Theorems · Theorem · general topology
IsExtrFilter.filter_mono
∀ {α : Type u} {β : Type v} [inst : Preorder β] {f : α → β} {l : Filter α} {a : α} {l' : Filter α},
IsExtrFilter f l a → l' ≤ l → IsExtrFilter f l' a- Defined in
- Mathlib.Order.Filter.Extr
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement and proof · cited by 8,121
- Preorderstatement and proof · cited by 7,952
- IsMaxFilterproof · cited by 38
- IsMinFilterproof · cited by 36
- IsExtrFilterstatement and proof · cited by 16
- IsMinFilter.isExtrproof · cited by 9
- IsMaxFilter.isExtrproof · cited by 8
- IsMinFilter.filter_monoproof · cited by 7
- IsMaxFilter.filter_monoproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- IsExtrOn.on_subsetproof · cited by 3
- IsExtrOn.localizeproof · cited by 1
- IsLocalExtrOn.on_subsetproof · cited by 1
- IsExtrFilter.filter_infproof · cited by 1