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