Theorems · Theorem · order theory
Set.dual_ordConnectedSection
∀ {α : Type u_1} [inst : LinearOrder α] (s : Set α),
(⇑OrderDual.ofDual ⁻¹' s).ordConnectedSection = ⇑OrderDual.ofDual ⁻¹' s.ordConnectedSection- Cited by
- 1 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Setstatement and proof · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Equivstatement · cited by 8,337
- Set.preimagestatement and proof · cited by 4,946
- Set.extproof · cited by 2,266
- OrderDualstatement and proof · cited by 927
- OrderDual.toDualproof · cited by 481
- OrderDual.ofDualstatement and proof · cited by 400
- Set.Nonempty.someproof · cited by 53
- Set.ordConnectedSectionstatement · cited by 7
- Set.Nonempty.some.congr_simpproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Set.compl_ordConnectedSection_ordSeparatingSet_mem_nhdsLEproof · cited by 1