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Bfr-iff

(bfr-iff x y) constructs the IFF of these BFRs.

Signature
(bfr-iff x y) → *

Definitions and Theorems

Function: bfr-iff

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

Theorem: bfr-eval-bfr-iff

(defthm bfr-eval-bfr-iff
  (equal (bfr-eval (bfr-iff x y) env)
         (iff (bfr-eval x env)
              (bfr-eval y env))))

Theorem: bfr-equiv-implies-bfr-equiv-bfr-iff-1

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

Theorem: bfr-equiv-implies-bfr-equiv-bfr-iff-2

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