
theorem Th76: :: VS10
  for G being _Graph, a,b being Vertex of G st a<>b & not a,b
are_adjacent for S being VertexSeparator of a,b for G2 being removeVertices of
  G,S holds a is Vertex of G2 & b is Vertex of G2
proof
  let G be _Graph;
  let a,b be Vertex of G such that
A1: a<>b and
A2: not a,b are_adjacent;
  let S be VertexSeparator of a,b, G2 be removeVertices of G,S;
  not b in S by A1,A2,Def8;
  then
A3: b in the_Vertices_of G\S by XBOOLE_0:def 5;
  not a in S by A1,A2,Def8;
  then a in the_Vertices_of G\S by XBOOLE_0:def 5;
  hence thesis by A3,GLIB_000:def 37;
end;
