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• 4v-sexprs

3v-syntax-sexprp

Recognizer for 4v-sexprs that cannot evaluate to Z.

Definitions and Theorems

Function: 3v-syntax-sexprp

(defun 3v-syntax-sexprp (x)
  (declare (xargs :guard t))
  (and (consp x)
       (let ((fn (car x)))
         (not (or (eq fn (4vz))
                  (eq fn 'id)
                  (eq fn 'res)
                  (eq fn 'zif)
                  (eq fn 'tristate))))))

Theorem: 3vp-of-4v-unfloat

(defthm 3vp-of-4v-unfloat
  (equal (equal (4vz) (4v-unfloat a))
         nil))

Theorem: 3vp-of-4v-not

(defthm 3vp-of-4v-not
  (equal (equal (4vz) (4v-not a)) nil))

Theorem: 3vp-of-4v-xdet

(defthm 3vp-of-4v-xdet
  (equal (equal (4vz) (4v-xdet a)) nil))

Theorem: 3vp-of-4v-and

(defthm 3vp-of-4v-and
  (equal (equal (4vz) (4v-and a b)) nil))

Theorem: 3vp-of-4v-or

(defthm 3vp-of-4v-or
  (equal (equal (4vz) (4v-or a b)) nil))

Theorem: 3vp-of-4v-xor

(defthm 3vp-of-4v-xor
  (equal (equal (4vz) (4v-xor a b)) nil))

Theorem: 3vp-of-4v-iff

(defthm 3vp-of-4v-iff
  (equal (equal (4vz) (4v-iff a b)) nil))

Theorem: 3vp-of-4v-ite

(defthm 3vp-of-4v-ite
  (equal (equal (4vz) (4v-ite c a b))
         nil))

Theorem: 3vp-of-4v-ite*

(defthm 3vp-of-4v-ite*
  (equal (equal (4vz) (4v-ite* c a b))
         nil))

Theorem: 3vp-of-4v-pullup

(defthm 3vp-of-4v-pullup
  (equal (equal (4vz) (4v-pullup a)) nil))

Theorem: 3vp-sexpr-eval-when-3v-syntax-sexprp

(defthm 3vp-sexpr-eval-when-3v-syntax-sexprp
  (implies (3v-syntax-sexprp x)
           (equal (equal (4vz) (4v-sexpr-eval x env))
                  nil)))