proposition: Lemma Zpow_pos_spec a n : Zpow_pos a n = a ^ Zpos n.
proof: Proof. revert a. induction n; intros a; simpl Zpow_pos. - rewrite IHn. replace (Z.pos n~1) with (1 + 2 * Z.pos n) by lia. rewrite Z.pow_add_r; try lia. rewrite Z.pow_mul_r; try lia. replace (a ^ 2) with (a * a) by lia. lia. - rewrite IHn. change (Z.pos n~0) with (2 * Z.pos n). rewrite Z.pow_mul_r; try lia. replace (a ^ 2) with (a * a) by lia. lia. - lia. Qed.
imports: Coq(PArith ZArith Lia Znumtheory) Coqtail(Ztools)