
theorem
  for G1 being _Graph, E being set, G2 being reverseEdgeDirections of G1, E
  holds G1.supDegree() = G2.supDegree() & G1.minDegree() = G2.minDegree()
proof
  let G1 be _Graph, E be set, G2 be reverseEdgeDirections of G1, E;
  set S1 = the set of all v.degree() where v is Vertex of G1;
  set S2 = the set of all v.degree() where v is Vertex of G2;
  now
    let x be object;
    hereby
      assume x in S1;
      then consider v1 being Vertex of G1 such that
        A1: x = v1.degree();
      reconsider v2 = v1 as Vertex of G2 by GLIB_007:4;
      x = v2.degree() by A1, GLIBPRE0:54;
      hence x in S2;
    end;
    assume x in S2;
    then consider v2 being Vertex of G2 such that
      A2: x = v2.degree();
    reconsider v1 = v2 as Vertex of G1 by GLIB_007:4;
    x = v1.degree() by A2, GLIBPRE0:54;
    hence x in S1;
  end;
  hence thesis by TARSKI:2;
end;
