\(i\)を階数、\(G:\mathord {\textnormal {\textsf {LocalGen}}}(i)\)を局所生成系とする。局所生成系\(\mathord {\textnormal {\textsf {D}}}(G):\mathord {\textnormal {\textsf {LocalGen}}}(i)\)を次のように定義する。

• -\(\mathord {\textnormal {\textsf {Index}}}\equiv G.\mathord {\textnormal {\textsf {Index}}}+G.\mathord {\textnormal {\textsf {Index}}}\)
• -\(\mathord {\textnormal {\textsf {fun}}}(\mathord {\textnormal {\textsf {in}}}_{1}(k))\equiv G.\mathord {\textnormal {\textsf {fun}}}(k)\)
• -\(\mathord {\textnormal {\textsf {fun}}}(\mathord {\textnormal {\textsf {in}}}_{2}(k))\equiv \mathord {\textnormal {\textsf {codiag}}}(G.\mathord {\textnormal {\textsf {fun}}}(k))\)
• -\(\mathord {\textnormal {\textsf {Dom}}}\)と\(\mathord {\textnormal {\textsf {Cod}}}\)は\(\mathord {\textnormal {\textsf {fun}}}\)から決まる。