 Claim (C0) holds for the [pseudobracket]{} $b'$ with ${\Delta}_{b'} := {\Delta}'_b$.  (0,0) circle (0); (0,-0) -(0,-0); (0,-0) -(0,-0.0); (-.0,0) -(.0,0); (0,-0) \[fill = black\] circle (.00); (0,-0) \[fill = black\] circle (.00); at (0,-0.0) [Fig. 0.0]{}; at (0,-.0) [$\Delta_b$]{}; at (-.0,-0.0) [$f$]{}; at (0,.0) [$