equivProd — Mathlib

English

The infimum of the toFilter and the principal filter at iUnion equals the toFilterDistortion-infimum form.

Русский

Нижняя граница между toFilter и главной фильтрующей структурой на iUnion равна toFilterDistortion.

LaTeX

$$$\\text{toFilter}(l,I) \\;\\inf\\; \\mathcal{P}\\{\\pi : \\pi.iUnion = \\pi_0.iUnion\\} = \\text{toFilteriUnion}(l,I,\\pi_0).$$$

Lean4

/-- Auxiliary equivalence with a product type used to lift an order. -/
def equivProd : IntegrationParams ≃ Bool × Boolᵒᵈ × Boolᵒᵈ
    where
  toFun l := ⟨l.1, OrderDual.toDual l.2, OrderDual.toDual l.3⟩
  invFun l := ⟨l.1, OrderDual.ofDual l.2.1, OrderDual.ofDual l.2.2⟩

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