type label =
  | Axiom
  | AndI
  | AndE
  | OrI
  | OrE
  | ArrI
  | ArrE
  | NegI
  | NegE
  | RAA
  | IffI
  | IffE
  | EqI
  | EqE
  | ForallI
  | ForallE
  | ExistsI
  | ExistsE

type pref = Linenum of int | Named of string
type t = { children : pref list; label : label; formula : Formula.t }

val valid : (pref -> t) -> Formula.t list -> t -> bool