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 Th34:
  the_Edges_of G = G.edgesBetween(the_Vertices_of G)
proof
  set EG = the_Edges_of G, SG = the_Source_of G, TG = the_Target_of G;
  now
    let x be object;
    hereby
      assume
A1:   x in EG;
      then SG.x in the_Vertices_of G & TG.x in the_Vertices_of G by FUNCT_2:5;
      hence x in G.edgesBetween(the_Vertices_of G) by A1,Lm5;
    end;
    assume x in G.edgesBetween(the_Vertices_of G);
    hence x in EG;
  end;
  hence thesis by TARSKI:2;
end;
