Section dfa_nfa_decider.
Hypothesis U: Set.
Hypothesis U0: U.
Hypothesis U_enc: U->positive.
Hypothesis U_enc_inj: is_inj U_enc.
Hypothesis U_list:list U.
Hypothesis U_list_spec:
forall s, In s U_list.
Hypothesis maxT:nat.
Hypothesis dfa: U->Σ->U.
Definition U_eqb(u1 u2:U) := Pos.eqb (U_enc u1) (U_enc u2).

Lemma U_eqb_spec:
forall u1 u2, if U_eqb u1 u2 then u1=u2 else u1<>u2.