Division of a value of type
Function:
(defun div-slong-ulong (x y) (declare (xargs :guard (and (slongp x) (ulongp y) (div-slong-ulong-okp x y)))) (div-ulong-ulong (ulong-from-slong x) y))
Theorem:
(defthm ulongp-of-div-slong-ulong (ulongp (div-slong-ulong x y)))
Theorem:
(defthm div-slong-ulong-of-slong-fix-x (equal (div-slong-ulong (slong-fix x) y) (div-slong-ulong x y)))
Theorem:
(defthm div-slong-ulong-slong-equiv-congruence-on-x (implies (slong-equiv x x-equiv) (equal (div-slong-ulong x y) (div-slong-ulong x-equiv y))) :rule-classes :congruence)
Theorem:
(defthm div-slong-ulong-of-ulong-fix-y (equal (div-slong-ulong x (ulong-fix y)) (div-slong-ulong x y)))
Theorem:
(defthm div-slong-ulong-ulong-equiv-congruence-on-y (implies (ulong-equiv y y-equiv) (equal (div-slong-ulong x y) (div-slong-ulong x y-equiv))) :rule-classes :congruence)