Check if the remainder of a value of type
Function:
(defun rem-uint-sshort-okp (x y) (declare (xargs :guard (and (uintp x) (sshortp y)))) (rem-uint-uint-okp x (uint-from-sshort y)))
Theorem:
(defthm booleanp-of-rem-uint-sshort-okp (booleanp (rem-uint-sshort-okp x y)))
Theorem:
(defthm rem-uint-sshort-okp-of-uint-fix-x (equal (rem-uint-sshort-okp (uint-fix x) y) (rem-uint-sshort-okp x y)))
Theorem:
(defthm rem-uint-sshort-okp-uint-equiv-congruence-on-x (implies (uint-equiv x x-equiv) (equal (rem-uint-sshort-okp x y) (rem-uint-sshort-okp x-equiv y))) :rule-classes :congruence)
Theorem:
(defthm rem-uint-sshort-okp-of-sshort-fix-y (equal (rem-uint-sshort-okp x (sshort-fix y)) (rem-uint-sshort-okp x y)))
Theorem:
(defthm rem-uint-sshort-okp-sshort-equiv-congruence-on-y (implies (sshort-equiv y y-equiv) (equal (rem-uint-sshort-okp x y) (rem-uint-sshort-okp x y-equiv))) :rule-classes :congruence)