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