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• Ipasir$a

Ipasir-add-lit$a

Logic form of ipasir-add-lit. See ipasir for usage.

Signature

(ipasir-add-lit$a solver lit) → new-solver

Arguments

solver — Guard (ipasir$a-p solver).

lit — Guard (litp lit).

Returns

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

Definitions and Theorems

Function: ipasir-add-lit$a

(defun ipasir-add-lit$a (solver lit)
 (declare (xargs :guard (and (ipasir$a-p solver) (litp lit))))
 (declare (xargs :guard (not (eq (ipasir-get-status$a solver)
                                 :undef))))
 (let ((__function__ 'ipasir-add-lit$a))
   (declare (ignorable __function__))
   (b*
    (((ipasir$a solver))
     (- (mbe :logic nil
             :exec (and (not (signed-byte-p 32 lit))
                        (raise "Out of bounds literal: ~x0" lit)))))
    (change-ipasir$a
         solver
         :new-clause (cons (lit-fix lit) solver.new-clause)
         :status :input
         :history (cons (cons ':add (cons (lit-fix lit) 'nil))
                        solver.history)))))

Theorem: ipasir$a-p-of-ipasir-add-lit$a

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

Theorem: status-of-ipasir-add-lit$a

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

Theorem: new-clause-of-ipasir-add-lit$a

(defthm new-clause-of-ipasir-add-lit$a
  (b* ((?new-solver (ipasir-add-lit$a solver lit)))
    (equal (ipasir$a->new-clause new-solver)
           (cons (lit-fix lit)
                 (ipasir$a->new-clause solver)))))

Theorem: formula-of-ipasir-add-lit$a

(defthm formula-of-ipasir-add-lit$a
  (b* ((?new-solver (ipasir-add-lit$a solver lit)))
    (equal (ipasir$a->formula new-solver)
           (ipasir$a->formula solver))))

Theorem: assumption-of-ipasir-add-lit$a

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

Theorem: ipasir-add-lit$a-of-ipasir$a-fix-solver

(defthm ipasir-add-lit$a-of-ipasir$a-fix-solver
  (equal (ipasir-add-lit$a (ipasir$a-fix solver)
                           lit)
         (ipasir-add-lit$a solver lit)))

Theorem: ipasir-add-lit$a-ipasir$a-equiv-congruence-on-solver

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

Theorem: ipasir-add-lit$a-of-lit-fix-lit

(defthm ipasir-add-lit$a-of-lit-fix-lit
  (equal (ipasir-add-lit$a solver (lit-fix lit))
         (ipasir-add-lit$a solver lit)))

Theorem: ipasir-add-lit$a-lit-equiv-congruence-on-lit

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