Greater-than relation of a value of type
Function:
(defun gt-sshort-ulong (x y) (declare (xargs :guard (and (sshortp x) (ulongp y)))) (gt-ulong-ulong (ulong-from-sshort x) y))
Theorem:
(defthm sintp-of-gt-sshort-ulong (sintp (gt-sshort-ulong x y)))
Theorem:
(defthm gt-sshort-ulong-of-sshort-fix-x (equal (gt-sshort-ulong (sshort-fix x) y) (gt-sshort-ulong x y)))
Theorem:
(defthm gt-sshort-ulong-sshort-equiv-congruence-on-x (implies (sshort-equiv x x-equiv) (equal (gt-sshort-ulong x y) (gt-sshort-ulong x-equiv y))) :rule-classes :congruence)
Theorem:
(defthm gt-sshort-ulong-of-ulong-fix-y (equal (gt-sshort-ulong x (ulong-fix y)) (gt-sshort-ulong x y)))
Theorem:
(defthm gt-sshort-ulong-ulong-equiv-congruence-on-y (implies (ulong-equiv y y-equiv) (equal (gt-sshort-ulong x y) (gt-sshort-ulong x y-equiv))) :rule-classes :congruence)