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Constrel

Constrel-fix

Fixing function for constrel structures.

Signature
(constrel-fix x) → new-x
Arguments: x — Guard (constrelp x).
Returns: new-x — Type (constrelp new-x).

Definitions and Theorems

Function: constrel-fix$inline

(defun constrel-fix$inline (x)
  (declare (xargs :guard (constrelp x)))
  (let ((__function__ 'constrel-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((name (str-fix (cdr (std::da-nth 0 x))))
              (args (expression-list-fix (cdr (std::da-nth 1 x)))))
           (list (cons 'name name)
                 (cons 'args args)))
         :exec x)))

Theorem: constrelp-of-constrel-fix

(defthm constrelp-of-constrel-fix
  (b* ((new-x (constrel-fix$inline x)))
    (constrelp new-x))
  :rule-classes :rewrite)

Theorem: constrel-fix-when-constrelp

(defthm constrel-fix-when-constrelp
  (implies (constrelp x)
           (equal (constrel-fix x) x)))

Function: constrel-equiv$inline

(defun constrel-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (constrelp acl2::x)
                              (constrelp acl2::y))))
  (equal (constrel-fix acl2::x)
         (constrel-fix acl2::y)))

Theorem: constrel-equiv-is-an-equivalence

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

Theorem: constrel-equiv-implies-equal-constrel-fix-1

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

Theorem: constrel-fix-under-constrel-equiv

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

Theorem: equal-of-constrel-fix-1-forward-to-constrel-equiv

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

Theorem: equal-of-constrel-fix-2-forward-to-constrel-equiv

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

Theorem: constrel-equiv-of-constrel-fix-1-forward

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

Theorem: constrel-equiv-of-constrel-fix-2-forward

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