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 p being Element of sproduct f
  ex s being Element of product f st p c= s
proof
  let f be non-empty Function,
  p be Element of sproduct f;
  set h = the Element of product f;
  reconsider s = h +* p as Element of product f by Th53;
  take s;
  thus thesis by FUNCT_4:25;
end;
