Theorems · Theorem · combinatorics
Finset.Colex.IsInitSeg.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 s- Defined in
- Mathlib.Combinatorics.Colex
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- SetLike.coeproof · cited by 8,199
- Fintypestatement and proof · cited by 7,736
- Set.preimageproof · cited by 4,946
- Finset.cardstatement and proof · cited by 2,327
- Finset.Nonemptystatement and proof · cited by 1,001
- Finset.extproof · cited by 565
- LE.le.eq_or_ltproof · cited by 220
- Finset.sup'proof · cited by 174
- toColexproof · cited by 90
Cited by2
Results whose statement or proof uses this declaration.
- Finset.Colex.IsInitSeg.shadowproof · cited by 1
- Finset.Colex.isInitSeg_iff_exists_initSegproof · cited by 0