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_sum_of_amalgams_of_squares & y is generated_from_squares
  implies x*y is generated_from_squares
proof
  assume that
A1: x is being_a_sum_of_amalgams_of_squares and
A2: y is generated_from_squares;
  x is generated_from_squares by A1,Th1;
  hence thesis by A2,Lm87;
end;
