
theorem
  for Y be non empty finite set,
  s be FinSequence of Y
  st Y={1} & s=<*1*> holds
  FDprobSEQ (s)=<*1*>
  proof
    let Y be non empty finite set, s be FinSequence of Y;
    assume
A1:  Y={1} & s=<*1*>;
    A2: dom s ={1} & s.1 = 1 by A1,FINSEQ_1:2,def 8;
    A3:len s=1&card Y =1 by A1,CARD_1:30;
    A4: dom s=Seg (card Y) by A2,A1,CARD_1:30,FINSEQ_1:2;
    rng s= {1} by A1,FINSEQ_1:39;
    then A5: 1 in rng s by TARSKI:def 1;
    A6: FDprobability((canFS(Y)).1,s)
    =FDprobability(<*1*>.1,s) by A1,FINSEQ_1:94
    .=FDprobability(1,s)
    .=1 by A1,A5,A3,FINSEQ_4:73;
    for n be Nat st n in dom s
    holds s.n=FDprobability((canFS(Y)).n,s)
    proof
      let n be Nat;
      assume n in dom s;
      then n=1 by A2,TARSKI:def 1;
      hence thesis by A6,A1;
    end;
    hence thesis by A4,A1,DIST_1:def 3;
  end;
