Theorems · Theorem · group theory
Subgroup.card_dvd_of_injective
∀ {α : Type u_1} [inst : Group α] {H : Type u_2} [inst_1 : Group H] (f : α →* H),
Function.Injective ⇑f → Nat.card α ∣ Nat.card H- Defined in
- Mathlib.GroupTheory.Coset.Card
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 96 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.
- DFunLike.coestatement and proof · cited by 62,936
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- Nat.cardstatement · cited by 844
- MonoidHom.rangeproof · cited by 314
- Nat.card_congrproof · cited by 133
- Equiv.ofInjectiveproof · cited by 64
- Subgroup.card_subgroup_dvd_cardproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- Subgroup.card_dvd_of_leproof · cited by 5
- IsCyclic.normalizer_le_centralizerproof · cited by 2
- NumberField.torsionOrder_dvd_absNorm_sub_oneproof · cited by 0