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