Ltac Inside_Square_Qsgn_ p1 p2 :=
  repeat
   match goal with
   | id1:(?X1 < ?X2)%Z |- _ =>
       unfold X2 in id1 || unfold X1 in id1;
        repeat
         match goal with
         | id1:(2 < outside_square ?X1 ?X2 ?X3 ?X4)%Z,id2:
         (~ (?X2 = 0%Z /\ ?X3 = 0%Z /\ ?X4 = 0%Z)) |- _ =>
             generalize
              (Qsgn_7 _ (outside_square_correct_1 X1 X2 X3 X4 p1 p2 id1 id2));
              clear id1
         | id1:(outside_square ?X1 ?X2 ?X3 ?X4 < -2)%Z,id2:
         (~ (?X2 = 0%Z /\ ?X3 = 0%Z /\ ?X4 = 0%Z)) |- _ =>
             generalize
              (Qsgn_8 _ (outside_square_correct_2 X1 X2 X3 X4 p1 p2 id1 id2));
              clear id1
         end
   end.

Lemma quadratic : forall (a b c d e f g h : Z) (s1 s2 : Q) (H_Qquadratic_denom_nonzero : Qquadratic_denom_nonzero e f g h s1 s2), Qquadratic a b c d e f g h s1 s2 H_Qquadratic_denom_nonzero = spec_q a b c d e f g h s1 s2.