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• Vl-repeateventcontrol

Vl-repeateventcontrol-fix

Fixing function for vl-repeateventcontrol structures.

Signature

(vl-repeateventcontrol-fix x) → new-x

Arguments

x — Guard (vl-repeateventcontrol-p x).

Returns

new-x — Type (vl-repeateventcontrol-p new-x).

Definitions and Theorems

Function: vl-repeateventcontrol-fix$inline

(defun vl-repeateventcontrol-fix$inline (x)
 (declare (xargs :guard (vl-repeateventcontrol-p x)))
 (let ((__function__ 'vl-repeateventcontrol-fix))
   (declare (ignorable __function__))
   (mbe :logic
        (b* ((expr (vl-expr-fix (std::prod-car (cdr x))))
             (ctrl (vl-eventcontrol-fix (std::prod-cdr (cdr x)))))
          (cons :vl-repeat-eventcontrol (std::prod-cons expr ctrl)))
        :exec x)))

Theorem: vl-repeateventcontrol-p-of-vl-repeateventcontrol-fix

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

Theorem: vl-repeateventcontrol-fix-when-vl-repeateventcontrol-p

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

Function: vl-repeateventcontrol-equiv$inline

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

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

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

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

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

Theorem: vl-repeateventcontrol-fix-under-vl-repeateventcontrol-equiv

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

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

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

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

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

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

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

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

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