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• Bfr

Bfr-depends-on

Signature

(bfr-depends-on k x) → *

Definitions and Theorems

Function: bfr-depends-on

(defun bfr-depends-on (k x)
  (declare (xargs :guard t))
  (let ((__function__ 'bfr-depends-on))
    (declare (ignorable __function__))
    (bfr-case :bdd (bfr-semantic-depends-on k x)
              :aig (set::in (bfr-varname-fix k)
                            (acl2::aig-vars x)))))

Theorem: bfr-eval-of-set-non-dep

(defthm bfr-eval-of-set-non-dep
  (implies (not (bfr-depends-on k x))
           (equal (bfr-eval x (bfr-set-var k v env))
                  (bfr-eval x env))))

Theorem: bfr-depends-on-of-bfr-var

(defthm bfr-depends-on-of-bfr-var
  (equal (bfr-depends-on m (bfr-var n))
         (equal (bfr-varname-fix m)
                (bfr-varname-fix n))))

Theorem: no-new-deps-of-bfr-not

(defthm no-new-deps-of-bfr-not
  (implies (not (bfr-depends-on k x))
           (not (bfr-depends-on k (bfr-not x)))))

Theorem: no-new-deps-of-bfr-and

(defthm no-new-deps-of-bfr-and
  (implies (and (not (bfr-depends-on k x))
                (not (bfr-depends-on k y)))
           (not (bfr-depends-on k (bfr-binary-and x y)))))

Theorem: no-new-deps-of-bfr-or

(defthm no-new-deps-of-bfr-or
  (implies (and (not (bfr-depends-on k x))
                (not (bfr-depends-on k y)))
           (not (bfr-depends-on k (bfr-binary-or x y)))))

Theorem: no-new-deps-of-bfr-xor

(defthm no-new-deps-of-bfr-xor
  (implies (and (not (bfr-depends-on k x))
                (not (bfr-depends-on k y)))
           (not (bfr-depends-on k (bfr-xor x y)))))

Theorem: no-new-deps-of-bfr-iff

(defthm no-new-deps-of-bfr-iff
  (implies (and (not (bfr-depends-on k x))
                (not (bfr-depends-on k y)))
           (not (bfr-depends-on k (bfr-iff x y)))))

Theorem: no-new-deps-of-bfr-ite

(defthm no-new-deps-of-bfr-ite
  (implies (and (not (bfr-depends-on k x))
                (not (bfr-depends-on k y))
                (not (bfr-depends-on k z)))
           (not (bfr-depends-on k (bfr-ite-fn x y z)))))

Theorem: no-deps-of-bfr-constants

(defthm no-deps-of-bfr-constants
  (and (not (bfr-depends-on k t))
       (not (bfr-depends-on k nil))))