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