Theorems · Theorem · general topology
Filter.map_val_Iio_atBot
∀ {α : Type u_3} [inst : Preorder α] [IsCodirectedOrder α] [NoMinOrder α] (a : α),
Filter.map Subtype.val Filter.atBot = Filter.atBotThe image of the filter atBot on Iio a under the coercion equals atBot.
- Defined in
- Mathlib.Order.Filter.AtTopBot.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Filterstatement · cited by 8,121
- Preorderstatement and proof · cited by 7,952
- Set.Iiostatement · cited by 1,166
- Filter.mapstatement and proof · cited by 819
- Filter.atBotstatement and proof · cited by 512
- NoMinOrderstatement and proof · cited by 247
- IsCodirectedOrderstatement and proof · cited by 95
- NoMinOrder.exists_ltproof · cited by 41
- Set.Iic_subset_Iioproof · cited by 12
- Filter.map_val_atBot_of_Iic_subsetproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Filter.tendsto_comp_val_Iio_atBotproof · cited by 0