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• Rlp-error

Rlp-error-equiv

Basic equivalence relation for rlp-error structures.

Definitions and Theorems

Function: rlp-error-equiv$inline

(defun rlp-error-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (rlp-error-p acl2::x)
                              (rlp-error-p acl2::y))))
  (equal (rlp-error-fix acl2::x)
         (rlp-error-fix acl2::y)))

Theorem: rlp-error-equiv-is-an-equivalence

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

Theorem: rlp-error-equiv-implies-equal-rlp-error-fix-1

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

Theorem: rlp-error-fix-under-rlp-error-equiv

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

Theorem: equal-of-rlp-error-fix-1-forward-to-rlp-error-equiv

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

Theorem: equal-of-rlp-error-fix-2-forward-to-rlp-error-equiv

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

Theorem: rlp-error-equiv-of-rlp-error-fix-1-forward

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

Theorem: rlp-error-equiv-of-rlp-error-fix-2-forward

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