λk. λf. λg. ∀ i, i < k ⇒ (f i) = (g i)

Definition sameF_upto : forall (A:Type), nat.nat -> (nat.nat -> A) -> (nat.nat -> A) -> Prop := fun (A:Type) => fun (k:nat.nat) => fun (f:(nat.nat -> A)) => fun (g:(nat.nat -> A)) => forall (i:nat.nat), (nat.lt i k) -> logic.eq (A) (f i) (g i)

definition sameF_upto : \forall A : Type[0] . nat -> (nat -> A) -> (nat -> A) -> Prop := \lambda A : Type[0]. \lambda k : nat. \lambda f : nat -> A. \lambda g : nat -> A. \forall (i:nat). ((lt) i k) -> (eq) (A) (f i) (g i)

def sameF_upto : forall (A : Type) , (nat.nat) -> ((nat.nat) -> A) -> ((nat.nat) -> A) -> Prop := fun (A : Type) , fun (k : nat.nat) , fun (f : (nat.nat) -> A) , fun (g : (nat.nat) -> A) , forall (i:nat.nat) , ((((nat.lt_) ) (i)) (k)) -> (((logic.eq_) (A)) ((f) (i))) ((g) (i))

sameF_upto [A:TYPE+] : [nat_sttfa_th.sttfa_nat -> [[nat_sttfa_th.sttfa_nat -> A] -> [[nat_sttfa_th.sttfa_nat -> A] -> bool]]] = (LAMBDA(k:nat_sttfa_th.sttfa_nat):(LAMBDA(f:[nat_sttfa_th.sttfa_nat -> A]):(LAMBDA(g:[nat_sttfa_th.sttfa_nat -> A]):(FORALL(i:nat_sttfa_th.sttfa_nat):(nat_sttfa_th.lt(i)(k) => logic_sttfa_th.eq[A](f(i))(g(i)))))))

Printing for OpenTheory is not working at the moment.