reserve A for set, x,y,z for object,
  k for Element of NAT;
reserve n for Nat,
  x for object;
reserve V, C for set;

theorem Th36:
  for f being Function holds support f c= dom f
proof
  let f be Function, x be object;
  assume x in support f;
  then f.x <> 0 by Def7;
  hence thesis by FUNCT_1:def 2;
end;
