Theorems · Theorem · ring theory
Subalgebra.op_sSup
∀ {R : Type u_2} {A : Type u_3} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
(S : Set (Subalgebra R A)), (sSup S).op = sSup (Subalgebra.unop ⁻¹' S)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Set.preimagestatement · cited by 4,946
- Subalgebrastatement and proof · cited by 1,353
- MulOppositestatement · cited by 1,135
- SupSet.sSupstatement · cited by 954
- Subalgebra.opstatement · cited by 30
- Subalgebra.unopstatement · cited by 21
- Subalgebra.opEquivproof · cited by 18
- OrderIso.map_sSup_eq_sSup_symm_preimageproof · cited by 18
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