Subtraction of a value of type
Function:
(defun sub-uint-ushort (x y) (declare (xargs :guard (and (uintp x) (ushortp y)))) (sub-uint-uint x (uint-from-ushort y)))
Theorem:
(defthm uintp-of-sub-uint-ushort (uintp (sub-uint-ushort x y)))
Theorem:
(defthm sub-uint-ushort-of-uint-fix-x (equal (sub-uint-ushort (uint-fix x) y) (sub-uint-ushort x y)))
Theorem:
(defthm sub-uint-ushort-uint-equiv-congruence-on-x (implies (uint-equiv x x-equiv) (equal (sub-uint-ushort x y) (sub-uint-ushort x-equiv y))) :rule-classes :congruence)
Theorem:
(defthm sub-uint-ushort-of-ushort-fix-y (equal (sub-uint-ushort x (ushort-fix y)) (sub-uint-ushort x y)))
Theorem:
(defthm sub-uint-ushort-ushort-equiv-congruence-on-y (implies (ushort-equiv y y-equiv) (equal (sub-uint-ushort x y) (sub-uint-ushort x y-equiv))) :rule-classes :congruence)