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

theorem Th27:
  (ex v st v is isolated) & G is c-regular implies c = 0
proof
  assume A1: (ex v st v is isolated) & G is c-regular;
  then consider v such that
    A2: v is isolated;
  thus c = v.degree() by A1
    .= 0 by A2, GLIB_000:157;
end;
