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

theorem
  (ex v st v is endvertex) & G is regular implies G is 1-regular
proof
  assume A1: (ex v st v is endvertex) & G is regular;
  then consider c being Cardinal such that
    A2: G is c-regular;
  c = 1 by A1, A2, Th28;
  hence thesis by A2;
end;
