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Representation-of-integer-operations

Boolean-from-sint

Check if a value of type signed int is not 0.

Definitions and Theorems

Function: boolean-from-sint

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

Theorem: booleanp-of-boolean-from-sint

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

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

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

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

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