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