reserve i,i1,i2,i9,i19,j,j1,j2,j9,j19,k,k1,k2,l,m,n for Nat;
reserve r,s,r9,s9 for Real;
reserve D for non empty set, f for FinSequence of D;
reserve f for FinSequence of TOP-REAL 2, G for Go-board;

theorem
  for G being Matrix of TOP-REAL 2 holds f is_sequence_on G implies rng
  f c= Values G
proof
  let G be Matrix of TOP-REAL 2;
  assume
A1: f is_sequence_on G;
  let y be object;
  assume y in rng f;
  then consider n being Element of NAT such that
A2: n in dom f and
A3: f/.n = y by PARTFUN2:2;
  ex i,j st [i,j] in Indices G & f/.n = G*(i,j) by A1,A2,GOBOARD1:def 9;
  then y in { G*(i,j): [i,j] in Indices G } by A3;
  hence thesis by MATRIX_0:39;
end;
