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 generated_from_squares 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 generated_from_squares implies x + y is generated_from_squares )
assume that
A1: x is being_a_sum_of_amalgams_of_squares and
A2: y is generated_from_squares ; :: thesis: x + y is generated_from_squares
x is generated_from_squares by A1, Th1;
hence x + y is generated_from_squares by A2, Lm64; :: thesis: verum