induction ls; intuition.
unfold compMap.
prog_simp.
intuition.
simpl.
prog_inline_first.
Hint Resolve list_inhabited : inhabited.
eapply comp_spec_seq; intuition;
eauto with inhabited.
eapply comp_spec_eq_trans.
2:{
eapply comp_spec_seq_eq; eauto with inhabited.
eapply comp_spec_eq_refl.
intuition.
eapply comp_spec_seq_eq; eauto with inhabited.
intuition.
eapply comp_spec_eq_refl.
}
prog_swap_r.
prog_inline_first.
prog_skip.
Qed.

Theorem compMap_map_fission_eq :
forall (A B C D : Set){eqdb : EqDec B}{eqdd : EqDec D}{eqdc : EqDec C}(ls : list A)(f1 : A -> Comp B)(f2 : A -> Comp C)(f3 : B -> D)(f4 : C -> D),
(forall a, comp_spec (fun b c => f3 b = f4 c)
(f1 a) (f2 a)) ->
comp_spec eq (lsb <-$ compMap _ f1 ls; ret (map f3 lsb))
(compMap _ (fun a => b <-$ f2 a; ret (f4 b)) ls).