apply BotC;mp;[is_ass|destruct a;simpl;apply OrI1];
try (apply ImpI;mp;[is_ass|apply OrI2;apply Clause_provable_3;in_solve]);
(apply BotC;mp;[constructor;constructor 2;in_solve|apply OrI2;apply Clause_provable_3;in_solve]).
apply OrI2;assumption.
Qed.

Theorem Clause_provable : forall l, Valid_Clause l -> Provable (ClausetoPropF l).
intros ? [?|(?&?&?)];apply in_split in H as (?&?&?);subst.