reserve m,k,j,j1,i,i1,i2,n for Nat,
  r,s for Real,
  C for compact non vertical non horizontal Subset of TOP-REAL 2,
  G for Go-board,
  p for Point of TOP-REAL 2;

theorem Th34:
  for f being non empty FinSequence of TOP-REAL 2, G being
Go-board st f is_sequence_on G & (ex i st [1,i] in Indices G & G*(1,i) in rng f
  ) & (ex i st [i,1] in Indices G & G*(i,1) in rng f) & (ex i st [len G,i] in
  Indices G & G*(len G,i) in rng f) & (ex i st [i,width G] in Indices G & G*(i,
  width G) in rng f) holds G = GoB f
proof
  let f be non empty FinSequence of TOP-REAL 2, G being Go-board such that
A1: f is_sequence_on G;
  given i1 being Nat such that
A2: [1,i1] in Indices G & G*(1,i1) in rng f;
  given i2 being Nat such that
A3: [i2,1] in Indices G & G*(i2,1) in rng f;
  given i3 being Nat such that
A4: [len G,i3] in Indices G & G*(len G,i3) in rng f;
  given i4 being Nat such that
A5: [i4,width G] in Indices G & G*(i4,width G) in rng f;
A6: proj2.:rng f = proj2.:Values G by A1,A3,A5,Th31;
  proj1.:rng f = proj1.:Values G by A1,A2,A4,Th30;
  hence thesis by A6,Th33;
end;
