
theorem Th38:
  for G1 being _Graph, E being set, G2 being removeEdges of G1, E
  for W1 being Walk of G1 st W1.edges() misses E holds W1 is Walk of G2
proof
  let G1 be _Graph, E be set, G2 be removeEdges of G1,E;
  let W1 be Walk of G1;
  assume A1: W1.edges() misses E;
  A2: W1.edges() c= the_Edges_of G1 & the_Edges_of G2 = the_Edges_of G1 \ E
    by GLIB_000:53;
  the_Vertices_of G1 = the_Vertices_of G2 by GLIB_000:53;
  then W1.vertices() c= the_Vertices_of G2;
  hence thesis by A1, A2, XBOOLE_1:86, GLIB_001:170;
end;
