proposition: Lemma BZprod_plt2r a b c: intp a -> intp b -> inc c BZps -> ((a *z c) <z (b *z c) <-> a <z b).
proof: Proof. move => pa pb pc; move: (BZps_sBZp pc)=> p'c. split; last by apply:BZprod_Mltgt0. move => h; case: (zleT_el pb pa) => //. move /(BZprod_ple2r pb pa pc) => h2; BZo_tac. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)