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

theorem Th34:
  for f being non constant standard special_circular_sequence,
      i1,i2 being Nat st 1<=i1 & i1<i2 & i2<len f holds
        mid(f,i1,1)^mid(f,len f-'1,i2) is_a_part<_of f,i1,i2
proof
  let f be non constant standard special_circular_sequence, i1,i2 be Nat;
  assume that
A1: 1<=i1 and
A2: i1<i2 and
A3: i2<len f;
  Rev (mid(f,i2,len f-'1)^mid(f,1,i1)) =Rev(mid(f,1,i1))^Rev(mid(f,i2,len
  f-'1)) by FINSEQ_5:64
    .=mid(f,i1,1)^Rev(mid(f,i2,len f-'1)) by FINSEQ_6:196
    .=mid(f,i1,1)^mid(f,len f-'1,i2) by FINSEQ_6:196;
  hence thesis by A1,A2,A3,Th29,Th33;
end;
