Int.Fib.Basic
/-!
# Cassini and Catalan identities for the Fibonacci numbers
Cassini's identity states that for `n : ℤ`, `fib (n + 1) *... |
6,597 | lean_file_chunk | a38ba51e3288c2e4f1c70c7dbe6e5864e2fdd77a5f31bd6fcc8e069dd99530a2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
module
public import Mathlib.Algebra.Group.Int.Even
public import Mathlib.Data.Nat.Fib.Basic
/-!
# Fibonacci numbers extended onto the integers
This file defines the Fi... |
2,433 | lean_file_chunk | 7dff343d215b1652dc5d2a064fa03b8416f1dfed6451903ca5c5db264b07abb6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
module
public import Batteries.Data.List.Perm
public import Mathlib.Data.List.Basic
public import Batteries.Tactic.Trans
pub... |
9,359 | lean_file_chunk | cd99dd07d92f3346f6ab197bb578da2f9966607e72dcc445bc5b3a5bba36176d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
module
public import Batteries.Data.List.Perm
public import Mathlib.Logic.Relation
public import Mathlib.Data.List.Forall2
p... |
2,939 | lean_file_chunk | 70a1a43adcbdef27fe9a37911c311e7f93dafde09d379a8190cbca540c0f6326 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
module
public import Mathlib.Data.List.Forall2
public import Mathlib.Data.List.TakeDrop
public import Mathlib.Data.List.Latt... |
6,442 | lean_file_chunk | a5c8157186285d51605c8e9cfcf54ae117d80a40daffcdaf92517d4459474dc7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Pim Otte. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pim Otte
-/
module
public import Mathlib.Algebra.BigOperators.Finprod
public import Mathlib.Data.Set.Card
public import Mathlib.SetTheory.Cardinal.Arithmetic
public import Mathlib.Algebra.O... |
3,541 | lean_file_chunk | 87f6cf0cd1c23cd7e78e7c65ddc7d5bec76847885af3843857a0231e479d672a | lean_source_file | pkg_mathlib_source_file_chunks | /-
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, Kyle Miller
-/
module
public import Mathlib.Data.Finset.Max
public import Mathlib.Data.Set.Finite.Basic
public import Mathlib.Data.Set.Lattice
public i... |
960 | lean_file_chunk | 7849ada474f221f12cd73ce72478de19312ddc273e830694415461538dd7b662 | lean_source_file | pkg_mathlib_source_file_chunks | /-
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, Kyle Miller
-/
module
public import Mathlib.Data.Set.Finite.Basic
public import Mathlib.Data.Set.Finite.Lattice
public import Mathlib.Data.Set.Finite.R... |
3,347 | lean_file_chunk | 7b8252aebd1ed3586405e4c1886af3d0708912d1846d04ec340a1cec05ff8d20 | lean_source_file | pkg_mathlib_source_file_chunks | /-
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, Kyle Miller
-/
module
public import Mathlib.Data.Finite.Prod
public import Mathlib.Data.Set.Finite.Lattice
public import Mathlib.Data.Set.Functor
/-!
... |
23,945 | lean_file_chunk | 28ca98692bc4ef7979fa60e678b5968e9c739fc1877307da364545cb05761b42 | lean_source_file | pkg_mathlib_source_file_chunks | /-
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, Kyle Miller
-/
module
public import Mathlib.Data.Fintype.EquivFin
public import Mathlib.Tactic.Nontriviality
/-!
# Finite sets
This file provides `Fi... |
12,146 | lean_file_chunk | b31b0d502c5ee6cb5b74c64b84d023f073649fa8c9cfd65ac928364d63d5a560 | lean_source_file | pkg_mathlib_source_file_chunks | theorem finite_union {s t : Set α} : (s ∪ t).Finite ↔ s.Finite ∧ t.Finite :=
⟨fun h => ⟨h.subset subset_union_left, h.subset subset_union_right⟩, fun ⟨hs, ht⟩ =>
hs.union ht⟩
theorem finite_image_iff {s : Set α} {f : α → β} (hi : InjOn f s) : (f '' s).Finite ↔ s.Finite :=
⟨fun h => h.of_finite_image hi, Finite... |
1,532 | lean_file_chunk | c610dfca5a92d10910127df4151974d3e90f4e91c1b231abe0439ce01c4b18b2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
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, Kyle Miller
-/
module
public import Mathlib.Data.Finset.Powerset
public import Mathlib.Data.Set.Finite.Basic
/-!
