proposition: Lemma BZs_prop: BZs = BZms \cup BZps.
proof: Proof. set_extens t. move =>/setC1_P [/BZ_i1P h xz]; apply /setU2_P; case: h; fprops. by move => tz; case: xz. move => /setU2_P; case. + by move/BZms_iP => [sa sb]; apply/setC1_P; split=> //; apply:BZm_sBZ. + by move/BZps_iP => [sa sb]; apply/setC1_P; split => //; apply:BZp_sBZ. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)