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