∀ n, leibniz (λm. match_nat_type false (λq. leb n q) m) (leb_body (n+1))

Theorem sym_eq_leb_body_S : forall (n:nat), leibniz.leibniz (nat -> bool.bool) (fun (m:nat) => match_nat_type (bool.bool) bool.false (fun (q:nat) => leb n q) m) (leb_body (S n)).

theorem sym_eq_leb_body_S : \forall (n:nat). (leibniz) (nat -> bool) (\lambda m : nat. (match_nat_type) (bool) (false) (\lambda q : nat. (leb) n q) m) ((leb_body) ((S) n)).

theorem sym_eq_leb_body_S : forall (n:nat.nat) , (((leibniz.leibniz) ((nat.nat) -> bool.bool)) (fun (m : nat.nat) , ((((nat.match_nat_type) (bool.bool)) ((bool.false) )) (fun (q : nat.nat) , (((nat.leb) ) (n)) (q))) (m))) (((nat.leb_body) ) (((nat.S) ) (n))).

sym_eq_leb_body_S : LEMMA (FORALL(n:nat_sttfa.sttfa_nat):leibniz_sttfa_th.leibniz[[nat_sttfa.sttfa_nat -> bool_sttfa_th.sttfa_bool]]((LAMBDA(m:nat_sttfa.sttfa_nat):nat_sttfa.match_nat_type[bool_sttfa_th.sttfa_bool](bool_sttfa_th.sttfa_false)((LAMBDA(q:nat_sttfa.sttfa_nat):nat_sttfa.leb(n)(q)))(m)))(nat_sttfa.leb_body(nat_sttfa.sttfa_S(n))))

Printing for OpenTheory is not working at the moment.