proposition: Lemma triv_cprod A B : (A \* B == 1) = (A == 1) && (B == 1).
proof: Proof. case A1: (A == 1); first by rewrite (eqP A1) cprod1g. apply/eqP=> /cprodP[[G H defA ->]] /eqP. by rewrite defA trivMg -defA A1. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(choice fintype bigop finset fingroup morphism) mathcomp(quotient action)