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            • Ubyte8-list
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            • Ubyte16-list
            • Ubyte11-list
            • Ubyte1-list
            • Sbyte8-list
            • Sbyte64-list
            • Sbyte4-list
            • Sbyte32-list
            • Sbyte3-list
            • Sbyte256-list
            • Sbyte2-list
            • Sbyte16-list
              • Sbyte16-list-fix
              • Sbyte16-list-equiv
              • Sbyte16-listp
            • Sbyte128-list
            • Sbyte1-list
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• Defbytelist-standard-instances

Sbyte16-list

Fixtype of true lists of signed bytes of size 16.

This is an ordinary fty::deflist.

Theorem: sbyte16-listp-forward-signed-byte-listp

(defthm sbyte16-listp-forward-signed-byte-listp
  (implies (sbyte16-listp x)
           (signed-byte-listp 16 x))
  :rule-classes :forward-chaining)

Theorem: sbyte16-listp-rewrite-signed-byte-listp

(defthm sbyte16-listp-rewrite-signed-byte-listp
  (equal (sbyte16-listp x)
         (signed-byte-listp 16 x)))

Theorem: signed-byte-listp-rewrite-sbyte16-listp

(defthm signed-byte-listp-rewrite-sbyte16-listp
  (equal (signed-byte-listp 16 x)
         (sbyte16-listp x)))

Theorem: true-listp-when-sbyte16-listp-rewrite

(defthm true-listp-when-sbyte16-listp-rewrite
  (implies (sbyte16-listp x)
           (true-listp x)))

Theorem: sbyte16-list-fix-of-take

(defthm sbyte16-list-fix-of-take
  (implies (<= (nfix n) (len x))
           (equal (sbyte16-list-fix (take n x))
                  (take n (sbyte16-list-fix x)))))

Theorem: sbyte16-list-fix-of-rcons

(defthm sbyte16-list-fix-of-rcons
  (equal (sbyte16-list-fix (rcons a x))
         (rcons (sbyte16-fix a)
                (sbyte16-list-fix x))))

Subtopics

Sbyte16-list-fix

(sbyte16-list-fix x) is a usual fty list fixing function.

Sbyte16-list-equiv

Basic equivalence relation for sbyte16-list structures.

Sbyte16-listp

(sbyte16-listp x) recognizes lists where every element satisfies sbyte16p.