theorem Th32:
  k <= d & cell(l,r) in cells(k,G) implies for i holds l.i in G.i & r.i in G.i
proof
  assume that
A1: k <= d and
A2: cell(l,r) in cells(k,G);
  let i;
  l.i < r.i & [l.i,r.i] is Gap of G.i or l.i = r.i & l.i in G.i or
  r.i < l.i & [l.i,r.i] is Gap of G.i by A1,A2,Th31;
  hence thesis by Th13;
end;
