let R be non empty doubleLoopStr ; :: thesis: for x, y being Scalar of R st x is being_a_square & y is generated_from_squares holds
x + y is generated_from_squares
let x, y be Scalar of R; :: thesis: ( x is being_a_square & y is generated_from_squares implies x + y is generated_from_squares )
assume A1: ( x is being_a_square & y is generated_from_squares ) ; :: thesis: x + y is generated_from_squares
then x is generated_from_squares by Lm31;
hence x + y is generated_from_squares by A1, Lm64; :: thesis: verum