Proof with try solve [simpl; auto|congruence].
intros. unfold clause_generate in H0.
destruct c... destruct delta... destruct p... destruct e0...
if_tac in H0... if_tac in H0... if_tac in H0...
Qed.

(* Specifications: *)
Lemma partial_mod_sound1 R R' acc l l' s :
listd clause_denote inter TT l s -> listd clause_denote inter TT acc s ->
partial_mod R acc l = inl _ (R', l') ->
listd clause_denote inter TT l' s.