reserve x,y for object,X,Y,A,B,C,M for set;
reserve P,Q,R,R1,R2 for Relation;
reserve X,X1,X2 for Subset of A;
reserve Y for Subset of B;
reserve R,R1,R2 for Subset of [:A,B:];
reserve FR for Subset-Family of [:A,B:];
reserve R for Relation of A,B;
reserve S for Relation of B,C;

theorem :: (18)
  S.:^(R.:X) = (R*S`)`.:^X
proof
  (S.:^(R.:X))` = S`.:(R.:X) by Th48
    .= ((R*(S`)).:X) by RELAT_1:126;
  then S.:^(R.:X) = ((R*(S`)).:X)` .= (R*S`)`.:^X by Th49;
  hence thesis;
end;
