intros w w' H; CaseEq (Qpositive_i w).
intros p q Heq.
rewrite <- construct_correct with (1 := Heq) (n := p + q).
apply construct_correct; auto.
rewrite <- H; auto.
auto.
Qed.

Theorem minus_decompose :
forall a b c d : nat, a = b -> c = d -> a - c = b - d.