Theorems · Theorem · ring theory
Algebra.iInf_toSubmodule
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] {ι : Sort u_1}
(S : ι → Subalgebra R A), Subalgebra.toSubmodule (⨅ i, S i) = ⨅ i, Subalgebra.toSubmodule (S i)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 77 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.
Cites14
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
- SetLike.coeproof · cited by 8,199
- Submodulestatement · cited by 7,192
- iInfstatement and proof · cited by 1,690
- Subalgebrastatement and proof · cited by 1,353
- Set.iInterproof · cited by 1,084
- OrderEmbeddingstatement · cited by 619
- SetLike.coe_injectiveproof · cited by 374
- Subalgebra.toSubmodulestatement and proof · cited by 141
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