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 Th55:
  for C being Chain of d,G holds C` = C + Omega(G)
proof
  let C be Chain of d,G;
  C /\ cells(d,G) = C by XBOOLE_1:28;
  hence thesis by XBOOLE_1:100;
end;
