
theorem Th4:
  for S be non empty finite set,
  D be Element of distribution_family(S),
  s,t be Element of D holds
  s,t -are_prob_equivalent
  proof
    let S be non empty finite set,
    D be Element of distribution_family(S),
    s,t be Element of D;
    consider x being FinSequence of S
    such that A1: D = Finseq-EQclass(x) by DIST_1:def 6;
    s,x -are_prob_equivalent
    & x,t -are_prob_equivalent by A1,DIST_1:7;
    hence thesis by DIST_1:6;
  end;
