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Classname/params

Classname/params-fix

Fixing function for classname/params structures.

Signature
(classname/params-fix x) → new-x
Arguments: x — Guard (classname/params-p x).
Returns: new-x — Type (classname/params-p new-x).

Definitions and Theorems

Function: classname/params-fix$inline

(defun classname/params-fix$inline (x)
  (declare (xargs :guard (classname/params-p x)))
  (let ((__function__ 'classname/params-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((name (str-fix (car x)))
              (params (vl-maybe-paramargs-fix (cdr x))))
           (hons name params))
         :exec x)))

Theorem: classname/params-p-of-classname/params-fix

(defthm classname/params-p-of-classname/params-fix
  (b* ((new-x (classname/params-fix$inline x)))
    (classname/params-p new-x))
  :rule-classes :rewrite)

Theorem: classname/params-fix-when-classname/params-p

(defthm classname/params-fix-when-classname/params-p
  (implies (classname/params-p x)
           (equal (classname/params-fix x) x)))

Function: classname/params-equiv$inline

(defun classname/params-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (classname/params-p acl2::x)
                              (classname/params-p acl2::y))))
  (equal (classname/params-fix acl2::x)
         (classname/params-fix acl2::y)))

Theorem: classname/params-equiv-is-an-equivalence

(defthm classname/params-equiv-is-an-equivalence
  (and (booleanp (classname/params-equiv x y))
       (classname/params-equiv x x)
       (implies (classname/params-equiv x y)
                (classname/params-equiv y x))
       (implies (and (classname/params-equiv x y)
                     (classname/params-equiv y z))
                (classname/params-equiv x z)))
  :rule-classes (:equivalence))

Theorem: classname/params-equiv-implies-equal-classname/params-fix-1

(defthm classname/params-equiv-implies-equal-classname/params-fix-1
  (implies (classname/params-equiv acl2::x x-equiv)
           (equal (classname/params-fix acl2::x)
                  (classname/params-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: classname/params-fix-under-classname/params-equiv

(defthm classname/params-fix-under-classname/params-equiv
  (classname/params-equiv (classname/params-fix acl2::x)
                          acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-classname/params-fix-1-forward-to-classname/params-equiv

(defthm
  equal-of-classname/params-fix-1-forward-to-classname/params-equiv
  (implies (equal (classname/params-fix acl2::x)
                  acl2::y)
           (classname/params-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-classname/params-fix-2-forward-to-classname/params-equiv

(defthm
  equal-of-classname/params-fix-2-forward-to-classname/params-equiv
  (implies (equal acl2::x (classname/params-fix acl2::y))
           (classname/params-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: classname/params-equiv-of-classname/params-fix-1-forward

(defthm classname/params-equiv-of-classname/params-fix-1-forward
  (implies (classname/params-equiv (classname/params-fix acl2::x)
                                   acl2::y)
           (classname/params-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: classname/params-equiv-of-classname/params-fix-2-forward

(defthm classname/params-equiv-of-classname/params-fix-2-forward
 (implies
     (classname/params-equiv acl2::x (classname/params-fix acl2::y))
     (classname/params-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)