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