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 _trivial _Graph, v being Vertex of G holds
    v.inDegree() = G.size() & v.outDegree() = G.size() &
    v.degree() = G.size() +` G.size()
proof
  let G be _trivial _Graph, v be Vertex of G;
  thus v.inDegree() = G.size() & v.outDegree() = G.size() by Th148;
  hence v.degree() = G.size() +` G.size();
end;
