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Fun-adeclor

Fun-adeclor-fix

Fixing function for fun-adeclor structures.

Signature
(fun-adeclor-fix x) → new-x
Arguments: x — Guard (fun-adeclorp x).
Returns: new-x — Type (fun-adeclorp new-x).

Definitions and Theorems

Function: fun-adeclor-fix$inline

(defun fun-adeclor-fix$inline (x)
 (declare (xargs :guard (fun-adeclorp x)))
 (let ((__function__ 'fun-adeclor-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (case (fun-adeclor-kind x)
    (:base
      (b* ((params (param-declon-list-fix (std::da-nth 0 (cdr x)))))
        (cons :base (list params))))
    (:pointer (b* ((decl (fun-adeclor-fix (std::da-nth 0 (cdr x)))))
                (cons :pointer (list decl)))))
   :exec x)))

Theorem: fun-adeclorp-of-fun-adeclor-fix

(defthm fun-adeclorp-of-fun-adeclor-fix
  (b* ((new-x (fun-adeclor-fix$inline x)))
    (fun-adeclorp new-x))
  :rule-classes :rewrite)

Theorem: fun-adeclor-fix-when-fun-adeclorp

(defthm fun-adeclor-fix-when-fun-adeclorp
  (implies (fun-adeclorp x)
           (equal (fun-adeclor-fix x) x)))

Function: fun-adeclor-equiv$inline

(defun fun-adeclor-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (fun-adeclorp acl2::x)
                              (fun-adeclorp acl2::y))))
  (equal (fun-adeclor-fix acl2::x)
         (fun-adeclor-fix acl2::y)))

Theorem: fun-adeclor-equiv-is-an-equivalence

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

Theorem: fun-adeclor-equiv-implies-equal-fun-adeclor-fix-1

(defthm fun-adeclor-equiv-implies-equal-fun-adeclor-fix-1
  (implies (fun-adeclor-equiv acl2::x x-equiv)
           (equal (fun-adeclor-fix acl2::x)
                  (fun-adeclor-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: fun-adeclor-fix-under-fun-adeclor-equiv

(defthm fun-adeclor-fix-under-fun-adeclor-equiv
  (fun-adeclor-equiv (fun-adeclor-fix acl2::x)
                     acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-fun-adeclor-fix-1-forward-to-fun-adeclor-equiv

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

Theorem: equal-of-fun-adeclor-fix-2-forward-to-fun-adeclor-equiv

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

Theorem: fun-adeclor-equiv-of-fun-adeclor-fix-1-forward

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

Theorem: fun-adeclor-equiv-of-fun-adeclor-fix-2-forward

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

Theorem: fun-adeclor-kind$inline-of-fun-adeclor-fix-x

(defthm fun-adeclor-kind$inline-of-fun-adeclor-fix-x
  (equal (fun-adeclor-kind$inline (fun-adeclor-fix x))
         (fun-adeclor-kind$inline x)))

Theorem: fun-adeclor-kind$inline-fun-adeclor-equiv-congruence-on-x

(defthm fun-adeclor-kind$inline-fun-adeclor-equiv-congruence-on-x
  (implies (fun-adeclor-equiv x x-equiv)
           (equal (fun-adeclor-kind$inline x)
                  (fun-adeclor-kind$inline x-equiv)))
  :rule-classes :congruence)

Theorem: consp-of-fun-adeclor-fix

(defthm consp-of-fun-adeclor-fix
  (consp (fun-adeclor-fix x))
  :rule-classes :type-prescription)