
theorem Th106: :: NeVSchFol:
  for G being _finite _Graph, S being VertexScheme of G, n being
  non zero Nat st n <= len S holds S.followSet(n) is non empty
proof
  let G be _finite _Graph, S be VertexScheme of G;
  let n be non zero Nat such that
A1: n <= len S;
  0+1 <= n by NAT_1:13;
  then
A2: len ((n, len S)-cut S) + n = len S + 1 by A1,FINSEQ_6:def 4;
  len S + 1 - n <> 0 by A1,NAT_1:13;
  then (n, len S)-cut S <> {} by A2;
  hence thesis;
end;
