let R be non empty doubleLoopStr ; :: thesis: for x, y being Scalar of R st x is being_a_sum_of_amalgams_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_sum_of_amalgams_of_squares & y is being_a_square implies x * y is generated_from_squares )
assume that
A1: x is being_a_sum_of_amalgams_of_squares and
A2: y is being_a_square ; :: thesis: x * y is generated_from_squares
A3: x is generated_from_squares by A1, Th1;
y is generated_from_squares by A2, Lm31;
hence x * y is generated_from_squares by A3, Lm87; :: thesis: verum