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• Tmp-occ

Tmp-occ-equiv

Basic equivalence relation for tmp-occ structures.

Definitions and Theorems

Function: tmp-occ-equiv$inline

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

Theorem: tmp-occ-equiv-is-an-equivalence

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

Theorem: tmp-occ-equiv-implies-equal-tmp-occ-fix-1

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

Theorem: tmp-occ-fix-under-tmp-occ-equiv

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

Theorem: equal-of-tmp-occ-fix-1-forward-to-tmp-occ-equiv

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

Theorem: equal-of-tmp-occ-fix-2-forward-to-tmp-occ-equiv

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

Theorem: tmp-occ-equiv-of-tmp-occ-fix-1-forward

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

Theorem: tmp-occ-equiv-of-tmp-occ-fix-2-forward

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