support_hsum_subset — Mathlib

English

The hsum of the sum of two summable families equals the sum of their hsum.

Русский

Сумма по Хана двух суммируемых семейств равна сумме их сумм по Хана.

LaTeX

$$$ (s+t).hsum = s.hsum + t.hsum $$$

Lean4

theorem support_hsum_subset {s : SummableFamily Γ R α} : s.hsum.support ⊆ ⋃ a : α, (s a).support := fun g hg =>
  by
  rw [mem_support, coeff_hsum, finsum_eq_sum _ (s.finite_co_support _)] at hg
  obtain ⟨a, _, h2⟩ := exists_ne_zero_of_sum_ne_zero hg
  rw [Set.mem_iUnion]
  exact ⟨a, h2⟩

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