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Hash-op

Hash-op-fix

Fixing function for hash-op structures.

Signature
(hash-op-fix x) → new-x
Arguments: x — Guard (hash-opp x).
Returns: new-x — Type (hash-opp new-x).

Definitions and Theorems

Function: hash-op-fix$inline

(defun hash-op-fix$inline (x)
  (declare (xargs :guard (hash-opp x)))
  (let ((__function__ 'hash-op-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (case (hash-op-kind x)
           (:hash.bhp256 (cons :hash.bhp256 (list)))
           (:hash.bhp512 (cons :hash.bhp512 (list)))
           (:hash.bhp768 (cons :hash.bhp768 (list)))
           (:hash.bhp1024 (cons :hash.bhp1024 (list)))
           (:hash.ped64 (cons :hash.ped64 (list)))
           (:hash.ped128 (cons :hash.ped128 (list)))
           (:hash.psd2 (cons :hash.psd2 (list)))
           (:hash.psd4 (cons :hash.psd4 (list)))
           (:hash.psd8 (cons :hash.psd8 (list))))
         :exec x)))

Theorem: hash-opp-of-hash-op-fix

(defthm hash-opp-of-hash-op-fix
  (b* ((new-x (hash-op-fix$inline x)))
    (hash-opp new-x))
  :rule-classes :rewrite)

Theorem: hash-op-fix-when-hash-opp

(defthm hash-op-fix-when-hash-opp
  (implies (hash-opp x)
           (equal (hash-op-fix x) x)))

Function: hash-op-equiv$inline

(defun hash-op-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (hash-opp acl2::x)
                              (hash-opp acl2::y))))
  (equal (hash-op-fix acl2::x)
         (hash-op-fix acl2::y)))

Theorem: hash-op-equiv-is-an-equivalence

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

Theorem: hash-op-equiv-implies-equal-hash-op-fix-1

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

Theorem: hash-op-fix-under-hash-op-equiv

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

Theorem: equal-of-hash-op-fix-1-forward-to-hash-op-equiv

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

Theorem: equal-of-hash-op-fix-2-forward-to-hash-op-equiv

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

Theorem: hash-op-equiv-of-hash-op-fix-1-forward

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

Theorem: hash-op-equiv-of-hash-op-fix-2-forward

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

Theorem: hash-op-kind$inline-of-hash-op-fix-x

(defthm hash-op-kind$inline-of-hash-op-fix-x
  (equal (hash-op-kind$inline (hash-op-fix x))
         (hash-op-kind$inline x)))

Theorem: hash-op-kind$inline-hash-op-equiv-congruence-on-x

(defthm hash-op-kind$inline-hash-op-equiv-congruence-on-x
  (implies (hash-op-equiv x x-equiv)
           (equal (hash-op-kind$inline x)
                  (hash-op-kind$inline x-equiv)))
  :rule-classes :congruence)

Theorem: consp-of-hash-op-fix

(defthm consp-of-hash-op-fix
  (consp (hash-op-fix x))
  :rule-classes :type-prescription)