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Vl-warningtree

Vl-warningtree-fix

Fixing function for vl-warningtree structures.

Signature
(vl-warningtree-fix x) → new-x
Arguments: x — Guard (vl-warningtree-p x).
Returns: new-x — Type (vl-warningtree-p new-x).

Definitions and Theorems

Function: vl-warningtree-fix$inline

(defun vl-warningtree-fix$inline (x)
 (declare (xargs :guard (vl-warningtree-p x)))
 (let ((__function__ 'vl-warningtree-fix))
  (declare (ignorable __function__))
  (mbe
    :logic
    (common-lisp::case (vl-warningtree-kind x)
      (:null nil)
      (:warning (b* ((warning (vl-warning-fix x)))
                  warning))
      (:context
           (b* ((context (cadr x))
                (subtree (vl-warningtree-fix (cddr x))))
             (cons :vl-warningtree-context (cons context subtree))))
      (:pair (b* ((left (vl-warningtree-fix (car x)))
                  (right (vl-warningtree-fix (cdr x))))
               (cons left right))))
    :exec x)))

Theorem: vl-warningtree-p-of-vl-warningtree-fix

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

Theorem: vl-warningtree-fix-when-vl-warningtree-p

(defthm vl-warningtree-fix-when-vl-warningtree-p
  (implies (vl-warningtree-p x)
           (equal (vl-warningtree-fix x) x)))

Function: vl-warningtree-equiv$inline

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

Theorem: vl-warningtree-equiv-is-an-equivalence

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

Theorem: vl-warningtree-equiv-implies-equal-vl-warningtree-fix-1

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

Theorem: vl-warningtree-fix-under-vl-warningtree-equiv

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

Theorem: equal-of-vl-warningtree-fix-1-forward-to-vl-warningtree-equiv

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

Theorem: equal-of-vl-warningtree-fix-2-forward-to-vl-warningtree-equiv

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

Theorem: vl-warningtree-equiv-of-vl-warningtree-fix-1-forward

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

Theorem: vl-warningtree-equiv-of-vl-warningtree-fix-2-forward

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

Theorem: vl-warningtree-kind$inline-of-vl-warningtree-fix-x

(defthm vl-warningtree-kind$inline-of-vl-warningtree-fix-x
  (equal (vl-warningtree-kind$inline (vl-warningtree-fix x))
         (vl-warningtree-kind$inline x)))

Theorem: vl-warningtree-kind$inline-vl-warningtree-equiv-congruence-on-x

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