
theorem Th1:
  for R be RelStr for S be full SubRelStr of R
  for T be full SubRelStr of S holds T is full SubRelStr of R
proof
  let R be RelStr;
  let S be full SubRelStr of R;
  let T be full SubRelStr of S;
  reconsider T1 = T as SubRelStr of R by YELLOW_6:7;
A1: the carrier of T c= the carrier of S by YELLOW_0:def 13;
  the InternalRel of S = (the InternalRel of R)|_2 the carrier of S by
YELLOW_0:def 14;
  then the InternalRel of T = ((the InternalRel of R)|_2 the carrier of S)|_2
  the carrier of T by YELLOW_0:def 14
    .= (the InternalRel of R)|_2 the carrier of T by A1,WELLORD1:22;
  then T1 is full by YELLOW_0:def 14;
  hence thesis;
end;
