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