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