
theorem Th40:
  for G being _Graph holds G.supOutDegree() c= G.supDegree()
proof
  let G be _Graph;
  now
    let x be object;
    assume x in G.supOutDegree();
    then consider X being set such that
      A1: x in X & X in the set of all v.outDegree() where v is Vertex of G
      by TARSKI:def 4;
    consider v being Vertex of G such that
      A2: X = v.outDegree() by A1;
    v.outDegree() c= v.degree() by CARD_2:94;
    then A3: x in v.degree() by A1, A2;
    v.degree() in the set of all w.degree() where w is Vertex of G;
    hence x in G.supDegree() by A3, TARSKI:def 4;
  end;
  hence thesis by TARSKI:def 3;
end;
