toIocMod_add_zsmul — Mathlib

English

For α with the given order and Archimedean property, the IcoMod with an added multiple of p is additive: toIcoMod hp a (b + m p) = toIcoMod hp a b + m p.

Русский

При заданном порядке и архимедовости: toIcoMod hp a (b + m p) = toIcoMod hp a b + m p.

LaTeX

$$$\operatorname{toIcoMod}\\_{hp} a (b + m \cdot p) = \operatorname{toIcoMod}\\_{hp} a b + m \cdot p$$$

Lean4

@[simp]
theorem toIocMod_add_zsmul (a b : α) (m : ℤ) : toIocMod hp a (b + m • p) = toIocMod hp a b :=
  by
  rw [toIocMod, toIocDiv_add_zsmul, toIocMod, add_smul]
  abel

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