Theorems · Theorem · general topology
IsMinFilter.filter_mono
∀ {α : Type u} {β : Type v} [inst : Preorder β] {f : α → β} {l : Filter α} {a : α} {l' : Filter α},
IsMinFilter f l a → l' ≤ l → IsMinFilter f l' a- Defined in
- Mathlib.Order.Filter.Extr
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Set.ofPredproof · cited by 6,101
- IsMinFilterstatement and proof · cited by 36
Cited by7
Results whose statement or proof uses this declaration.
- IsExtrFilter.filter_monoproof · cited by 4
- IsMinOn.localizeproof · cited by 3
- IsLocalMinOn.isLocalMinproof · cited by 2
- IsMinOn.of_isLocalMinOn_of_convexOn_Iccproof · cited by 1
- IsMinOn.on_subsetproof · cited by 1
- IsLocalMinOn.on_subsetproof · cited by 1
- IsMinFilter.filter_infproof · cited by 1