theorem :: O_RING_1:10

for R being non empty doubleLoopStr
for x, y being Scalar of R st x is being_a_square & ( y is being_a_sum_of_squares or y is being_a_product_of_squares or y is being_a_sum_of_products_of_squares or y is being_an_amalgam_of_squares or y is being_a_sum_of_amalgams_of_squares or y is generated_from_squares ) holds
x + y is generated_from_squares by Lm70, Lm71, Lm72, Lm73, Lm74, Lm75;