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