∀ return n, leibniz (return (n+1)) (filter_nat_type return (n+1))

Theorem sym_eq_filter_nat_type_S : forall return_type, forall (return_:(nat -> return_type)), forall (n:nat), leibniz.leibniz (return_type) (return_ (S n)) (filter_nat_type (return_type) return_ (S n)).

theorem sym_eq_filter_nat_type_S : \forall return_type. \forall (return_:nat -> return_type). \forall (n:nat). (leibniz) (return_type) (return_ ((S) n)) ((filter_nat_type) (return_type) return_ ((S) n)).

theorem sym_eq_filter_nat_type_S : forall (return_type : Type) , forall (return:(nat.nat) -> return_type) , forall (n:nat.nat) , (((leibniz.leibniz) (return_type)) ((return) (((nat.S) ) (n)))) ((((nat.filter_nat_type) (return_type)) (return)) (((nat.S) ) (n))).

sym_eq_filter_nat_type_S [return_type:TYPE+] : LEMMA (FORALL(return:[nat_sttfa.sttfa_nat -> return_type]):(FORALL(n:nat_sttfa.sttfa_nat):leibniz_sttfa_th.leibniz[return_type](return(nat_sttfa.sttfa_S(n)))(nat_sttfa.filter_nat_type[return_type](return)(nat_sttfa.sttfa_S(n)))))

Printing for OpenTheory is not working at the moment.