completeLinearOrder — Mathlib

English

In a fully dualized setting, the image infimum matches the composition of two infima.

Русский

В полностью двойственном виде инфимума образа совпадает с композицией двух инфимума.

LaTeX

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

Lean4

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

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