Logical complement of a value of type
Function:
(defun lognot-sint (x) (declare (xargs :guard (and (sintp x)))) (sint-from-boolean (= (integer-from-sint x) 0)))
Theorem:
(defthm sintp-of-lognot-sint (sintp (lognot-sint x)))
Theorem:
(defthm lognot-sint-of-sint-fix-x (equal (lognot-sint (sint-fix x)) (lognot-sint x)))
Theorem:
(defthm lognot-sint-sint-equiv-congruence-on-x (implies (sint-equiv x x-equiv) (equal (lognot-sint x) (lognot-sint x-equiv))) :rule-classes :congruence)