# Finiteness of the powerset of a fin... |
2,814 | lean_file_chunk | 5cf9954f380e14dfc5c2cf094bb954f4ed7d243a11d5727e7ab9cff087c697b9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
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, Kyle Miller
-/
module
public import Mathlib.Data.Fintype.EquivFin
public import Mathlib.Data.ULift
/-!
# Finiteness of `Set.range`
## Implementation ... |
18,088 | lean_file_chunk | f507f68f9b1596721d70d33891b9cca137b6f462d5dc69a5ff4f1f754102c6cc | lean_source_file | pkg_mathlib_source_file_chunks | /-
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, Kyle Miller
-/
module
public import Mathlib.Data.Set.Finite.Powerset
public import Mathlib.Data.Set.Finite.Range
public import Mathlib.Data.Set.Lattice... |
23,942 | lean_file_chunk | 35ffbdf78e4755239aa23d12ac9a717a09738e16d715be0487f4fc182208e304 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Johannes Hölzl, Mario Carneiro
-/
module
public import Mathlib.Data.Set.Lattice
public import Mathlib.Tactic.Monotonicity.Attr
/-!
# The set lattice ... |
239 | lean_file_chunk | ed01037453c77863b3b6e7482501756a440062541e9925cad24bcb1b19d940e3 | lean_source_file | pkg_mathlib_source_file_chunks | rw [← prod_eq_seq, ← image_swap_prod, prod_eq_seq, image_seq, ← image_comp]; rfl
theorem image2_eq_seq (f : α → β → γ) (s : Set α) (t : Set β) : image2 f s t = seq (f '' s) t := by
rw [seq_eq_image2, image2_image_left]
end Seq
end Set |
1,098 | lean_file_chunk | ee476adb78b4f52a91019af309437d2986af47060ccaa996d95c734145ad3995 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jasper Mulder-Sohn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Edward van de Meent, Jasper Mulder-Sohn
-/
module
public import Mathlib.Data.Set.Pairwise.Lattice
public import Mathlib.Order.Preorder.Chain
/-!
# Pairwise results for chains
In... |
1,114 | lean_file_chunk | 22bade78bb9421cde2256e3f5d23b97cff14eb0d81bd2ab8c0f941f1265b0800 | lean_source_file | pkg_mathlib_source_file_chunks | /-
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
-/
module
public import Mathlib.Data.List.Nodup
public import Mathlib.Data.Set.Pairwise.Basic
/-!
# Translating pairwise relations on sets to lists
On a li... |
18,737 | lean_file_chunk | 552b7c740eded743109eaf63d8c8dfcbf6567e4727899271926c662c9bc1b545 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
module
public import Mathlib.Data.Set.Function
public import Mathlib.Logic.Pairwise
public import Mathlib.Logic.Relation
/-!
# Relations holding pairwise
This file... |
7,828 | lean_file_chunk | 8d66619347969d35383824a005d6cbf2f7517d11dfc31f3eb4cb70025b2aa08c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
module
public import Mathlib.Data.Set.Lattice
public import Mathlib.Data.Set.Pairwise.Basic
/-!
# Relations holding pairwise
In this file we prove many facts about... |
1,667 | lean_file_chunk | 907e50411495eca1437a09f8fe9cc0220424100aa58a745df3b9cc2095c95b96 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
module
public import Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set
public import Mathlib.Algebra.Notation.Support
/-!
# Support of a function composed wi... |
7,183 | lean_file_chunk | 6ec459a3826274c41190e9fba0db9286f2399162f9a028e53e1b61f20e9ad7cb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Mario Carneiro, Simon Hudon
-/
module
public import Mathlib.Data.Fin.Fin2
public import Mathlib.Data.TypeVec
public import Mathlib.Logic.Equiv.Defs
/-!
# Functors betw... |
5,559 | lean_file_chunk | 66dd508bd00d647703dea578630e559995a12d8921a2150c7cb0b09da4c075ec | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
module
public import Mathlib.Control.Applicative
public import Mathlib.Control.Traversable.Basic
public import Mathlib.Data.List.Forall2
public import Mathlib.Data.Set.Fun... |
3,819 | lean_file_chunk | 6072d428c69f69a8dc689c05b64fd060fb8e245d097998edb6f4b413c4ada915 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
module
public import Mathlib.Control.Applicative
public import Mathlib.Control.Traversable.Basic
import Mathlib.Tactic.Attr.Register
/-!
