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Representation-of-integer-operations

Lognot-uint

Logical complement of a value of type unsigned int [C17:6.5.3].

Definitions and Theorems

Function: lognot-uint

(defun lognot-uint (x)
  (declare (xargs :guard (and (uintp x))))
  (sint-from-boolean (= (integer-from-uint x) 0)))

Theorem: sintp-of-lognot-uint

(defthm sintp-of-lognot-uint
  (sintp (lognot-uint x)))

Theorem: lognot-uint-of-uint-fix-x

(defthm lognot-uint-of-uint-fix-x
  (equal (lognot-uint (uint-fix x))
         (lognot-uint x)))

Theorem: lognot-uint-uint-equiv-congruence-on-x

(defthm lognot-uint-uint-equiv-congruence-on-x
  (implies (uint-equiv x x-equiv)
           (equal (lognot-uint x)
                  (lognot-uint x-equiv)))
  :rule-classes :congruence)