Remark mult_minus_distr_l : forall a b c : nat, a * (b - c) = a * b - a * c.Remark minus_eq_decompose :
 forall a b c d : nat, a = b -> c = d -> a - c = b - d.

(* Specifications: *)
Theorem new_equality : (3 * p - 4 * q) * (3 * p - 4 * q) = 2 * ((3 * q - 2 * p) * (3 * q - 2 * p)).
Theorem sqrt2_not_rational : forall p q : nat, q <> 0 -> p * p = 2 * (q * q) -> False.