Theorems · Theorem · general topology
IsMaxOn.iSup_eq
∀ {α : Type u} {β : Type v} [inst : ConditionallyCompleteLinearOrder α] {f : β → α} {s : Set β} {x₀ : β},
x₀ ∈ s → IsMaxOn f s x₀ → ⨆ x, f ↑x = f x₀- Defined in
- Mathlib.Order.Filter.Extr
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Set.Elemstatement and proof · cited by 7,166
- iSupstatement · cited by 2,415
- ConditionallyCompleteLinearOrderstatement and proof · cited by 542
- IsMaxOnstatement and proof · cited by 114
- ciSup_eq_of_forall_le_of_forall_lt_exists_gtproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- IsMinOn.iInf_eqproof · cited by 1
- IsSelfAdjoint.hasEigenvector_of_isMaxOnproof · cited by 1