Theorems · Theorem · order theory
Set.encard_le_chainHeight_of_isChain
∀ {α : Type u_1} {r : α → α → Prop} (s t : Set α), t ⊆ s → IsChain r t → t.encard ≤ s.chainHeight r- Defined in
- Mathlib.Order.Height
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 and proof · cited by 4,985
- Set.encardstatement and proof · cited by 327
- IsChainstatement and proof · cited by 158
- Set.chainHeightstatement · cited by 22
- le_iSup_iffproof · cited by 16
Cited by6
Results whose statement or proof uses this declaration.
- Set.chainHeight_eq_of_relEmbeddingproof · cited by 2
- Set.not_isChain_of_chainHeight_lt_encardproof · cited by 1
- Set.chainHeight_flipproof · cited by 0
- Set.chainHeight_monoproof · cited by 0
- Set.finite_of_chainHeight_ne_topproof · cited by 0
- Set.encard_eq_chainHeight_of_isChainproof · cited by 0