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Bfr-andc2

(bfr-andc2 x y) constructs the ANDC2 of these BFRs.

Signature
(bfr-andc2 x y) → *

Definitions and Theorems

Function: bfr-andc2

(defun bfr-andc2 (x y)
  (declare (xargs :guard t))
  (let ((__function__ 'bfr-andc2))
    (declare (ignorable __function__))
    (mbe :logic
         (bfr-case :bdd (acl2::q-and-c2 x y)
                   :aig (acl2::aig-andc2 x y))
         :exec
         (if (and (booleanp x) (booleanp y))
             (and x (not y))
           (bfr-case :bdd (acl2::q-and-c2 x y)
                     :aig (acl2::aig-andc2 x y))))))

Theorem: bfr-eval-bfr-andc2

(defthm bfr-eval-bfr-andc2
  (equal (bfr-eval (bfr-andc2 x y) env)
         (and (bfr-eval x env)
              (not (bfr-eval y env)))))

Theorem: bfr-equiv-implies-bfr-equiv-bfr-andc2-1

(defthm bfr-equiv-implies-bfr-equiv-bfr-andc2-1
  (implies (bfr-equiv x x-equiv)
           (bfr-equiv (bfr-andc2 x y)
                      (bfr-andc2 x-equiv y)))
  :rule-classes (:congruence))

Theorem: bfr-equiv-implies-bfr-equiv-bfr-andc2-2

(defthm bfr-equiv-implies-bfr-equiv-bfr-andc2-2
  (implies (bfr-equiv y y-equiv)
           (bfr-equiv (bfr-andc2 x y)
                      (bfr-andc2 x y-equiv)))
  :rule-classes (:congruence))