  Focusing, introduced by Jean-Marc Andreoli in the context of classical linear
logic, defines a normal form for sequent calculus derivations that cuts down on
the number of possible derivations by eagerly applying invertible rules and
grouping sequences of non-invertible rules. A focused sequent calculus is
defined relative to some non-focused sequent calculus; focalization is the
property that every non-focused derivation can be transformed into a focused
derivation.
  In this paper, we present a focused sequent calculus for propositional
intuitionistic logic and prove the focalization property relative to a standard
presentation of propositional intuitionistic logic. Compared to existing
approaches, the proof is quite concise, depending only on the internal
soundness and completeness of the focused logic. In turn, both of these
properties can be established (and mechanically verified) by structural
induction in the style of Pfenning's structural cut elimination without the
need for any tedious and repetitious invertibility lemmas. The proof of cut
admissibility for the focused system, which establishes internal soundness, is
not particularly novel. The proof of identity expansion, which establishes
internal completeness, is a major contribution of this work.
