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(in-package "PROOF-CHECKER-ARRAY")
(include-book "literal")
(include-book "unique")
(include-book "sets")
(include-book "clause")
;; ===================================================================
;; ========================== ALL-LITERALS ===========================
(defun all-literals (formula)
(declare (xargs :guard (formulap formula)))
(remove-duplicate-literals (flatten-formula formula)))
(defthm literal-listp-all-literals
(implies (formulap formula)
(literal-listp (all-literals formula))))
(defthm unique-literalsp-all-literals
(implies (formulap formula)
(unique-literalsp (all-literals formula))))
(defthm member-append
(iff (member e (append x y))
(or (member e x)
(member e y))))
; this rule is not firing because of free variable
(defthm member-all-literals
(implies (and (member literal clause)
(member clause formula))
(member literal (all-literals formula))))
(defthm subsetp-all-literals
(implies (member clause formula)
(subsetp clause (all-literals formula))))
(defthm subsetp-list-all-literals
(subsetp-list formula (all-literals formula)))
(in-theory (disable all-literals))
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