theorem Th80:
  for X be set, S be add-associative right_zeroed right_complementable
    right-distributive non empty doubleLoopStr
  for p be Series of X,S, a be Element of S
  for V be set st vars p c= V holds vars (a * p) c= V
proof
  let X be set, S be add-associative right_zeroed right_complementable
  right-distributive non empty doubleLoopStr;
  let p be Series of X,S, a be Element of S;
  let V be set; assume A1: vars p c= V;
  vars (a * p) c= vars p by Th44;
  hence thesis by A1;
end;
