		Search-engine friendly clone of the ACL2 documentation.

Expr-sort

Expr-sort-fix

Fixing function for expr-sort structures.

Signature
(expr-sort-fix x) → new-x
Arguments: x — Guard (expr-sortp x).
Returns: new-x — Type (expr-sortp new-x).

Definitions and Theorems

Function: expr-sort-fix$inline

(defun expr-sort-fix$inline (x)
  (declare (xargs :guard (expr-sortp x)))
  (let ((__function__ 'expr-sort-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (case (expr-sort-kind x)
           (:constant (cons :constant (list)))
           (:nonconst (cons :nonconst (list)))
           (:location (cons :location (list))))
         :exec x)))

Theorem: expr-sortp-of-expr-sort-fix

(defthm expr-sortp-of-expr-sort-fix
  (b* ((new-x (expr-sort-fix$inline x)))
    (expr-sortp new-x))
  :rule-classes :rewrite)

Theorem: expr-sort-fix-when-expr-sortp

(defthm expr-sort-fix-when-expr-sortp
  (implies (expr-sortp x)
           (equal (expr-sort-fix x) x)))

Function: expr-sort-equiv$inline

(defun expr-sort-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (expr-sortp acl2::x)
                              (expr-sortp acl2::y))))
  (equal (expr-sort-fix acl2::x)
         (expr-sort-fix acl2::y)))

Theorem: expr-sort-equiv-is-an-equivalence

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

Theorem: expr-sort-equiv-implies-equal-expr-sort-fix-1

(defthm expr-sort-equiv-implies-equal-expr-sort-fix-1
  (implies (expr-sort-equiv acl2::x x-equiv)
           (equal (expr-sort-fix acl2::x)
                  (expr-sort-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: expr-sort-fix-under-expr-sort-equiv

(defthm expr-sort-fix-under-expr-sort-equiv
  (expr-sort-equiv (expr-sort-fix acl2::x)
                   acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-expr-sort-fix-1-forward-to-expr-sort-equiv

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

Theorem: equal-of-expr-sort-fix-2-forward-to-expr-sort-equiv

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

Theorem: expr-sort-equiv-of-expr-sort-fix-1-forward

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

Theorem: expr-sort-equiv-of-expr-sort-fix-2-forward

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

Theorem: expr-sort-kind$inline-of-expr-sort-fix-x

(defthm expr-sort-kind$inline-of-expr-sort-fix-x
  (equal (expr-sort-kind$inline (expr-sort-fix x))
         (expr-sort-kind$inline x)))

Theorem: expr-sort-kind$inline-expr-sort-equiv-congruence-on-x

(defthm expr-sort-kind$inline-expr-sort-equiv-congruence-on-x
  (implies (expr-sort-equiv x x-equiv)
           (equal (expr-sort-kind$inline x)
                  (expr-sort-kind$inline x-equiv)))
  :rule-classes :congruence)

Theorem: consp-of-expr-sort-fix

(defthm consp-of-expr-sort-fix
  (consp (expr-sort-fix x))
  :rule-classes :type-prescription)