Theorems · Theorem · number theory
IsApproximateSubgroup.card_pow_le
∀ {G : Type u_1} [inst : Group G] {K : ℝ} [inst_1 : DecidableEq G] {A : Finset G},
IsApproximateSubgroup K ↑A → ∀ {n : ℕ}, ↑(A ^ n).card ≤ K ^ (n - 1) * ↑A.card- Cited by
- 1 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
- Finset.cardstatement and proof · cited by 2,327
- pow_zeroproof · cited by 1,094
- pow_oneproof · cited by 894
- mul_le_mul_of_nonneg_rightproof · cited by 301
- Nat.cast_nonneg'proof · cited by 245
- tsub_selfproof · cited by 154
Cited by1
Results whose statement or proof uses this declaration.
- IsApproximateSubgroup.card_mul_self_leproof · cited by 0