Theorems · Theorem · group theory
Subgroup.card_comap_dvd_of_injective
∀ {α : Type u_1} [inst : Group α] {H : Type u_2} [inst_1 : Group H] (K : Subgroup H) (f : α →* H),
Function.Injective ⇑f → Nat.card ↥(Subgroup.comap f K) ∣ Nat.card ↥K- Defined in
- Mathlib.GroupTheory.Coset.Card
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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
- Subgroupstatement and proof · cited by 3,593
- Nat.cardstatement · cited by 844
- Subgroup.comapstatement and proof · cited by 154
- Nat.card_congrproof · cited by 133
- MulEquiv.toEquivproof · cited by 126
- Subgroup.equivMapOfInjectiveproof · cited by 7
- Subgroup.card_dvd_of_leproof · cited by 5
- Subgroup.map_comap_leproof · cited by 3
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