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• Nibble

Nibble-fix

Fixer for nibble.

Signature

(nibble-fix x) → fixed-x

Arguments

x — Guard (nibblep x).

Returns

fixed-x — Type (nibblep fixed-x).

Definitions and Theorems

Function: nibble-fix

(defun nibble-fix (x)
  (declare (xargs :guard (nibblep x)))
  (mbe :logic (if (nibblep x) x 0)
       :exec x))

Theorem: nibblep-of-nibble-fix

(defthm nibblep-of-nibble-fix
  (b* ((fixed-x (nibble-fix x)))
    (nibblep fixed-x))
  :rule-classes :rewrite)

Theorem: nibble-fix-when-nibblep

(defthm nibble-fix-when-nibblep
  (implies (nibblep x)
           (equal (nibble-fix x) x)))