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Var/const-dinfo

Var/const-dinfo-fix

Fixing function for var/const-dinfo structures.

Signature
(var/const-dinfo-fix x) → new-x
Arguments: x — Guard (var/const-dinfop x).
Returns: new-x — Type (var/const-dinfop new-x).

Definitions and Theorems

Function: var/const-dinfo-fix$inline

(defun var/const-dinfo-fix$inline (x)
  (declare (xargs :guard (var/const-dinfop x)))
  (let ((__function__ 'var/const-dinfo-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((value (value-fix (cdr (std::da-nth 0 x))))
              (constp (acl2::bool-fix (cdr (std::da-nth 1 x)))))
           (list (cons 'value value)
                 (cons 'constp constp)))
         :exec x)))

Theorem: var/const-dinfop-of-var/const-dinfo-fix

(defthm var/const-dinfop-of-var/const-dinfo-fix
  (b* ((new-x (var/const-dinfo-fix$inline x)))
    (var/const-dinfop new-x))
  :rule-classes :rewrite)

Theorem: var/const-dinfo-fix-when-var/const-dinfop

(defthm var/const-dinfo-fix-when-var/const-dinfop
  (implies (var/const-dinfop x)
           (equal (var/const-dinfo-fix x) x)))

Function: var/const-dinfo-equiv$inline

(defun var/const-dinfo-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (var/const-dinfop acl2::x)
                              (var/const-dinfop acl2::y))))
  (equal (var/const-dinfo-fix acl2::x)
         (var/const-dinfo-fix acl2::y)))

Theorem: var/const-dinfo-equiv-is-an-equivalence

(defthm var/const-dinfo-equiv-is-an-equivalence
  (and (booleanp (var/const-dinfo-equiv x y))
       (var/const-dinfo-equiv x x)
       (implies (var/const-dinfo-equiv x y)
                (var/const-dinfo-equiv y x))
       (implies (and (var/const-dinfo-equiv x y)
                     (var/const-dinfo-equiv y z))
                (var/const-dinfo-equiv x z)))
  :rule-classes (:equivalence))

Theorem: var/const-dinfo-equiv-implies-equal-var/const-dinfo-fix-1

(defthm var/const-dinfo-equiv-implies-equal-var/const-dinfo-fix-1
  (implies (var/const-dinfo-equiv acl2::x x-equiv)
           (equal (var/const-dinfo-fix acl2::x)
                  (var/const-dinfo-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: var/const-dinfo-fix-under-var/const-dinfo-equiv

(defthm var/const-dinfo-fix-under-var/const-dinfo-equiv
  (var/const-dinfo-equiv (var/const-dinfo-fix acl2::x)
                         acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-var/const-dinfo-fix-1-forward-to-var/const-dinfo-equiv

(defthm
    equal-of-var/const-dinfo-fix-1-forward-to-var/const-dinfo-equiv
  (implies (equal (var/const-dinfo-fix acl2::x)
                  acl2::y)
           (var/const-dinfo-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-var/const-dinfo-fix-2-forward-to-var/const-dinfo-equiv

(defthm
    equal-of-var/const-dinfo-fix-2-forward-to-var/const-dinfo-equiv
  (implies (equal acl2::x (var/const-dinfo-fix acl2::y))
           (var/const-dinfo-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: var/const-dinfo-equiv-of-var/const-dinfo-fix-1-forward

(defthm var/const-dinfo-equiv-of-var/const-dinfo-fix-1-forward
  (implies (var/const-dinfo-equiv (var/const-dinfo-fix acl2::x)
                                  acl2::y)
           (var/const-dinfo-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: var/const-dinfo-equiv-of-var/const-dinfo-fix-2-forward

(defthm var/const-dinfo-equiv-of-var/const-dinfo-fix-2-forward
  (implies
       (var/const-dinfo-equiv acl2::x (var/const-dinfo-fix acl2::y))
       (var/const-dinfo-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)