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].

Lemma minset_eq P1 P2 A : P1 =1 P2 -> minset P1 A = minset P2 A.