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• Addr-scope

Addr-scope-equiv

Definitions and Theorems

Function: addr-scope-equiv$inline

(defun addr-scope-equiv$inline (x y)
  (declare (xargs :guard (and (addr-scope-p x)
                              (addr-scope-p y))))
  (equal (addr-scope-fix x)
         (addr-scope-fix y)))

Theorem: addr-scope-equiv-is-an-equivalence

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

Theorem: addr-scope-equiv-implies-equal-addr-scope-fix-1

(defthm addr-scope-equiv-implies-equal-addr-scope-fix-1
  (implies (addr-scope-equiv x x-equiv)
           (equal (addr-scope-fix x)
                  (addr-scope-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: addr-scope-fix-under-addr-scope-equiv

(defthm addr-scope-fix-under-addr-scope-equiv
  (addr-scope-equiv (addr-scope-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-addr-scope-fix-1-forward-to-addr-scope-equiv

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

Theorem: equal-of-addr-scope-fix-2-forward-to-addr-scope-equiv

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

Theorem: addr-scope-equiv-of-addr-scope-fix-1-forward

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

Theorem: addr-scope-equiv-of-addr-scope-fix-2-forward

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