Theorems · Theorem · general topology
IsMaxOn.on_subset
∀ {α : Type u} {β : Type v} [inst : Preorder β] {f : α → β} {s : Set α} {a : α} {t : Set α},
IsMaxOn f t a → s ⊆ t → IsMaxOn f s a- Defined in
- Mathlib.Order.Filter.Extr
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- IsMaxOnstatement and proof · cited by 114
- Filter.principal_monoproof · cited by 30
- IsMaxFilter.filter_monoproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- Complex.norm_eq_norm_of_isMaxOn_of_ball_subsetproof · cited by 3
- Complex.exists_mem_frontier_isMaxOn_normproof · cited by 1
- IsMaxOn.interproof · cited by 0