Definition advance_next (gl: list (ident * globdef F V)) (x: positive) :=
  List.fold_left (fun n g => Pos.succ n) gl x.Remark genv_next_add_globals:
  forall gl ge,
  genv_next (add_globals ge gl) = advance_next gl (genv_next ge).Remark genv_public_add_globals:
  forall gl ge,
  genv_public (add_globals ge gl) = genv_public ge.

Theorem globalenv_public: forall p, genv_public (globalenv p) = prog_public p.