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