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