proposition: Lemma infinite_set_pr1 a b: inc b a -> a \Eq (a -s1 b) -> infinite_set (a -s1 b).
proof: Proof. move=> ab => h. move: (infinite_set_pr ab h);rewrite /infinite_set. by move /card_eqP:h => <-. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)