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 Th18:
  |.Kv.| c= [#]Kv implies [#]BCS(n,Kv) = [#]Kv
 proof
  assume|.Kv.|c=[#]Kv;
  then BCS(n,Kv)=subdivision(n,center_of_mass V,Kv) by Def6;
  hence thesis by SIMPLEX0:64;
 end;
