theorem
  x is being_a_square & y is being_a_product_of_squares implies x*y is
  being_an_amalgam_of_squares
proof
  assume x is being_a_square & y is being_a_product_of_squares;
  then x is being_an_amalgam_of_squares & y is being_an_amalgam_of_squares by
Lm17,Lm19;
  hence thesis by Lm86;
end;
