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