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            • Sbyte8-list
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            • Sbyte32-list
              • Sbyte32-list-fix
              • Sbyte32-list-equiv
              • Sbyte32-listp
            • Sbyte3-list
            • Sbyte256-list
            • Sbyte2-list
            • Sbyte16-list
            • Sbyte128-list
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• Defbytelist-standard-instances

Sbyte32-list

Fixtype of true lists of signed bytes of size 32.

This is an ordinary fty::deflist.

Theorem: sbyte32-listp-forward-signed-byte-listp

(defthm sbyte32-listp-forward-signed-byte-listp
  (implies (sbyte32-listp x)
           (signed-byte-listp 32 x))
  :rule-classes :forward-chaining)

Theorem: sbyte32-listp-rewrite-signed-byte-listp

(defthm sbyte32-listp-rewrite-signed-byte-listp
  (equal (sbyte32-listp x)
         (signed-byte-listp 32 x)))

Theorem: signed-byte-listp-rewrite-sbyte32-listp

(defthm signed-byte-listp-rewrite-sbyte32-listp
  (equal (signed-byte-listp 32 x)
         (sbyte32-listp x)))

Theorem: true-listp-when-sbyte32-listp-rewrite

(defthm true-listp-when-sbyte32-listp-rewrite
  (implies (sbyte32-listp x)
           (true-listp x)))

Theorem: sbyte32-list-fix-of-take

(defthm sbyte32-list-fix-of-take
  (implies (<= (nfix n) (len x))
           (equal (sbyte32-list-fix (take n x))
                  (take n (sbyte32-list-fix x)))))

Theorem: sbyte32-list-fix-of-rcons

(defthm sbyte32-list-fix-of-rcons
  (equal (sbyte32-list-fix (rcons a x))
         (rcons (sbyte32-fix a)
                (sbyte32-list-fix x))))

Subtopics

Sbyte32-list-fix

(sbyte32-list-fix x) is a usual fty list fixing function.

Sbyte32-list-equiv

Basic equivalence relation for sbyte32-list structures.

Sbyte32-listp

(sbyte32-listp x) recognizes lists where every element satisfies sbyte32p.