proposition: Lemma pow_IPR (q p: positive) : IPR (q ^ p) = pow (IPR q) (Pos.to_nat p).
proof: Proof. induction p as [| p IH] using Pos.peano_ind. - now simpl; rewrite Pos.pow_1_r, Rmult_1_r. - now rewrite Pos.pow_succ_r, mult_IPR, Pos2Nat.inj_succ; simpl; rewrite IH. Qed.
imports: RelationClasses Raxioms Rpow_def ZArith ZArithRing RealField