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