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