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