reserve x for object, X,Y for set;
reserve C for non empty set;
reserve c for Element of C;
reserve f,f1,f2,f3,g,g1 for complex-valued Function;
reserve r,p for Complex;
reserve r,r1,r2,p for Real;
reserve f,f1,f2 for PartFunc of C,REAL;
reserve f for real-valued Function;

theorem
  X misses dom f implies f|X is bounded
proof
  assume X /\ dom f = {};
  then dom(f|X) = {} by RELAT_1:61;
  then f|X = {};
  hence thesis;
end;
