Bitwise conjunction of a value of type
Function:
(defun bitand-sshort-ulong (x y) (declare (xargs :guard (and (sshortp x) (ulongp y)))) (bitand-ulong-ulong (ulong-from-sshort x) y))
Theorem:
(defthm ulongp-of-bitand-sshort-ulong (ulongp (bitand-sshort-ulong x y)))
Theorem:
(defthm bitand-sshort-ulong-of-sshort-fix-x (equal (bitand-sshort-ulong (sshort-fix x) y) (bitand-sshort-ulong x y)))
Theorem:
(defthm bitand-sshort-ulong-sshort-equiv-congruence-on-x (implies (sshort-equiv x x-equiv) (equal (bitand-sshort-ulong x y) (bitand-sshort-ulong x-equiv y))) :rule-classes :congruence)
Theorem:
(defthm bitand-sshort-ulong-of-ulong-fix-y (equal (bitand-sshort-ulong x (ulong-fix y)) (bitand-sshort-ulong x y)))
Theorem:
(defthm bitand-sshort-ulong-ulong-equiv-congruence-on-y (implies (ulong-equiv y y-equiv) (equal (bitand-sshort-ulong x y) (bitand-sshort-ulong x y-equiv))) :rule-classes :congruence)