Theorems · Theorem · group theory
AddSubmonoid.unop_closure
∀ {M : Type u_2} [inst : AddZeroClass M] (s : Set Mᵃᵒᵖ),
(AddSubmonoid.closure s).unop = AddSubmonoid.closure (AddOpposite.op ⁻¹' s)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddZeroClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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 and proof · cited by 4,946
- AddZeroClassstatement and proof · cited by 1,237
- AddSubmonoidstatement and proof · cited by 1,178
- AddOppositestatement and proof · cited by 452
- AddSubmonoid.closurestatement and proof · cited by 224
- AddOpposite.opstatement and proof · cited by 192
- Set.preimage_preimageproof · cited by 36
- AddSubmonoid.opproof · cited by 28
- AddSubmonoid.unopstatement · cited by 25
- AddSubmonoid.op_closureproof · cited by 2
- AddSubmonoid.op_unopproof · cited by 1
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