let R be non empty doubleLoopStr ; :: thesis: for x, y being Scalar of R st x is being_an_amalgam_of_squares & 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_an_amalgam_of_squares & y is being_a_product_of_squares implies x * y is being_an_amalgam_of_squares )
assume that
A1: x is being_an_amalgam_of_squares and
A2: y is being_a_product_of_squares ; :: thesis: x * y is being_an_amalgam_of_squares
y is being_an_amalgam_of_squares by A2, Lm19;
hence x * y is being_an_amalgam_of_squares by A1, Lm86; :: thesis: verum