theorem
  for KX be subset-closed SimplicialComplexStr of X
    for A be Subset of KX for S be finite-membered Subset-Family of A st
        S c= the topology of KX
      holds Complex_of S is strict SubSimplicialComplex of KX
 proof
  let KX be subset-closed SimplicialComplexStr of X;
  let A be Subset of KX;
  let S be finite-membered Subset-Family of A;
  A1: the_family_of KX is subset-closed;
  assume S c=the topology of KX;
  hence thesis by A1,Th3,Th28;
 end;
