
theorem Th4:
  for R being RelStr, X being Subset of R, x being set st X is
  lower & x in X holds (the InternalRel of R)-Seg x c= X
proof
  let R be RelStr, X be Subset of R, x be set such that
A1: X is lower & x in X;
  let z be object;
  assume z in (the InternalRel of R)-Seg x;
  then [z,x] in (the InternalRel of R) by WELLORD1:1;
  hence thesis by A1;
end;
