proposition: Lemma set_lt_2inf x: Sinfinite x -> C2 <s x.
proof: Proof. move: Sfinite2 => ha xi. case: (p_or_not_p (x\Eq Nat)) => en. exact:(set_lt_i2 ha (EqS en)). split; last by move => hb; move:(set_lt_i1 ha hb). case:(set_compare_to_finite x NS2) => // - [lx2 _]; case:xi. split => //; apply:(set_leT lx2 (proj1 ha)). Qed.
imports: mathcomp(ssreflect ssrbool eqtype ssrfun)