reserve V for set;

theorem
  for M being PseudoMetricSpace, V,Q being Element of M-neighbour, v1,v2
  being Element of REAL holds V,Q is_dst v1 & V,Q is_dst v2 implies v1=v2
proof
  let M be PseudoMetricSpace, V,Q be Element of M-neighbour , v1,v2 be Element
  of REAL;
  assume that
A1: V,Q is_dst v1 and
A2: V,Q is_dst v2;
  consider p1 being Element of M such that
A3: V=p1-neighbour by Th15;
  consider q1 being Element of M such that
A4: Q=q1-neighbour by Th15;
A5: q1 in Q by A4,Th4;
A6: p1 in V by A3,Th4;
  then dist(p1,q1)=v1 by A1,A5;
  hence thesis by A2,A6,A5;
end;
