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Bitwise exclusive disjunction of a value of type
Function:
(defun bitxor-slong-schar (x y) (declare (xargs :guard (and (slongp x) (scharp y)))) (bitxor-slong-slong x (slong-from-schar y)))
Theorem:
(defthm slongp-of-bitxor-slong-schar (slongp (bitxor-slong-schar x y)))
Theorem:
(defthm bitxor-slong-schar-of-slong-fix-x (equal (bitxor-slong-schar (slong-fix x) y) (bitxor-slong-schar x y)))
Theorem:
(defthm bitxor-slong-schar-slong-equiv-congruence-on-x (implies (slong-equiv x x-equiv) (equal (bitxor-slong-schar x y) (bitxor-slong-schar x-equiv y))) :rule-classes :congruence)
Theorem:
(defthm bitxor-slong-schar-of-schar-fix-y (equal (bitxor-slong-schar x (schar-fix y)) (bitxor-slong-schar x y)))
Theorem:
(defthm bitxor-slong-schar-schar-equiv-congruence-on-y (implies (schar-equiv y y-equiv) (equal (bitxor-slong-schar x y) (bitxor-slong-schar x y-equiv))) :rule-classes :congruence)