Remainder of a value of type
Function:
(defun rem-schar-ulong (x y) (declare (xargs :guard (and (scharp x) (ulongp y) (rem-schar-ulong-okp x y)))) (rem-ulong-ulong (ulong-from-schar x) y))
Theorem:
(defthm ulongp-of-rem-schar-ulong (ulongp (rem-schar-ulong x y)))
Theorem:
(defthm rem-schar-ulong-of-schar-fix-x (equal (rem-schar-ulong (schar-fix x) y) (rem-schar-ulong x y)))
Theorem:
(defthm rem-schar-ulong-schar-equiv-congruence-on-x (implies (schar-equiv x x-equiv) (equal (rem-schar-ulong x y) (rem-schar-ulong x-equiv y))) :rule-classes :congruence)
Theorem:
(defthm rem-schar-ulong-of-ulong-fix-y (equal (rem-schar-ulong x (ulong-fix y)) (rem-schar-ulong x y)))
Theorem:
(defthm rem-schar-ulong-ulong-equiv-congruence-on-y (implies (ulong-equiv y y-equiv) (equal (rem-schar-ulong x y) (rem-schar-ulong x y-equiv))) :rule-classes :congruence)