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