Bitwise exclusive disjunction of a value of type
Function:
(defun bitxor-ulong-sint (x y) (declare (xargs :guard (and (ulongp x) (sintp y)))) (bitxor-ulong-ulong x (ulong-from-sint y)))
Theorem:
(defthm ulongp-of-bitxor-ulong-sint (ulongp (bitxor-ulong-sint x y)))
Theorem:
(defthm bitxor-ulong-sint-of-ulong-fix-x (equal (bitxor-ulong-sint (ulong-fix x) y) (bitxor-ulong-sint x y)))
Theorem:
(defthm bitxor-ulong-sint-ulong-equiv-congruence-on-x (implies (ulong-equiv x x-equiv) (equal (bitxor-ulong-sint x y) (bitxor-ulong-sint x-equiv y))) :rule-classes :congruence)
Theorem:
(defthm bitxor-ulong-sint-of-sint-fix-y (equal (bitxor-ulong-sint x (sint-fix y)) (bitxor-ulong-sint x y)))
Theorem:
(defthm bitxor-ulong-sint-sint-equiv-congruence-on-y (implies (sint-equiv y y-equiv) (equal (bitxor-ulong-sint x y) (bitxor-ulong-sint x y-equiv))) :rule-classes :congruence)