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

theorem Th31:
  for f being non empty FinSequence of TOP-REAL 2 for g being non
trivial FinSequence of TOP-REAL 2 st j+1 < len g & f/.len f = g/.1 holds LSeg(f
  ^'g,len f+j) = LSeg(g,j+1)
proof
  let f be non empty FinSequence of TOP-REAL 2;
  let g be non trivial FinSequence of TOP-REAL 2 such that
A1: j+1 < len g and
A2: f/.len f = g/.1;
  per cases by NAT_1:14;
  suppose
    j = 0;
    hence thesis by A2,Th30;
  end;
  suppose
    1 <= j;
    hence thesis by A1,Th29;
  end;
end;
