Theorems · Theorem · combinatorics
Finset.Colex.IsInitSeg.total
∀ {α : Type u_1} [inst : LinearOrder α] {𝒜₁ 𝒜₂ : Finset (Finset α)} {r : ℕ},
Finset.Colex.IsInitSeg 𝒜₁ r → Finset.Colex.IsInitSeg 𝒜₂ r → 𝒜₁ ⊆ 𝒜₂ ∨ 𝒜₂ ⊆ 𝒜₁Initial segments are nested in some way. In particular, if they're the same size they're equal.
- Defined in
- Mathlib.Combinatorics.Colex
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 83 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Finsetstatement and proof · cited by 13,712
- LinearOrderstatement and proof · cited by 8,572
- Finset.Nonemptyproof · cited by 1,001
- Colexproof · cited by 131
- toColexproof · cited by 90
- Finset.mem_sdiffproof · cited by 44
- trichotomous_ofproof · cited by 9
- Finset.Colex.IsInitSegstatement and proof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- Finset.kruskal_katonaproof · cited by 1