Theorems · Theorem · group theory
Subgroup.eq_of_le_of_card_ge
∀ {G : Type u_1} [inst : Group G] {H K : Subgroup G} [Finite ↥K], H ≤ K → Nat.card ↥K ≤ Nat.card ↥H → H = K- Defined in
- Mathlib.Algebra.Group.Subgroup.Finite
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coeproof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Finitestatement and proof · cited by 3,029
- Nat.cardstatement and proof · cited by 844
- SetLike.coe_injectiveproof · cited by 374
- Set.toFiniteproof · cited by 174
- Set.Finite.eq_of_subset_of_card_leproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.zpowers_eqproof · cited by 3
- Subgroup.eq_top_of_le_cardproof · cited by 2
- NumberField.Units.map_complexEmbedding_torsionproof · cited by 1