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