reserve f for non empty FinSequence of TOP-REAL 2,
  i,j,k,k1,k2,n,i1,i2,j1,j2 for Nat,
  r,s,r1,r2 for Real,
  p,q,p1,q1 for Point of TOP-REAL 2,
  G for Go-board;
reserve f for non constant standard special_circular_sequence;

theorem Th37:
  for i,j being Nat st 1 < i & i < j & j <= len f holds f/.i <> f/.j
proof
  let i,j be Nat such that
A1: 1 < i and
A2: i < j and
A3: j <= len f;
  per cases by A3,XXREAL_0:1;
  suppose
    j < len f;
    hence thesis by A1,A2,Th36;
  end;
  suppose
    j = len f;
    then
A4: f/.j = f/.1 by FINSEQ_6:def 1;
    i < len f by A2,A3,XXREAL_0:2;
    hence thesis by A1,A4,Th36;
  end;
end;
