\begin{array} { r l } & { \{ a _ { 1 } \otimes b _ { 1 } , \dotsc , a _ { n - 1 } \otimes b _ { n - 1 } , a ^ { \prime } a ^ { \prime \prime } \otimes b ^ { \prime } b ^ { \prime \prime } \} _ { n } } \\ & { = \sum _ { \sigma \in \operatorname { S h } _ { k , l } ^ { - 1 } , \sigma ( k ) = n } ( - 1 ) ^ { \sigma } a _ { \sigma ( k + 1 ) } \cdots a _ { \sigma ( k + l ) } \{ a _ { \sigma ( 1 ) } , \dotsc , a _ { \sigma ( k - 1 ) } , a ^ { \prime } a ^ { \prime \prime } \} _ { k } \otimes b _ { \sigma ( 1 ) } \cdots b _ { \sigma ( k - 1 ) } b ^ { \prime } b ^ { \prime \prime } \{ b _ { \sigma ( k + 1 ) } , \dotsc , b _ { \sigma ( n ) } \} _ { l } } \\ & { + \sum _ { \sigma \in \operatorname { S h } _ { k , l } ^ { - 1 } , \sigma ( n ) = n } ( - 1 ) ^ { \sigma } a _ { \sigma ( k + 1 ) } \cdots a _ { \sigma ( n - 1 ) } a ^ { \prime } a ^ { \prime \prime } \{ a _ { \sigma ( 1 ) } , \dotsc , a _ { \sigma ( k ) } \} _ { k } \otimes b _ { \sigma ( 1 ) } \cdots b _ { \sigma ( k ) } \{ b _ { \sigma ( k + 1 ) } , \dotsc , b _ { \sigma ( n - 1 ) } b ^ { \prime } b ^ { \prime \prime } \} _ { l } } \\ & { = a ^ { \prime } \otimes b ^ { \prime } \sum _ { \sigma \in \operatorname { S h } _ { k , l } ^ { - 1 } , \sigma ( k ) = n } ( - 1 ) ^ { \sigma } a _ { \sigma ( k + 1 ) } \cdots a _ { \sigma ( k + l ) } \{ a _ { \sigma ( 1 ) } , \dotsc , a _ { \sigma ( k - 1 ) } , a ^ { \prime \prime } \} _ { k } \otimes b _ { \sigma ( 1 ) } \cdots b _ { \sigma ( k - 1 ) } b ^ { \prime \prime } \{ b _ { \sigma ( k + 1 ) } , \dotsc , b _ { \sigma ( n ) } \} _ { l } } \\ & { + a ^ { \prime \prime } \otimes b ^ { \prime \prime } \sum _ { \sigma \in \operatorname { S h } _ { k , l } ^ { - 1 } , \sigma ( k ) = n } ( - 1 ) ^ { \sigma } a _ { \sigma ( k + 1 ) } \cdots a _ { \sigma ( k + l ) } \{ a _ { \sigma ( 1 ) } , \dotsc , a _ { \sigma ( k - 1 ) } , a ^ { \prime } \} _ { k } \otimes b _ { \sigma ( 1 ) } \cdots b _ { \sigma ( k - 1 ) } b ^ { \prime } \{ b _ { \sigma ( k + 1 ) } , \dotsc , b _ { \sigma ( n ) } \} _ { l } } \\ & { + a ^ { \prime \prime } \otimes b ^ { \prime \prime } \sum _ { \sigma \in \operatorname { S h } _ { k , l } ^ { - 1 } , \sigma ( n ) = n } ( - 1 ) ^ { \sigma } a _ { \sigma ( k + 1 ) } \cdots a _ { \sigma ( n - 1 ) } a ^ { \prime } \{ a _ { \sigma ( 1 ) } , \dotsc , a _ { \sigma ( k ) } \} _ { k } \otimes b _ { \sigma ( 1 ) } \cdots b _ { \sigma ( k ) } \{ b _ { \sigma ( k + 1 ) } , \dotsc , b _ { \sigma ( n - 1 ) } b ^ { \prime } \} _ { l } } \\ & { + a ^ { \prime } \otimes b ^ { \prime } \sum _ { \sigma \in \operatorname { S h } _ { k , l } ^ { - 1 } , \sigma ( n ) = n } ( - 1 ) ^ { \sigma } a _ { \sigma ( k + 1 ) } \cdots a _ { \sigma ( n - 1 ) } a ^ { \prime \prime } \{ a _ { \sigma ( 1 ) } , \dotsc , a _ { \sigma ( k ) } \} _ { k } \otimes b _ { \sigma ( 1 ) } \cdots b _ { \sigma ( k ) } \{ b _ { \sigma ( k + 1 ) } , \dotsc , b _ { \sigma ( n - 1 ) } b ^ { \prime \prime } \} _ { l } } \\ & { = ( a ^ { \prime } \otimes b ^ { \prime } ) \{ a _ { 1 } \otimes b _ { 1 } , \dotsc , a _ { n - 1 } \otimes b _ { n - 1 } , a ^ { \prime \prime } \otimes b ^ { \prime \prime } \} _ { n } + ( a ^ { \prime \prime } \otimes b ^ { \prime \prime } ) \{ a _ { 1 } \otimes b _ { 1 } , \dotsc , a _ { n - 1 } \otimes b _ { n - 1 } , a ^ { \prime } \otimes b ^ { \prime } \} _ { n } . } \end{array}