proposition: Lemma prod_rel_ltrans : left_Transitive R -> left_Transitive S -> left_Transitive prod_rel.
proof: Proof. move=> pR pS [a1 b1] [a2 b2] [R12 S12] [a3 b3] /=. by rewrite (pR _ _ R12 a3) (pS _ _ S12 b3). Qed.
imports: Coq(ssreflect ssrbool ssrfun Setoid) mathcomp(ssrnat seq eqtype) pcm(options)