proposition: Lemma mult_IZR : forall n m:Z, IZR (n * m) = IZR n * IZR m.
proof: Proof. intros [| p | p] [| q | q]; rewrite ?Rmult_0_l, ?Rmult_0_r, ?Z.mul_0_l, ?Z.mul_0_r; try easy; unfold IZR; simpl. - now apply mult_IPR. - now rewrite mult_IPR, Ropp_mult_distr_r. - now rewrite mult_IPR, Ropp_mult_distr_l. - now rewrite mult_IPR, Rmult_opp_opp. Qed.
imports: RelationClasses Raxioms Rpow_def ZArith ZArithRing RealField