let R be non empty doubleLoopStr ; :: thesis: for x being Scalar of R st x is being_a_square holds
x is being_a_product_of_squares
let x be Scalar of R; :: thesis: ( x is being_a_square implies x is being_a_product_of_squares )
assume x is being_a_square ; :: thesis: x is being_a_product_of_squares
then A1: <*x*> is being_a_Product_of_squares by Lm8;
( len <*x*> = 1 & <*x*> /. 1 = x ) by Lm2;
hence x is being_a_product_of_squares by A1; :: thesis: verum