reserve i, j, n for Element of NAT,
  f, g, h, k for FinSequence of REAL,
  M, N for non empty MetrSpace;

theorem
  [:TopSpaceMetr Euclid i,TopSpaceMetr Euclid j:],
    TopSpaceMetr Euclid (i+j) are_homeomorphic
proof
 consider f be Function of [:TopSpaceMetr Euclid i,TopSpaceMetr Euclid j:],
   TopSpaceMetr Euclid (i+j) such that
A1:f is being_homeomorphism and
  for fi,fj be FinSequence st [fi,fj] in dom f holds f.(fi,fj) = fi^fj by Lm2;
 take f;
 thus thesis by A1;
end;
