let R be non empty doubleLoopStr ; :: thesis: for x, y being Scalar of R st x is being_a_sum_of_products_of_squares & y is being_a_sum_of_squares holds
x + y is generated_from_squares
let x, y be Scalar of R; :: thesis: ( x is being_a_sum_of_products_of_squares & y is being_a_sum_of_squares implies x + y is generated_from_squares )
assume ( x is being_a_sum_of_products_of_squares & y is being_a_sum_of_squares ) ; :: thesis: x + y is generated_from_squares
then ( x is generated_from_squares & y is generated_from_squares ) by Lm38, Lm54;
hence x + y is generated_from_squares by Lm64; :: thesis: verum