Lemma Qquadratic_Qpositive_to_Q_3 : forall (a b c d e f g h : Z) (p1 p2 : Qpositive) (H_Qquadratic_sg_denom_nonzero : Qquadratic_sg_denom_nonzero e f g h p1 p2) (He : e <> 0%Z), same_ratio a b c d e f g h -> Qquadratic_Qpositive_to_Q a b c d e f g h p1 p2 H_Qquadratic_sg_denom_nonzero = fraction_encoding a e He.