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_products_of_squares implies
  x*y is generated_from_squares
proof
  assume x is being_a_square & y is being_a_sum_of_products_of_squares;
  then x is generated_from_squares & y is generated_from_squares by Lm31,Lm54;
  hence thesis by Lm87;
end;
