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