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
  X c= Y implies G.edgesBetween(X) c= G.edgesBetween(Y)
proof
  assume
A1: X c= Y;
    let x be object;
    assume
A2: x in G.edgesBetween(X);
    then (the_Source_of G).x in X & (the_Target_of G).x in X by Lm5;
    hence x in G.edgesBetween(Y) by A1,A2,Lm5;
end;
