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Param-declon

Param-declon-fix

Fixing function for param-declon structures.

Signature
(param-declon-fix x) → new-x
Arguments: x — Guard (param-declonp x).
Returns: new-x — Type (param-declonp new-x).

Definitions and Theorems

Function: param-declon-fix$inline

(defun param-declon-fix$inline (x)
 (declare (xargs :guard (param-declonp x)))
 (let ((__function__ 'param-declon-fix))
  (declare (ignorable __function__))
  (mbe :logic
       (b* ((tyspec (tyspecseq-fix (cdr (std::da-nth 0 (cdr x)))))
            (declor (obj-declor-fix (cdr (std::da-nth 1 (cdr x))))))
         (cons :param-declon (list (cons 'tyspec tyspec)
                                   (cons 'declor declor))))
       :exec x)))

Theorem: param-declonp-of-param-declon-fix

(defthm param-declonp-of-param-declon-fix
  (b* ((new-x (param-declon-fix$inline x)))
    (param-declonp new-x))
  :rule-classes :rewrite)

Theorem: param-declon-fix-when-param-declonp

(defthm param-declon-fix-when-param-declonp
  (implies (param-declonp x)
           (equal (param-declon-fix x) x)))

Function: param-declon-equiv$inline

(defun param-declon-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (param-declonp acl2::x)
                              (param-declonp acl2::y))))
  (equal (param-declon-fix acl2::x)
         (param-declon-fix acl2::y)))

Theorem: param-declon-equiv-is-an-equivalence

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

Theorem: param-declon-equiv-implies-equal-param-declon-fix-1

(defthm param-declon-equiv-implies-equal-param-declon-fix-1
  (implies (param-declon-equiv acl2::x x-equiv)
           (equal (param-declon-fix acl2::x)
                  (param-declon-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: param-declon-fix-under-param-declon-equiv

(defthm param-declon-fix-under-param-declon-equiv
  (param-declon-equiv (param-declon-fix acl2::x)
                      acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-param-declon-fix-1-forward-to-param-declon-equiv

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

Theorem: equal-of-param-declon-fix-2-forward-to-param-declon-equiv

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

Theorem: param-declon-equiv-of-param-declon-fix-1-forward

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

Theorem: param-declon-equiv-of-param-declon-fix-2-forward

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