Theorems · Theorem · ring theory
Subsemiring.unop_closure
∀ {R : Type u_2} [inst : NonAssocSemiring R] (s : Set Rᵐᵒᵖ),
(Subsemiring.closure s).unop = Subsemiring.closure (MulOpposite.op ⁻¹' s)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonAssocSemiring
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
- MulOppositestatement and proof · cited by 1,135
- NonAssocSemiringstatement and proof · cited by 805
- MulOpposite.opstatement and proof · cited by 520
- Subsemiringstatement and proof · cited by 456
- Subsemiring.closurestatement and proof · cited by 53
- Subsemiring.opproof · cited by 43
- Set.preimage_preimageproof · cited by 36
- Subsemiring.unopstatement · cited by 26
- Subsemiring.op_closureproof · cited by 2
- Subsemiring.op_injproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Subalgebra.unop_adjoinproof · cited by 0