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(in-package "PROOF-CHECKER-ARRAY")
(include-book "literal")
(include-book "unique")
;; ===================================================================
;; ============================= CLAUSE ==============================
(defun clausep (clause)
(declare (xargs :guard t))
(and (literal-listp clause)
(unique-literalsp clause)
(no-conflicting-literalsp clause)))
(defthm clausep-true-listp
(implies (clausep clause)
(true-listp clause)))
(defthm clausep-member
(implies (and (clausep clause)
(member e clause))
(literalp e)))
(defthm clausep-cdr
(implies (and (clausep clause)
(consp clause))
(clausep (cdr clause))))
;; ===================================================================
;; ============================= FORMULA =============================
(defun formulap (formula)
(declare (xargs :guard t))
(if (atom formula)
(null formula)
(and (clausep (car formula))
(formulap (cdr formula)))))
(defthm formulap-true-listp
(implies (formulap formula)
(true-listp formula)))
(defthm formulap-member
(implies (and (formulap formula)
(member e formula))
(clausep e)))
(defthm formulap-cdr
(implies (and (formulap formula)
(consp formula))
(formulap (cdr formula))))
(defthm formulap-implies-clausep-car
(implies (and (formulap formula)
(consp formula))
(clausep (car formula))))
;; ===================================================================
;; ========================= FLATTEN-FORMULA =========================
(defun flatten-formula (formula)
(declare (xargs :guard (formulap formula)))
(if (atom formula)
nil
(append (car formula)
(flatten-formula (cdr formula)))))
(defthm literal-listp-flatten-formula
(implies (formulap formula)
(literal-listp (flatten-formula formula))))
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