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

theorem Th91:
  for G2, V for G1 being addVertices of G2, V
  for x,y,e being object holds e Joins x,y,G1 iff e Joins x,y,G2
proof
  let G2, V;
  let G1 be addVertices of G2, V;
  let x,y,e be object;
  e Joins x,y,G1 iff (e DJoins x,y,G1 or e DJoins y,x,G1) by GLIB_000:16;
  then e Joins x,y,G1 iff (e DJoins x,y,G2 or e DJoins y,x,G2) by Th89;
  hence thesis by GLIB_000:16;
end;
