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

theorem Th26:
  for f being special non empty FinSequence of TOP-REAL 2 for g
being special non trivial FinSequence of TOP-REAL 2 st f/.len f = g/.1 holds f
  ^'g is special
proof
  let f be special non empty FinSequence of TOP-REAL 2;
  let g be special non trivial FinSequence of TOP-REAL 2 such that
A1: f/.len f = g/.1;
  set h = (2, len g)-cut g;
A2: f^'g = f^(2, len g)-cut g by FINSEQ_6:def 5;
A3: 1+1 <= len g by NAT_D:60;
  then
A4: (g/.1)`1 = (g/.(1+1))`1 or (g/.1)`2 = (g/.(1+1))`2 by TOPREAL1:def 5;
  len g <= len g +1 by NAT_1:11;
  then
A5: 2<=len g+1 by A3,XXREAL_0:2;
  len h +1+1 = len h +(1+1) .= len g+1 by A5,Lm1;
  then 1 <= len h by A3,XREAL_1:6;
  then
A6: h/.1 = h.1 by FINSEQ_4:15
    .= g.(1+1) by A3,FINSEQ_6:138
    .= g/.(1+1) by A3,FINSEQ_4:15;
  h is special by Th25;
  hence thesis by A1,A2,A6,A4,GOBOARD2:8;
end;
