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
  GS is [Graph-like] iff _GraphSelectors c= dom GS & the_Vertices_of GS
is non empty & the_Source_of GS is Function of the_Edges_of GS,the_Vertices_of
GS & the_Target_of GS is Function of the_Edges_of GS,the_Vertices_of GS by Lm1;
