Less-than relation of a value of type
Function:
(defun lt-sshort-ushort (x y) (declare (xargs :guard (and (sshortp x) (ushortp y)))) (lt-sint-sint (sint-from-sshort x) (sint-from-ushort y)))
Theorem:
(defthm sintp-of-lt-sshort-ushort (sintp (lt-sshort-ushort x y)))
Theorem:
(defthm lt-sshort-ushort-of-sshort-fix-x (equal (lt-sshort-ushort (sshort-fix x) y) (lt-sshort-ushort x y)))
Theorem:
(defthm lt-sshort-ushort-sshort-equiv-congruence-on-x (implies (sshort-equiv x x-equiv) (equal (lt-sshort-ushort x y) (lt-sshort-ushort x-equiv y))) :rule-classes :congruence)
Theorem:
(defthm lt-sshort-ushort-of-ushort-fix-y (equal (lt-sshort-ushort x (ushort-fix y)) (lt-sshort-ushort x y)))
Theorem:
(defthm lt-sshort-ushort-ushort-equiv-congruence-on-y (implies (ushort-equiv y y-equiv) (equal (lt-sshort-ushort x y) (lt-sshort-ushort x y-equiv))) :rule-classes :congruence)