PB; have /set0Pn[x Bx]: B != set0 := memPn notP0 B PB.
apply/cards1P; exists (odflt x [pick y in pblock P x]); apply/esym/eqP.
rewrite eqEsubset sub1set inE -andbA; apply/andP; split.by apply/mem_imset/bigcupP; exists B.case: {1}_ / pickP => [t zPt Bt | /(_ z)/idP[]]; last by rewrite mem_pblock.
by rewrite -(same_pblt11.
Qed.

(* Specifications: *)
Lemma minsetP P A :
by apply/implyP=> sBA; apply/eqP; apply/eqP/idP=> [-> //