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