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