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• Transunit-info

Transunit-info-fix

Fixing function for transunit-info structures.

Signature

(transunit-info-fix x) → new-x

Arguments

x — Guard (transunit-infop x).

Returns

new-x — Type (transunit-infop new-x).

Definitions and Theorems

Function: transunit-info-fix$inline

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

Theorem: transunit-infop-of-transunit-info-fix

(defthm transunit-infop-of-transunit-info-fix
  (b* ((new-x (transunit-info-fix$inline x)))
    (transunit-infop new-x))
  :rule-classes :rewrite)

Theorem: transunit-info-fix-when-transunit-infop

(defthm transunit-info-fix-when-transunit-infop
  (implies (transunit-infop x)
           (equal (transunit-info-fix x) x)))

Function: transunit-info-equiv$inline

(defun transunit-info-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (transunit-infop acl2::x)
                              (transunit-infop acl2::y))))
  (equal (transunit-info-fix acl2::x)
         (transunit-info-fix acl2::y)))

Theorem: transunit-info-equiv-is-an-equivalence

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

Theorem: transunit-info-equiv-implies-equal-transunit-info-fix-1

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

Theorem: transunit-info-fix-under-transunit-info-equiv

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

Theorem: equal-of-transunit-info-fix-1-forward-to-transunit-info-equiv

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

Theorem: equal-of-transunit-info-fix-2-forward-to-transunit-info-equiv

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

Theorem: transunit-info-equiv-of-transunit-info-fix-1-forward

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

Theorem: transunit-info-equiv-of-transunit-info-fix-2-forward

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