reserve i,j,k,m,n for Nat;
reserve R for non empty doubleLoopStr;
reserve x,y for Scalar of R;
reserve f,g,h for FinSequence of R;

theorem
  x is being_a_product_of_squares implies x is
  being_a_sum_of_products_of_squares & x is being_an_amalgam_of_squares & x is
being_a_sum_of_amalgams_of_squares & x is generated_from_squares by Lm13,Lm19
