Hint Resolve lt_word_le_nat.

(* Specifications: *)
Lemma wordToNat_natToWord_idempotent' : forall sz n,
(n < pow2 sz)%nat
-> wordToNat (natToWord sz n) = n.
Lemma le_word_le_nat': forall (sz:nat) n m,
(n < pow2 sz)%nat ->
(natToWord sz n <= m)%word ->
(n <= wordToNat m)%nat.
Lemma wordToNat_natToWord_bound : forall sz n (bound : word sz),
(n <= wordToNat bound)%nat
-> wordToNat (natToWord sz n) = n.
Lemma wordToNat_natToWord_le : forall sz n,
(wordToNat (natToWord sz n) <= n)%nat.
Lemma wordToNat_natToWord_lt : forall sz n b,
(n < b -> wordToNat (natToWord sz n) < b)%nat.
Lemma wordToNat_eq_natToWord : forall sz (w : word sz) n,
wordToNat w = n
-> w = natToWord sz n.
Lemma wlt_lt_bound: forall sz (a : word sz) (b bound : nat),
(a < natToWord sz b)%word
-> (b <= wordToNat (natToWord sz bound))%nat
-> (wordToNat a < b)%nat.
Lemma natplus1_wordplus1_eq:
forall sz (a bound : word sz),
(0 < sz)%nat ->
(a < bound)%word ->
(wordToNat a) + 1 = wordToNat (a ^+ (natToWord sz 1)).
Lemma lt_wlt: forall sz (n : word sz) m, (wordToNat n < wordToNat m)%nat ->
n < m.
Lemma le_wle: forall sz (n : word sz) m, (wordToNat n <= wordToNat m)%nat ->
n <= m.
Lemma wlt_wle_incl : forall sz (a b : word sz),
(a < b)%word -> (a <= b)%word.
Lemma wminus_Alt2: forall sz x y, y <= x ->
@wminusN sz x y = wordBinN minus x y.
Theorem wlt_wf:
forall sz, well_founded (@wlt sz).