reserve A,B,a,b,c,d,e,f,g,h for set;

theorem Th13:
  for R being RelStr holds id the carrier of R misses the
  InternalRel of ComplRelStr R
proof
  let R be RelStr;
  assume not thesis;
  then id (the carrier of R) /\ the InternalRel of ComplRelStr R <> {};
  then consider a being object such that
A1: a in id (the carrier of R) /\ the InternalRel of ComplRelStr R by
XBOOLE_0:def 1;
  a in the InternalRel of ComplRelStr R by A1,XBOOLE_0:def 4;
  then
A2: a in (the InternalRel of R)` \ id the carrier of R by NECKLACE:def 8;
  a in id (the carrier of R) by A1,XBOOLE_0:def 4;
  hence contradiction by A2,XBOOLE_0:def 5;
end;
