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• Ipasir-formula

Ipasir-add-clauses

Add a list of clauses to the formula

Signature

(ipasir-add-clauses ipasir clauses) → new-ipasir

Arguments

clauses — Guard (lit-list-listp clauses).

Definitions and Theorems

Function: ipasir-add-clauses

(defun ipasir-add-clauses (ipasir clauses)
 (declare (xargs :stobjs (ipasir)))
 (declare (xargs :guard (lit-list-listp clauses)))
 (declare
     (xargs :guard (and (not (eq (ipasir-get-status ipasir) :undef))
                        (ipasir-empty-new-clause ipasir))))
 (let ((__function__ 'ipasir-add-clauses))
   (declare (ignorable __function__))
   (if (atom clauses)
       (b* ((ipasir (ipasir-cancel-new-clause ipasir)))
         (ipasir-input ipasir))
     (b* ((ipasir (ipasir-add-list ipasir (car clauses))))
       (ipasir-add-clauses ipasir (cdr clauses))))))

Theorem: ipasir-add-clauses-status

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

Theorem: ipasir-add-clauses-formula

(defthm ipasir-add-clauses-formula
  (b* ((?new-ipasir (ipasir-add-clauses ipasir clauses)))
    (equal (ipasir$a->formula new-ipasir)
           (append (rev (rev-each (lit-list-list-fix clauses)))
                   (ipasir$a->formula ipasir)))))

Theorem: ipasir-add-clauses-eval-formula

(defthm ipasir-add-clauses-eval-formula
  (b* ((?new-ipasir (ipasir-add-clauses ipasir clauses)))
    (equal (eval-formula (ipasir$a->formula new-ipasir)
                         env)
           (eval-formula (append clauses (ipasir$a->formula ipasir))
                         env))))

Theorem: ipasir-add-clauses-new-clause

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

Theorem: ipasir-add-clauses-assumption

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