Theorems · Theorem · combinatorics
Finset.sup_preimage_self
∀ {α : Type u_1} {β : Type u_2} [Nonempty α] [inst : SemilatticeSup β] [inst_1 : OrderBot β] {s : Finset β} {f : α → β}
(hf : Set.BijOn f (f ⁻¹' ↑s) ↑s), (s.preimage f ⋯).sup f = s.sup id- Defined in
- Mathlib.Data.Finset.Preimage
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Set.preimagestatement and proof · cited by 4,946
- OrderBotstatement and proof · cited by 1,055
- Finset.imageproof · cited by 910
- SemilatticeSupstatement and proof · cited by 785
- Set.MapsTostatement · cited by 732
- Set.InjOnstatement · cited by 543
- Finset.supstatement and proof · cited by 530
- Set.SurjOnstatement · cited by 186
- Set.BijOnstatement and proof · cited by 168
- Finset.preimagestatement and proof · cited by 108
Cited by1
Results whose statement or proof uses this declaration.
- Finset.sup_preimage_val_idproof · cited by 0