
theorem
  for G being _Graph holds G.minOutDegree() c= G.minDegree()
proof
  let G be _Graph;
  consider v1 being Vertex of G such that
    A1: v1.outDegree() = G.minOutDegree() and
    A2: for w being Vertex of G holds v1.outDegree() c= w.outDegree() by Th38;
  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.outDegree() c= G.minDegree() by A3, CARD_2:94;
  v1.outDegree() c= v2.outDegree() by A2;
  hence thesis by A1, A4, XBOOLE_1:1;
end;
