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• Sponge

Sponge-equiv

Basic equivalence relation for sponge structures.

Definitions and Theorems

Function: sponge-equiv$inline

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

Theorem: sponge-equiv-is-an-equivalence

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

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

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

Theorem: sponge-fix-under-sponge-equiv

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

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

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

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

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

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

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

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

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