Theorems · Theorem · group theory
AddSubsemigroup.unop_sSup
∀ {M : Type u_2} [inst : Add M] (S : Set (AddSubsemigroup Mᵃᵒᵖ)), (sSup S).unop = sSup (AddSubsemigroup.op ⁻¹' S)- Cited by
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- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Add
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.preimagestatement · cited by 4,946
- SupSet.sSupstatement · cited by 954
- OrderIso.symmproof · cited by 475
- AddOppositestatement and proof · cited by 452
- AddSubsemigroupstatement and proof · cited by 262
- AddSubsemigroup.opstatement · cited by 28
- AddSubsemigroup.unopstatement · cited by 25
- AddSubsemigroup.opEquivproof · cited by 18
- OrderIso.map_sSup_eq_sSup_symm_preimageproof · cited by 18
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