Mathlib Map

Theorems · Theorem · general topology

OrderIso.map_atBot

∀ {α : Type u_3} {β : Type u_4} [inst : Preorder α] [inst_1 : Preorder β] (e : α ≃o β),
  Filter.map (⇑e) Filter.atBot = Filter.atBot
Defined in
Mathlib.Order.Filter.AtTopBot.Map
Cited by
4 results in Mathlib
Foundations
Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PreorderPreorder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Real.map_exp_atBot · cited by 2Real.map_exp_atBotOrderIso.tendsto_atBot · cited by 1OrderIso.tendsto_atBotFilter.map_inv_atBot · cited by 1Filter.map_inv_atBotFilter.map_neg_atBot · cited by 1Filter.map_neg_atBotDFunLike.coe · cited by 62936DFunLike.coeFilter · cited by 8121FilterPreorder · cited by 7952PreorderOrderIso · cited by 874OrderIsoFilter.map · cited by 819Filter.mapFilter.atBot · cited by 512Filter.atBotOrderIso.dual · cited by 24OrderIso.dualOrderIso.map_atTop · cited by 11OrderIso.map_atTopOrderIso.map_atBotCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by4

Results whose statement or proof uses this declaration.