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