
theorem Th14:
  for L being add-associative right_zeroed right_complementable
  well-unital right-distributive non trivial doubleLoopStr, X being
non empty set, x1, x2 being Element of X st 1_1(x1,L) = 1_1(x2,L) holds x1 = x2
proof
  let L be add-associative right_zeroed right_complementable well-unital
  right-distributive non trivial doubleLoopStr, X be non empty set,
  x1, x2 be Element of X such that
A1: 1_1(x1,L) = 1_1(x2,L) and
A2: x1 <> x2;
  1_L = 1_1(x2,L).UnitBag x1 by A1,Th12
    .= 0.L by A2,Th10,Th12;
  hence contradiction;
end;
