Theorems · Theorem · ring theory
Subalgebra.mem_op
∀ {R : Type u_2} {A : Type u_3} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] {x : Aᵐᵒᵖ}
{S : Subalgebra R A}, x ∈ S.op ↔ MulOpposite.unop x ∈ S- Cited by
- 0 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Subalgebrastatement and proof · cited by 1,353
- MulOppositestatement and proof · cited by 1,135
- MulOpposite.unopstatement · cited by 268
- Subalgebra.opstatement · cited by 30
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