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• Init-declor-info

Init-declor-info-fix

Fixing function for init-declor-info structures.

Signature

(init-declor-info-fix x) → new-x

Arguments

x — Guard (init-declor-infop x).

Returns

new-x — Type (init-declor-infop new-x).

Definitions and Theorems

Function: init-declor-info-fix$inline

(defun init-declor-info-fix$inline (x)
  (declare (xargs :guard (init-declor-infop x)))
  (mbe :logic
       (b* ((type (type-fix (cdr (std::da-nth 0 x))))
            (typedefp (bool-fix (cdr (std::da-nth 1 x))))
            (uid? (uid-option-fix (cdr (std::da-nth 2 x)))))
         (list (cons 'type type)
               (cons 'typedefp typedefp)
               (cons 'uid? uid?)))
       :exec x))

Theorem: init-declor-infop-of-init-declor-info-fix

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

Theorem: init-declor-info-fix-when-init-declor-infop

(defthm init-declor-info-fix-when-init-declor-infop
  (implies (init-declor-infop x)
           (equal (init-declor-info-fix x) x)))

Function: init-declor-info-equiv$inline

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

Theorem: init-declor-info-equiv-is-an-equivalence

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

Theorem: init-declor-info-equiv-implies-equal-init-declor-info-fix-1

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

Theorem: init-declor-info-fix-under-init-declor-info-equiv

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

Theorem: equal-of-init-declor-info-fix-1-forward-to-init-declor-info-equiv

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

Theorem: equal-of-init-declor-info-fix-2-forward-to-init-declor-info-equiv

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

Theorem: init-declor-info-equiv-of-init-declor-info-fix-1-forward

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

Theorem: init-declor-info-equiv-of-init-declor-info-fix-2-forward

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

Theorem: init-declor-info-fix$inline-of-init-declor-info-fix-x

(defthm init-declor-info-fix$inline-of-init-declor-info-fix-x
  (equal (init-declor-info-fix$inline (init-declor-info-fix x))
         (init-declor-info-fix$inline x)))

Theorem: init-declor-info-fix$inline-init-declor-info-equiv-congruence-on-x

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