Theorems · Theorem · group theory
AddSubgroup.index_comap_of_surjective
∀ {G : Type u_1} {G' : Type u_2} [inst : AddGroup G] [inst_1 : AddGroup G'] (H : AddSubgroup G) {f : G' →+ G},
Function.Surjective ⇑f → (AddSubgroup.comap f H).index = H.index- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- QuotientAddGroup.mkproof · cited by 348
- Nat.card_congrproof · cited by 133
- Quotient.mk''proof · cited by 132
- AddSubgroup.comapstatement and proof · cited by 123
- AddSubgroup.indexstatement · cited by 104
- Equiv.ofBijectiveproof · cited by 70
- AddMonoidHom.map_addproof · cited by 48
- Quotient.eq''proof · cited by 44
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.index_comapproof · cited by 4
- Module.Basis.SmithNormalForm.toAddSubgroup_index_eq_pow_mul_prodproof · cited by 1