let R be non empty doubleLoopStr ; :: thesis: for x being Scalar of R st x is being_a_sum_of_products_of_squares holds
x is being_a_sum_of_amalgams_of_squares
let x be Scalar of R; :: thesis: ( x is being_a_sum_of_products_of_squares implies x is being_a_sum_of_amalgams_of_squares )
assume x is being_a_sum_of_products_of_squares ; :: thesis: x is being_a_sum_of_amalgams_of_squares
then consider f being FinSequence of R such that
A1: ( f is being_a_Sum_of_products_of_squares & x = f /. (len f) ) by Def9;
( f is being_a_Sum_of_amalgams_of_squares & x = f /. (len f) ) by A1, Lm26;
hence x is being_a_sum_of_amalgams_of_squares by Def13; :: thesis: verum