Theorems · Theorem · ring theory
Algebra.mem_top
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] {x : A}, x ∈ ⊤- Cited by
- 10 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.
Cites6
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
- Top.topstatement · cited by 9,680
- Subalgebrastatement · cited by 1,353
- Set.mem_univproof · cited by 416
Cited by10
Results whose statement or proof uses this declaration.
- Algebra.eq_top_iffproof · cited by 13
- Polynomial.Gal.extproof · cited by 5
- Algebra.surjective_algebraMap_iffproof · cited by 4
- polynomialFunctions_separatesPointsproof · cited by 2
- Algebra.comap_topproof · cited by 1
- Algebra.FiniteType.iff_quotient_mvPolynomialproof · cited by 1
- IsCyclotomicExtension.union_leftproof · cited by 1
- Polynomial.Monic.quotient_isIntegralproof · cited by 0
- IsCyclotomicExtension.subsingleton_iffproof · cited by 0