reserve x,y, X,Y,Z for set,
        D for non empty set,
        n,k for Nat,
        i,i1,i2 for Integer;
reserve K for SimplicialComplexStr;
reserve KX for SimplicialComplexStr of X,
        SX for SubSimplicialComplex of KX;
reserve SC for SimplicialComplex of X;
reserve K for non void subset-closed SimplicialComplexStr;
reserve P for Function;

theorem Th61:
  subdivision(0,P,KX) = KX
 proof
  ex F be Function st F.0=KX & F.0=subdivision(0,P,KX) & dom F=NAT & for k for
KX1 be SimplicialComplexStr of X st KX1=F.k holds
F.(k+1)=subdivision(P,KX1) by Def21;
  hence thesis;
 end;
