hasSum_iff_hasSum_compl — Mathlib

English

Analogous to congr_cofinite₀ but stated in the Multipliable namespace; if f is Multipliable and tail of equality holds, then g is Multipliable.

Русский

Аналогично congr_cofinite₀, но в пространстве Multipliable; если f Multipliable и выполняется условие равенств на хвосте, то g Multipliable.

LaTeX

$$$$ \text{Multipliable}(f) \rightarrow (\forall^\infty a, f(a)=g(a)) \rightarrow \text{Multipliable}(g). $$$$

Lean4

/-- A function `f` has a sum in an uniform additive group `α` if and only if it has that sum in the
completion of `α`. -/
theorem hasSum_iff_hasSum_compl (f : β → α) (a : α) : HasSum (toCompl ∘ f) a L ↔ HasSum f a L :=
  (isDenseInducing_toCompl α).hasSum_iff f a

Похожие утверждения