hsum_add — Mathlib

English

Equivalences of summable families induced by a bijection between index types preserve the family structure.

Русский

Эквивалентности суммируемых семейств, порожденные биекция между индексами, сохраняют структуру семейства.

LaTeX

$$$\\text{Equiv}(e,s):\\ \\text{SummableFamily } Γ R α \\to SummableFamily Γ R β$ is defined by$ toFun b := s(e^{-1}(b))$$$

Lean4

@[simp]
theorem hsum_add {s t : SummableFamily Γ R α} : (s + t).hsum = s.hsum + t.hsum :=
  by
  ext g
  simp only [coeff_hsum, coeff_add, add_apply]
  exact finsum_add_distrib (s.finite_co_support _) (t.finite_co_support _)

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