let R be non empty doubleLoopStr ; :: thesis: for x being Scalar of R st x is being_a_sum_of_squares holds
x is being_a_sum_of_products_of_squares
let x be Scalar of R; :: thesis: ( x is being_a_sum_of_squares implies x is being_a_sum_of_products_of_squares )
assume x is being_a_sum_of_squares ; :: thesis: x is being_a_sum_of_products_of_squares
then consider f being FinSequence of R such that
A1: f is being_a_Sum_of_squares and
A2: x = f /. (len f) by Def5;
f is being_a_Sum_of_products_of_squares by A1, Lm14;
hence x is being_a_sum_of_products_of_squares by A2, Def9; :: thesis: verum