Theorems · Theorem · order theory
LowerSet.coe_map_apply
∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] (f : α ≃o β) (s : LowerSet α),
↑((LowerSet.map f) s) = ⇑f '' ↑s- Defined in
- Mathlib.Order.UpperLower.CompleteLattice
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- SetLike.coestatement · cited by 8,199
- Preorderstatement and proof · cited by 7,952
- Set.imagestatement · cited by 5,609
- OrderIsostatement and proof · cited by 874
- LowerSetstatement and proof · cited by 230
- LowerSet.mapstatement · cited by 12
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