Check if the multiplication of a value of type
Function:
(defun mul-slong-sint-okp (x y) (declare (xargs :guard (and (slongp x) (sintp y)))) (mul-slong-slong-okp x (slong-from-sint y)))
Theorem:
(defthm booleanp-of-mul-slong-sint-okp (booleanp (mul-slong-sint-okp x y)))
Theorem:
(defthm mul-slong-sint-okp-of-slong-fix-x (equal (mul-slong-sint-okp (slong-fix x) y) (mul-slong-sint-okp x y)))
Theorem:
(defthm mul-slong-sint-okp-slong-equiv-congruence-on-x (implies (slong-equiv x x-equiv) (equal (mul-slong-sint-okp x y) (mul-slong-sint-okp x-equiv y))) :rule-classes :congruence)
Theorem:
(defthm mul-slong-sint-okp-of-sint-fix-y (equal (mul-slong-sint-okp x (sint-fix y)) (mul-slong-sint-okp x y)))
Theorem:
(defthm mul-slong-sint-okp-sint-equiv-congruence-on-y (implies (sint-equiv y y-equiv) (equal (mul-slong-sint-okp x y) (mul-slong-sint-okp x y-equiv))) :rule-classes :congruence)