ringEquiv_mixedSpace_apply — Mathlib

English

Reiteration of how ringEquiv_mixedSpace acts on an adele when interpreted through the mixed space representation.

Русский

Повторное изложение действия ringEquiv_mixedSpace на аделе через смешанное пространство.

LaTeX

$$$\\forall x,\\ ringEquiv\\_mixedSpace(K)\\, x = (\\text{fst}, \\text{snd})$$$

Lean4

@[simp]
theorem ringEquiv_mixedSpace_apply (x : InfiniteAdeleRing K) :
    ringEquiv_mixedSpace K x =
      (fun (v : { w : InfinitePlace K // IsReal w }) => extensionEmbeddingOfIsReal v.2 (x v),
        fun (v : { w : InfinitePlace K // IsComplex w }) => extensionEmbedding v.1 (x v)) :=
  rfl

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