Theorems · Theorem · ring theory
Subring.unop_closure
∀ {R : Type u_2} [inst : NonAssocRing R] (s : Set Rᵐᵒᵖ),
(Subring.closure s).unop = Subring.closure (MulOpposite.op ⁻¹' s)- Defined in
- Mathlib.Algebra.Ring.Subring.MulOpposite
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonAssocRing
Around this declaration
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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
- MulOppositestatement and proof · cited by 1,135
- Subringstatement and proof · cited by 602
- MulOpposite.opstatement and proof · cited by 520
- NonAssocRingstatement and proof · cited by 483
- Subring.closurestatement and proof · cited by 78
- Set.preimage_preimageproof · cited by 36
- Subring.opproof · cited by 32
- Subring.unopstatement · cited by 25
- Subring.op_unopproof · cited by 1
- Subring.op_closureproof · cited by 1
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