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
  implies x*y is being_an_amalgam_of_squares
proof
  assume that
A1: x is being_an_amalgam_of_squares and
A2: y is being_a_product_of_squares;
  y is being_an_amalgam_of_squares by A2,Lm19;
  hence thesis by A1,Lm86;
end;
