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• Struct-sinfo

Struct-sinfo-fix

Fixing function for struct-sinfo structures.

Signature

(struct-sinfo-fix x) → new-x

Arguments

x — Guard (struct-sinfop x).

Returns

new-x — Type (struct-sinfop new-x).

Definitions and Theorems

Function: struct-sinfo-fix$inline

(defun struct-sinfo-fix$inline (x)
 (declare (xargs :guard (struct-sinfop x)))
 (let ((__function__ 'struct-sinfo-fix))
  (declare (ignorable __function__))
  (mbe
     :logic
     (b* ((components (type-map-fix (cdr (std::da-nth 0 (cdr x))))))
       (cons :struct-sinfo (list (cons 'components components))))
     :exec x)))

Theorem: struct-sinfop-of-struct-sinfo-fix

(defthm struct-sinfop-of-struct-sinfo-fix
  (b* ((new-x (struct-sinfo-fix$inline x)))
    (struct-sinfop new-x))
  :rule-classes :rewrite)

Theorem: struct-sinfo-fix-when-struct-sinfop

(defthm struct-sinfo-fix-when-struct-sinfop
  (implies (struct-sinfop x)
           (equal (struct-sinfo-fix x) x)))

Function: struct-sinfo-equiv$inline

(defun struct-sinfo-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (struct-sinfop acl2::x)
                              (struct-sinfop acl2::y))))
  (equal (struct-sinfo-fix acl2::x)
         (struct-sinfo-fix acl2::y)))

Theorem: struct-sinfo-equiv-is-an-equivalence

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

Theorem: struct-sinfo-equiv-implies-equal-struct-sinfo-fix-1

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

Theorem: struct-sinfo-fix-under-struct-sinfo-equiv

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

Theorem: equal-of-struct-sinfo-fix-1-forward-to-struct-sinfo-equiv

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

Theorem: equal-of-struct-sinfo-fix-2-forward-to-struct-sinfo-equiv

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

Theorem: struct-sinfo-equiv-of-struct-sinfo-fix-1-forward

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

Theorem: struct-sinfo-equiv-of-struct-sinfo-fix-2-forward

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