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Theorems · Theorem · group theory

AddSubgroup.op_inj

∀ {G : Type u_2} [inst : AddGroup G] {S T : AddSubgroup G}, S.op = T.op ↔ S = T
Defined in
Mathlib.Algebra.Group.Subgroup.MulOpposite
Cited by
2 results in Mathlib
Foundations
Depth 30 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.unop_closure · cited by 0AddSubgroup.unop_closureAddSubgroup.unop_normalizer · cited by 0AddSubgroup.unop_normaliz…AddGroup · cited by 4410AddGroupAddSubgroup · cited by 3232AddSubgroupAddOpposite · cited by 452AddOppositeAddSubgroup.op · cited by 57AddSubgroup.opRelIso.eq_iff_eq · cited by 18RelIso.eq_iff_eqAddSubgroup.opEquiv · cited by 18AddSubgroup.opEquivAddSubgroup.op_injCITED BYCITES

Cites6

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

Cited by2

Results whose statement or proof uses this declaration.