Section FsfunTheory.
Variables (key : unit) (K : choiceType) (V : eqType) (default : K -> V).

Lemma fsinjectivebP f :
reflect (exists2 S : {fset K}, (finsupp f `<=` S)
& {in S &, injective f} /\ forall a : S, f (val a) \in S)
(fsinjectiveb f).