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• Vl-parsed-interface-head

Vl-parsed-interface-head-fix

Fixing function for vl-parsed-interface-head structures.

Signature

(vl-parsed-interface-head-fix x) → new-x

Arguments

x — Guard (vl-parsed-interface-head-p x).

Returns

new-x — Type (vl-parsed-interface-head-p new-x).

Definitions and Theorems

Function: vl-parsed-interface-head-fix$inline

(defun vl-parsed-interface-head-fix$inline (x)
 (declare (xargs :guard (vl-parsed-interface-head-p x)))
 (let ((__function__ 'vl-parsed-interface-head-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (b* ((ifname (str-fix (std::prod-car (cdr x))))
        (modport (maybe-string-fix (std::prod-cdr (cdr x)))))
    (cons
         :vl-parsed-interface-head (std::prod-cons ifname modport)))
   :exec x)))

Theorem: vl-parsed-interface-head-p-of-vl-parsed-interface-head-fix

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

Theorem: vl-parsed-interface-head-fix-when-vl-parsed-interface-head-p

(defthm vl-parsed-interface-head-fix-when-vl-parsed-interface-head-p
  (implies (vl-parsed-interface-head-p x)
           (equal (vl-parsed-interface-head-fix x)
                  x)))

Function: vl-parsed-interface-head-equiv$inline

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

Theorem: vl-parsed-interface-head-equiv-is-an-equivalence

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

Theorem: vl-parsed-interface-head-equiv-implies-equal-vl-parsed-interface-head-fix-1

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

Theorem: vl-parsed-interface-head-fix-under-vl-parsed-interface-head-equiv

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

Theorem: equal-of-vl-parsed-interface-head-fix-1-forward-to-vl-parsed-interface-head-equiv

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

Theorem: equal-of-vl-parsed-interface-head-fix-2-forward-to-vl-parsed-interface-head-equiv

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

Theorem: vl-parsed-interface-head-equiv-of-vl-parsed-interface-head-fix-1-forward

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

Theorem: vl-parsed-interface-head-equiv-of-vl-parsed-interface-head-fix-2-forward

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