Theorems · Theorem · order theory
Set.exists_isChain_of_le_chainHeight
∀ {α : Type u_1} {r : α → α → Prop} {s : Set α} (n : ℕ), ↑n ≤ s.chainHeight r → ∃ t ⊆ s, t.encard = ↑n ∧ IsChain r t- Defined in
- Mathlib.Order.Height
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Setstatement and proof · cited by 53,352
- ENatstatement · cited by 4,985
- LE.le.transproof · cited by 3,151
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- Set.encardstatement and proof · cited by 327
- IsChainstatement and proof · cited by 158
- Set.chainHeightstatement and proof · cited by 22
- Set.encard_emptyproof · cited by 17
- IsChain.monoproof · cited by 3
- Set.exists_subset_encard_eqproof · cited by 3
- iSup_lt_iffproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Set.chainHeight_eq_of_relEmbeddingproof · cited by 2
- Set.chainHeight_eq_top_iffproof · cited by 0
- Set.chainHeight_flipproof · cited by 0
- Set.chainHeight_monoproof · cited by 0