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
  for G being _Graph, e being object st e in the_Edges_of G
  holds e in G.edgesBetween({(the_Source_of G).e,(the_Target_of G).e})
proof
  let G be _Graph, e be object;
  set v = (the_Source_of G).e, w = (the_Target_of G).e;
  assume A1: e in the_Edges_of G;
  v in {v,w} & w in {v,w} by TARSKI:def 2;
  hence e in G.edgesBetween({v,w}) by A1, Lm5;
end;
