proposition: Lemma cleSSP a b: cardinalp a -> cardinalp b -> (csucc a <=c csucc b <-> a <=c b).
proof: Proof. move => ca cb; split => h; last by apply: cleSS. have le1 := (cleS0 ca); have le2 := (cleT le1 h). case: (Nat_dichot cb) => bN; last by move/csucc_inf: bN => ->. by move /(cltSleP bN):(clt_leT (cltS (NS_le_nat le2 (NS_succ bN))) h). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)