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Deftreeops-rep-info

Deftreeops-rep-info-fix

Fixing function for deftreeops-rep-info structures.

Signature
(deftreeops-rep-info-fix x) → new-x
Arguments: x — Guard (deftreeops-rep-infop x).
Returns: new-x — Type (deftreeops-rep-infop new-x).

Definitions and Theorems

Function: deftreeops-rep-info-fix$inline

(defun deftreeops-rep-info-fix$inline (x)
 (declare (xargs :guard (deftreeops-rep-infop x)))
 (let ((__function__ 'deftreeops-rep-info-fix))
  (declare (ignorable __function__))
  (mbe
    :logic
    (b*
      ((get-tree-list-fn (acl2::symbol-fix (cdr (std::da-nth 0 x))))
       (matching-thm (acl2::symbol-fix (cdr (std::da-nth 1 x))))
       (get-len-fn (acl2::symbol-fix (cdr (std::da-nth 2 x))))
       (get-tree-fn (acl2::symbol-fix (cdr (std::da-nth 3 x)))))
      (list (cons 'get-tree-list-fn
                  get-tree-list-fn)
            (cons 'matching-thm matching-thm)
            (cons 'get-len-fn get-len-fn)
            (cons 'get-tree-fn get-tree-fn)))
    :exec x)))

Theorem: deftreeops-rep-infop-of-deftreeops-rep-info-fix

(defthm deftreeops-rep-infop-of-deftreeops-rep-info-fix
  (b* ((new-x (deftreeops-rep-info-fix$inline x)))
    (deftreeops-rep-infop new-x))
  :rule-classes :rewrite)

Theorem: deftreeops-rep-info-fix-when-deftreeops-rep-infop

(defthm deftreeops-rep-info-fix-when-deftreeops-rep-infop
  (implies (deftreeops-rep-infop x)
           (equal (deftreeops-rep-info-fix x) x)))

Function: deftreeops-rep-info-equiv$inline

(defun deftreeops-rep-info-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (deftreeops-rep-infop acl2::x)
                              (deftreeops-rep-infop acl2::y))))
  (equal (deftreeops-rep-info-fix acl2::x)
         (deftreeops-rep-info-fix acl2::y)))

Theorem: deftreeops-rep-info-equiv-is-an-equivalence

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

Theorem: deftreeops-rep-info-equiv-implies-equal-deftreeops-rep-info-fix-1

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

Theorem: deftreeops-rep-info-fix-under-deftreeops-rep-info-equiv

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

Theorem: equal-of-deftreeops-rep-info-fix-1-forward-to-deftreeops-rep-info-equiv

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

Theorem: equal-of-deftreeops-rep-info-fix-2-forward-to-deftreeops-rep-info-equiv

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

Theorem: deftreeops-rep-info-equiv-of-deftreeops-rep-info-fix-1-forward

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

Theorem: deftreeops-rep-info-equiv-of-deftreeops-rep-info-fix-2-forward

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