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_square implies x is being_a_sum_of_squares & x is
  being_a_product_of_squares & 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 Lm7,Lm9,Lm11,Lm17,Lm21,Lm31;
