Theorems · Theorem · group theory
AddSubgroup.index_ker
∀ {G : Type u_1} {G' : Type u_2} [inst : AddGroup G] [inst_1 : AddGroup G'] (f : G →+ G'),
f.ker.index = Nat.card ↥f.range- Defined in
- Mathlib.GroupTheory.Index
- 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botproof · cited by 4,720
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- Nat.cardstatement and proof · cited by 844
- AddMonoidHom.kerstatement · cited by 158
- AddMonoidHom.rangestatement and proof · cited by 142
- AddSubgroup.indexstatement and proof · cited by 104
- AddMonoidHom.comap_botproof · cited by 6
- AddSubgroup.relIndex_bot_leftproof · cited by 4
- AddSubgroup.index_comapproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- AddGroup.isAddCyclic_of_coprime_card_range_card_kerproof · cited by 1
- IsAddCyclic.index_nsmulAddMonoidHom_kerproof · cited by 1
- AddSubgroup.index_rangeproof · cited by 1