completeLinearOrder — Mathlib

English

With dual Galois connections, the image infimum equals the dual-infimum composition.

Русский

При двойственных Гало-соединениях образ инфимума равен двойственной композиции инфимума.

LaTeX

$$$(h_1 : ∀ b, GaloisConnection (toDual ∘ l_1 b) (swap u b)) (h_2 : ∀ a, GaloisConnection (toDual ∘ l_2 a) (u a)) : s.Nonempty → BddBelow s → t.Nonempty → BddAbove t → sInf (image2 u s t) = u (sInf s) (sInf t)$$$

Lean4

noncomputable instance completeLinearOrder {α : Type*} [ConditionallyCompleteLinearOrder α] :
    CompleteLinearOrder (WithTop (WithBot α)) where
  __ := completeLattice
  __ := linearOrder
  __ := linearOrder.toBiheytingAlgebra

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