Theorems · Theorem · ring theory
Algebra.map_iInf
∀ {R : Type u} {A : Type v} {B : Type w} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
[inst_3 : Semiring B] [inst_4 : Algebra R B] {ι : Sort u_1} [Nonempty ι] (f : A →ₐ[R] B),
Function.Injective ⇑f → ∀ (s : ι → Subalgebra R A), Subalgebra.map f (iInf s) = ⨅ i, Subalgebra.map f (s i)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Set.imageproof · cited by 5,609
- AlgHomstatement and proof · cited by 3,236
- iInfstatement and proof · cited by 1,690
- Subalgebrastatement and proof · cited by 1,353
- Set.iInterproof · cited by 1,084
- SetLike.coe_injectiveproof · cited by 374
- Subalgebra.mapstatement and proof · cited by 90
- Set.injOn_of_injectiveproof · cited by 28
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