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 & (y is being_a_sum_of_squares or y is
  being_a_product_of_squares or y is being_a_sum_of_products_of_squares or y is
being_an_amalgam_of_squares or y is being_a_sum_of_amalgams_of_squares or y is
generated_from_squares) implies x+y is generated_from_squares by Lm70,Lm71,Lm72
