 We’ve called this way of presenting proofs “sequent natural deduction” to honour the way it is developed from sequent calculus. However, many…maybe even all…elementary logic textbooks that use such a system as their object to be taught call it simply “natural deduction”. Of these books, some even take the space (in an authorial introduction, usually) to argue that this is superior to other ways of doing natural deduction, especially from a pedogogical point of view. However, they don’t remark on the relation of this method to that of Gentzen’s single-conclusion sequent calculus.