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• Ipasir$a

Ipasir-init$a

Logic form of ipasir-init. See ipasir for usage.

Signature

(ipasir-init$a solver state) → (mv new-solver new-state)

Arguments

solver — Guard (ipasir$a-p solver).

Returns

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

new-state — Type (equal new-state (mv-nth 2 (read-acl2-oracle state))).

Definitions and Theorems

Function: ipasir-init$a

(defun ipasir-init$a (solver state)
 (declare (xargs :stobjs (state)))
 (declare (xargs :guard (ipasir$a-p solver)))
 (declare (xargs :guard (eq (ipasir-get-status$a solver)
                            :undef)))
 (let ((__function__ 'ipasir-init$a))
  (declare (ignorable __function__))
  (b* (((ipasir$a solver))
       ((mv & initval state)
        (read-acl2-oracle state)))
   (mv
     (make-ipasir$a :status :input
                    :callback-count 0
                    :history (cons (cons ':init (cons initval 'nil))
                                   solver.history))
     state))))

Theorem: ipasir$a-p-of-ipasir-init$a.new-solver

(defthm ipasir$a-p-of-ipasir-init$a.new-solver
  (b* (((mv ?new-solver ?new-state)
        (ipasir-init$a solver state)))
    (ipasir$a-p new-solver))
  :rule-classes :rewrite)

Theorem: return-type-of-ipasir-init$a.new-state

(defthm return-type-of-ipasir-init$a.new-state
  (b* (((mv ?new-solver ?new-state)
        (ipasir-init$a solver state)))
    (equal new-state
           (mv-nth 2 (read-acl2-oracle state))))
  :rule-classes :rewrite)

Theorem: ipasir-init$a-status

(defthm ipasir-init$a-status
  (b* (((mv ?new-solver ?new-state)
        (ipasir-init$a solver state)))
    (equal (ipasir$a->status new-solver)
           :input)))

Theorem: ipasir-init$a-formula

(defthm ipasir-init$a-formula
  (b* (((mv ?new-solver ?new-state)
        (ipasir-init$a solver state)))
    (equal (ipasir$a->formula new-solver)
           nil)))

Theorem: ipasir-init$a-assumption

(defthm ipasir-init$a-assumption
  (b* (((mv ?new-solver ?new-state)
        (ipasir-init$a solver state)))
    (equal (ipasir$a->assumption new-solver)
           nil)))

Theorem: ipasir-init$a-new-clause

(defthm ipasir-init$a-new-clause
  (b* (((mv ?new-solver ?new-state)
        (ipasir-init$a solver state)))
    (equal (ipasir$a->new-clause new-solver)
           nil)))

Theorem: ipasir-init$a-of-ipasir$a-fix-solver

(defthm ipasir-init$a-of-ipasir$a-fix-solver
  (equal (ipasir-init$a (ipasir$a-fix solver)
                        state)
         (ipasir-init$a solver state)))

Theorem: ipasir-init$a-ipasir$a-equiv-congruence-on-solver

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