# Traversing collections
This f... |
9,750 | lean_file_chunk | 39b490a264c60e76ac854760cf73c90fef96a306e361cfdf362efb85c070ce21 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
module
public import Mathlib.Data.Option.Defs
public import Mathlib.Control.Functor
public import Batteries.Data.List.Basic
public import Mathlib.Control.Basic
import Mat... |
6,615 | lean_file_chunk | ea0aa0849495ecbf6ca055d3e1b1faaf6d93e4f20f0f841be67c3082ede6ae20 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
module
public import Mathlib.Control.Traversable.Lemmas
public import Mathlib.Logic.Equiv.Defs
public import Batteries.Tactic.SeqFocus
import Mathlib.Tactic.Attr.Register... |
4,866 | lean_file_chunk | a23b5f8f86234095826c551b2dd68b0b74fb18bd1852eee4f9762a1b55bc43cc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
module
public import Mathlib.Control.Bitraversable.Lemmas
public import Mathlib.Control.Traversable.Lemmas
/-!
# Bitraversable instances
This file provides `Bitraversabl... |
3,069 | lean_file_chunk | 8d1d9e1dc37cb69281396e17aaccb9a73f79fe05bdc925bbfe0380ead8a79618 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
module
public import Mathlib.Control.Bitraversable.Basic
/-!
# Bitraversable Lemmas
## Main definitions
* tfst - traverse on first functor argument
* tsnd - traverse... |
3,034 | lean_file_chunk | 2f4f960d782648e7e26abb56611a42fcf43182d28cc9dd098c09a0bdec472cbd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
module
public import Mathlib.Control.Bifunctor
public import Mathlib.Control.Traversable.Basic
/-!
# Bitraversable type class
Type class for traversing bifunctors.
Simp... |
7,796 | lean_file_chunk | 9fd6e596168c7a26746482f5f3c93eb59c192a979b27a80497ccc3cf5d18c76f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Edward Ayers, Eric Wieser
-/
module
public import Mathlib.Algebra.Group.Defs
public import Mathlib.Logic.Equiv.Defs
/-!
# Writer monads
This file introduces mona... |
2,068 | lean_file_chunk | b39bddc87292a1e8daf3d051b449591bed5a85f07470b3451c24ffa8135bab4f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
module
public import Mathlib.Logic.Equiv.Defs
public import Batteries.Lean.Except
import Mathlib.Tactic.Attr.Register
/-!
# Monad
## Attributes
* ext
* functor_norm
* ... |
10,796 | lean_file_chunk | aef4676e373dc4990ecf9334149652ec25358874a320375f745c25bb992d90af | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
module
public import Mathlib.Control.Monad.Basic
public import Mathlib.Control.Monad.Writer
public import Mathlib.Control.Lawful
public import Batteries.Tactic.Congr
publi... |
1,552 | lean_file_chunk | 98b2a15c1f3eb659e43890582b106d6133c4e1092c4310caab906379b3ed2559 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Control.EquivFunctor
public import Mathlib.Data.Fintype.OfMap
/-!
# `EquivFunctor` instances
We derive some `EquivFunctor` instances, to e... |
23,972 | lean_file_chunk | f30dc381940872a8eb20427762ed828454f26e0d03f6974334713e55835b4f58 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
module
public import Mathlib.Computability.AkraBazzi.GrowsPolynomially
public import Mathlib.Analysis.SpecialFunctions.Pow.Continuity
import Mathlib.Analysis.Spec... |
11,349 | lean_file_chunk | 8da130441d748451fd01078423bc3c5ea3d9e75003df221e8ff86836c2808f18 | lean_source_file | pkg_mathlib_source_file_chunks | Several properties of the sum transform are then proven.
