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

theorem Th27:
  for x,y being object holds y in neighbourhood(x,T) iff [x,y] in T
proof
  let x,y be object;
  hereby
    assume y in neighbourhood(x,T);
    then [y,x] in T by EQREL_1:19;
    hence [x,y] in T by EQREL_1:6;
  end;
  assume [x,y] in T;
  then [y,x] in T by EQREL_1:6;
  hence thesis by EQREL_1:19;
end;
