logMap_unit_smul — Mathlib

English

For x,y ∈ 𝓞 K and u ∈ units, u • mixedEmbedding(K,x) = mixedEmbedding(K,y) iff u*x = y.

Русский

Для x,y ∈ 𝓞 K и u ∈ единицы, u • вложение(x) = вложение(y) тогда и только тогда, когда u*x = y.

LaTeX

$$$u \cdot \text{mixedEmbedding}(K,x) = \text{mixedEmbedding}(K,y) \iff u x = y$$$

Lean4

theorem logMap_unit_smul (u : (𝓞 K)ˣ) (hx : mixedEmbedding.norm x ≠ 0) :
    logMap (u • x) = logEmbedding K (Additive.ofMul u) + logMap x := by
  rw [unitSMul_smul, logMap_mul (by rw [norm_unit]; norm_num) hx, logMap_eq_logEmbedding]

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