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3805fe5 bff4ec7 3805fe5 bff4ec7 3805fe5 bff4ec7 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | Require Export PVbench.Algorithms.integer_divide.rocq.spec_lib.
From Coq Require Import ZArith List Znumtheory Sorting.Sorted.
Import ListNotations.
Local Open Scope Z_scope.
From Coq Require Import Lia.
(** Internal mathematical state shared by both trial-division loop heads.
Machine ranges, [cnt]/list-length bindings, modulo guards, and array
ownership deliberately remain visible in the C annotation. *)
Definition FactorizationProgress
(original : Z) (factors : list Z) (remaining candidate : Z) : Prop :=
fold_right Z.mul 1 factors * remaining = original /\
Forall prime factors /\
Sorted Z.le factors /\
Forall (fun factor => factor <= candidate) factors /\
(forall d : Z,
2 <= d < candidate -> ~ Z.divide d remaining).
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