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