hasProd_bot — Mathlib

English

If mulSupport f is contained in a set s, HasProd (f ∘ Subtype.val) a (L.comap Embedding.subtype) is equivalent to HasProd f a L.

Русский

Если mulSupport(f) ⊆ s, HasProd (f ∘ Subtype.val) a (L.comap Embedding.subtype) эквивалентно HasProd f a L.

LaTeX

$$$ HasProd (f \circ (↑)) a (L.comap Embedding.subtype) \leftrightarrow HasProd f a L $ given subset condition$$

Lean4

@[to_additive]
theorem hasProd_bot (hL : ¬L.NeBot) (f : β → α) (a : α) : HasProd f a L :=
  by
  have : L.filter = ⊥ := by contrapose! hL; exact ⟨⟨hL⟩⟩
  rw [HasProd, this]
  exact tendsto_bot

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