reserve c,c1,c2 for Cardinal, G,G1,G2 for _Graph, v for Vertex of G;

theorem
  G is regular iff G.minDegree() = G.supDegree()
proof
  hereby
    assume G is regular;
    then consider c being Cardinal such that
      A1: G is c-regular;
    thus G.minDegree() = c by A1, Th22
      .= G.supDegree() by A1, Th22;
  end;
  assume G.minDegree() = G.supDegree();
  then G is G.minDegree()-regular by Th23;
  hence thesis;
end;
