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