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