reserve X,Z for set;
reserve x,y,z for object;
reserve A,B,C for Subset of X;

theorem
  for A being transitive RelStr, B being finite Subset of A st
    the InternalRel of A is_connected_in B holds
      ex s being FinSequence of A st s is B-desc_ordering
proof
  let A be transitive RelStr;
  let B be finite Subset of A;
  assume the InternalRel of A is_connected_in B;
  then consider s being FinSequence of A such that
    A1: s is B-asc_ordering by Th89;
  take Rev s;
  thus thesis by A1, Th75;
end;
