proposition: Lemma BigZring : ring_theory 0 1 BigZ.add BigZ.mul BigZ.sub BigZ.opp BigZ.eq.
proof: Proof. constructor. exact BigZ.add_0_l. exact BigZ.add_comm. exact BigZ.add_assoc. exact BigZ.mul_1_l. exact BigZ.mul_comm. exact BigZ.mul_assoc. exact BigZ.mul_add_distr_r. symmetry. apply BigZ.add_opp_r. exact BigZ.add_opp_diag_r. Qed.
imports: BigN ZProperties ZDivFloor ZSig ZSigZAxioms ZMake Ring Lia