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Valid-table

Valid-table-fix

Fixing function for valid-table structures.

Signature
(valid-table-fix x) → new-x
Arguments: x — Guard (valid-tablep x).
Returns: new-x — Type (valid-tablep new-x).

Definitions and Theorems

Function: valid-table-fix$inline

(defun valid-table-fix$inline (x)
 (declare (xargs :guard (valid-tablep x)))
 (let ((__function__ 'valid-table-fix))
  (declare (ignorable __function__))
  (mbe :logic
       (b* ((scopes (valid-scope-list-fix (cdr (std::da-nth 0 x)))))
         (list (cons 'scopes scopes)))
       :exec x)))

Theorem: valid-tablep-of-valid-table-fix

(defthm valid-tablep-of-valid-table-fix
  (b* ((new-x (valid-table-fix$inline x)))
    (valid-tablep new-x))
  :rule-classes :rewrite)

Theorem: valid-table-fix-when-valid-tablep

(defthm valid-table-fix-when-valid-tablep
  (implies (valid-tablep x)
           (equal (valid-table-fix x) x)))

Function: valid-table-equiv$inline

(defun valid-table-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (valid-tablep acl2::x)
                              (valid-tablep acl2::y))))
  (equal (valid-table-fix acl2::x)
         (valid-table-fix acl2::y)))

Theorem: valid-table-equiv-is-an-equivalence

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

Theorem: valid-table-equiv-implies-equal-valid-table-fix-1

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

Theorem: valid-table-fix-under-valid-table-equiv

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

Theorem: equal-of-valid-table-fix-1-forward-to-valid-table-equiv

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

Theorem: equal-of-valid-table-fix-2-forward-to-valid-table-equiv

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

Theorem: valid-table-equiv-of-valid-table-fix-1-forward

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

Theorem: valid-table-equiv-of-valid-table-fix-2-forward

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