proposition: Lemma fin_disj_fam_prop10d A (c := fin_disj_fam_card A): fin_disj_fam A -> ~ (exists2 i, intp i & nonempty (Vg A i)) -> zint_k2 (fin_disj_fam_enum_range A).
proof: Proof. move => ha hb; apply/set0_P => i /Zo_P [iz [x /setUb_P [k ka kb]]]. case: hb; exists k; [by rewrite /intp - (proj42 ha) | ex_tac ]. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype)