reserve i,j,k,n for Nat,
  D for non empty set,
  f, g for FinSequence of D;

theorem Th2:
  (for n holds f|n = g|n) implies f = g
proof
  assume
A1: for n holds f|n = g|n;
A2: now
    assume
A3: len f <> len g;
    per cases by A3,XXREAL_0:1;
    suppose
A4:   len f < len g;
A5:   g|len g = g by FINSEQ_1:58;
      f|len g = f by A4,FINSEQ_1:58;
      hence contradiction by A1,A4,A5;
    end;
    suppose
A6:   len g < len f;
      then f|len f = f & g|len f = g by FINSEQ_1:58;
      hence contradiction by A1,A6;
    end;
  end;
  f|len f = f & g|len g = g by FINSEQ_1:58;
  hence thesis by A1,A2;
end;
