theorem Th6:
  B is commutative implies product(B,n) is commutative
proof
  assume
A1: B is commutative;
  now
    let x,y be Element of n-tuples_on D;
    thus product(B,n).(x,y) = B.:(x,y) by Def1
      .= B.:(y,x) by A1,FINSEQOP:33
      .= product(B,n).(y,x) by Def1;
  end;
  hence thesis;
end;
