Section measure_double_rect_paired.
Let Q c := match c with (x,y) => P x y end.
Let Fix_F_2_Acc_irr x y f g : @Fix_F_2 x y f = Fix_F_2 g.

Theorem measure_double_rect_fix x y :
measure_double_rect x y = @F x y (fun x' y' _ => measure_double_rect x' y').