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