Check if the remainder of a value of type
Function:
(defun rem-slong-slong-okp (x y) (declare (xargs :guard (and (slongp x) (slongp y)))) (and (not (equal (integer-from-slong y) 0)) (slong-integerp (rem (integer-from-slong x) (integer-from-slong y)))))
Theorem:
(defthm booleanp-of-rem-slong-slong-okp (booleanp (rem-slong-slong-okp x y)))
Theorem:
(defthm rem-slong-slong-okp-of-slong-fix-x (equal (rem-slong-slong-okp (slong-fix x) y) (rem-slong-slong-okp x y)))
Theorem:
(defthm rem-slong-slong-okp-slong-equiv-congruence-on-x (implies (slong-equiv x x-equiv) (equal (rem-slong-slong-okp x y) (rem-slong-slong-okp x-equiv y))) :rule-classes :congruence)
Theorem:
(defthm rem-slong-slong-okp-of-slong-fix-y (equal (rem-slong-slong-okp x (slong-fix y)) (rem-slong-slong-okp x y)))
Theorem:
(defthm rem-slong-slong-okp-slong-equiv-congruence-on-y (implies (slong-equiv y y-equiv) (equal (rem-slong-slong-okp x y) (rem-slong-slong-okp x y-equiv))) :rule-classes :congruence)