proposition: Lemma oprod2_comm3 x y: oprod2_comm_P4 x y -> oprod_comm x y.
proof: Proof. move=> [a [g [c1 [c2 [ ]anz vp og[c1N c2N xv dx yv]]]]]. rewrite yv xv. have oc1:= OS_nat c1N. have oc2:= OS_nat c2N. apply:(oprod2_comm2 anz vp (OS_prod2 og oc2)). rewrite dx - (oprodD oc1 oc2 og) - (oprodD oc2 oc1 og). by rewrite (osum2_2int c1N c2N) (osum2_2int c2N c1N) csumC. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)