let R be non empty doubleLoopStr ; :: thesis: for x, y being Scalar of R st x is being_a_square & y is being_a_product_of_squares holds
x * y is being_an_amalgam_of_squares
let x, y be Scalar of R; :: thesis: ( x is being_a_square & y is being_a_product_of_squares implies x * y is being_an_amalgam_of_squares )
assume ( x is being_a_square & y is being_a_product_of_squares ) ; :: thesis: x * y is being_an_amalgam_of_squares
then ( x is being_an_amalgam_of_squares & y is being_an_amalgam_of_squares ) by Lm17, Lm19;
hence x * y is being_an_amalgam_of_squares by Lm86; :: thesis: verum