theorem Th61:
  x = y & r > 0 implies Ball(y,r) is a_neighborhood of x
  proof
    assume that
A1: x = y and
A2: r > 0;
    reconsider S = ]. x - r , x + r .[ as Subset of FMT_R^1
      by TOPMETR:17,FINTOPO7:def 15;
    S is a_neighborhood of x by A2,Th58;
    hence thesis by A1,FRECHET:7;
  end;
