for R being non empty doubleLoopStr
for x being Scalar of R st x is being_a_square holds
( x is being_a_sum_of_squares & x is being_a_product_of_squares & x is being_a_sum_of_products_of_squares & x is being_an_amalgam_of_squares & x is being_a_sum_of_amalgams_of_squares & x is generated_from_squares ) by Lm7, Lm9, Lm11, Lm17, Lm21, Lm31;