reserve A,B,C for Ordinal,
  K,L,M,N for Cardinal,
  x,y,y1,y2,z,u for object,X,Y,Z,Z1,Z2 for set,
  n for Nat,
  f,f1,g,h for Function,
  Q,R for Relation;
reserve ff for Cardinal-Function;
reserve F,G for Cardinal-Function;
reserve A,B for set;

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;
