theorem
  variables_in H1 <=> H2 = variables_in H1 \/ variables_in H2
proof
  thus variables_in H1 <=> H2 = variables_in H1 => H2 \/ variables_in H2 => H1
  by Th141
    .= variables_in H1 \/ variables_in H2 \/ variables_in H2 => H1 by Th144
    .= variables_in H1 \/ variables_in H2 \/ (variables_in H1 \/
  variables_in H2) by Th144
    .= variables_in H1 \/ variables_in H2;
end;
