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