Mathlib Map

Theorems · Theorem · group theory

AddSubgroup.map_id

∀ {G : Type u_1} [inst : AddGroup G] (K : AddSubgroup G), AddSubgroup.map (AddMonoidHom.id G) K = K
Defined in
Mathlib.Algebra.Group.Subgroup.Map
Cited by
3 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext, Quot.sound
Assumes
AddGroup
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AddSubgroup.addCommutator_sum_sum · cited by 1AddSubgroup.addCommutator…AddSubgroup.normalCore_eq_iInf_map_addConj · cited by 1AddSubgroup.normalCore_eq…AddSubgroup.map_symm_eq_iff_map_eq · cited by 0AddSubgroup.map_symm_eq_i…SetLike.coe · cited by 8199SetLike.coeAddGroup · cited by 4410AddGroupAddSubgroup · cited by 3232AddSubgroupSetLike.coe_injective · cited by 374SetLike.coe_injectiveAddSubgroup.map · cited by 189AddSubgroup.mapAddMonoidHom.id · cited by 107AddMonoidHom.idSet.image_id · cited by 60Set.image_idAddSubgroup.map_idCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.