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