proposition: Lemma cpow_less_pr1 x y: \0c <c x -> cardinalp y -> x ^<c y <=c x ^c y.
proof: Proof. move=> [[_ cx _] xnz] cy; apply:card_ub_sup; fprops. move => t /funI_P [z zy ->]; apply: cpow_Mlele => //. - by apply:nesym. - by apply:cleR. - by move: zy => /cardinals_ltP []. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)