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bff4ec7 3805fe5 bff4ec7 3805fe5 bff4ec7 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | From Coq Require Import ZArith List Znumtheory Sorting.Sorted.
Import ListNotations.
Local Open Scope Z_scope.
From Coq Require Import Lia.
(** [PrimeFactorization original factors] is the public mathematical meaning of
the initialized output segment. Membership is deliberately bidirectional:
the segment contains no non-prime/non-divisor and omits no prime divisor of
[original]. [Sorted Z.le] records the program's increasing trial-divisor
order, while the product equation fixes multiplicities to the actual prime
factorization rather than merely listing each distinct divisor once. *)
Definition PrimeFactorization (original : Z) (factors : list Z) : Prop :=
Forall prime factors /\
Sorted Z.le factors /\
fold_right Z.mul 1 factors = original /\
(forall q : Z,
In q factors <-> prime q /\ Z.divide q original).
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