reserve G for _Graph;
reserve G2 for _Graph, G1 for Supergraph of G2;
reserve V for set;

theorem Th95:
  for G2, V for G1 being addVertices of G2, V, W being Walk of G1
  st W.vertices() misses V \ the_Vertices_of G2 holds W is Walk of G2
proof
  let G2, V;
  let G1 be addVertices of G2, V, W be Walk of G1;
  A1: G2 is Subgraph of G1 by Th61;
  assume A2: W.vertices() misses V \ the_Vertices_of G2;
  the_Vertices_of G1 = the_Vertices_of G2 \/ V by Def10;
  then A3: the_Vertices_of G1 = the_Vertices_of G2 \/ (V \ the_Vertices_of G2)
    by XBOOLE_1:39;
  A4: W.vertices() c= the_Vertices_of G2 by A2, A3, XBOOLE_1:73;
  W.edges() c= the_Edges_of G1;
  then W.edges() c= the_Edges_of G2 by Def10;
  hence thesis by A1, A4, GLIB_001:170;
end;
