fact: Axiom thm_DEPENDENT_CHOICE_FIXED : forall {A : Type'}, forall P : nat -> A -> Prop, forall R : nat -> A -> A -> Prop, forall a : A, ((P (NUMERAL 0) a) /\ (forall n : nat, forall x : A, (P n x) -> exists y : A, (P (S n) y) /\ (R n x y))) -> exists f : nat -> A, ((f (NUMERAL 0)) = a) /\ ((forall n : nat, P n (f n)) /\ (forall n : nat, R n (f n) (f (S n)))).
imports: coq theory_hol types terms axioms