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_an_amalgam_of_squares & (y is being_a_product_of_squares or
y is being_an_amalgam_of_squares) or x is being_a_sum_of_amalgams_of_squares &
  (y is being_a_square or y is being_a_product_of_squares or y is
being_an_amalgam_of_squares) implies x+y is being_a_sum_of_amalgams_of_squares
  by Lm60,Lm66,Lm67,Lm68,Lm69;
