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• Vl-clocking-block-item

Vl-clocking-block-item-fix

(vl-clocking-block-item-fix x) is a fty fixing function.

Signature

(vl-clocking-block-item-fix x) → fty::newx

Arguments

x — Guard (vl-clocking-block-item-p x).

Returns

fty::newx — Type (vl-clocking-block-item-p fty::newx).

Note that in the execution this is just an inline identity function.

Definitions and Theorems

Function: vl-clocking-block-item-fix$inline

(defun vl-clocking-block-item-fix$inline (x)
  (declare (xargs :guard (vl-clocking-block-item-p x)))
  (let ((__function__ 'vl-clocking-block-item-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (common-lisp::case (tag x)
           ((:vl-defaultskew)
            (vl-defaultskew-item-fix x))
           ((:vl-clkassign) (vl-clkassign-fix x))
           ((:vl-property) (vl-property-fix x))
           (otherwise (vl-sequence-fix x)))
         :exec x)))

Theorem: vl-clocking-block-item-p-of-vl-clocking-block-item-fix

(defthm vl-clocking-block-item-p-of-vl-clocking-block-item-fix
  (b* ((fty::newx (vl-clocking-block-item-fix$inline x)))
    (vl-clocking-block-item-p fty::newx))
  :rule-classes :rewrite)

Theorem: vl-clocking-block-item-fix-when-vl-clocking-block-item-p

(defthm vl-clocking-block-item-fix-when-vl-clocking-block-item-p
  (implies (vl-clocking-block-item-p x)
           (equal (vl-clocking-block-item-fix x)
                  x)))

Function: vl-clocking-block-item-equiv$inline

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

Theorem: vl-clocking-block-item-equiv-is-an-equivalence

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

Theorem: vl-clocking-block-item-equiv-implies-equal-vl-clocking-block-item-fix-1

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

Theorem: vl-clocking-block-item-fix-under-vl-clocking-block-item-equiv

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

Theorem: equal-of-vl-clocking-block-item-fix-1-forward-to-vl-clocking-block-item-equiv

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

Theorem: equal-of-vl-clocking-block-item-fix-2-forward-to-vl-clocking-block-item-equiv

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

Theorem: vl-clocking-block-item-equiv-of-vl-clocking-block-item-fix-1-forward

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

Theorem: vl-clocking-block-item-equiv-of-vl-clocking-block-item-fix-2-forward

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

Theorem: tag-of-vl-clocking-block-item-fix-forward

(defthm tag-of-vl-clocking-block-item-fix-forward
  (or (equal (tag (vl-clocking-block-item-fix x))
             :vl-defaultskew)
      (equal (tag (vl-clocking-block-item-fix x))
             :vl-clkassign)
      (equal (tag (vl-clocking-block-item-fix x))
             :vl-property)
      (equal (tag (vl-clocking-block-item-fix x))
             :vl-sequence))
  :rule-classes
  ((:forward-chaining
        :trigger-terms ((tag (vl-clocking-block-item-fix x))))))