Multiplication of a value of type
Function:
(defun mul-uint-sshort (x y) (declare (xargs :guard (and (uintp x) (sshortp y)))) (mul-uint-uint x (uint-from-sshort y)))
Theorem:
(defthm uintp-of-mul-uint-sshort (uintp (mul-uint-sshort x y)))
Theorem:
(defthm mul-uint-sshort-of-uint-fix-x (equal (mul-uint-sshort (uint-fix x) y) (mul-uint-sshort x y)))
Theorem:
(defthm mul-uint-sshort-uint-equiv-congruence-on-x (implies (uint-equiv x x-equiv) (equal (mul-uint-sshort x y) (mul-uint-sshort x-equiv y))) :rule-classes :congruence)
Theorem:
(defthm mul-uint-sshort-of-sshort-fix-y (equal (mul-uint-sshort x (sshort-fix y)) (mul-uint-sshort x y)))
Theorem:
(defthm mul-uint-sshort-sshort-equiv-congruence-on-y (implies (sshort-equiv y y-equiv) (equal (mul-uint-sshort x y) (mul-uint-sshort x y-equiv))) :rule-classes :congruence)