
theorem Th71:
  for G being _finite _Graph holds (MCS:CSeq(G))``1 is eventually-constant
proof
  let G be _finite _Graph;
  set CS = (MCS:CSeq(G));
  set S = CS``1;
  now
    consider n being Nat such that
A1: for m being Nat st n <= m holds CS.n = CS.m by Def6;
    take n;
    let m be Nat such that
A2: n <= m;
    thus S.n = (CS.n)`1 by Def24
      .= (CS.m)`1 by A1,A2
      .= S.m by Def24;
  end;
  hence thesis;
end;
