map_val_Iic_atBot — Mathlib

English

The dual version: the mirror of gc on the dual order also yields map atTop = atTop.

Русский

Двойственная версия gc на двойственном порядке также даёт map atTop = atTop.

LaTeX

$$$\text{Предположим }\text{gc на }\alpha^\mathrm{op},\beta^\mathrm{op}:\map f\ atTop = atTop$$$

Lean4

/-- The `atBot` filter for an open interval `Iic a` comes from the `atBot` filter in the ambient
order. -/
@[simp]
theorem map_val_Iic_atBot [Preorder α] [IsDirected α (· ≥ ·)] (a : α) : map ((↑) : Iic a → α) atBot = atBot :=
  map_val_Ici_atTop (OrderDual.toDual a)

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