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• Lift-info

Lift-info-fix

Fixing function for lift-info structures.

Signature

(lift-info-fix x) → new-x

Arguments

x — Guard (lift-infop x).

Returns

new-x — Type (lift-infop new-x).

Definitions and Theorems

Function: lift-info-fix$inline

(defun lift-info-fix$inline (x)
  (declare (xargs :guard (lift-infop x)))
  (let ((__function__ 'lift-info-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((def (definition-fix (cdr (std::da-nth 0 x))))
              (hyps (list-fix (cdr (std::da-nth 1 x)))))
           (list (cons 'def def)
                 (cons 'hyps hyps)))
         :exec x)))

Theorem: lift-infop-of-lift-info-fix

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

Theorem: lift-info-fix-when-lift-infop

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

Function: lift-info-equiv$inline

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

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

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

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

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

Theorem: lift-info-fix-under-lift-info-equiv

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

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

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

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

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

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

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

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

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