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 Th55:
  sproduct f c= PFuncs(dom f,union rng f)
proof
  let x be object;
  assume x in sproduct f;
  then x is PartFunc of dom f, union rng f by Th52;
  hence thesis by PARTFUN1:45;
end;
