theorem Th25:
  I is non empty trivial implies vol I = 0
  proof
    assume I is non empty trivial;
    then consider x be object such that
A1: I = {x} by ZFMISC_1:131;
    x in I by A1,TARSKI:def 1;
    then reconsider x as Real;
    vol {x} = 0 by COUSIN:41;
    hence thesis by A1;
  end;
