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Smtlink-process-user-hint

Smt-solver-params

Definitions and Theorems

Function: smt-solver-params-p

(defun smt-solver-params-p (term)
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'smt-solver-params-p))
    (declare (ignorable acl2::__function__))
    (true-listp term)))

Theorem: booleanp-of-smt-solver-params-p

(defthm booleanp-of-smt-solver-params-p
  (b* ((syntax-good? (smt-solver-params-p term)))
    (booleanp syntax-good?))
  :rule-classes :rewrite)

Function: smt-solver-params-fix

(defun smt-solver-params-fix (term)
  (declare (xargs :guard (smt-solver-params-p term)))
  (let ((acl2::__function__ 'smt-solver-params-fix))
    (declare (ignorable acl2::__function__))
    (mbe :logic
         (if (smt-solver-params-p term)
             term
           (true-list-fix term))
         :exec term)))

Theorem: smt-solver-params-p-of-smt-solver-params-fix

(defthm smt-solver-params-p-of-smt-solver-params-fix
  (b* ((fixed-term (smt-solver-params-fix term)))
    (smt-solver-params-p fixed-term))
  :rule-classes :rewrite)

Function: smt-solver-params-equiv$inline

(defun smt-solver-params-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (smt-solver-params-p acl2::x)
                              (smt-solver-params-p acl2::y))))
  (equal (smt-solver-params-fix acl2::x)
         (smt-solver-params-fix acl2::y)))

Theorem: smt-solver-params-equiv-is-an-equivalence

(defthm smt-solver-params-equiv-is-an-equivalence
  (and (booleanp (smt-solver-params-equiv x y))
       (smt-solver-params-equiv x x)
       (implies (smt-solver-params-equiv x y)
                (smt-solver-params-equiv y x))
       (implies (and (smt-solver-params-equiv x y)
                     (smt-solver-params-equiv y z))
                (smt-solver-params-equiv x z)))
  :rule-classes (:equivalence))

Theorem: smt-solver-params-equiv-implies-equal-smt-solver-params-fix-1

(defthm
      smt-solver-params-equiv-implies-equal-smt-solver-params-fix-1
  (implies (smt-solver-params-equiv acl2::x x-equiv)
           (equal (smt-solver-params-fix acl2::x)
                  (smt-solver-params-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: smt-solver-params-fix-under-smt-solver-params-equiv

(defthm smt-solver-params-fix-under-smt-solver-params-equiv
  (smt-solver-params-equiv (smt-solver-params-fix acl2::x)
                           acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-smt-solver-params-fix-1-forward-to-smt-solver-params-equiv

(defthm
 equal-of-smt-solver-params-fix-1-forward-to-smt-solver-params-equiv
 (implies (equal (smt-solver-params-fix acl2::x)
                 acl2::y)
          (smt-solver-params-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: equal-of-smt-solver-params-fix-2-forward-to-smt-solver-params-equiv

(defthm
 equal-of-smt-solver-params-fix-2-forward-to-smt-solver-params-equiv
 (implies (equal acl2::x (smt-solver-params-fix acl2::y))
          (smt-solver-params-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: smt-solver-params-equiv-of-smt-solver-params-fix-1-forward

(defthm smt-solver-params-equiv-of-smt-solver-params-fix-1-forward
  (implies (smt-solver-params-equiv (smt-solver-params-fix acl2::x)
                                    acl2::y)
           (smt-solver-params-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: smt-solver-params-equiv-of-smt-solver-params-fix-2-forward

(defthm smt-solver-params-equiv-of-smt-solver-params-fix-2-forward
 (implies
   (smt-solver-params-equiv acl2::x (smt-solver-params-fix acl2::y))
   (smt-solver-params-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Subtopics

Smt-solver-params-fix: Fixing function for smt-solver-params.
Smt-solver-params-p: Recognizer for smt-solver-params.