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