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• Deftreeops-table-value

Deftreeops-table-value-fix

Fixing function for deftreeops-table-value structures.

Signature

(deftreeops-table-value-fix x) → new-x

Arguments

x — Guard (deftreeops-table-valuep x).

Returns

new-x — Type (deftreeops-table-valuep new-x).

Definitions and Theorems

Function: deftreeops-table-value-fix$inline

(defun deftreeops-table-value-fix$inline (x)
 (declare (xargs :guard (deftreeops-table-valuep x)))
 (let ((__function__ 'deftreeops-table-value-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (b*
    ((rulename-info-alist
       (deftreeops-rulename-info-alist-fix (cdr (std::da-nth 0 x))))
     (numrange-info-alist
       (deftreeops-numrange-info-alist-fix (cdr (std::da-nth 1 x))))
     (charval-info-alist
        (deftreeops-charval-info-alist-fix (cdr (std::da-nth 2 x))))
     (event-alist (acl2::symbol-pseudoeventform-alist-fix
                       (cdr (std::da-nth 3 x))))
     (call (acl2::pseudo-event-form-fix (cdr (std::da-nth 4 x)))))
    (list (cons 'rulename-info-alist
                rulename-info-alist)
          (cons 'numrange-info-alist
                numrange-info-alist)
          (cons 'charval-info-alist
                charval-info-alist)
          (cons 'event-alist event-alist)
          (cons 'call call)))
   :exec x)))

Theorem: deftreeops-table-valuep-of-deftreeops-table-value-fix

(defthm deftreeops-table-valuep-of-deftreeops-table-value-fix
  (b* ((new-x (deftreeops-table-value-fix$inline x)))
    (deftreeops-table-valuep new-x))
  :rule-classes :rewrite)

Theorem: deftreeops-table-value-fix-when-deftreeops-table-valuep

(defthm deftreeops-table-value-fix-when-deftreeops-table-valuep
  (implies (deftreeops-table-valuep x)
           (equal (deftreeops-table-value-fix x)
                  x)))

Function: deftreeops-table-value-equiv$inline

(defun deftreeops-table-value-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (deftreeops-table-valuep acl2::x)
                              (deftreeops-table-valuep acl2::y))))
  (equal (deftreeops-table-value-fix acl2::x)
         (deftreeops-table-value-fix acl2::y)))

Theorem: deftreeops-table-value-equiv-is-an-equivalence

(defthm deftreeops-table-value-equiv-is-an-equivalence
  (and (booleanp (deftreeops-table-value-equiv x y))
       (deftreeops-table-value-equiv x x)
       (implies (deftreeops-table-value-equiv x y)
                (deftreeops-table-value-equiv y x))
       (implies (and (deftreeops-table-value-equiv x y)
                     (deftreeops-table-value-equiv y z))
                (deftreeops-table-value-equiv x z)))
  :rule-classes (:equivalence))

Theorem: deftreeops-table-value-equiv-implies-equal-deftreeops-table-value-fix-1

(defthm
 deftreeops-table-value-equiv-implies-equal-deftreeops-table-value-fix-1
 (implies (deftreeops-table-value-equiv acl2::x x-equiv)
          (equal (deftreeops-table-value-fix acl2::x)
                 (deftreeops-table-value-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: deftreeops-table-value-fix-under-deftreeops-table-value-equiv

(defthm
      deftreeops-table-value-fix-under-deftreeops-table-value-equiv
  (deftreeops-table-value-equiv (deftreeops-table-value-fix acl2::x)
                                acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-deftreeops-table-value-fix-1-forward-to-deftreeops-table-value-equiv

(defthm
 equal-of-deftreeops-table-value-fix-1-forward-to-deftreeops-table-value-equiv
 (implies (equal (deftreeops-table-value-fix acl2::x)
                 acl2::y)
          (deftreeops-table-value-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: equal-of-deftreeops-table-value-fix-2-forward-to-deftreeops-table-value-equiv

(defthm
 equal-of-deftreeops-table-value-fix-2-forward-to-deftreeops-table-value-equiv
 (implies (equal acl2::x
                 (deftreeops-table-value-fix acl2::y))
          (deftreeops-table-value-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: deftreeops-table-value-equiv-of-deftreeops-table-value-fix-1-forward

(defthm
 deftreeops-table-value-equiv-of-deftreeops-table-value-fix-1-forward
 (implies
  (deftreeops-table-value-equiv (deftreeops-table-value-fix acl2::x)
                                acl2::y)
  (deftreeops-table-value-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: deftreeops-table-value-equiv-of-deftreeops-table-value-fix-2-forward

(defthm
 deftreeops-table-value-equiv-of-deftreeops-table-value-fix-2-forward
 (implies (deftreeops-table-value-equiv
               acl2::x
               (deftreeops-table-value-fix acl2::y))
          (deftreeops-table-value-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)