Theorems · Theorem · group theory
AddSubgroup.relIndex_ker
∀ {G : Type u_1} {G' : Type u_2} [inst : AddGroup G] [inst_1 : AddGroup G'] (K : AddSubgroup G) (f : G →+ G'),
f.ker.relIndex K = Nat.card ↥(AddSubgroup.map f K)- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 97 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.
- 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
- AddSubgroup.mapstatement and proof · cited by 189
- AddMonoidHom.kerstatement · cited by 158
- AddSubgroup.relIndexstatement and proof · cited by 67
- AddSubgroup.relIndex_comapproof · cited by 7
- AddMonoidHom.comap_botproof · cited by 6
- AddSubgroup.relIndex_bot_leftproof · cited by 4
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