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_product_of_squares implies x*y is
  being_an_amalgam_of_squares
proof
  assume x is being_a_square & y is being_a_product_of_squares;
  then x is being_an_amalgam_of_squares & y is being_an_amalgam_of_squares by
Lm17,Lm19;
  hence thesis by Lm86;
end;
