reserve G for Go-board,
  i,j,k,m,n for Nat;

theorem Th3:
  for D being non trivial set for f being non constant circular
  FinSequence of D holds len f > 2
proof
  let D be non trivial set;
  let f be non constant circular FinSequence of D;
  assume
A1: len f <= 2;
  per cases by A1,XXREAL_0:1;
  suppose
    len f < 1+1;
    then len f <= 1 by NAT_1:13;
    then reconsider f as trivial Function by Th2;
    f is constant;
    hence contradiction;
  end;
  suppose
A2: len f = 2;
    then
A3: dom f = {1,2} by FINSEQ_1:2,def 3;
    for n,m being Nat st n in dom f & m in dom f holds f.n=f.m
    proof
      let n,m be Nat such that
A4:   n in dom f and
A5:   m in dom f;
      per cases by A3,A4,A5,TARSKI:def 2;
      suppose
        n = 1 & m = 1 or n = 2 & m = 2;
        hence thesis;
      end;
      suppose that
A6:     n = 1 and
A7:     m = 2;
A8:     m in dom f by A3,A7,TARSKI:def 2;
        n in dom f by A3,A6,TARSKI:def 2;
        hence f.n = f/.1 by A6,PARTFUN1:def 6
          .= f/.len f by FINSEQ_6:def 1
          .= f.m by A2,A7,A8,PARTFUN1:def 6;
      end;
      suppose that
A9:     n = 2 and
A10:    m = 1;
A11:    n in dom f by A3,A9,TARSKI:def 2;
        m in dom f by A3,A10,TARSKI:def 2;
        hence f.m = f/.1 by A10,PARTFUN1:def 6
          .= f/.len f by FINSEQ_6:def 1
          .= f.n by A2,A9,A11,PARTFUN1:def 6;
      end;
    end;
    hence contradiction by SEQM_3:def 10;
  end;
end;
