
theorem Th24:
  for X be non empty TopSpace
  for a be Real,f be RealMap of X holds
    support(a(#)f) c= support(f)
proof
  let X be non empty TopSpace;
  let  a be Real,f be RealMap of X;
  set CX= the carrier of X;
  reconsider h=a(#)f as RealMap of X;
    now let x be object;
      assume x in support(a(#)f); then
      (a(#)f).x <>0 by PRE_POLY:def 7; then
A1:   a*f.x <> 0 by VALUED_1:6;
      f.x <> 0 by A1;
      hence x in support(f) by PRE_POLY:def 7;
    end;
    hence thesis;
end;
