fact: Axiom thm_CHOICE_PAIRED_THM : forall {A B : Type'}, forall P : A -> B -> Prop, forall Q : (prod A B) -> Prop, ((exists x : A, exists y : B, P x y) /\ (forall x : A, forall y : B, (P x y) -> Q (@pair A B x y))) -> Q (@ε (prod A B) (@GABS ((prod A B) -> Prop) (fun f : (prod A B) -> Prop => forall x : A, forall y : B, @GEQ Prop (f (@pair A B x y)) (P x y)))).
imports: coq theory_hol types terms axioms