Theorems · Theorem · group theory
AddSubgroup.index_map_of_bijective
∀ {G : Type u_1} {G' : Type u_2} [inst : AddGroup G] [inst_1 : AddGroup G'] {f : G →+ G'},
Function.Bijective ⇑f → ∀ (H : AddSubgroup G), (AddSubgroup.map f H).index = H.index- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Function.Bijectivestatement and proof · cited by 863
- bot_leproof · cited by 306
- AddSubgroup.mapstatement · cited by 189
- AddSubgroup.indexstatement · cited by 104
- AddMonoidHom.ker_eq_botproof · cited by 7
- AddSubgroup.index_map_eqproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.index_map_equivproof · cited by 2
- AddSubgroup.index_smulproof · cited by 0