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    • Ubyte32-list

    Ubyte32-list-equiv

    Basic equivalence relation for ubyte32-list structures.

    Definitions and Theorems

    Function: ubyte32-list-equiv$inline

    (defun ubyte32-list-equiv$inline (x y)
      (declare (xargs :guard (and (ubyte32-listp x)
                                  (ubyte32-listp y))))
      (equal (ubyte32-list-fix x)
             (ubyte32-list-fix y)))

    Theorem: ubyte32-list-equiv-is-an-equivalence

    (defthm ubyte32-list-equiv-is-an-equivalence
      (and (booleanp (ubyte32-list-equiv x y))
           (ubyte32-list-equiv x x)
           (implies (ubyte32-list-equiv x y)
                    (ubyte32-list-equiv y x))
           (implies (and (ubyte32-list-equiv x y)
                         (ubyte32-list-equiv y z))
                    (ubyte32-list-equiv x z)))
      :rule-classes (:equivalence))

    Theorem: ubyte32-list-equiv-implies-equal-ubyte32-list-fix-1

    (defthm ubyte32-list-equiv-implies-equal-ubyte32-list-fix-1
      (implies (ubyte32-list-equiv x x-equiv)
               (equal (ubyte32-list-fix x)
                      (ubyte32-list-fix x-equiv)))
      :rule-classes (:congruence))

    Theorem: ubyte32-list-fix-under-ubyte32-list-equiv

    (defthm ubyte32-list-fix-under-ubyte32-list-equiv
      (ubyte32-list-equiv (ubyte32-list-fix x)
                          x)
      :rule-classes (:rewrite :rewrite-quoted-constant))

    Theorem: equal-of-ubyte32-list-fix-1-forward-to-ubyte32-list-equiv

    (defthm equal-of-ubyte32-list-fix-1-forward-to-ubyte32-list-equiv
      (implies (equal (ubyte32-list-fix x) y)
               (ubyte32-list-equiv x y))
      :rule-classes :forward-chaining)

    Theorem: equal-of-ubyte32-list-fix-2-forward-to-ubyte32-list-equiv

    (defthm equal-of-ubyte32-list-fix-2-forward-to-ubyte32-list-equiv
      (implies (equal x (ubyte32-list-fix y))
               (ubyte32-list-equiv x y))
      :rule-classes :forward-chaining)

    Theorem: ubyte32-list-equiv-of-ubyte32-list-fix-1-forward

    (defthm ubyte32-list-equiv-of-ubyte32-list-fix-1-forward
      (implies (ubyte32-list-equiv (ubyte32-list-fix x)
                                   y)
               (ubyte32-list-equiv x y))
      :rule-classes :forward-chaining)

    Theorem: ubyte32-list-equiv-of-ubyte32-list-fix-2-forward

    (defthm ubyte32-list-equiv-of-ubyte32-list-fix-2-forward
      (implies (ubyte32-list-equiv x (ubyte32-list-fix y))
               (ubyte32-list-equiv x y))
      :rule-classes :forward-chaining)