let n be Nat; :: thesis: for V being RealLinearSpace
for Kv being non void SimplicialComplex of V st |.Kv.| c= [#] Kv holds
[#] (BCS (n,Kv)) = [#] Kv
let V be RealLinearSpace; :: thesis: for Kv being non void SimplicialComplex of V st |.Kv.| c= [#] Kv holds
[#] (BCS (n,Kv)) = [#] Kv
let Kv be non void SimplicialComplex of V; :: thesis: ( |.Kv.| c= [#] Kv implies [#] (BCS (n,Kv)) = [#] Kv )
assume |.Kv.| c= [#] Kv ; :: thesis: [#] (BCS (n,Kv)) = [#] Kv
then BCS (n,Kv) = subdivision (n,(center_of_mass V),Kv) by Def6;
hence [#] (BCS (n,Kv)) = [#] Kv by SIMPLEX0:64; :: thesis: verum