theorem Th68:
  TS is deterministic implies for P, Q being RedSequence of
  ==>.-relation(TS) st P.1 = Q.1 & len P = len Q holds P = Q
proof
  assume
A1: TS is deterministic;
  let P, Q be RedSequence of ==>.-relation(TS) such that
A2: P.1 = Q.1 and
A3: len P = len Q;
  now
    let k;
    assume
A4: k in dom P;
    then 1 <= k & k <= len P by FINSEQ_3:25;
    then k in dom Q by A3,FINSEQ_3:25;
    hence P.k = Q.k by A1,A2,A4,Th67;
  end;
  hence thesis by A3,FINSEQ_2:9;
end;
