Check if the addition of a value of type
Function:
(defun add-sint-sint-okp (x y) (declare (xargs :guard (and (sintp x) (sintp y)))) (sint-integerp (+ (integer-from-sint x) (integer-from-sint y))))
Theorem:
(defthm booleanp-of-add-sint-sint-okp (booleanp (add-sint-sint-okp x y)))
Theorem:
(defthm add-sint-sint-okp-of-sint-fix-x (equal (add-sint-sint-okp (sint-fix x) y) (add-sint-sint-okp x y)))
Theorem:
(defthm add-sint-sint-okp-sint-equiv-congruence-on-x (implies (sint-equiv x x-equiv) (equal (add-sint-sint-okp x y) (add-sint-sint-okp x-equiv y))) :rule-classes :congruence)
Theorem:
(defthm add-sint-sint-okp-of-sint-fix-y (equal (add-sint-sint-okp x (sint-fix y)) (add-sint-sint-okp x y)))
Theorem:
(defthm add-sint-sint-okp-sint-equiv-congruence-on-y (implies (sint-equiv y y-equiv) (equal (add-sint-sint-okp x y) (add-sint-sint-okp x y-equiv))) :rule-classes :congruence)