Definition assert := { p:pred (K0.knot * KI.other) | boxy expandM p }.Module KI := Input.Module K0 := K0.Definition predicate: Type := assert.

Lemma boxy_expand_spec: forall (p: pred (K0.knot*KI.other)), boxy expandM p <-> (fun p: pred (K0.knot*KI.other) => forall x y, expandR x y -> proj1_sig p x -> proj1_sig p y) p.