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