English
When the left argument of the energy is the entire set (univ), E_m[univ, t] equals |α| times |t|^2 for a finite type α with a group structure.
Русский
Если в левой аргументе энергии взять все элементы множества (univ), то E_m[univ, t] равно |α|·|t|^2 для конечного типа α с групповой структурой.
LaTeX
$$E_m[univ, t] = |α| · |t|^2$$
Lean4
@[to_additive]
theorem mulEnergy_comm (s t : Finset α) : Eₘ[s, t] = Eₘ[t, s] :=
by
rw [mulEnergy, ← Finset.card_map (Equiv.prodComm _ _).toEmbedding, map_filter]
simp [-Finset.card_map, mulEnergy, mul_comm, map_eq_image, Function.comp_def]