// This prints the left floatting menu

### Theorembigops.sym_eq_bigop_body_S

Statement

∀ n, leibniz (λp. λnil. λop. λf. if (p n) then (op (f n) (bigop n p nil op f)) else (bigop n p nil op f)) (bigop_body (n+1))

Main Dependencies
Theory

Statement

Theorem sym_eq_bigop_body_S : forall H, forall (n:nat.nat), leibniz.leibniz ((nat.nat -> bool.bool) -> H -> (H -> H -> H) -> (nat.nat -> H) -> H) (fun (p:(nat.nat -> bool.bool)) => fun (nil:H) => fun (op:(H -> H -> H)) => fun (f:(nat.nat -> H)) => bool.match_bool_type (H) (op (f n) (bigop (H) n p nil op f)) (bigop (H) n p nil op f) (p n)) (bigop_body (H) (nat.S n)).

Statement

theorem sym_eq_bigop_body_S : \forall H. \forall (n:nat). (leibniz) ((nat -> bool) -> H -> (H -> H -> H) -> (nat -> H) -> H) (\lambda p : nat -> bool. \lambda nil : H. \lambda op : H -> H -> H. \lambda f : nat -> H. (match_bool_type) (H) (op (f n) ((bigop) (H) n p nil op f)) ((bigop) (H) n p nil op f) (p n)) ((bigop_body) (H) ((S) n)).

Statement

theorem sym_eq_bigop_body_S : forall (H : Type) , forall (n:nat.nat) , (((leibniz.leibniz) (((nat.nat) -> bool.bool) -> (H) -> ((H) -> (H) -> H) -> ((nat.nat) -> H) -> H)) (fun (p : (nat.nat) -> bool.bool) , fun (nil : H) , fun (op : (H) -> (H) -> H) , fun (f : (nat.nat) -> H) , ((((bool.match_bool_type) (H)) (((op) ((f) (n))) (((((((bigops.bigop) (H)) (n)) (p)) (nil)) (op)) (f)))) (((((((bigops.bigop) (H)) (n)) (p)) (nil)) (op)) (f))) ((p) (n)))) (((bigops.bigop_body) (H)) (((nat.S) ) (n))).

Statement

sym_eq_bigop_body_S [H:TYPE+] : LEMMA (FORALL(n:nat_sttfa_th.sttfa_nat):leibniz_sttfa_th.leibniz[[[nat_sttfa_th.sttfa_nat -> bool_sttfa_th.sttfa_bool] -> [H -> [[H -> [H -> H]] -> [[nat_sttfa_th.sttfa_nat -> H] -> H]]]]]((LAMBDA(p:[nat_sttfa_th.sttfa_nat -> bool_sttfa_th.sttfa_bool]):(LAMBDA(nil:H):(LAMBDA(op:[H -> [H -> H]]):(LAMBDA(f:[nat_sttfa_th.sttfa_nat -> H]):bool_sttfa_th.match_bool_type[H](op(f(n))(bigops_sttfa.bigop[H](n)(p)(nil)(op)(f)))(bigops_sttfa.bigop[H](n)(p)(nil)(op)(f))(p(n)))))))(bigops_sttfa.bigop_body[H](nat_sttfa_th.sttfa_S(n))))

Printing for OpenTheory is not working at the moment.