\(i\)を階数、\(A:\mathord {\textnormal {\textsf {Span}}}(i)\)をスパン、\(B:\mathord {\textnormal {\textsf {SpanOver}}}(A)\)を\(A\)上のスパンとする。スパン\(\mathord {\textnormal {\textsf {Total}}}(B):\mathord {\textnormal {\textsf {Span}}}(i)\)を次のように定義する。

• -\(\mathord {\textnormal {\textsf {Left}}}\equiv \sum _{x:A.\mathord {\textnormal {\textsf {Left}}}}B.\mathord {\textnormal {\textsf {Left}}}(x)\)
• -\(\mathord {\textnormal {\textsf {Right}}}\equiv \sum _{x:A.\mathord {\textnormal {\textsf {Right}}}}B.\mathord {\textnormal {\textsf {Right}}}(x)\)
• -\(\mathord {\textnormal {\textsf {Center}}}\equiv \sum _{x:A.\mathord {\textnormal {\textsf {Center}}}}B.\mathord {\textnormal {\textsf {Center}}}(x)\)
• -\(\mathord {\textnormal {\textsf {leg-l}}}(x)\equiv \mathord {\textnormal {\textsf {pair}}}(A.\mathord {\textnormal {\textsf {leg-l}}}(\mathord {\textnormal {\textsf {proj}}}_{1}(x)),B.\mathord {\textnormal {\textsf {leg-l}}}(\mathord {\textnormal {\textsf {proj}}}_{2}(x)))\)
• -\(\mathord {\textnormal {\textsf {leg-r}}}(x)\equiv \mathord {\textnormal {\textsf {pair}}}(A.\mathord {\textnormal {\textsf {leg-r}}}(\mathord {\textnormal {\textsf {proj}}}_{1}(x)),B.\mathord {\textnormal {\textsf {leg-r}}}(\mathord {\textnormal {\textsf {proj}}}_{2}(x)))\)