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