theorem :: O_RING_1:4

for R being non empty doubleLoopStr
for x being Scalar of R st x is being_a_product_of_squares holds
( 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 Lm13, Lm19, Lm25, Lm49;