
theorem Th35:
  for G being _Graph, v being Vertex of G holds
    G.minDegree() c= v.degree() & v.degree() c= G.supDegree() &
    G.minInDegree() c= v.inDegree() & v.inDegree() c= G.supInDegree() &
    G.minOutDegree() c= v.outDegree() & v.outDegree() c= G.supOutDegree()
proof
  let G be _Graph, v be Vertex of G;
  v.degree() in the set of all w.degree() where w is Vertex of G;
  hence G.minDegree() c= v.degree() & v.degree() c= G.supDegree()
    by ZFMISC_1:74, SETFAM_1:3;
  v.inDegree() in the set of all w.inDegree() where w is Vertex of G;
  hence G.minInDegree() c= v.inDegree() & v.inDegree() c= G.supInDegree()
    by ZFMISC_1:74, SETFAM_1:3;
  v.outDegree() in the set of all w.outDegree() where w is Vertex of G;
  hence G.minOutDegree() c= v.outDegree() & v.outDegree() c= G.supOutDegree()
    by ZFMISC_1:74, SETFAM_1:3;
end;
