Check if the remainder of a value of type
Function:
(defun rem-ushort-ullong-okp (x y) (declare (xargs :guard (and (ushortp x) (ullongp y)))) (rem-ullong-ullong-okp (ullong-from-ushort x) y))
Theorem:
(defthm booleanp-of-rem-ushort-ullong-okp (booleanp (rem-ushort-ullong-okp x y)))
Theorem:
(defthm rem-ushort-ullong-okp-of-ushort-fix-x (equal (rem-ushort-ullong-okp (ushort-fix x) y) (rem-ushort-ullong-okp x y)))
Theorem:
(defthm rem-ushort-ullong-okp-ushort-equiv-congruence-on-x (implies (ushort-equiv x x-equiv) (equal (rem-ushort-ullong-okp x y) (rem-ushort-ullong-okp x-equiv y))) :rule-classes :congruence)
Theorem:
(defthm rem-ushort-ullong-okp-of-ullong-fix-y (equal (rem-ushort-ullong-okp x (ullong-fix y)) (rem-ushort-ullong-okp x y)))
Theorem:
(defthm rem-ushort-ullong-okp-ullong-equiv-congruence-on-y (implies (ullong-equiv y y-equiv) (equal (rem-ushort-ullong-okp x y) (rem-ushort-ullong-okp x y-equiv))) :rule-classes :congruence)