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Theorems · Theorem · group theory

QuotientAddGroup.map_id_apply

∀ {G : Type u_1} [inst : AddGroup G] (N : AddSubgroup G) [nN : N.Normal]
  (h : optParam (N ≤ AddSubgroup.comap (AddMonoidHom.id G) N) ⋯) (x : G ⧸ N),
  (QuotientAddGroup.map N N (AddMonoidHom.id G) h) x = x
Defined in
Mathlib.GroupTheory.QuotientGroup.Defs
Cited by
1 results in Mathlib
Foundations
Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddGroupAddSubgroup.Normal
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Around this declaration

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

QuotientAddGroup.map_id · cited by 0QuotientAddGroup.map_idDFunLike.coe · cited by 62936DFunLike.coeAddGroup · cited by 4410AddGroupAddSubgroup · cited by 3232AddSubgroupAddMonoidHom · cited by 3230AddMonoidHomHasQuotient.Quotient · cited by 2301HasQuotient.QuotientEq.le · cited by 605Eq.leAddSubgroup.Normal · cited by 183AddSubgroup.NormalAddSubgroup.comap · cited by 123AddSubgroup.comapAddMonoidHom.id · cited by 107AddMonoidHom.idQuotientAddGroup.induction_on · cited by 33QuotientAddGroup.inductio…QuotientAddGroup.map · cited by 10QuotientAddGroup.mapAddSubgroup.comap_id · cited by 2AddSubgroup.comap_idQuotientAddGroup.map_id_applyCITED BYCITES

Cites12

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Cited by1

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