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