Theorems · Theorem · general topology
IsExtrOn.on_preimage
∀ {α : Type u} {β : Type v} {δ : Type x} [inst : Preorder β] {f : α → β} {s : Set α} (g : δ → α) {b : δ},
IsExtrOn f s (g b) → IsExtrOn (f ∘ g) (g ⁻¹' s) b- Defined in
- Mathlib.Order.Filter.Extr
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
- Assumes
- Preorder
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Cites11
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
- Set.preimagestatement · cited by 4,946
- IsMaxOnproof · cited by 114
- IsMinOnproof · cited by 96
- IsExtrOnstatement and proof · cited by 30
- IsMaxOn.isExtrproof · cited by 6
- IsMinOn.isExtrproof · cited by 6
- IsExtrOn.elimproof · cited by 5
- IsMinOn.on_preimageproof · cited by 1
- IsMaxOn.on_preimageproof · cited by 1
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