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• Pprint-options

Pprint-options-equiv

Basic equivalence relation for pprint-options structures.

Definitions and Theorems

Function: pprint-options-equiv$inline

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

Theorem: pprint-options-equiv-is-an-equivalence

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

Theorem: pprint-options-equiv-implies-equal-pprint-options-fix-1

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

Theorem: pprint-options-fix-under-pprint-options-equiv

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

Theorem: equal-of-pprint-options-fix-1-forward-to-pprint-options-equiv

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

Theorem: equal-of-pprint-options-fix-2-forward-to-pprint-options-equiv

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

Theorem: pprint-options-equiv-of-pprint-options-fix-1-forward

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

Theorem: pprint-options-equiv-of-pprint-options-fix-2-forward

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