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