proposition: Lemma beth_inaccessible1 k : inaccessible k -> beth k = k.
proof: Proof. move => ik. move: beth_normal => [sa sb]. have infk:= (proj1 (proj1 (proj1 ik))). have ck := (proj1 infk); have ok := (proj1 ck). apply: cleA. rewrite (sb _ (infinite_card_limit2 infk)); apply:card_ub_sup => //. move => i /funI_P [z /(oltP ok) zk ->]. exact: (proj1(beth_inaccessible ik zk)). move:(ocle1 (osi_gex sa ok)). by rewrite (card_card ck) (card_card (CS_beth ok)). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)