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Strunispec

Strunispec-equiv

Basic equivalence relation for strunispec structures.

Definitions and Theorems

Function: strunispec-equiv$inline

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

Theorem: strunispec-equiv-is-an-equivalence

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

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

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

Theorem: strunispec-fix-under-strunispec-equiv

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

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

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

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

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

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

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

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

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