proposition: Lemma powerRZ_inv' x alpha : powerRZ (/ x) alpha = Rinv (powerRZ x alpha).
proof: Proof. destruct (intP alpha). - now simpl; rewrite Rinv_1. - now rewrite <-!pow_powerRZ, ?pow_inv, ?pow_powerRZ. - unfold powerRZ. destruct (- n). + now rewrite Rinv_1. + apply pow_inv. + now rewrite pow_inv. Qed.
imports: ArithRing Rdefinitions Raxioms RIneq Rpow_def R_Ifp Rbasic_fun R_sqr SplitAbsolu SplitRmult ArithProp Zpower Ztac