
theorem
  for S be non empty finite set,
  p be distProbFinS of S,
  s be FinSequence of S st FDprobSEQ (s)=p holds
  distribution( p,S )=Finseq-EQclass(s) &
  s in distribution( p,S )
  proof
    let S be non empty finite set,
    p be distProbFinS of S,
    s be FinSequence of S;
    assume A1: FDprobSEQ (s)=p;
    set D=Finseq-EQclass(s);
    reconsider D as Element of distribution_family(S) by DIST_1:def 6;
    (GenProbSEQ S).(Finseq-EQclass(s)) = p by A1,DIST_1:12; then
    D=distribution(p,S) by A1,DIST_1:def 8;
    hence thesis;
  end;
