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• Vl-emodwire-p

Vl-emodwire-fix

Signature

(vl-emodwire-fix x) → x-prime

Arguments

x — Guard (vl-emodwire-p x).

Returns

x-prime — Type (vl-emodwire-p x-prime).

Definitions and Theorems

Function: vl-emodwire-fix$inline

(defun vl-emodwire-fix$inline (x)
  (declare (xargs :guard (vl-emodwire-p x)))
  (let ((__function__ 'vl-emodwire-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (if (vl-emodwire-p x)
             x
           'acl2::bad-default-emodwire)
         :exec x)))

Theorem: vl-emodwire-p-of-vl-emodwire-fix

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

Theorem: vl-emodwire-fix-when-vl-emodwire-p

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

Function: vl-emodwire-equiv$inline

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

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

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

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

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

Theorem: vl-emodwire-fix-under-vl-emodwire-equiv

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