isCoatomistic — Mathlib

English

If every π(i) is topologically complete and coatomistic, then the Pi-product ∀ i, π(i) is coatomistic.

Русский

Если каждый π(i) кограничен и коатомарен, то произведение Pi ∀ i, π(i) коатомарно.

LaTeX

$$$ IsCoatomistic\left(\forall i,\ π(i)\right) $$$

Lean4

instance isCoatomistic [∀ i, CompleteLattice (π i)] [∀ i, IsCoatomistic (π i)] : IsCoatomistic (∀ i, π i) :=
  isAtomistic_dual_iff_isCoatomistic.1 <| show IsAtomistic (∀ i, (π i)ᵒᵈ) from inferInstance

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