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• Prune-config

Prune-config-fix

Fixing function for prune-config structures.

Signature

(prune-config-fix x) → new-x

Arguments

x — Guard (prune-config-p x).

Returns

new-x — Type (prune-config-p new-x).

Definitions and Theorems

Function: prune-config-fix$inline

(defun prune-config-fix$inline (x)
  (declare (xargs :guard (prune-config-p x)))
  (let ((__function__ 'prune-config-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((gatesimp (gatesimp-fix (cdr x))))
           (cons :prune-config gatesimp))
         :exec x)))

Theorem: prune-config-p-of-prune-config-fix

(defthm prune-config-p-of-prune-config-fix
  (b* ((new-x (prune-config-fix$inline x)))
    (prune-config-p new-x))
  :rule-classes :rewrite)

Theorem: prune-config-fix-when-prune-config-p

(defthm prune-config-fix-when-prune-config-p
  (implies (prune-config-p x)
           (equal (prune-config-fix x) x)))

Function: prune-config-equiv$inline

(defun prune-config-equiv$inline (x acl2::y)
  (declare (xargs :guard (and (prune-config-p x)
                              (prune-config-p acl2::y))))
  (equal (prune-config-fix x)
         (prune-config-fix acl2::y)))

Theorem: prune-config-equiv-is-an-equivalence

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

Theorem: prune-config-equiv-implies-equal-prune-config-fix-1

(defthm prune-config-equiv-implies-equal-prune-config-fix-1
  (implies (prune-config-equiv x x-equiv)
           (equal (prune-config-fix x)
                  (prune-config-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: prune-config-fix-under-prune-config-equiv

(defthm prune-config-fix-under-prune-config-equiv
  (prune-config-equiv (prune-config-fix x)
                      x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-prune-config-fix-1-forward-to-prune-config-equiv

(defthm equal-of-prune-config-fix-1-forward-to-prune-config-equiv
  (implies (equal (prune-config-fix x) acl2::y)
           (prune-config-equiv x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-prune-config-fix-2-forward-to-prune-config-equiv

(defthm equal-of-prune-config-fix-2-forward-to-prune-config-equiv
  (implies (equal x (prune-config-fix acl2::y))
           (prune-config-equiv x acl2::y))
  :rule-classes :forward-chaining)

Theorem: prune-config-equiv-of-prune-config-fix-1-forward

(defthm prune-config-equiv-of-prune-config-fix-1-forward
  (implies (prune-config-equiv (prune-config-fix x)
                               acl2::y)
           (prune-config-equiv x acl2::y))
  :rule-classes :forward-chaining)

Theorem: prune-config-equiv-of-prune-config-fix-2-forward

(defthm prune-config-equiv-of-prune-config-fix-2-forward
  (implies (prune-config-equiv x (prune-config-fix acl2::y))
           (prune-config-equiv x acl2::y))
  :rule-classes :forward-chaining)