Local Coercion bool2Prop (b: bool) := b = true.

(* Specifications: *)
Lemma loop_sound n sigma nc s cl st : clause_denote nc st -> space_denote sigma st -> setd clause_denote inter TT s st -> the_loop n sigma nc s cl = Valid -> clause_denote empty_clause st.
Theorem check_entailment_sound: forall (e: entailment), VeriStar.check_entailment e = VeriStar.Valid -> entailment_denote e.