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 Th48:
  for A being Cell of k,G, C being Chain of (k + 1),G holds
  A in del C iff k + 1 <= d & card(star A /\ C) is odd
proof
  let A be Cell of k,G, C be Chain of (k + 1),G;
  defpred P[Cell of k,G] means k + 1 <= d & card(star $1 /\ C) is odd;
A1: del C = { A9 where A9 is Cell of k,G : P[A9] };
  thus A in del C iff P[A] from LMOD_7:sch 7(A1);
end;
