Mathlib Map

Theorems · Definition · group theory

AddSubgroup.unop

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

Pull an opposite additive subgroup back to an additive subgroup along AddOpposite.op

Defined in
Mathlib.Algebra.Group.Subgroup.MulOpposite
Cited by
30 results in Mathlib
Foundations
Depth 27 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.opEquiv · cited by 18AddSubgroup.opEquivAddSubgroup.op_unop · cited by 3AddSubgroup.op_unopAddSubgroup.unop_injective · cited by 2AddSubgroup.unop_injectiveAddSubgroup.normal_unop · cited by 2AddSubgroup.normal_unopAddSubgroup.unop_bot · cited by 1AddSubgroup.unop_botAddSubgroup.unop_top · cited by 1AddSubgroup.unop_topAddSubgroup.coe_unop · cited by 1AddSubgroup.coe_unopAddSubgroup.op_sInf · cited by 1AddSubgroup.op_sInfAddSubgroup.unop_closure · cited by 0AddSubgroup.unop_closureAddSubgroup.unop_eq_bot · cited by 0AddSubgroup.unop_eq_botAddSubgroup.unop_eq_top · cited by 0AddSubgroup.unop_eq_topAddSubgroup.le_op_iff · cited by 0AddSubgroup.le_op_iffAddSubgroup.unop_iInf · cited by 0AddSubgroup.unop_iInfAddSubgroup.unop_iSup · cited by 0AddSubgroup.unop_iSupAddSubgroup.unop_inf · cited by 0AddSubgroup.unop_infSetLike.coe · cited by 8199SetLike.coeSet.preimage · cited by 4946Set.preimageAddGroup · cited by 4410AddGroupAddSubgroup · cited by 3232AddSubgroupAddOpposite · cited by 452AddOppositeAddOpposite.op · cited by 192AddOpposite.opAddSubgroup.unopCITED BYCITES

Cites6

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

Cited by31

Results whose statement or proof uses this declaration.