theorem
  x is being_a_square & y is being_an_amalgam_of_squares implies x*y is
  being_an_amalgam_of_squares
proof
  assume that
A1: x is being_a_square and
A2: y is being_an_amalgam_of_squares;
  x is being_an_amalgam_of_squares by A1,Lm17;
  hence thesis by A2,Lm86;
end;
