∀ case_O case_S n, equal (match_nat_type case_O case_S (n+1)) (case_S n)

Axiom axiom_match_nat_type_S : forall return_type, forall (case_O:return_type), forall (case_S:(nat -> return_type)), forall (n:nat), connectives.equal (return_type) (match_nat_type (return_type) case_O case_S (S n)) (case_S n)

axiom axiom_match_nat_type_S : \forall return_type. \forall (case_O:return_type). \forall (case_S:nat -> return_type). \forall (n:nat). (equal) (return_type) ((match_nat_type) (return_type) case_O case_S ((S) n)) (case_S n)

axiom axiom_match_nat_type_S : forall (return_type : Type) , forall (case_O:return_type) , forall (case_S:(nat.nat) -> return_type) , forall (n:nat.nat) , (((connectives.equal) (return_type)) (((((nat.match_nat_type) (return_type)) (case_O)) (case_S)) (((nat.S) ) (n)))) ((case_S) (n))

axiom_match_nat_type_S [return_type:TYPE+] : AXIOM (FORALL(case_O:return_type):(FORALL(case_S:[nat_sttfa.sttfa_nat -> return_type]):(FORALL(n:nat_sttfa.sttfa_nat):connectives_sttfa_th.equal[return_type](nat_sttfa.match_nat_type[return_type](case_O)(case_S)(nat_sttfa.sttfa_S(n)))(case_S(n)))))

Printing for OpenTheory is not working at the moment.