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

theorem Th30:
  for f being non empty FinSequence of TOP-REAL 2 for g being non
  trivial FinSequence of TOP-REAL 2 st f/.len f = g/.1 holds LSeg(f^'g,len f) =
  LSeg(g,1)
proof
  let f be non empty FinSequence of TOP-REAL 2;
A1: 1 <= len f by NAT_1:14;
  let g be non trivial FinSequence of TOP-REAL 2;
  assume f/.len f = g/.1;
  then
A2: (f^'g)/.(len f +0) = g/.(0+1) by A1,FINSEQ_6:159;
A3: 1 < len g by Th2;
  then
A4: (f^'g)/.(len f +0+1) = g/.(0+1+1) by FINSEQ_6:160;
A5: 1+1 <= len g by A3,NAT_1:13;
  len f + 0+1 < len f + len g by A3,XREAL_1:6;
  then len f +0+1 < len (f^'g)+1 by FINSEQ_6:139;
  then len f +0+1 <= len (f^'g) by NAT_1:13;
  hence LSeg(f^'g,len f) = LSeg((f^'g)/.(len f+0),(f^'g)/.(len f+0+1)) by A1,
TOPREAL1:def 3
    .= LSeg(g,1) by A2,A4,A5,TOPREAL1:def 3;
end;
