proposition: Lemma fin_disj_fam_prop1 A x (i := (fin_disj_fam_rank A x)): fin_disj_fam A -> inc x (unionb A) -> inc x (Vg A i) /\ intp i.
proof: Proof. move =>[qa qb qc qd] /setUb_P [k]; rewrite qb => kd kv. apply: select_pr; first by exists k. hnf; rewrite - qb; move => i1 i2 i1z i1v i2z i2v. move: (qc i1 i2 i1z i2z); case => // fi; empty_tac1 x. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype)