
theorem
  for G being _Graph holds G.minInDegree() c= G.minDegree()
proof
  let G be _Graph;
  consider v1 being Vertex of G such that
    A1: v1.inDegree() = G.minInDegree() and
    A2: for w being Vertex of G holds v1.inDegree() c= w.inDegree() by Th37;
  consider v2 being Vertex of G such that
    A3: v2.degree() = G.minDegree() and
    for w being Vertex of G holds v2.degree() c= w.degree() by Th36;
  A4: v2.inDegree() c= G.minDegree() by A3, CARD_2:94;
  v1.inDegree() c= v2.inDegree() by A2;
  hence thesis by A1, A4, XBOOLE_1:1;
end;
