Theorems · Theorem · group theory
AddSubgroup.card_comap_dvd_of_injective
∀ {α : Type u_1} [inst : AddGroup α] {H : Type u_2} [inst_1 : AddGroup H] (K : AddSubgroup H) (f : α →+ H),
Function.Injective ⇑f → Nat.card ↥(AddSubgroup.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
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- Nat.cardstatement · cited by 844
- AddEquiv.toEquivproof · cited by 174
- Nat.card_congrproof · cited by 133
- AddSubgroup.comapstatement and proof · cited by 123
- AddSubgroup.equivMapOfInjectiveproof · cited by 3
- AddSubgroup.card_dvd_of_leproof · cited by 2
- AddSubgroup.map_comap_leproof · cited by 2
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