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_sum_of_squares implies x is
being_a_sum_of_products_of_squares & x is being_a_sum_of_amalgams_of_squares &
  x is generated_from_squares by Lm15,Lm23,Lm38;
