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• Bfr

Bfr-varname-fix

Signature

(bfr-varname-fix x) → new-x

Arguments

x — Guard (bfr-varname-p x).

Returns

new-x — Type (bfr-varname-p new-x).

Definitions and Theorems

Function: bfr-varname-fix

(defun bfr-varname-fix (x)
  (declare (xargs :guard (bfr-varname-p x)))
  (let ((__function__ 'bfr-varname-fix))
    (declare (ignorable __function__))
    (bfr-case :bdd (nfix x)
              :aig (aig-var-fix x))))

Theorem: bfr-varname-p-of-bfr-varname-fix

(defthm bfr-varname-p-of-bfr-varname-fix
  (b* ((new-x (bfr-varname-fix x)))
    (bfr-varname-p new-x))
  :rule-classes :rewrite)

Theorem: bfr-varname-fix-when-bfr-varname-p

(defthm bfr-varname-fix-when-bfr-varname-p
  (implies (bfr-varname-p x)
           (equal (bfr-varname-fix x) x)))

Function: bfr-varname-equiv$inline

(defun bfr-varname-equiv$inline (x y)
  (declare (xargs :guard (and (bfr-varname-p x)
                              (bfr-varname-p y))))
  (equal (bfr-varname-fix x)
         (bfr-varname-fix y)))

Theorem: bfr-varname-equiv-is-an-equivalence

(defthm bfr-varname-equiv-is-an-equivalence
  (and (booleanp (bfr-varname-equiv x y))
       (bfr-varname-equiv x x)
       (implies (bfr-varname-equiv x y)
                (bfr-varname-equiv y x))
       (implies (and (bfr-varname-equiv x y)
                     (bfr-varname-equiv y z))
                (bfr-varname-equiv x z)))
  :rule-classes (:equivalence))

Theorem: bfr-varname-equiv-implies-equal-bfr-varname-fix-1

(defthm bfr-varname-equiv-implies-equal-bfr-varname-fix-1
  (implies (bfr-varname-equiv x x-equiv)
           (equal (bfr-varname-fix x)
                  (bfr-varname-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: bfr-varname-fix-under-bfr-varname-equiv

(defthm bfr-varname-fix-under-bfr-varname-equiv
  (bfr-varname-equiv (bfr-varname-fix x)
                     x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: nfix-of-bfr-varname-fix

(defthm nfix-of-bfr-varname-fix
  (equal (nfix (bfr-varname-fix x))
         (nfix x)))

Theorem: bfr-varname-fix-of-nfix

(defthm bfr-varname-fix-of-nfix
  (equal (bfr-varname-fix (nfix x))
         (nfix x)))

Theorem: bfr-varname-p-when-natp

(defthm bfr-varname-p-when-natp
  (implies (natp x) (bfr-varname-p x)))