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        • Ipasir-set-or
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        • Ipasir-set-buf
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      • Ipasir-val
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      • Ipasir-set-limit
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• Ipasir-formula

Ipasir-set-buf

Add clauses restricting out to have the same value as in.

Signature

(ipasir-set-buf ipasir out in) → new-ipasir

Arguments

out — Guard (litp out).

in — Guard (litp in).

Definitions and Theorems

Function: ipasir-set-buf

(defun ipasir-set-buf (ipasir out in)
 (declare (xargs :stobjs (ipasir)))
 (declare (xargs :guard (and (litp out) (litp in))))
 (declare
     (xargs :guard (and (not (eq (ipasir-get-status ipasir) :undef))
                        (ipasir-empty-new-clause ipasir))))
 (let ((__function__ 'ipasir-set-buf))
   (declare (ignorable __function__))
   (b* ((ipasir (ipasir-cancel-new-clause ipasir))
        (ipasir (ipasir-add-binary ipasir (l- out) in)))
     (ipasir-add-binary ipasir out (l- in)))))

Theorem: ipasir-set-buf-status

(defthm ipasir-set-buf-status
  (b* ((?new-ipasir (ipasir-set-buf ipasir out in)))
    (equal (ipasir$a->status new-ipasir)
           :input)))

Theorem: ipasir-set-buf-formula

(defthm ipasir-set-buf-formula
 (b* ((?new-ipasir (ipasir-set-buf ipasir out in)))
  (implies
      (syntaxp (not (equal ipasir ''nil)))
      (equal (ipasir$a->formula new-ipasir)
             (append (ipasir$a->formula (ipasir-set-buf nil out in))
                     (ipasir$a->formula ipasir))))))

Theorem: ipasir-set-buf-eval-formula

(defthm ipasir-set-buf-eval-formula
  (b* ((?new-ipasir (ipasir-set-buf ipasir out in)))
    (equal (eval-formula (ipasir$a->formula new-ipasir)
                         env)
           (b-and (b-eqv (eval-lit out env)
                         (eval-lit in env))
                  (eval-formula (ipasir$a->formula ipasir)
                                env)))))

Theorem: ipasir-set-buf-new-clause

(defthm ipasir-set-buf-new-clause
  (b* ((?new-ipasir (ipasir-set-buf ipasir out in)))
    (not (ipasir$a->new-clause new-ipasir))))

Theorem: ipasir-set-buf-assumption

(defthm ipasir-set-buf-assumption
  (b* ((?new-ipasir (ipasir-set-buf ipasir out in)))
    (equal (ipasir$a->assumption new-ipasir)
           (ipasir$a->assumption ipasir))))