reserve x,X,Y for set;
reserve C for non empty set;
reserve c for Element of C;
reserve V for RealNormSpace;
reserve f,f1,f2,f3 for PartFunc of C,V;
reserve r,r1,r2,p for Real;

theorem
  for f1 be PartFunc of C,REAL holds (f1 is total & f2 is total
  iff f1(#)f2 is total)
proof
  let f1 be PartFunc of C,REAL;
  thus f1 is total & f2 is total implies f1(#)f2 is total;
  assume f1(#)f2 is total;
  then dom f1 /\ dom f2 = C by Def3;
  hence dom f1 = C & dom f2 = C by XBOOLE_1:17;
end;
