Ltac solve_comparison :=
  apply root_monotonic; repeat rewrite square_recompose; rewrite hyp_sqrt;
   rewrite mult2_recompose; apply mult_lt; auto with arith.

(* Specifications: *)
Theorem comparison1 : q < p.
Theorem comparison2 : 2 * p < 3 * q.
Theorem comparison3 : 4 * q < 3 * p.
Theorem comparison4 : 3 * q - 2 * p < q.