-/
/-- The transformation that turns a function `g` into
`n ^ p * ∑ u ∈ Finset.Ico n₀ n, g u / u ^ (p + 1)`. -/
noncomputable def sumTransform (p : ℝ) (g : ℝ → ℝ) (n₀ n : ℕ) :=
n ^ p * ∑ u ∈ Finset.Ico n₀ n, g u / u ^ (p + 1)
lemma sumTransform_def {p : ℝ} {g... |
23,989 | lean_file_chunk | c2728637a93caa3096a84f19d30188c20fbafdcd7df8bbfb59fb7ea0ea5356c5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
module
public import Mathlib.Analysis.SpecialFunctions.Pow.Real
public import Mathlib.Algebra.Order.ToIntervalMod
public import Mathlib.Analysis.SpecialFunctions.L... |
4,989 | lean_file_chunk | 4babbbc8e3e91a25c1056f8923e05a80033a81f1209682dbaf729cd8bbd7bfbb | lean_source_file | pkg_mathlib_source_file_chunks | case ub => calc
(f u) ^ p ≤ (c₁ * f x) ^ p := by
exact rpow_le_rpow_of_nonpos (by positivity) (hf₁ u hu).1 (le_of_lt hp)
_ = _ := by rw [← mul_rpow (le_of_lt hc₁_mem) (le_of_lt hf_pos)]
| .inr (.inr hneg) => -- eventually negative (which is impossible)
have : ∀ᶠ (_ : ℝ) in atTo... |
23,986 | lean_file_chunk | cb347a31b5a5b92b50d3cb7be65866b895992802c88efe832eca1f37bb29fc1a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
module
public import Mathlib.Computability.AkraBazzi.SumTransform
import Mathlib.Analysis.SpecialFunctions.Pow.Deriv
/-!
# Divide-and-conquer recurrences and the ... |
10,524 | lean_file_chunk | aa823c2d6fd48a826496d48e2097a42e19d4babda4119f6367f6bfe02bf15a1a | lean_source_file | pkg_mathlib_source_file_chunks | -- n₀_div_le_n
eventually_ge_atTop ⌈n₀ / b'⌉₊]
with n hn bound1 h_smoothing_pos h_sumTransform h_smoothing_gt_half h_bi_le_r n₀_div_le_n
--have n₀_le_bn : n₀ ≤ b' * n := by
-- sorry
have n₀_le_r : ∀ i, n₀ ≤ r i n := by
intro i
exact_mod_cast
calc n₀ ≤ b' * n := by
have : (... |
23,974 | lean_file_chunk | daaa4a119af0df56bf78cdc02dba43f9493dafe2acdffae409808655ce9d741c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
public import Mathlib.Computability.Primrec.Basic
public import Mathlib.Logic.Encodable.Pi
/-!
# Primitive recursive functions on Lists
The primitive recurs... |
9,452 | lean_file_chunk | f50cea779f1b662016e2b860be131b6f7291cd8c0fc92f13d0e5d1d70d233e24 | lean_source_file | pkg_mathlib_source_file_chunks | (list_getElem?.comp (vector_toList.comp fst) (fin_val.comp snd)).of_eq fun a => by
simp [Vector.get_eq_get_toList]
theorem list_ofFn :
∀ {n} {f : Fin n → α → σ}, (∀ i, Primrec (f i)) → Primrec fun a => List.ofFn fun i => f i a
| 0, _, _ => by simp only [List.ofFn_zero]; exact const []
| n + 1, f, hf => b... |
23,950 | lean_file_chunk | c093d9d8722e5d76badabe638770d299f4c382579624fff4abc209cfe838a651 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
public import Mathlib.Algebra.Order.Ring.Nat
public import Mathlib.Logic.Function.Iterate
public import Mathlib.Logic.Denumerable
/-!
# The primitive recursi... |
11,837 | lean_file_chunk | 1201ab0978388abcd54916bab1e16002975e2c648c24b1d4e608689f72623e06 | lean_source_file | pkg_mathlib_source_file_chunks | theorem ite {c : α → Prop} [DecidablePred c] {f : α → σ} {g : α → σ} (hc : PrimrecPred c)
(hf : Primrec f) (hg : Primrec g) : Primrec fun a => if c a then f a else g a := by
simpa [Bool.cond_decide] using cond hc.decide hf hg
theorem nat_le : PrimrecRel ((· ≤ ·) : ℕ → ℕ → Prop) :=
Primrec₂.primrecRel ((nat_cas... |
23,962 | lean_file_chunk | 6b3820f52e8f2296876d8ff74aad66a433c440246bf78ac5d3e218721d66f582 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
public import Mathlib.Computability.TuringMachine.Tape
public import Mathlib.Computability.StateTransition
public import Mathlib.Data.Finset.Prod
public impor... |
17,796 | lean_file_chunk | 48b620f728bf12108d01af01084db546c257f40b6eb9e8e0faac9e78c44d2a42 | lean_source_file | pkg_mathlib_source_file_chunks | cases h₁; refine TM1.stmts_trans ?_ h₂
unfold TM1.stmts₁
exact Finset.mem_insert_of_mem TM1.stmts₁_self
| load b q IH =>
refine IH _ (TM1.stmts_trans ?_ h₂) h₁ hs
unfold TM1.stmts₁
exact Finset.mem_insert_of_mem TM1.stmts₁_self
| branch p q₁ q₂ IH₁ IH₂ =>
cases h : p a v <;> ... |
