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