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Lstmt-gin

Lstmt-gin-fix

Fixing function for lstmt-gin structures.

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

Definitions and Theorems

Function: lstmt-gin-fix$inline

(defun lstmt-gin-fix$inline (x)
 (declare (xargs :guard (lstmt-ginp x)))
 (let ((__function__ 'lstmt-gin-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (b*
    ((context (atc-context-fix (cdr (std::da-nth 0 x))))
     (typed-formals
          (atc-symbol-varinfo-alist-fix (cdr (std::da-nth 1 x))))
     (inscope
        (atc-symbol-varinfo-alist-list-fix (cdr (std::da-nth 2 x))))
     (fn (symbol-fix (cdr (std::da-nth 3 x))))
     (fn-guard (symbol-fix (cdr (std::da-nth 4 x))))
     (compst-var (symbol-fix (cdr (std::da-nth 5 x))))
     (fenv-var (symbol-fix (cdr (std::da-nth 6 x))))
     (limit-var (symbol-fix (cdr (std::da-nth 7 x))))
     (measure-for-fn (symbol-fix (cdr (std::da-nth 8 x))))
     (measure-formals (symbol-list-fix (cdr (std::da-nth 9 x))))
     (prec-fns
          (atc-symbol-fninfo-alist-fix (cdr (std::da-nth 10 x))))
     (prec-tags
          (atc-string-taginfo-alist-fix (cdr (std::da-nth 11 x))))
     (prec-objs
          (atc-string-objinfo-alist-fix (cdr (std::da-nth 12 x))))
     (thm-index (acl2::pos-fix (cdr (std::da-nth 13 x))))
     (names-to-avoid (symbol-list-fix (cdr (std::da-nth 14 x))))
     (proofs (acl2::bool-fix (cdr (std::da-nth 15 x)))))
    (list (cons 'context context)
          (cons 'typed-formals typed-formals)
          (cons 'inscope inscope)
          (cons 'fn fn)
          (cons 'fn-guard fn-guard)
          (cons 'compst-var compst-var)
          (cons 'fenv-var fenv-var)
          (cons 'limit-var limit-var)
          (cons 'measure-for-fn measure-for-fn)
          (cons 'measure-formals measure-formals)
          (cons 'prec-fns prec-fns)
          (cons 'prec-tags prec-tags)
          (cons 'prec-objs prec-objs)
          (cons 'thm-index thm-index)
          (cons 'names-to-avoid names-to-avoid)
          (cons 'proofs proofs)))
   :exec x)))

Theorem: lstmt-ginp-of-lstmt-gin-fix

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

Theorem: lstmt-gin-fix-when-lstmt-ginp

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

Function: lstmt-gin-equiv$inline

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

Theorem: lstmt-gin-equiv-is-an-equivalence

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

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

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

Theorem: lstmt-gin-fix-under-lstmt-gin-equiv

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

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

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

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

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

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

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

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

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