reserve G for Go-board,
  i,j,k,m,n for Nat;
reserve f,g,g1,g2 for FinSequence of TOP-REAL 2;

theorem Th35:
  f is non empty & g is non trivial & f/.len f = g/.1 implies
  L~(f^'g) = L~f \/ L~g
proof
  assume that
A1: f is non empty and
A2: g is non trivial and
A3: f/.len f = g/.1;
  set c = (1+1, len g)-cut g;
A4: c = g/^1 by Th13;
A5: len g > 1 by A2,Th2;
  then len c = len g - 1 by A4,RFINSEQ:def 1;
  then len c > 1-1 by A5,XREAL_1:9;
  then len c > 0;
  then
A6: c is non empty;
  g is not empty by A2;
  then g = <*g/.1*>^c by A4,FINSEQ_5:29;
  then
A7: LSeg(g/.1,c/.1) \/ L~c = L~g by A6,SPPOL_2:20;
  L~(f^c) = L~f \/ LSeg(f/.(len f),c/.1) \/ L~c by A1,A6,SPPOL_2:23
    .= L~f \/ (LSeg(g/.1,c/.1) \/ L~c) by A3,XBOOLE_1:4;
  hence thesis by A7,FINSEQ_6:def 5;
end;
