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
  f is total iff -f is total
proof
  thus f is total implies -f is total;
  assume
A1: -f is total;
  -f = (-1)(#)f by Th23;
  hence thesis by A1,Def4;
end;
