Theorems · Theorem · ring theory
Subsemiring.op_closure
∀ {R : Type u_2} [inst : NonAssocSemiring R] (s : Set R),
(Subsemiring.closure s).op = Subsemiring.closure (MulOpposite.unop ⁻¹' s)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 68 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.
Cites17
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
- SetLike.coeproof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- Set.preimagestatement and proof · cited by 4,946
- MulOppositestatement and proof · cited by 1,135
- InfSet.sInfproof · cited by 935
- NonAssocSemiringstatement and proof · cited by 805
- MulOpposite.opproof · cited by 520
- Subsemiringstatement and proof · cited by 456
- MulOpposite.unopstatement and proof · cited by 268
- Function.Surjective.forallproof · cited by 214
- InfSetproof · cited by 145
Cited by2
Results whose statement or proof uses this declaration.
- Subsemiring.unop_closureproof · cited by 1
- Subalgebra.op_adjoinproof · cited by 0