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 generated_from_squares & y is being_a_square or x is
  generated_from_squares & y is being_a_sum_of_squares or x is
  generated_from_squares & y is being_a_product_of_squares or x is
  generated_from_squares & y is being_a_sum_of_products_of_squares or x is
  generated_from_squares & y is being_an_amalgam_of_squares or x is
  generated_from_squares & y is being_a_sum_of_amalgams_of_squares or x is
  generated_from_squares & y is generated_from_squares implies x+y is
  generated_from_squares by Lm36,Lm43,Lm64,Lm76,Lm77,Lm78,Lm79;
