Mathlib Map

Theorems · Theorem · group theory

AddSubgroup.op_sInf

∀ {G : Type u_2} [inst : AddGroup G] (S : Set (AddSubgroup G)), (sInf S).op = sInf (AddSubgroup.unop ⁻¹' S)
Defined in
Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas
Cited by
1 results in Mathlib
Foundations
Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddGroup
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AddSubgroup.op_closure · cited by 2AddSubgroup.op_closureSet · cited by 53352SetSet.preimage · cited by 4946Set.preimageAddGroup · cited by 4410AddGroupAddSubgroup · cited by 3232AddSubgroupInfSet.sInf · cited by 935InfSet.sInfAddOpposite · cited by 452AddOppositeAddSubgroup.op · cited by 57AddSubgroup.opAddSubgroup.unop · cited by 30AddSubgroup.unopAddSubgroup.opEquiv · cited by 18AddSubgroup.opEquivOrderIso.map_sInf_eq_sInf_symm_preimage · cited by 18OrderIso.map_sInf_eq_sInf…AddSubgroup.op_sInfCITED BYCITES

Cites10

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

Cited by1

Results whose statement or proof uses this declaration.