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 implies x*y is
  generated_from_squares
proof
  assume that
A1: x is generated_from_squares and
A2: y is being_a_square;
  y is generated_from_squares by A2,Lm31;
  hence thesis by A1,Lm87;
end;
