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 Th6:
  RealOrd linearly_orders REAL
proof
  thus RealOrd is_reflexive_in REAL;
  thus RealOrd is_transitive_in REAL by Lm3;
  thus RealOrd is_antisymmetric_in REAL by Lm2;
  thus thesis by Lm4;
end;
