Theorems · Theorem · combinatorics
Finset.Colex.isInitSeg_iff_exists_initSeg
∀ {α : Type u_1} [inst : LinearOrder α] {𝒜 : Finset (Finset α)} {r : ℕ} [inst_1 : Fintype α],
Finset.Colex.IsInitSeg 𝒜 r ∧ 𝒜.Nonempty ↔ ∃ s, s.card = r ∧ 𝒜 = Finset.Colex.initSeg sBeing a nonempty initial segment of colex is equivalent to being an initSeg.
- Defined in
- Mathlib.Combinatorics.Colex
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderFintype
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- LinearOrderstatement and proof · cited by 8,572
- Fintypestatement and proof · cited by 7,736
- Finset.cardstatement and proof · cited by 2,327
- Finset.Nonemptystatement and proof · cited by 1,001
- Finset.Colex.IsInitSegstatement and proof · cited by 9
- Finset.Colex.initSegstatement and proof · cited by 8
- Finset.Colex.IsInitSeg.exists_initSegproof · cited by 2
- Finset.Colex.isInitSeg_initSegproof · cited by 2
- Finset.Colex.initSeg_nonemptyproof · cited by 1
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