
theorem Th1:
  for G1 being _Graph, G2 being Subgraph of G1
  for v1 being Vertex of G1, v2 being Vertex of G2 st v1 = v2
  holds v2.inDegree() c= v1.inDegree() &
    v2.outDegree() c= v1.outDegree() & v2.degree() c= v1.degree()
proof
  let G1 be _Graph, G2 be Subgraph of G1;
  let v1 be Vertex of G1, v2 be Vertex of G2;
  assume A1: v1 = v2;
  then v2.edgesIn() c= v1.edgesIn() by GLIB_000:78;
  hence A2: v2.inDegree() c= v1.inDegree() by CARD_1:11;
  thus v2.outDegree() c= v1.outDegree() by A1, GLIB_000:78, CARD_1:11;
  hence v2.degree() c= v1.degree() by A2, CARD_2:83;
end;
