Check if the multiplication of a value of type
Function:
(defun mul-sllong-sshort-okp (x y) (declare (xargs :guard (and (sllongp x) (sshortp y)))) (mul-sllong-sllong-okp x (sllong-from-sshort y)))
Theorem:
(defthm booleanp-of-mul-sllong-sshort-okp (booleanp (mul-sllong-sshort-okp x y)))
Theorem:
(defthm mul-sllong-sshort-okp-of-sllong-fix-x (equal (mul-sllong-sshort-okp (sllong-fix x) y) (mul-sllong-sshort-okp x y)))
Theorem:
(defthm mul-sllong-sshort-okp-sllong-equiv-congruence-on-x (implies (sllong-equiv x x-equiv) (equal (mul-sllong-sshort-okp x y) (mul-sllong-sshort-okp x-equiv y))) :rule-classes :congruence)
Theorem:
(defthm mul-sllong-sshort-okp-of-sshort-fix-y (equal (mul-sllong-sshort-okp x (sshort-fix y)) (mul-sllong-sshort-okp x y)))
Theorem:
(defthm mul-sllong-sshort-okp-sshort-equiv-congruence-on-y (implies (sshort-equiv y y-equiv) (equal (mul-sllong-sshort-okp x y) (mul-sllong-sshort-okp x y-equiv))) :rule-classes :congruence)