English
The coercion of the difference of cusp forms equals the difference of their coercions: coe(f − g) = coe(f) − coe(g).
Русский
Приведение к функции разности кадрированных форм эквивалентно разности их приведённых значений: coe(f − g) = coe(f) − coe(g).
LaTeX
$$$\bigl(\text{CuspForm}.funLike\, \Gamma \ k \bigr).coe (f - g) = \bigl(\text{CuspForm}.funLike\, \Gamma \ k \bigr).coe f - \bigl(\text{CuspForm}.funLike\, \Gamma \ k \bigr).coe g$$$
Lean4
theorem sModNatTR_eq_sModNat (q i : ℕ) : sModNatTR q i = sModNat q i := by rw [sModNatTR, helper, sModNat_aux_eq]
where helper b q k : sModNatTR.go q k b = sModNat_aux b q k := by
induction k generalizing b with
| zero => rfl
| succ k ih =>
rw [sModNatTR.go, ih, sModNat_aux]
clear ih
induction k with
| zero => rfl
| succ k ih => rw [sModNat_aux, ih, sModNat_aux]
