theorem
  R is being_linear-order implies R linearly_orders field R
proof
  assume that
A1: R is_reflexive_in field R and
A2: R is_transitive_in field R and
A3: R is_antisymmetric_in field R and
A4: R is_connected_in field R;
  thus R is_reflexive_in field R & R is_transitive_in field R & R
  is_antisymmetric_in field R & R is_connected_in field R by A1,A2,A3,A4;
end;
