theorem
  for G1 being _Graph, G2 being Subgraph of G1, x,y,e being set st e in
the_Edges_of G2 holds (e Joins x,y,G1 implies e Joins x,y,G2) & (e DJoins x,y,
  G1 implies e DJoins x,y,G2) & (e SJoins x,y,G1 implies e SJoins x,y,G2) & (e
  DSJoins x,y,G1 implies e DSJoins x,y,G2)
by Def32;
