Mathlib Map

Theorems · Theorem · group theory

AddSubgroup.range_subtype

∀ {G : Type u_1} [inst : AddGroup G] (H : AddSubgroup G), H.subtype.range = H
Defined in
Mathlib.Algebra.Group.Subgroup.Ker
Cited by
16 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddGroup

Around this declaration

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

AddSubgroup.relIndex_comap · cited by 7AddSubgroup.relIndex_comapAddSubgroup.isAddCyclic_iff_exists_zmultiples_eq_top · cited by 4AddSubgroup.isAddCyclic_i…AddMonoidHom.ker_eq_bot_of_cancel · cited by 2AddMonoidHom.ker_eq_bot_o…AddSubgroup.map_subtype_addCommutator · cited by 2AddSubgroup.map_subtype_a…AddSubgroup.map_subtype_le · cited by 2AddSubgroup.map_subtype_leAddSubgroup.IsSubnormal.trans' · cited by 2IsSubnormal.trans'AddSubgroup.subtype_range · cited by 1AddSubgroup.subtype_rangeAddSubgroup.addSubgroupOf_normalizer_eq · cited by 1AddSubgroup.addSubgroupOf…AddSubgroup.addSubgroupOf_sup · cited by 1AddSubgroup.addSubgroupOf…AddSubgroup.injective_noncommPiCoprod_of_iSupIndep · cited by 0AddSubgroup.injective_non…AddSubgroup.noncommPiCoprod_range · cited by 0AddSubgroup.noncommPiCopr…AddSubgroup.independent_of_coprime_order · cited by 0AddSubgroup.independent_o…AddSubgroup.relIndex_inter_ne_zero · cited by 0AddSubgroup.relIndex_inte…AddSubgroup.Normal.addCommutator_le_of_self_sup_commutative_eq_top · cited by 0Normal.addCommutator_le_o…AddSubgroup.index_map_subtype · cited by 0AddSubgroup.index_map_sub…AddGroup · cited by 4410AddGroupAddSubgroup · cited by 3232AddSubgroupSetLike.coe_injective · cited by 374SetLike.coe_injectiveAddMonoidHom.range · cited by 142AddMonoidHom.rangeSubtype.range_coe · cited by 98Subtype.range_coeAddSubgroup.subtype · cited by 82AddSubgroup.subtypeAddMonoidHom.coe_range · cited by 4AddMonoidHom.coe_rangeAddSubgroup.range_subtypeCITED BYCITES

Cites7

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

Cited by16

Results whose statement or proof uses this declaration.