reserve n for Nat;

theorem
  for G be Go-board for f,g be FinSequence of TOP-REAL 2 for k be
  Nat holds 1 <= k & k < len f & f^g is_sequence_on G implies
left_cell(f^g,k,G) = left_cell(f,k,G) & right_cell(f^g,k,G) = right_cell(f,k,G)
proof
  let G be Go-board;
  let f,g be FinSequence of TOP-REAL 2;
  let k be Nat;
  assume that
A1: 1 <= k and
A2: k < len f and
A3: f^g is_sequence_on G;
A4: k+1 <= len f by A2,NAT_1:13;
A5: (f^g)|len f = f by FINSEQ_5:23;
  len f <= len f + len g by NAT_1:11;
  then len f <= len (f^g) by FINSEQ_1:22;
  then k+1 <= len (f^g) by A4,XXREAL_0:2;
  hence thesis by A1,A3,A5,A4,GOBRD13:31;
end;
