Section BigSetOps.
Variables T I : finType.
Implicit Types (U : {pred T}) (P : pred I) (A B : {set I}) (F :  I -> {set T}).
End Curry.

Lemma trivIimset J F (P := F @: J) :
{in J &, forall i j, j != i -> [disjoint F i & F j]} -> set0 \notin P ->
trivIset P /\ {in J &, injective F}.