
theorem Th39:
  for f being Function, X being set, i being object st i in dom f & X c= f.i
  holds product(f +* (i,X)) c= product(f)
proof
let f be Function, X be set, i be object;
 I: i is set by TARSKI:1;
assume i in dom f & X c= f.i;
  then product(f +* (i,X)) c= product(f +* (i,f.i)) by Th38;
  hence thesis by I, FUNCT_7:35;
end;
