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Theorems · Theorem · group theory

AddSubsemigroup.op_sInf

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

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

AddSubsemigroup.op_closure · cited by 1AddSubsemigroup.op_closureSet · cited by 53352SetSet.preimage · cited by 4946Set.preimageInfSet.sInf · cited by 935InfSet.sInfAddOpposite · cited by 452AddOppositeAddSubsemigroup · cited by 262AddSubsemigroupAddSubsemigroup.op · cited by 28AddSubsemigroup.opAddSubsemigroup.unop · cited by 25AddSubsemigroup.unopAddSubsemigroup.opEquiv · cited by 18AddSubsemigroup.opEquivOrderIso.map_sInf_eq_sInf_symm_preimage · cited by 18OrderIso.map_sInf_eq_sInf…AddSubsemigroup.op_sInfCITED BYCITES

Cites9

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Cited by1

Results whose statement or proof uses this declaration.