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 Th20:
  x in cell(l,r) iff ((for i holds l.i <= x.i & x.i <= r.i) or
  ex i st r.i < l.i & (x.i <= r.i or l.i <= x.i) )
proof
  defpred P[Element of REAL d] means (for i holds l.i <= $1.i & $1.i <= r.i) or
  (ex i st r.i < l.i & ($1.i <= r.i or l.i <= $1.i));
A1: cell(l,r) = { x9 :  P[x9] };
  thus x in cell(l,r) iff P[x] from LMOD_7:sch 7(A1);
end;
