instSemilatticeSupOfAddLeftMonoOfAddRightMono

English

For a proper space α and any x ∈ α, comap (dist x) atTop equals cocompact α.

Русский

Для правильного пространства α и любого x, comap (dist x) atTop совпадает с cocompact α.

LaTeX

$$$\operatorname{comap}(\operatorname{dist} x)\; \operatorname{atTop} = \operatorname{cocompact}(\alpha).$$$

Lean4

instance [AddZeroClass R] [SemilatticeSup R] [AddLeftMono R] [AddRightMono R] : SemilatticeSup (PseudoMetric X R)
    where
  sup := max
  le_sup_left := by simp [← PseudoMetric.coe_le_coe]
  le_sup_right := by simp [← PseudoMetric.coe_le_coe]
  sup_le _ _ _ := fun h h' _ _ ↦ sup_le (h _ _) (h' _ _)

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