Theorems · Theorem · field theory
Subfield.prod_mem
∀ {K : Type u} [inst : Field K] (s : Subfield K) {ι : Type u_1} {t : Finset ι} {f : ι → K},
(∀ c ∈ t, f c ∈ s) → ∏ i ∈ t, f i ∈ sProduct of elements of a subfield indexed by a Finset is in the subfield.
- Defined in
- Mathlib.Algebra.Field.Subfield.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
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Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Fieldstatement and proof · cited by 7,404
- Finset.prodstatement · cited by 2,356
- Subfieldstatement and proof · cited by 303
- prod_memproof · cited by 16
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