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

theorem Th30:
  for F being PGraphMapping of G1, G2 st F is isomorphism
  holds G1 is c-regular iff G2 is c-regular
proof
  let F be PGraphMapping of G1, G2;
  assume A1: F is isomorphism;
  hence G1 is c-regular implies G2 is c-regular by Lm2;
  reconsider F0 = F as one-to-one PGraphMapping of G1, G2 by A1;
  F0" is isomorphism by A1, GLIB_010:75;
  hence thesis by Lm2;
end;
