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 G1 being _Graph, G2 being spanning Subgraph of G1, G3 being
  spanning Subgraph of G2 holds G3 is spanning Subgraph of G1
proof
  let G1 be _Graph, G2 be spanning Subgraph of G1, G3 be spanning Subgraph of
  G2;
  the_Vertices_of G3 = the_Vertices_of G2 by Def33
    .= the_Vertices_of G1 by Def33;
  hence thesis by Def33,Th43;
end;
