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 Th6:
  for G being Matrix of TOP-REAL 2 for f being FinSequence of
  TOP-REAL 2 st f is_sequence_on G
  for k being Nat st 1 <= k & k <= len f holds f/.k in
  Values G
proof
  let G be Matrix of TOP-REAL 2;
  let f be FinSequence of TOP-REAL 2;
  assume that
A1: f is_sequence_on G;
  let k be Nat such that
A2: 1 <= k & k <= len f;
A3: k in dom f by A2,FINSEQ_3:25;
  then f/.k = f.k by PARTFUN1:def 6;
  then
A4: f/.k in rng f by A3,FUNCT_1:def 3;
  rng f c= Values G by A1,GOBRD13:8;
  hence thesis by A4;
end;
