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
 |.Kv.| c= [#]Kv implies |.BCS(n,Kv).| = |.Kv.| by Th10;
