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Vl-op-p

Signature

(vl-op-p x) → *

Definitions and Theorems

Function: vl-op-p

(defun vl-op-p (x)
  (declare (xargs :guard t))
  (let ((__function__ 'vl-op-p))
    (declare (ignorable __function__))
    (or (vl-unaryop-p x)
        (vl-binaryop-p x))))

Function: vl-op-fix

(defun vl-op-fix (x)
  (declare (xargs :guard (vl-op-p x)))
  (let ((__function__ 'vl-op-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (if (vl-binaryop-p x)
             x
           (vl-unaryop-fix x))
         :exec x)))

Theorem: vl-op-p-of-vl-op-fix

(defthm vl-op-p-of-vl-op-fix
  (b* ((xx (vl-op-fix x))) (vl-op-p xx))
  :rule-classes :rewrite)

Theorem: vl-op-fix-when-vl-op-p

(defthm vl-op-fix-when-vl-op-p
  (b* ((?xx (vl-op-fix x)))
    (implies (vl-op-p x) (equal xx x))))

Function: vl-op-equiv$inline

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

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

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

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

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

Theorem: vl-op-fix-under-vl-op-equiv

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

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

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

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

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

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

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

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

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

Theorem: vl-op-p-when-unary-or-binary

(defthm vl-op-p-when-unary-or-binary
  (implies (or (vl-unaryop-p x) (vl-binaryop-p x))
           (vl-op-p x)))