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Gin-fix

Fixing function for gin structures.

Signature
(gin-fix x) → new-x
Arguments: x — Guard (ginp x).
Returns: new-x — Type (ginp new-x).

Definitions and Theorems

Function: gin-fix$inline

(defun gin-fix$inline (x)
 (declare (xargs :guard (ginp x)))
 (let ((__function__ 'gin-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (b*
    ((ienv (c$::ienv-fix (cdr (std::da-nth 0 x))))
     (const-new (acl2::symbol-fix (cdr (std::da-nth 1 x))))
     (vartys (c::ident-type-map-fix (cdr (std::da-nth 2 x))))
     (events
         (acl2::pseudo-event-form-list-fix (cdr (std::da-nth 3 x))))
     (thm-index (pos-fix (cdr (std::da-nth 4 x)))))
    (list (cons 'ienv ienv)
          (cons 'const-new const-new)
          (cons 'vartys vartys)
          (cons 'events events)
          (cons 'thm-index thm-index)))
   :exec x)))

Theorem: ginp-of-gin-fix

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

Theorem: gin-fix-when-ginp

(defthm gin-fix-when-ginp
  (implies (ginp x)
           (equal (gin-fix x) x)))

Function: gin-equiv$inline

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

Theorem: gin-equiv-is-an-equivalence

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

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

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

Theorem: gin-fix-under-gin-equiv

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

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

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

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

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

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

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

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

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