proposition: Lemma pow_Rsqr : forall (x:R) (n:nat), x ^ (2 * n) = Rsqr x ^ n.
proof: Proof. intros; induction n as [| n Hrecn]. - reflexivity. - replace (2 * S n)%nat with (S (S (2 * n))). + replace (x ^ S (S (2 * n))) with (x * x * x ^ (2 * n)). * rewrite Hrecn; reflexivity. * simpl; ring. + ring. Qed.
imports: ArithRing Rdefinitions Raxioms RIneq Rpow_def R_Ifp Rbasic_fun R_sqr SplitAbsolu SplitRmult ArithProp Zpower Ztac