Theorems · Theorem · order theory
Set.exists_eq_chainHeight_of_chainHeight_ne_top
∀ {α : Type u_1} (s : Set α) (r : α → α → Prop), s.chainHeight r ≠ ⊤ → ∃ t ⊆ s, t.encard = s.chainHeight r ∧ IsChain r t- Defined in
- Mathlib.Order.Height
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Top.topstatement and proof · cited by 9,680
- ENatstatement and proof · cited by 4,985
- iSupproof · cited by 2,415
- Set.encardstatement and proof · cited by 327
- IsChainstatement and proof · cited by 158
- lt_top_iff_ne_topproof · cited by 95
- Set.chainHeightstatement and proof · cited by 22
- ENat.exists_eq_iSup_of_lt_topproof · cited by 5
- Set.chainHeight_eq_iSupproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Set.exists_eq_chainHeight_of_finiteproof · cited by 0