Section MaxSetMinSet.
Variable T : finType.
Notation sT := {set T}.
Implicit Types A B C : sT.
Implicit Type P : pred sT.
Definition minset P A := [forall (B : sT | B \subset A), (B == A) == P B].
Arguments minsetP {P A}.

Lemma minset_exists P C : P C -> {A | minset P A & A \subset C}.