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• Ipasir$a

Ipasir-finalize-clause$a

Logic form of ipasir-finalize-clause. See ipasir for usage.

Signature

(ipasir-finalize-clause$a solver) → new-solver

Arguments

solver — Guard (ipasir$a-p solver).

Returns

new-solver — Type (ipasir$a-p new-solver).

Definitions and Theorems

Function: ipasir-finalize-clause$a

(defun ipasir-finalize-clause$a (solver)
 (declare (xargs :guard (ipasir$a-p solver)))
 (declare (xargs :guard (not (eq (ipasir-get-status$a solver)
                                 :undef))))
 (let ((__function__ 'ipasir-finalize-clause$a))
  (declare (ignorable __function__))
  (b* (((ipasir$a solver)))
   (change-ipasir$a solver
                    :formula (cons solver.new-clause solver.formula)
                    :new-clause nil
                    :status :input
                    :history (cons :finalize solver.history)))))

Theorem: ipasir$a-p-of-ipasir-finalize-clause$a

(defthm ipasir$a-p-of-ipasir-finalize-clause$a
  (b* ((new-solver (ipasir-finalize-clause$a solver)))
    (ipasir$a-p new-solver))
  :rule-classes :rewrite)

Theorem: status-of-ipasir-finalize-clause$a

(defthm status-of-ipasir-finalize-clause$a
  (b* ((?new-solver (ipasir-finalize-clause$a solver)))
    (equal (ipasir$a->status new-solver)
           :input)))

Theorem: new-clause-of-ipasir-finalize-clause$a

(defthm new-clause-of-ipasir-finalize-clause$a
  (b* ((?new-solver (ipasir-finalize-clause$a solver)))
    (equal (ipasir$a->new-clause new-solver)
           nil)))

Theorem: formula-of-ipasir-finalize-clause$a

(defthm formula-of-ipasir-finalize-clause$a
  (b* ((?new-solver (ipasir-finalize-clause$a solver)))
    (equal (ipasir$a->formula new-solver)
           (cons (ipasir$a->new-clause solver)
                 (ipasir$a->formula solver)))))

Theorem: assumption-of-ipasir-finalize-clause$a

(defthm assumption-of-ipasir-finalize-clause$a
  (b* ((?new-solver (ipasir-finalize-clause$a solver)))
    (equal (ipasir$a->assumption new-solver)
           (ipasir$a->assumption solver))))

Theorem: ipasir-finalize-clause$a-of-ipasir$a-fix-solver

(defthm ipasir-finalize-clause$a-of-ipasir$a-fix-solver
  (equal (ipasir-finalize-clause$a (ipasir$a-fix solver))
         (ipasir-finalize-clause$a solver)))

Theorem: ipasir-finalize-clause$a-ipasir$a-equiv-congruence-on-solver

(defthm ipasir-finalize-clause$a-ipasir$a-equiv-congruence-on-solver
  (implies (ipasir$a-equiv solver solver-equiv)
           (equal (ipasir-finalize-clause$a solver)
                  (ipasir-finalize-clause$a solver-equiv)))
  :rule-classes :congruence)