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• Snapshot-config

Snapshot-config-equiv

Basic equivalence relation for snapshot-config structures.

Definitions and Theorems

Function: snapshot-config-equiv$inline

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

Theorem: snapshot-config-equiv-is-an-equivalence

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

Theorem: snapshot-config-equiv-implies-equal-snapshot-config-fix-1

(defthm snapshot-config-equiv-implies-equal-snapshot-config-fix-1
  (implies (snapshot-config-equiv x x-equiv)
           (equal (snapshot-config-fix x)
                  (snapshot-config-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: snapshot-config-fix-under-snapshot-config-equiv

(defthm snapshot-config-fix-under-snapshot-config-equiv
  (snapshot-config-equiv (snapshot-config-fix x)
                         x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-snapshot-config-fix-1-forward-to-snapshot-config-equiv

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

Theorem: equal-of-snapshot-config-fix-2-forward-to-snapshot-config-equiv

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

Theorem: snapshot-config-equiv-of-snapshot-config-fix-1-forward

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

Theorem: snapshot-config-equiv-of-snapshot-config-fix-2-forward

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