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