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• Vttree

Vttree-fix

Fixing function for vttree structures.

Signature

(vttree-fix x) → new-x

Arguments

x — Guard (vttree-p x).

Returns

new-x — Type (vttree-p new-x).

Definitions and Theorems

Function: vttree-fix$inline

(defun vttree-fix$inline (x)
  (declare (xargs :guard (vttree-p x)))
  (let ((__function__ 'vttree-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (common-lisp::case (vttree-kind x)
           (:none nil)
           (:warnings (b* ((warnings (vl-warninglist-fix (cdr x))))
                        (cons :warnings warnings)))
           (:constraints
                (b* ((constraints (sv::constraintlist-fix (cdr x))))
                  (cons :constraints constraints)))
           (:context (b* ((ctx (cadr x))
                          (subtree (vttree-fix (cddr x))))
                       (cons :context (cons ctx subtree))))
           (:branch (b* ((left (vttree-fix (car x)))
                         (right (vttree-fix (cdr x))))
                      (cons left right))))
         :exec x)))

Theorem: vttree-p-of-vttree-fix

(defthm vttree-p-of-vttree-fix
  (b* ((new-x (vttree-fix$inline x)))
    (vttree-p new-x))
  :rule-classes :rewrite)

Theorem: vttree-fix-when-vttree-p

(defthm vttree-fix-when-vttree-p
  (implies (vttree-p x)
           (equal (vttree-fix x) x)))

Function: vttree-equiv$inline

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

Theorem: vttree-equiv-is-an-equivalence

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

Theorem: vttree-equiv-implies-equal-vttree-fix-1

(defthm vttree-equiv-implies-equal-vttree-fix-1
  (implies (vttree-equiv acl2::x x-equiv)
           (equal (vttree-fix acl2::x)
                  (vttree-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: vttree-fix-under-vttree-equiv

(defthm vttree-fix-under-vttree-equiv
  (vttree-equiv (vttree-fix acl2::x)
                acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-vttree-fix-1-forward-to-vttree-equiv

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

Theorem: equal-of-vttree-fix-2-forward-to-vttree-equiv

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

Theorem: vttree-equiv-of-vttree-fix-1-forward

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

Theorem: vttree-equiv-of-vttree-fix-2-forward

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

Theorem: vttree-kind$inline-of-vttree-fix-x

(defthm vttree-kind$inline-of-vttree-fix-x
  (equal (vttree-kind$inline (vttree-fix x))
         (vttree-kind$inline x)))

Theorem: vttree-kind$inline-vttree-equiv-congruence-on-x

(defthm vttree-kind$inline-vttree-equiv-congruence-on-x
  (implies (vttree-equiv x x-equiv)
           (equal (vttree-kind$inline x)
                  (vttree-kind$inline x-equiv)))
  :rule-classes :congruence)