theorem
  for f being non-empty Function
  for s,ss being Element of product f, A being set
  holds (ss +* s | A) | A = s | A
proof
  let f be non-empty Function;
  let s,ss be Element of product f;
  let A be set;
  dom s = dom f by Th9
    .= dom ss by Th9;
  then A /\ dom ss c= A /\ dom s;
  hence thesis by FUNCT_4:88;
end;
