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• Vl-moditem

Vl-moditem-fix

(vl-moditem-fix x) is a ACL2::fty fixing function.

Signature

(vl-moditem-fix x) → fty::newx

Arguments

x — Guard (vl-moditem-p x).

Returns

fty::newx — Type (vl-moditem-p fty::newx).

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

Definitions and Theorems

Function: vl-moditem-fix$inline

(defun vl-moditem-fix$inline (x)
  (declare (xargs :guard (vl-moditem-p x)))
  (let ((__function__ 'vl-moditem-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (common-lisp::case (tag x)
           ((:vl-vardecl) (vl-vardecl-fix x))
           ((:vl-paramdecl) (vl-paramdecl-fix x))
           ((:vl-fundecl) (vl-fundecl-fix x))
           ((:vl-taskdecl) (vl-taskdecl-fix x))
           ((:vl-modinst) (vl-modinst-fix x))
           (otherwise (vl-gateinst-fix x)))
         :exec x)))

Theorem: vl-moditem-p-of-vl-moditem-fix

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

Theorem: vl-moditem-fix-when-vl-moditem-p

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

Function: vl-moditem-equiv$inline

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

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

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

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

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

Theorem: vl-moditem-fix-under-vl-moditem-equiv

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

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

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

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

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

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

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

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

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

Theorem: tag-of-vl-moditem-fix-forward

(defthm tag-of-vl-moditem-fix-forward
  (or (equal (tag (vl-moditem-fix x))
             :vl-vardecl)
      (equal (tag (vl-moditem-fix x))
             :vl-paramdecl)
      (equal (tag (vl-moditem-fix x))
             :vl-fundecl)
      (equal (tag (vl-moditem-fix x))
             :vl-taskdecl)
      (equal (tag (vl-moditem-fix x))
             :vl-modinst)
      (equal (tag (vl-moditem-fix x))
             :vl-gateinst))
  :rule-classes
  ((:forward-chaining :trigger-terms ((tag (vl-moditem-fix x))))))