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• Ipasir-formula

Ipasir-add-binary

Add a binary clause to the formula

Signature

(ipasir-add-binary ipasir a b) → new-ipasir

Arguments

a — Guard (litp a).

b — Guard (litp b).

Definitions and Theorems

Function: ipasir-add-binary

(defun ipasir-add-binary (ipasir a b)
 (declare (xargs :stobjs (ipasir)))
 (declare (xargs :guard (and (litp a) (litp b))))
 (declare
     (xargs :guard (and (not (eq (ipasir-get-status ipasir) :undef))
                        (ipasir-empty-new-clause ipasir))))
 (let ((__function__ 'ipasir-add-binary))
   (declare (ignorable __function__))
   (b* ((ipasir (ipasir-cancel-new-clause ipasir))
        (ipasir (ipasir-add-lit ipasir a))
        (ipasir (ipasir-add-lit ipasir b)))
     (ipasir-finalize-clause ipasir))))

Theorem: ipasir-add-binary-status

(defthm ipasir-add-binary-status
  (b* ((?new-ipasir (ipasir-add-binary ipasir a b)))
    (equal (ipasir$a->status new-ipasir)
           :input)))

Theorem: ipasir-add-binary-formula

(defthm ipasir-add-binary-formula
  (b* ((?new-ipasir (ipasir-add-binary ipasir a b)))
    (equal (ipasir$a->formula new-ipasir)
           (cons (lit-list-fix (list b a))
                 (ipasir$a->formula ipasir)))))

Theorem: ipasir-add-binary-eval-formula

(defthm ipasir-add-binary-eval-formula
  (b* ((?new-ipasir (ipasir-add-binary ipasir a b)))
    (equal (eval-formula (ipasir$a->formula new-ipasir)
                         assum)
           (eval-formula (cons (list a b)
                               (ipasir$a->formula ipasir))
                         assum))))

Theorem: ipasir-add-binary-new-clause

(defthm ipasir-add-binary-new-clause
  (b* ((?new-ipasir (ipasir-add-binary ipasir a b)))
    (not (ipasir$a->new-clause new-ipasir))))

Theorem: ipasir-add-binary-assumption

(defthm ipasir-add-binary-assumption
  (b* ((?new-ipasir (ipasir-add-binary ipasir a b)))
    (equal (ipasir$a->assumption new-ipasir)
           (ipasir$a->assumption ipasir))))