(** ** The axiom of infinity **)
(** The set denoted by the pointed graph ((opt nat), OMEGA, (none nat)) contains zero (i.e. the empty set)... *)

(** ... and is closed under successor: *)
Theorem omega_succ :
forall (X : Typ1) (A : Rel X) (a : X),
ELT X A a (opt nat) OMEGA (none nat) ->
ELT (opt X) (SUCC X A a) (none X) (opt nat) OMEGA (none nat).