Mathlib Map

Theorems · Definition · group theory

AddSubgroup.opEquiv

{G : Type u_2} → [inst : AddGroup G] → AddSubgroup G ≃o AddSubgroup Gᵃᵒᵖ

An additive subgroup H of G determines an additive subgroup H.op of the opposite additive group Gᵃᵒᵖ.

Defined in
Mathlib.Algebra.Group.Subgroup.MulOpposite
Cited by
18 results in Mathlib
Foundations
Depth 29 from the axioms · uses propext, Quot.sound
Assumes
AddGroup
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AddSubgroup.unop_injective · cited by 2AddSubgroup.unop_injectiveAddSubgroup.op_inj · cited by 2AddSubgroup.op_injAddSubgroup.op_injective · cited by 2AddSubgroup.op_injectiveAddSubgroup.unop_bot · cited by 1AddSubgroup.unop_botAddSubgroup.op_bot · cited by 1AddSubgroup.op_botAddSubgroup.op_sInf · cited by 1AddSubgroup.op_sInfAddSubgroup.unop_iInf · cited by 0AddSubgroup.unop_iInfAddSubgroup.unop_iSup · cited by 0AddSubgroup.unop_iSupAddSubgroup.unop_inj · cited by 0AddSubgroup.unop_injAddSubgroup.unop_sInf · cited by 0AddSubgroup.unop_sInfAddSubgroup.unop_sSup · cited by 0AddSubgroup.unop_sSupAddSubgroup.unop_sup · cited by 0AddSubgroup.unop_supAddSubgroup.opEquiv_apply · cited by 0AddSubgroup.opEquiv_applyAddSubgroup.opEquiv_symm_apply · cited by 0AddSubgroup.opEquiv_symm_…AddSubgroup.op_iInf · cited by 0AddSubgroup.op_iInfAddGroup · cited by 4410AddGroupAddSubgroup · cited by 3232AddSubgroupOrderIso · cited by 874OrderIsoAddOpposite · cited by 452AddOppositeAddSubgroup.op · cited by 57AddSubgroup.opAddSubgroup.unop · cited by 30AddSubgroup.unopAddSubgroup.op_unop · cited by 3AddSubgroup.op_unopAddSubgroup.unop_op · cited by 0AddSubgroup.unop_opAddSubgroup.op_le_op_iff · cited by 0AddSubgroup.op_le_op_iffAddSubgroup.opEquivCITED BYCITES

Cites9

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

Cited by18

Results whose statement or proof uses this declaration.