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• Ipasir-formula

Ipasir-set-iff

Add clauses restricting out to be the IFF of in1 and in2.

Signature

(ipasir-set-iff ipasir out in1 in2) → new-ipasir

Arguments

out — Guard (litp out).

in1 — Guard (litp in1).

in2 — Guard (litp in2).

Definitions and Theorems

Function: ipasir-set-iff$inline

(defun ipasir-set-iff$inline (ipasir out in1 in2)
 (declare (xargs :stobjs (ipasir)))
 (declare (xargs :guard (and (litp out) (litp in1) (litp in2))))
 (declare
     (xargs :guard (and (not (eq (ipasir-get-status ipasir) :undef))
                        (ipasir-empty-new-clause ipasir))))
 (let ((__function__ 'ipasir-set-iff))
   (declare (ignorable __function__))
   (ipasir-set-xor ipasir out (l- in1)
                   in2)))

Theorem: ipasir-set-iff-status

(defthm ipasir-set-iff-status
  (b* ((?new-ipasir (ipasir-set-iff$inline ipasir out in1 in2)))
    (equal (ipasir$a->status new-ipasir)
           :input)))

Theorem: ipasir-set-iff-formula

(defthm ipasir-set-iff-formula
 (b* ((?new-ipasir (ipasir-set-iff$inline ipasir out in1 in2)))
  (implies
   (syntaxp (not (equal ipasir ''nil)))
   (equal
        (ipasir$a->formula new-ipasir)
        (append (ipasir$a->formula (ipasir-set-iff nil out in1 in2))
                (ipasir$a->formula ipasir))))))

Theorem: ipasir-set-iff-eval-formula

(defthm ipasir-set-iff-eval-formula
  (b* ((?new-ipasir (ipasir-set-iff$inline ipasir out in1 in2)))
    (equal (eval-formula (ipasir$a->formula new-ipasir)
                         env)
           (b-and (b-eqv (eval-lit out env)
                         (b-eqv (eval-lit in1 env)
                                (eval-lit in2 env)))
                  (eval-formula (ipasir$a->formula ipasir)
                                env)))))

Theorem: ipasir-set-iff-new-clause

(defthm ipasir-set-iff-new-clause
  (b* ((?new-ipasir (ipasir-set-iff$inline ipasir out in1 in2)))
    (not (ipasir$a->new-clause new-ipasir))))

Theorem: ipasir-set-iff-assumption

(defthm ipasir-set-iff-assumption
  (b* ((?new-ipasir (ipasir-set-iff$inline ipasir out in1 in2)))
    (equal (ipasir$a->assumption new-ipasir)
           (ipasir$a->assumption ipasir))))