Mathlib Map

Theorems · Definition · group theory

AddSubmonoid.unop

{M : Type u_2} → [inst : AddZeroClass M] → AddSubmonoid Mᵃᵒᵖ → AddSubmonoid M

Pull an opposite additive submonoid back to a submonoid along AddOpposite.op

Defined in
Mathlib.Algebra.Group.Submonoid.MulOpposite
Cited by
25 results in Mathlib
Foundations
Depth 20 from the axioms · uses Quot.sound
Assumes
AddZeroClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AddSubmonoid.opEquiv · cited by 18AddSubmonoid.opEquivAddSubmonoid.unop_injective · cited by 2AddSubmonoid.unop_injecti…AddSubmonoid.op_sInf · cited by 1AddSubmonoid.op_sInfAddSubmonoid.op_unop · cited by 1AddSubmonoid.op_unopAddSubmonoid.unop_bot · cited by 1AddSubmonoid.unop_botAddSubmonoid.coe_unop · cited by 1AddSubmonoid.coe_unopAddSubmonoid.unop_top · cited by 1AddSubmonoid.unop_topAddSubmonoid.op_le_iff · cited by 0AddSubmonoid.op_le_iffAddSubmonoid.op_sSup · cited by 0AddSubmonoid.op_sSupAddSubmonoid.opEquiv_symm_apply · cited by 0AddSubmonoid.opEquiv_symm…AddSubgroup.unop_toAddSubmonoid · cited by 0AddSubgroup.unop_toAddSub…AddSubmonoid.unop_sInf · cited by 0AddSubmonoid.unop_sInfAddSubmonoid.unop_sSup · cited by 0AddSubmonoid.unop_sSupAddSubmonoid.mem_unop · cited by 0AddSubmonoid.mem_unopAddSubmonoid.unop_closure · cited by 0AddSubmonoid.unop_closureSetLike.coe · cited by 8199SetLike.coeSet.preimage · cited by 4946Set.preimageAddZeroClass · cited by 1237AddZeroClassAddSubmonoid · cited by 1178AddSubmonoidAddOpposite · cited by 452AddOppositeAddOpposite.op · cited by 192AddOpposite.opAddSubmonoid.unopCITED BYCITES

Cites6

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

Cited by26

Results whose statement or proof uses this declaration.