If Min is given (as an integer or FD variable) then SetVariable is constrained to have such minimum. If Min is a free variable, then it is unified with the set's minimum as an FD variable or an integer (if it is already known).
minimum/2 can thus be used either to declare (or constrain) a minimum function or to retrieve it.
?- S`::..[1,2], minimum(S,M). ?- set(S,,[1,2],[minimum:1], minimum(S,M). M = 1 ?- S`::+[1,2], minimum(S,2). S =  ?- set(S,,[1,2],[minimum:2], minimum(S,M). S =  M = 2