induction n; destruct i; intuition; try omega.
unfold computeHybrid.
unfold minus.
fold minus.
rewrite <- minus_n_O.
unfold forNats.
fold forNats.
unfold compMap.
fold compMap.
inline_first.
comp_skip.
inline_first.
comp_simp.
comp_irr_l.
inline_first.
comp_skip.
simpl.
intuition.
unfold computeHybrid.
unfold minus.
fold minus.
unfold forNats.
fold forNats.
unfold compMap.
fold compMap.
inline_first.
do 2 comp_at comp_inline leftc 1%nat.
comp_swap_l.
comp_skip.
assert
(evalDist
(a1 <-$
(lsb' <-$
(b <-$ (c1 a);
lsb' <-$ compMap B_EqDec (fun _ : nat => (c1 a)) (forNats i);
ret b :: lsb'); ret x0 :: lsb');
a2 <-$ compMap B_EqDec (fun _ : nat => (c2 a)) (forNats (n0 - S i));
ret a1 ++ a2) x ==
evalDist
(ls <-$ (computeHybrid n0 (S i) a);
ret (x0 :: ls)) x).
unfold computeHybrid.
unfold forNats.
fold forNats.
unfold compMap.
fold compMap.
inline_first.
comp_skip.
inline_first.
comp_skip.
comp_simp.
inline_first.
comp_skip.
comp_simp.
simpl.
intuition.
rewrite H1.
clear H1.
eapply eqRat_trans.
2:{
comp_skip.
eapply eqRat_refl.
}
unfold computeHybrid.
inline_first.
comp_skip.
inline_first.
comp_skip.
inline_first.
comp_skip.
comp_simp.
simpl.
intuition.
Qed.

Theorem hybrid_replace_c2_equiv :
forall i x a,
i < n ->
evalDist
(b <-$ (c2 a);
hybrid <-$ computeHybrid n i a;
ret (listReplace hybrid i b b)) x ==
evalDist (computeHybrid n i a) x.