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• Observability-config

Observability-config-fix

Fixing function for observability-config structures.

Signature

(observability-config-fix x) → new-x

Arguments

x — Guard (observability-config-p x).

Returns

new-x — Type (observability-config-p new-x).

Definitions and Theorems

Function: observability-config-fix$inline

(defun observability-config-fix$inline (x)
 (declare (xargs :guard (observability-config-p x)))
 (let ((__function__ 'observability-config-fix))
  (declare (ignorable __function__))
  (mbe
     :logic
     (b* ((hyp-max-size
               (acl2::maybe-natp-fix (cdr (std::da-nth 0 (cdr x)))))
          (concl-min-size
               (acl2::maybe-natp-fix (cdr (std::da-nth 1 (cdr x)))))
          (min-ratio (rfix (cdr (std::da-nth 2 (cdr x)))))
          (gatesimp (gatesimp-fix (cdr (std::da-nth 3 (cdr x))))))
       (cons :observability-config
             (list (cons 'hyp-max-size hyp-max-size)
                   (cons 'concl-min-size concl-min-size)
                   (cons 'min-ratio min-ratio)
                   (cons 'gatesimp gatesimp))))
     :exec x)))

Theorem: observability-config-p-of-observability-config-fix

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

Theorem: observability-config-fix-when-observability-config-p

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

Function: observability-config-equiv$inline

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

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

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

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

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

Theorem: observability-config-fix-under-observability-config-equiv

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

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

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

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

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

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

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

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

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