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