reserve X,Y,Z,x,y,z for set;
reserve T,R for Tolerance of X;

theorem
  for x for Y being TolClass of T st x in Y holds Y c= neighbourhood(x,T )
proof
  let x;
  let Y be TolClass of T such that
A1: x in Y;
  for y being object st y in Y holds y in neighbourhood(x,T)
  proof
    let y be object;
    assume y in Y;
    then [x,y] in T by A1,Def1;
    hence thesis by Th27;
  end;
  hence thesis;
end;
