Theorems · Theorem · order theory
UpperSet.map_Ioi
∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] (f : α ≃o β) (a : α),
(UpperSet.map f) (UpperSet.Ioi a) = UpperSet.Ioi (f a)- Defined in
- Mathlib.Order.UpperLower.Principal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Preorderstatement and proof · cited by 7,952
- Set.extproof · cited by 2,266
- OrderIsostatement and proof · cited by 874
- UpperSetstatement · cited by 245
- UpperSet.extproof · cited by 29
- UpperSet.Ioistatement · cited by 15
- UpperSet.mapstatement · cited by 12
- OrderIso.image_Ioiproof · cited by 3
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