Section Properties.
Variable (X Y: Type).
Variable (r: retract X Y).
Context {D: Dis Y}.
Global Instance dis_retract: Dis X.
Definition tight (y: Y) :=
match R y with
| Some x => if I x == y then Some x else None
| None => None
end.

Lemma tight_is_tight x y:
tight y = Some x -> I x = y.