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