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• Stringlit

Stringlit-equiv

Basic equivalence relation for stringlit structures.

Definitions and Theorems

Function: stringlit-equiv$inline

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

Theorem: stringlit-equiv-is-an-equivalence

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

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

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

Theorem: stringlit-fix-under-stringlit-equiv

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

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

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

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

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

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

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

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

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