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