Theorems · Theorem · number theory
Finset.divConst_le_mulConst_sq
∀ {G : Type u_1} [inst : Group G] [inst_1 : DecidableEq G] {A : Finset G}, A.divConst A ≤ A.mulConst A ^ 2If A has small doubling, then it has small difference, with the constant squared.
This is a consequence of the Ruzsa triangle inequality.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupDecidableEq
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Cites19
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
- Groupstatement and proof · cited by 6,238
- Finset.cardproof · cited by 2,327
- mul_assocproof · cited by 1,667
- Finset.Nonemptyproof · cited by 1,001
- NNRatstatement and proof · cited by 523
- mul_posproof · cited by 374
- zero_powproof · cited by 361
- Nat.cast_pos'proof · cited by 219
- Finset.eq_empty_or_nonemptyproof · cited by 104
- Finset.Nonempty.card_posproof · cited by 55
- le_of_mul_le_mul_rightproof · cited by 26
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