Definition nthB (b: list int) (i: nat) (n: Z) :=
nth (Z.to_nat (Z.of_nat i - 16 + n)) (rev (generate_word (rev b) 48)) Int.zero.

Lemma nth_rev_generate_word:
forall i b,
length b = 16%nat ->
(16 <= i < 64)%nat ->
nth i (rev (generate_word (rev b) 48)) Int.zero =
Int.add (nthB b i 0)
(Int.add (Int.add (sigma_0 (nthB b i 1)) (sigma_1 (nthB b i 14)))
(nthB b i 9)).