reserve i,j,k,n for Nat,
  D for non empty set,
  f, g for FinSequence of D;
reserve G for Go-board,
  f, g for FinSequence of TOP-REAL 2,
  p for Point of TOP-REAL 2,
  r, s for Real,
  x for set;

theorem Th23:
  2 <= len G & 2 <= width G & f is_sequence_on G & 1 <= k & k+1 <=
  len f & p in Values G & p in LSeg(f,k) implies p = f/.k or p = f/.(k+1)
proof
  assume that
A1: 2 <= len G & 2 <= width G & f is_sequence_on G and
A2: 1 <= k & k+1 <= len f and
A3: p in Values G and
A4: p in LSeg(f,k);
A5: LSeg(f,k) = LSeg(f/.k, f/.(k+1)) by A2,TOPREAL1:def 3;
  consider i,j being Nat such that
A6: 1 <= i & i+1 <= len G & 1 <= j & j+1 <= width G and
A7: LSeg(f,k) c= cell(G,i,j) by A1,A2,Th22;
  p is_extremal_in cell(G,i,j) by A3,A4,A6,A7,Th21;
  hence thesis by A4,A7,A5,SPPOL_1:def 1;
end;