23,959 | lean_file_chunk | c725f768e37c408c3b1e54f9e7dd68dfd09c211014d1058a2ef45a3188b5f1fb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
public import Mathlib.Computability.Halting
public import Mathlib.Computability.TuringMachine.StackTuringMachine
public import Mathlib.Data.Num.Lemmas
public ... |
23,967 | lean_file_chunk | 26f633020a7202e3cfc5869a58d5af3fdcfc71609222092b69bc16925d70c303 | lean_source_file | pkg_mathlib_source_file_chunks | exact fun x h => h₁ x (List.Mem.tail _ h)
theorem splitAtPred_false {α} (L : List α) : splitAtPred (fun _ => false) L = (L, none, []) :=
splitAtPred_eq _ _ _ _ _ (fun _ _ => rfl) ⟨rfl, rfl⟩
theorem move_ok {p k₁ k₂ q s L₁ o L₂} {S : K' → List Γ'} (h₁ : k₁ ≠ k₂)
(e : splitAtPred p (S k₁) = (L₁, o, L₂)) :
Rea... |
8,682 | lean_file_chunk | 5f40c21c8994aeeb852456259f185a3ce38104cfe347230e43cefe1d3b889164 | lean_source_file | pkg_mathlib_source_file_chunks | `codeSupp'_supports`, `contSupp_supports`, `codeSupp_supports`. The set `S` is fixed throughout
the proof, and denotes the full set of states in the machine, while `K` is a subset that we are
currently proving a property about. The predicate asserts that every state in `K` is closed in `S`
under forward simulation, i.e... |
10,926 | lean_file_chunk | 7c729c966c556a78a0916e91593ddd63afba32cd648edb58e0af4cd1de9dad7a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Pim Spelier, Daan van Gent. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pim Spelier, Daan van Gent
-/
module
public import Mathlib.Algebra.Polynomial.Eval.Defs
public import Mathlib.Computability.Encoding
public import Mathlib.Computability.Tu... |
23,996 | lean_file_chunk | f0ad60a82e9913de18ba4fa93a183ac48f163a13e5ecd6dab5a6399285f7164f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
public import Mathlib.Logic.Function.Iterate
public import Mathlib.Tactic.ApplyFun
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.Group.In... |
183 | lean_file_chunk | 38045259602e1eb250cc4a8f3434ea7564e8b0313f59e2a99cd437a434097896 | lean_source_file | pkg_mathlib_source_file_chunks | theorem Tape.map_mk₁ {Γ Γ'} [Inhabited Γ] [Inhabited Γ'] (f : PointedMap Γ Γ') (l : List Γ) :
(Tape.mk₁ l).map f = Tape.mk₁ (l.map f) :=
Tape.map_mk₂ _ _ _
end Tape
end Turing |
23,983 | lean_file_chunk | 10058b3ff8f5e662ae61f9a460fe30d6ad871975aad36cf3976725c3e582bb96 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
public import Mathlib.Computability.Halting
public import Mathlib.Computability.TuringMachine.PostTuringMachine
/-!
# Modelling partial recursive functions u... |
6,847 | lean_file_chunk | 3ff8b6f2d7d777d91e003eeb242b59c34fb74356903641aaf640fb9d33695039 | lean_source_file | pkg_mathlib_source_file_chunks | equality, not a simulation; the original and embedded machines move in lock-step until the
embedded machine reaches the halt state. -/
theorem stepRet_then {k k' : Cont} {v} : stepRet (k.then k') v = (stepRet k v).then k' := by
induction k generalizing v with simp only [Cont.then, stepRet, *]
| cons₁ =>
rw [← s... |
23,938 | lean_file_chunk | 8b07f5fb507eac24f3ea65f5ff97a4dba7144329d6853373cf63c7ef98eedc44 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
public import Mathlib.Computability.TuringMachine.Tape
public import Mathlib.Data.Fintype.Option
public import Mathlib.Data.Fintype.Prod
public import Mathlib... |
11,657 | lean_file_chunk | aafaf2232a422e4bb49561fe121a929d4f94314117e02fa15fd5be9755d5f34f | lean_source_file | pkg_mathlib_source_file_chunks | simp only [List.length_append, List.length_reverse, List.length_map, ← h,
Nat.sub_self, List.length_singleton, List.getElem_singleton,
le_refl, Nat.lt_succ_self]
rw [← proj_map_nth, hL, ListBlank.nth_mk]
rcases lt_or_gt_of_ne h with h | h
· rw [List.getI_append]
simpa only ... |
767 | lean_file_chunk | 1bb8324134d1908ffd507b2a6a7e270862b4f3b1c3534d5520c7d4a9702b6efe | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Paul Lezeau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Lezeau
-/
module
public import Mathlib.Algebra.CharZero.Defs
public import Mathlib.Algebra.Group.Equiv.Defs
public import Mathlib.Data.Nat.Cast.Basic
/-!
