theorem Th34:
  R is being_partial-order implies R partially_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;
  thus R is_reflexive_in field R & R is_transitive_in field R & R
  is_antisymmetric_in field R by A1,A2,A3;
end;
