Theorems · Theorem · ring theory
StarSubalgebra.sInf_toSubalgebra
∀ {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 (StarSubalgebra R A)),
(sInf S).toSubalgebra = sInf (StarSubalgebra.toSubalgebra '' S)- Defined in
- Mathlib.Algebra.Star.Subalgebra
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites20
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- 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
- SetLike.coeproof · cited by 8,199
- Set.imagestatement and proof · cited by 5,609
- StarRingstatement and proof · cited by 1,686
- Subalgebrastatement and proof · cited by 1,353
- Set.iInterproof · cited by 1,084
- InfSet.sInfstatement and proof · cited by 935
- StarModulestatement and proof · cited by 570
- SetLike.coe_injectiveproof · cited by 374
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