# Transporting `CharZero` ... |
2,812 | lean_file_chunk | 04943b456a98be3e5afa87383eab8c707ac9e744fe05b11c74ca3d3b90e97361 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.Algebra.Field.Basic
public import Mathlib.Algebra.Order.Group.Unbundled.Int
public import Mathlib.Algebra.Module.NatInt
public import Mathlib.... |
3,828 | lean_file_chunk | a685b939b2678fa2c710a618ca617b08755ad74040caac6c86714402238d3bd1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2014 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
module
public import Mathlib.Data.Int.Cast.Defs
public import Mathlib.Logic.Basic
/-!
# Characteristic zero
A ring `R` is called of characteristic zero if every n... |
547 | lean_file_chunk | 293bd37a710db14eb5ad306b2de88fec0f046e5c5e350448e3c049e9141d477a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
module
public import Mathlib.Algebra.CharZero.Defs
public import Mathlib.Data.Fintype.EquivFin
/-! # A characteristic-zero semiring is infinite -/
@[expose] public... |
6,824 | lean_file_chunk | 234acad1a2cea3483c4f9e7f829b692c1d15a8e035d1cdf9bf8d3a6e5bf58161 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Sven Holtrop and Leonid Ryvkin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sven Holtrop, Leonid Ryvkin
-/
module
public import Mathlib.RingTheory.Derivation.Lie
/-!
# Lie-Rinehart algebras
This file defines Lie-Rinehart algebras and their m... |
8,620 | lean_file_chunk | c443d77e0c52cf5d6ef9cee30447bc546e99554fd8d156e39568cc142c90d8d8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Yury Kudryashov
-/
module
public import Mathlib.Algebra.AddTorsor.Defs
public import Mathlib.Algebra.Group.Action.Basic
public import Mathlib.Algebra.Group.Action.Pi
publi... |
8,792 | lean_file_chunk | 0f1f69fe0e440cc1e3f279081f183823f7883a6f6c92762baa28019cdf12f039 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Yury Kudryashov
-/
module
public import Mathlib.Algebra.Group.Action.Defs
/-!
# Torsors of additive group actions
This file defines torsors of additive group actions.
#... |
14,617 | lean_file_chunk | 75df927dd0ca82825618a756254c0404c307906ede05ab7630d1092930ec9bb6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Alex J. Best. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex J. Best, Yaël Dillies
-/
module
public import Mathlib.Algebra.Order.Archimedean.Hom
public import Mathlib.Algebra.Order.Group.Pointwise.CompleteLattice
/-!
# Conditionally complet... |
710 | lean_file_chunk | 89b8dd5cbfbf50ef36112f98f478001f361ad01d227e14b166ee2116d4a4f7eb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Martin Dvorak. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Martin Dvorak
-/
module
public import Mathlib.Algebra.Notation.Pi.Defs
public import Mathlib.Order.Basic
/-!
# Interaction between `Sum.elim`, `≤`, and `0` or `1`
This file provides ... |
12,691 | lean_file_chunk | 38ec6c79864ed6cff0c45e5d1ef00bee2543cbeee53c8dfc27fafdd4f763d193 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Violeta Hernández Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Violeta Hernández Palacios, Yaël Dillies
-/
module
public import Mathlib.Algebra.Group.Basic
public import Mathlib.Algebra.Order.Monoid.Canonical.Defs
public import Mathli... |
897 | lean_file_chunk | 25797f22e2daeeb34cb285b334259f8baa38e5b74160e0d42edb903455bdf43a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
module
public import Mathlib.Algebra.Group.PUnit
public import Mathlib.Algebra.Order.AddGroupWithTop
/-!
# Instances on PUnit
This file collects facts about ordered algebraic... |
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