let R be non empty doubleLoopStr ; :: thesis: for x, y being Scalar of R st x is being_a_square & 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_square & y is being_a_sum_of_squares implies x * y is generated_from_squares )
assume A1: ( x is being_a_square & y is being_a_sum_of_squares ) ; :: thesis: x * y is generated_from_squares
then A2: x is generated_from_squares by Lm31;
y is generated_from_squares by A1, Lm38;
hence x * y is generated_from_squares by A2, Lm87; :: thesis: verum