adjoin_contains_field_as_subfield

English

Adjoining a second set T to an already adjoined set S is the same as adjoining S ∪ T, up to restriction of scalars to F.

Русский

Объединение adjoin F S с T эквивалентно адьюнту S ∪ T (с ограничением скаляров к F).

LaTeX

$$$(\operatorname{adjoin}(\operatorname{adjoin}_F S) T).\restrictionScalars _ = \operatorname{adjoin}_F(S \cup T)$$$

Lean4

theorem adjoin_contains_field_as_subfield (F : Subfield E) : (F : Set E) ⊆ adjoin F S := fun x hx =>
  adjoin.algebraMap_mem F S ⟨x, hx⟩

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