(** Proof that Sqrt(2) cannot be rational *)
Ltac mysimpl := simplify_eq; repeat rewrite Pmult_xO_permute_r.

(* Specifications: *)
Theorem main_thm : forall p q: positive, (p*p <> 2*(q*q))%positive.
Coercion inject_Z : Z >-> Q.
Theorem sqrt2_not_rational : forall q:Q, ~ q^2 == 2.
Open Scope Z_scope.