theorem shareFunction_iia [NeZero J] {w : Fin J → ℝ}
(hw : ∀ j, 0 < w j) (j k : Fin J) :
shareFunction w j / shareFunction w k = w j / w k := by
simp only [shareFunction]
have hsum : (0 : ℝ) < ∑ i, w i :=
Finset.sum_pos (fun i _ => hw i) Finset.univ_nonempty
field_simp [ne_of_gt hsum, ne_of_gt (hw k)]Ten Views of a Single Object: