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_square 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_square implies x * y is being_an_amalgam_of_squares )
assume A1: ( x is being_an_amalgam_of_squares & y is being_a_square ) ; :: thesis: x * y is being_an_amalgam_of_squares
then y is being_an_amalgam_of_squares by Lm17;
hence x * y is being_an_amalgam_of_squares by A1, Lm86; :: thesis: verum