
theorem
  for A being connected transitive RelStr, B being finite Subset of A
    st B is non empty holds
      ex x being Element of A st x in B &
        for y being Element of A st y in B & x <> y holds
          y <= x
proof
  let A be connected transitive RelStr;
  let B be finite Subset of A;
  assume A1: B is non empty;
  the InternalRel of A is_connected_in B by Def1, Th16;
  hence thesis by A1, Th33;
end;
