pi_pure — Mathlib

English

Equivalence for mem_pi_pure including simplified simp lemmas.

Русский

Эквивалентность mem_pi_pure с упрощёнными леммами simp.

LaTeX

$$$\text{mem\_pi\_pure} \iff ...$$$

Lean4

/-- The indexed product of finitely many pure filters `pure (f i)` is the pure filter `pure f`.

If the index type is infinite, then `mem_pi_pure` and `hasBasis_pi_pure` below may be useful. -/
@[simp]
theorem pi_pure [Finite ι] (f : (i : ι) → α i) : pi (pure <| f ·) = pure f := by
  simp only [← principal_singleton, pi_principal, univ_pi_singleton]

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