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• Vl-elabtask

Vl-elabtask-fix

Fixing function for vl-elabtask structures.

Signature

(vl-elabtask-fix x) → new-x

Arguments

x — Guard (vl-elabtask-p x).

Returns

new-x — Type (vl-elabtask-p new-x).

Definitions and Theorems

Function: vl-elabtask-fix$inline

(defun vl-elabtask-fix$inline (x)
  (declare (xargs :guard (vl-elabtask-p x)))
  (let ((__function__ 'vl-elabtask-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((stmt (vl-stmt-fix (cdr x))))
           (cons :vl-elabtask stmt))
         :exec x)))

Theorem: vl-elabtask-p-of-vl-elabtask-fix

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

Theorem: vl-elabtask-fix-when-vl-elabtask-p

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

Function: vl-elabtask-equiv$inline

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

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

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

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

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

Theorem: vl-elabtask-fix-under-vl-elabtask-equiv

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

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

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

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

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

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

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

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

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