theorem OrderedSpectrum.gap_ge_one (spec : OrderedSpectrum M) (k : Fin M)
(hk : (k : ℕ) + 1 < M) :
1 ≤ spec.gap k hk := by
unfold OrderedSpectrum.gap
rw [le_div_iff₀ (spec.pos ⟨(k : ℕ) + 1, hk⟩), one_mul]
exact spec.mono (Fin.mk_le_mk.mpr (Nat.le_succ _))Endogenous Hierarchy: Why N Levels?