| import AUXLib.ListLib | |
| import AUXLib.Prime | |
| namespace Algorithms.integer_divide.lean | |
| open AUXLib | |
| export AUXLib.Prime (prime) | |
| inductive HdRel {A : Type u} (R : A → A → Prop) (a : A) : List A → Prop where | |
| | HdRel_nil : HdRel R a [] | |
| | HdRel_cons (b : A) (l : List A) : R a b → HdRel R a (b :: l) | |
| inductive Sorted {A : Type u} (R : A → A → Prop) : List A → Prop where | |
| | Sorted_nil : Sorted R [] | |
| | Sorted_cons (a : A) (l : List A) : Sorted R l → HdRel R a l → Sorted R (a :: l) | |
| def PrimeFactorization (original : Int) (factors : List Int) : Prop := | |
| Forall prime factors ∧ Sorted (· ≤ ·) factors ∧ | |
| factors.foldr (· * ·) 1 = original ∧ | |
| ∀ q : Int, q ∈ factors ↔ prime q ∧ Z.divide q original | |
| end Algorithms.integer_divide.lean | |