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.

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