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Representation-of-integer-operations

Boolean-from-ushort

Check if a value of type unsigned short is not 0.

Definitions and Theorems

Function: boolean-from-ushort

(defun boolean-from-ushort (x)
  (declare (xargs :guard (and (ushortp x))))
  (/= (integer-from-ushort x) 0))

Theorem: booleanp-of-boolean-from-ushort

(defthm booleanp-of-boolean-from-ushort
  (booleanp (boolean-from-ushort x)))

Theorem: boolean-from-ushort-of-ushort-fix-x

(defthm boolean-from-ushort-of-ushort-fix-x
  (equal (boolean-from-ushort (ushort-fix x))
         (boolean-from-ushort x)))

Theorem: boolean-from-ushort-ushort-equiv-congruence-on-x

(defthm boolean-from-ushort-ushort-equiv-congruence-on-x
  (implies (ushort-equiv x x-equiv)
           (equal (boolean-from-ushort x)
                  (boolean-from-ushort x-equiv)))
  :rule-classes :congruence)