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Bfr-nand

(bfr-nand x y) constructs the NAND of these BFRs.

Signature
(bfr-nand x y) → *

Definitions and Theorems

Function: bfr-nand

(defun bfr-nand (x y)
  (declare (xargs :guard t))
  (let ((__function__ 'bfr-nand))
    (declare (ignorable __function__))
    (mbe :logic
         (bfr-case :bdd (acl2::q-nand x y)
                   :aig (acl2::aig-nand x y))
         :exec
         (if (and (booleanp x) (booleanp y))
             (not (and x y))
           (bfr-case :bdd (acl2::q-nand x y)
                     :aig (acl2::aig-nand x y))))))

Theorem: bfr-eval-bfr-nand

(defthm bfr-eval-bfr-nand
  (equal (bfr-eval (bfr-nand x y) env)
         (not (and (bfr-eval x env)
                   (bfr-eval y env)))))

Theorem: bfr-equiv-implies-bfr-equiv-bfr-nand-1

(defthm bfr-equiv-implies-bfr-equiv-bfr-nand-1
  (implies (bfr-equiv x x-equiv)
           (bfr-equiv (bfr-nand x y)
                      (bfr-nand x-equiv y)))
  :rule-classes (:congruence))

Theorem: bfr-equiv-implies-bfr-equiv-bfr-nand-2

(defthm bfr-equiv-implies-bfr-equiv-bfr-nand-2
  (implies (bfr-equiv y y-equiv)
           (bfr-equiv (bfr-nand x y)
                      (bfr-nand x y-equiv)))
  :rule-classes (:congruence))