theorem Th17:
  |.Kv.| c= [#]Kv implies BCS(1,Kv) = BCS Kv
 proof
  assume A1: |.Kv.|c=[#]Kv;
  hence BCS(1,Kv)=subdivision(1,center_of_mass V,Kv) by Def6
   .=subdivision(center_of_mass V,Kv) by SIMPLEX0:62
   .=BCS Kv by A1,Def5;
 end;
