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Parametrize-config

Parametrize-config-fix

Fixing function for parametrize-config structures.

Signature
(parametrize-config-fix x) → new-x
Arguments: x — Guard (parametrize-config-p x).
Returns: new-x — Type (parametrize-config-p new-x).

Definitions and Theorems

Function: parametrize-config-fix$inline

(defun parametrize-config-fix$inline (x)
 (declare (xargs :guard (parametrize-config-p x)))
 (let ((__function__ 'parametrize-config-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (b* ((build-limit (nfix (cdr (std::da-nth 0 (cdr x)))))
        (conjoin-limit (nfix (cdr (std::da-nth 1 (cdr x)))))
        (output-types (parametrize-output-type-map-fix
                           (cdr (std::da-nth 2 (cdr x))))))
    (cons
      :parametrize-config (list (cons 'build-limit build-limit)
                                (cons 'conjoin-limit conjoin-limit)
                                (cons 'output-types output-types))))
   :exec x)))

Theorem: parametrize-config-p-of-parametrize-config-fix

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

Theorem: parametrize-config-fix-when-parametrize-config-p

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

Function: parametrize-config-equiv$inline

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

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

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

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

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

Theorem: parametrize-config-fix-under-parametrize-config-equiv

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

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

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

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

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

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

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

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

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