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• Fundef-info

Fundef-info-fix

Fixing function for fundef-info structures.

Signature

(fundef-info-fix x) → new-x

Arguments

x — Guard (fundef-infop x).

Returns

new-x — Type (fundef-infop new-x).

Definitions and Theorems

Function: fundef-info-fix$inline

(defun fundef-info-fix$inline (x)
  (declare (xargs :guard (fundef-infop x)))
  (mbe :logic
       (b* ((type (type-fix (cdr (std::da-nth 0 x))))
            (uid (uid-fix (cdr (std::da-nth 1 x)))))
         (list (cons 'type type)
               (cons 'uid uid)))
       :exec x))

Theorem: fundef-infop-of-fundef-info-fix

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

Theorem: fundef-info-fix-when-fundef-infop

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

Function: fundef-info-equiv$inline

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

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

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

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

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

Theorem: fundef-info-fix-under-fundef-info-equiv

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

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

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

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

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

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

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

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

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

Theorem: fundef-info-fix$inline-of-fundef-info-fix-x

(defthm fundef-info-fix$inline-of-fundef-info-fix-x
  (equal (fundef-info-fix$inline (fundef-info-fix x))
         (fundef-info-fix$inline x)))

Theorem: fundef-info-fix$inline-fundef-info-equiv-congruence-on-x

(defthm fundef-info-fix$inline-fundef-info-equiv-congruence-on-x
  (implies (fundef-info-equiv x x-equiv)
           (equal (fundef-info-fix$inline x)
                  (fundef-info-fix$inline x-equiv)))
  :rule-classes :congruence)