(0 \otimes \Delta) \Delta = (\Delta \otimes 0)\Delta: {\U^{\imath}}_q(\mathfrak{sl}_{0r+0}) \longrightarrow {\U^{\imath}}_q(\mathfrak{sl}_{0r+0}) \otimes \U_q(\mathfrak{sl}_{0r+0}) \otimes \U_q(\mathfrak{sl}_{0r+0})