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
  G.edgesBetween(X) c= G.edgesInOut(X)
proof
  let z be object;
  assume z in G.edgesBetween(X);
  then z in G.edgesInto(X) by XBOOLE_0:def 4;
  hence z in G.edgesInOut(X) by XBOOLE_0:def 3;
end;
