Theorems · Definition · order theory
Set.ordConnectedProj
{α : Type u_1} → [LinearOrder α] → (s : Set α) → ↑s → αProjection from s : Set α to α sending each order connected component of s to a single
point of this component.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 22 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.
Cites4
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
- LinearOrderstatement and proof · cited by 8,572
- Set.Elemstatement and proof · cited by 7,166
- Set.Nonempty.someproof · cited by 53
Cited by8
Results whose statement or proof uses this declaration.
- Set.ordConnectedSectionproof · cited by 7
- Set.ordConnectedProj_mem_ordConnectedComponentstatement · cited by 3
- Set.mem_ordConnectedComponent_ordConnectedProjstatement · cited by 2
- Set.ordConnectedComponent_ordConnectedProjstatement · cited by 1
- Set.ordConnectedProj_eqstatement and proof · cited by 1
- Set.ordConnectedSection_subsetproof · cited by 1
- Set.eq_of_mem_ordConnectedSection_of_uIcc_subsetproof · cited by 1
- Set.disjoint_ordT5Nhdproof · cited by 0