Check if the division of a value of type
Function:
(defun div-sshort-ullong-okp (x y) (declare (xargs :guard (and (sshortp x) (ullongp y)))) (div-ullong-ullong-okp (ullong-from-sshort x) y))
Theorem:
(defthm booleanp-of-div-sshort-ullong-okp (booleanp (div-sshort-ullong-okp x y)))
Theorem:
(defthm div-sshort-ullong-okp-of-sshort-fix-x (equal (div-sshort-ullong-okp (sshort-fix x) y) (div-sshort-ullong-okp x y)))
Theorem:
(defthm div-sshort-ullong-okp-sshort-equiv-congruence-on-x (implies (sshort-equiv x x-equiv) (equal (div-sshort-ullong-okp x y) (div-sshort-ullong-okp x-equiv y))) :rule-classes :congruence)
Theorem:
(defthm div-sshort-ullong-okp-of-ullong-fix-y (equal (div-sshort-ullong-okp x (ullong-fix y)) (div-sshort-ullong-okp x y)))
Theorem:
(defthm div-sshort-ullong-okp-ullong-equiv-congruence-on-y (implies (ullong-equiv y y-equiv) (equal (div-sshort-ullong-okp x y) (div-sshort-ullong-okp x y-equiv))) :rule-classes :congruence)