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 Th35:
  cell(l,r) in cells(0,G) iff l = r & for i holds l.i in G.i
proof
  hereby
    assume cell(l,r) in cells(0,G);
    then consider x such that
A1: cell(l,r) = cell(x,x) and
A2: for i holds x.i in G.i by Th34;
A3: for i holds x.i <= x.i;
    then l = x by A1,Th28;
    hence l = r & for i holds l.i in G.i by A1,A2,A3,Th28;
  end;
  thus thesis by Th34;
end;
