Mathlib Map

Theorems · Definition · group theory

AddSubgroup.op

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

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

Defined in
Mathlib.Algebra.Group.Subgroup.MulOpposite
Cited by
57 results in Mathlib
Foundations
Depth 26 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.

QuotientAddGroup.leftRel · cited by 34QuotientAddGroup.leftRelAddSubgroup.opEquiv · cited by 18AddSubgroup.opEquivAddSubgroup.equivOp · cited by 5AddSubgroup.equivOpAddSubgroup.normal_op · cited by 3AddSubgroup.normal_opAddSubgroup.op_unop · cited by 3AddSubgroup.op_unopAddSubgroup.mem_op · cited by 3AddSubgroup.mem_opisAddFundamentalDomain_Ioc' · cited by 2isAddFundamentalDomain_Io…QuotientAddGroup.sound · cited by 2QuotientAddGroup.soundAddSubgroup.op_closure · cited by 2AddSubgroup.op_closureAddSubgroup.op_inj · cited by 2AddSubgroup.op_injAddSubgroup.op_injective · cited by 2AddSubgroup.op_injectiveMeasureTheory.AddQuotientMeasureEqMeasurePreimage.addInvariantMeasure_quotient · cited by 2AddQuotientMeasureEqMeasu…AddSubgroup.op_normalizer · cited by 2AddSubgroup.op_normalizerMeasureTheory.Measure.IsAddLeftInvariant.addQuotientMeasureEqMeasurePreimage_of_set · cited by 2IsAddLeftInvariant.addQuo…QuotientAddGroup.orbit_eq_out_vadd · cited by 1QuotientAddGroup.orbit_eq…SetLike.coe · cited by 8199SetLike.coeSet.preimage · cited by 4946Set.preimageAddGroup · cited by 4410AddGroupAddSubgroup · cited by 3232AddSubgroupAddOpposite · cited by 452AddOppositeAddOpposite.unop · cited by 125AddOpposite.unopAddSubgroup.zero_mem · cited by 23AddSubgroup.zero_memAddSubgroup.opCITED BYCITES

Cites7

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

Cited by60

Results whose statement or proof uses this declaration.