  This article proves that an irreducible subfactor planar algebra with a
distributive biprojection lattice admits a minimal 2-box projection generating
the identity biprojection. It is a generalization (conjectured in 2013) of a
theorem of Oystein Ore on distributive intervals of finite groups (1938), and a
corollary of a natural subfactor extension of a conjecture of Kenneth S. Brown
in algebraic combinatorics (2000). We deduce a link between combinatorics and
representations in finite group theory.
