Addition of a value of type
Function:
(defun add-uint-slong (x y) (declare (xargs :guard (and (uintp x) (slongp y) (add-uint-slong-okp x y)))) (add-slong-slong (slong-from-uint x) y))
Theorem:
(defthm slongp-of-add-uint-slong (slongp (add-uint-slong x y)))
Theorem:
(defthm add-uint-slong-of-uint-fix-x (equal (add-uint-slong (uint-fix x) y) (add-uint-slong x y)))
Theorem:
(defthm add-uint-slong-uint-equiv-congruence-on-x (implies (uint-equiv x x-equiv) (equal (add-uint-slong x y) (add-uint-slong x-equiv y))) :rule-classes :congruence)
Theorem:
(defthm add-uint-slong-of-slong-fix-y (equal (add-uint-slong x (slong-fix y)) (add-uint-slong x y)))
Theorem:
(defthm add-uint-slong-slong-equiv-congruence-on-y (implies (slong-equiv y y-equiv) (equal (add-uint-slong x y) (add-uint-slong x y-equiv))) :rule-classes :congruence)