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• Jexpr

Jexpr-equiv

Basic equivalence relation for jexpr structures.

Definitions and Theorems

Function: jexpr-equiv$inline

(defun jexpr-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (jexprp acl2::x)
                              (jexprp acl2::y))))
  (equal (jexpr-fix acl2::x)
         (jexpr-fix acl2::y)))

Theorem: jexpr-equiv-is-an-equivalence

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

Theorem: jexpr-equiv-implies-equal-jexpr-fix-1

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

Theorem: jexpr-fix-under-jexpr-equiv

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

Theorem: equal-of-jexpr-fix-1-forward-to-jexpr-equiv

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

Theorem: equal-of-jexpr-fix-2-forward-to-jexpr-equiv

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

Theorem: jexpr-equiv-of-jexpr-fix-1-forward

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

Theorem: jexpr-equiv-of-jexpr-fix-2-forward

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