Theorems · Theorem · field theory
IntermediateField.multiset_sum_mem
∀ {K : Type u_1} {L : Type u_2} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] (S : IntermediateField K L)
(m : Multiset L), (∀ a ∈ m, a ∈ S) → m.sum ∈ SSum of a multiset of elements in an IntermediateField is in the IntermediateField.
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- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Multisetstatement and proof · cited by 2,627
- IntermediateFieldstatement and proof · cited by 988
- Multiset.sumstatement · cited by 388
- multiset_sum_memproof · cited by 10
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