reserve x,y,X for set,
        r for Real,
        n,k for Nat;
reserve RLS for non empty RLSStruct,
        Kr,K1r,K2r for SimplicialComplexStr of RLS,
        V for RealLinearSpace,
        Kv for non void SimplicialComplex of V;

theorem Th16:
  |.Kv.| c= [#]Kv implies BCS(0,Kv) = Kv
 proof
  assume|.Kv.|c=[#]Kv;
  hence BCS(0,Kv)=subdivision(0,center_of_mass V,Kv) by Def6
   .=Kv by SIMPLEX0:61;
 end;
