reserve X,x,y,z for set;
reserve n,m,k,k9,d9 for Nat;
reserve d for non zero Nat;
reserve i,i0,i1 for Element of Seg d;
reserve l,r,l9,r9,l99,r99,x,x9,l1,r1,l2,r2 for Element of REAL d;
reserve Gi for non trivial finite Subset of REAL;
reserve li,ri,li9,ri9,xi,xi9 for Real;
reserve G for Grating of d;

theorem Th47:
  for A being Cell of k,G, B being Cell of (k + 1),G holds
  B in star A iff A c= B
proof
  let A be Cell of k,G, B be Cell of (k + 1),G;
  defpred P[set] means A c= $1;
A1: star A = { B9 where B9 is Cell of (k + 1),G : P[B9] };
  thus B in star A iff P[B] from LMOD_7:sch 7(A1);
end;
