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• Stat32i

Stat32i-equiv

Basic equivalence relation for stat32i structures.

Definitions and Theorems

Function: stat32i-equiv$inline

(defun stat32i-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (stat32ip acl2::x)
                              (stat32ip acl2::y))))
  (equal (stat32i-fix acl2::x)
         (stat32i-fix acl2::y)))

Theorem: stat32i-equiv-is-an-equivalence

(defthm stat32i-equiv-is-an-equivalence
  (and (booleanp (stat32i-equiv x y))
       (stat32i-equiv x x)
       (implies (stat32i-equiv x y)
                (stat32i-equiv y x))
       (implies (and (stat32i-equiv x y)
                     (stat32i-equiv y z))
                (stat32i-equiv x z)))
  :rule-classes (:equivalence))

Theorem: stat32i-equiv-implies-equal-stat32i-fix-1

(defthm stat32i-equiv-implies-equal-stat32i-fix-1
  (implies (stat32i-equiv acl2::x x-equiv)
           (equal (stat32i-fix acl2::x)
                  (stat32i-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: stat32i-fix-under-stat32i-equiv

(defthm stat32i-fix-under-stat32i-equiv
  (stat32i-equiv (stat32i-fix acl2::x)
                 acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-stat32i-fix-1-forward-to-stat32i-equiv

(defthm equal-of-stat32i-fix-1-forward-to-stat32i-equiv
  (implies (equal (stat32i-fix acl2::x) acl2::y)
           (stat32i-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-stat32i-fix-2-forward-to-stat32i-equiv

(defthm equal-of-stat32i-fix-2-forward-to-stat32i-equiv
  (implies (equal acl2::x (stat32i-fix acl2::y))
           (stat32i-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: stat32i-equiv-of-stat32i-fix-1-forward

(defthm stat32i-equiv-of-stat32i-fix-1-forward
  (implies (stat32i-equiv (stat32i-fix acl2::x)
                          acl2::y)
           (stat32i-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: stat32i-equiv-of-stat32i-fix-2-forward

(defthm stat32i-equiv-of-stat32i-fix-2-forward
  (implies (stat32i-equiv acl2::x (stat32i-fix acl2::y))
           (stat32i-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)