for R being non empty doubleLoopStr
for x, y being Scalar of R st ( ( x is being_a_sum_of_products_of_squares & y is being_a_square ) or ( x is being_a_sum_of_products_of_squares & y is being_a_product_of_squares ) ) holds
x + y is being_a_sum_of_products_of_squares by Lm58, Lm65;