Theorems · Theorem · ring theory
Subsemiring.op_sInf
∀ {R : Type u_2} [inst : NonAssocSemiring R] (S : Set (Subsemiring R)), (sInf S).op = sInf (Subsemiring.unop ⁻¹' S)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 67 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.
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
- MulOppositestatement · cited by 1,135
- InfSet.sInfstatement · cited by 935
- NonAssocSemiringstatement and proof · cited by 805
- Subsemiringstatement and proof · cited by 456
- Subsemiring.opstatement · cited by 43
- Subsemiring.unopstatement · cited by 26
- Subsemiring.opEquivproof · cited by 18
- OrderIso.map_sInf_eq_sInf_symm_preimageproof · cited by 18
Cited by1
Results whose statement or proof uses this declaration.
- Subsemiring.op_closureproof · cited by 2