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Theorems · Theorem · group theory

AddSubmonoid.op_sInf

∀ {M : Type u_2} [inst : AddZeroClass M] (S : Set (AddSubmonoid M)), (sInf S).op = sInf (AddSubmonoid.unop ⁻¹' S)
Defined in
Mathlib.Algebra.Group.Submonoid.MulOpposite
Cited by
1 results in Mathlib
Foundations
Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddZeroClass
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Around this declaration

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

AddSubmonoid.op_closure · cited by 2AddSubmonoid.op_closureSet · cited by 53352SetSet.preimage · cited by 4946Set.preimageAddZeroClass · cited by 1237AddZeroClassAddSubmonoid · cited by 1178AddSubmonoidInfSet.sInf · cited by 935InfSet.sInfAddOpposite · cited by 452AddOppositeAddSubmonoid.op · cited by 28AddSubmonoid.opAddSubmonoid.unop · cited by 25AddSubmonoid.unopOrderIso.map_sInf_eq_sInf_symm_preimage · cited by 18OrderIso.map_sInf_eq_sInf…AddSubmonoid.opEquiv · cited by 18AddSubmonoid.opEquivAddSubmonoid.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.