
theorem Th3:
  for L being associative commutative well-unital distributive
almost_left_invertible non empty doubleLoopStr, z,z1 being Element of L holds
  z <> 0.L implies z1 = (z1 * z) / z
proof
  let L be associative commutative well-unital distributive
  almost_left_invertible non empty doubleLoopStr, z,z1 be Element of L;
  assume
A1: z <> 0.L;
  thus (z1 * z) / z = z1 * (z * z") by GROUP_1:def 3
    .= z1 * 1.L by A1,VECTSP_1:def 10
    .= z1;
end;
