let R be non empty doubleLoopStr ; :: thesis: for x, y being Scalar of R st x is being_a_product_of_squares & y is being_a_square holds
x + y is generated_from_squares
let x, y be Scalar of R; :: thesis: ( x is being_a_product_of_squares & y is being_a_square implies x + y is generated_from_squares )
assume ( x is being_a_product_of_squares & y is being_a_square ) ; :: thesis: x + y is generated_from_squares
then ( x is generated_from_squares & y is generated_from_squares ) by Lm31, Lm49;
hence x + y is generated_from_squares by Lm64; :: thesis: verum