QVT14 — QVTr: Deletion semantics

I’m having trouble with the semantics of DELETE on p. 189 of the QVT Specification (v1.1). It reads in part:

FORALL OBJVAR IN MAKESET(<DOMAIN_K_VARIABLE_SET>) (
…
AND BELONGSTO(OBJVAR, MAKESET(<DOMAIN_K_VARIABLE_SET>))

I guess I don’t understand MAKESET and BELONGSTO. First of all, <DOMAIN_K_VARIABLE_SET> is already a set, so what’s the MAKESET function do? Second, the FORALL iterates OBJVAR over the results of the same MAKESET that BELONGSTO tests. So how can BELONGSTO be false? That is, I would assume BELONGSTO is defined as follows:

BELONGSTO(e, S) º e ÎS

except that under this definition the expression above is always satisfied.

Any and all help appreciated. Thank you very much.