proposition: Lemma oprod_fix1 a y (x := a ^o omega0 *o y): \0o <o a -> ordinalp y -> a *o x = x.
proof: Proof. move => ap oy. have oa:= proj32_1 ap. rewrite (oprodA oa (OS_pow oa OS_omega) oy) -{1} (opowx1 oa). by rewrite - (opow_sum oa OS1 OS_omega) (osum_int_omega olt_1omega). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)