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

theorem Th22:
  for G being c-regular _Graph holds G.minDegree() = c & G.maxDegree() = c
proof
  let G be c-regular _Graph;
  now
    set v = the Vertex of G;
    take v;
    thus A1: v.degree() = c by Def4;
    let w be Vertex of G;
    thus v.degree() c= w.degree() by A1, Def4;
  end;
  hence G.minDegree() = c by GLIB_013:36;
  now
    set v = the Vertex of G;
    take v;
    thus A2: v.degree() = c by Def4;
    let w be Vertex of G;
    thus w.degree() c= v.degree() by A2, Def4;
  end;
  hence G.maxDegree() = c by GLIB_013:48;
end;
