
theorem
  for G1 being _Graph, G2 being spanning Subgraph of G1 holds
    G2.minDegree() c= G1.minDegree() &
    G2.minInDegree() c= G1.minInDegree() &
    G2.minOutDegree() c= G1.minOutDegree()
proof
  let G1 be _Graph, G2 be spanning Subgraph of G1;
  set F = (id G1) | G2;
  A1: F is directed weak_SG-embedding by GLIB_010:57;
  rng F_V = rng ((id G1)_V | the_Vertices_of G1) by GLIB_000:def 33
    .= the_Vertices_of G1;
  hence thesis by A1, Th52, Th57;
end;
