
theorem Th26:
  for L1,L2 be non empty RelStr st the RelStr of L1 = the RelStr
  of L2 holds L1,L2 are_isomorphic
proof
  let L1,L2 be non empty RelStr;
  assume
A1: the RelStr of L1 = the RelStr of L2;
  ex f be Function of L1,L2 st f is isomorphic
  proof
    reconsider f = id the carrier of L1 as Function of L1,L2 by A1;
    take f;
    now
      let z be object;
      assume
A2:   z in the carrier of L2;
      take v = z;
      thus v in the carrier of L1 by A1,A2;
      thus z = f.v by A1,A2,FUNCT_1:18;
    end;
    then
A3: rng f = the carrier of L2 by FUNCT_2:10;
    for x,y be Element of L1 holds x <= y iff f.x <= f.y
    by A1,YELLOW_0:1;
    hence thesis by A3,WAYBEL_0:66;
  end;
  hence thesis by WAYBEL_1:def 8;
end;
