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

theorem Th14:
  for D being set, f being FinSequence of D st k <= len f holds (1
  , k)-cut f = f|k
proof
  let D be set, f being FinSequence of D such that
A1: k <= len f;
  per cases;
  suppose
A2: 0+1 > k;
A3: f|0 = {};
    k = 0 by A2,NAT_1:13;
    hence thesis by A3,FINSEQ_6:def 4;
  end;
  suppose
A4: 1 <= k;
A5: len(f|k)+1 = k+1 by A1,FINSEQ_1:59;
    for i being Nat st i<len(f|k) holds (f|k).(i+1)= f.(1+i)
    proof
      let i be Nat;
      assume i<len(f|k);
      then i+1 <= k by A5,NAT_1:13;
      hence thesis by FINSEQ_3:112;
    end;
    hence thesis by A1,A4,A5,FINSEQ_6:def 4;
  end;
end;
