reserve i, i1, i2, j, k for Nat,
  r, s for Real;
reserve D for non empty set,
  f1 for FinSequence of D;

theorem
  for f being non constant standard special_circular_sequence,
      g being FinSequence of TOP-REAL 2,i1,i2 being Nat st
    g is_a_part_of f,i1,i2 holds
    1<=i1 & i1+1<=len f & 1<=i2 & i2+1<=len f & g.len g=f.i2 & 1<=len g &
    len g<len f & ((for i being Nat st 1<=i & i<=len g holds
      g.i=f.S_Drop((i1+i)-'1,f)) or
      for i being Nat st 1<=i & i<=len g holds
        g.i=f.S_Drop (len f +i1-'i,f) )
proof
  let f be non constant standard special_circular_sequence, g be FinSequence
  of TOP-REAL 2,i1,i2 be Nat;
  assume
A1: g is_a_part_of f,i1,i2;
  now
    per cases by A1;
    case
      g is_a_part>_of f,i1,i2;
      hence thesis;
    end;
    case
      g is_a_part<_of f,i1,i2;
      hence thesis;
    end;
  end;
  hence thesis;
end;
