reserve GS for GraphStruct;
reserve G,G1,G2,G3 for _Graph;
reserve e,x,x1,x2,y,y1,y2,E,V,X,Y for set;
reserve n,n1,n2 for Nat;
reserve v,v1,v2 for Vertex of G;

theorem Th98:
  for G being _Graph, G1,G2 being Subgraph of G st G1 c< G2 holds
(the_Vertices_of G1 c< the_Vertices_of G2 or the_Edges_of G1 c< the_Edges_of G2
  )
proof
  let G be _Graph, G1,G2 be Subgraph of G;
  assume
A1: G1 c< G2;
  then G1 c= G2;
  then
A2: G1 is Subgraph of G2;
  then
A3: the_Vertices_of G1 c= the_Vertices_of G2 by Def32;
A4: the_Edges_of G1 c= the_Edges_of G2 by A2,Def32;
A5: not G1 == G2 by A1;
  now
    per cases by A5,Th86;
    suppose
      the_Vertices_of G1 <> the_Vertices_of G2;
      hence thesis by A3,XBOOLE_0:def 8;
    end;
    suppose
      the_Edges_of G1 <> the_Edges_of G2;
      hence thesis by A4,XBOOLE_0:def 8;
    end;
  end;
  hence thesis;
end;
