Fixpoint Fix_F_2 (x:A) (x':B) (a:Acc R (x, x')) : P x x' :=
    F
      (fun (y:A) (y':B) (h:R (y, y') (x, x')) =>
         Fix_F_2 (x:=y) (x':=y') (Acc_inv a (y,y') h)).

Theorem well_founded_induction_type_2 : (forall (x:A) (x':B), (forall (y:A) (y':B), R (y, y') (x, x') -> P y y') -> P x x') -> forall (a:A) (b:B), P a b.