let R be non empty doubleLoopStr ; :: thesis: for x being Scalar of R st x is being_a_product_of_squares holds
x is generated_from_squares
let x be Scalar of R; :: thesis: ( x is being_a_product_of_squares implies x is generated_from_squares )
assume x is being_a_product_of_squares ; :: thesis: x is generated_from_squares
then consider f being FinSequence of R such that
A1: f is being_a_Product_of_squares and
A2: x = f /. (len f) by Def7;
0 <> len f by A1, Def6;
hence x is generated_from_squares by A1, A2, Lm48; :: thesis: verum