Theorems · Theorem · ring theory
StarAlgebra.mem_adjoin_of_mem
∀ (R : Type u_2) {A : Type u_3} [inst : CommSemiring R] [inst_1 : StarRing R] [inst_2 : Semiring A]
[inst_3 : Algebra R A] [inst_4 : StarRing A] [inst_5 : StarModule R A] {s : Set A} {x : A},
x ∈ s → x ∈ StarAlgebra.adjoin R s- Defined in
- Mathlib.Algebra.Star.Subalgebra
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
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
- StarRingstatement and proof · cited by 1,686
- StarModulestatement and proof · cited by 570
- StarSubalgebrastatement · cited by 194
- StarAlgebra.adjoinstatement · cited by 42
- StarAlgebra.subset_adjoinproof · cited by 10
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