Theorems · Theorem · number theory
ThreeAPFree.le_rothNumberNat
∀ {k n : ℕ} (s : Finset ℕ), ThreeAPFree ↑s → (∀ x ∈ s, x < n) → s.card = k → k ≤ rothNumberNat nA verbose specialization of threeAPFree.le_addRothNumber, sometimes convenient in
practice.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- LE.le.transproof · cited by 3,151
- Finset.cardstatement and proof · cited by 2,327
- OrderHomstatement · cited by 934
- Eq.geproof · cited by 375
- Finset.mem_rangeproof · cited by 140
- ThreeAPFreestatement and proof · cited by 38
- rothNumberNatstatement · cited by 17
- ThreeAPFree.le_addRothNumberproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- Behrend.card_sphere_le_rothNumberNatproof · cited by 1