Theorems · Theorem · combinatorics
Finset.Colex.mem_initSeg
∀ {α : Type u_1} [inst : LinearOrder α] {s t : Finset α} [inst_1 : Fintype α],
t ∈ Finset.Colex.initSeg s ↔ s.card = t.card ∧ toColex t ≤ toColex s- Defined in
- Mathlib.Combinatorics.Colex
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 68 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Finsetstatement and proof · cited by 13,712
- LinearOrderstatement and proof · cited by 8,572
- Equivstatement · cited by 8,337
- Fintypestatement and proof · cited by 7,736
- Finset.cardstatement and proof · cited by 2,327
- Colexstatement · cited by 131
- toColexstatement and proof · cited by 90
- Finset.Colex.initSegstatement · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- Finset.Colex.IsInitSeg.exists_initSegproof · cited by 2
- Finset.Colex.isInitSeg_initSegproof · cited by 2