apply — Mathlib

English

For nonzero x, the value of AddValuation x equals x.addValuationDef in the top-inflated sense.

Русский

Для ненулевого x значение AddValuation x равно x.addValuationDef в расширении вверх.

LaTeX

$$AddValuation(x) = x.addValuationDef$$

Lean4

@[simp]
theorem apply {x : ℚ_[p]} (hx : x ≠ 0) : Padic.addValuation x = (x.valuation : WithTop ℤ) := by
  simp only [Padic.addValuation, AddValuation.of_apply, addValuationDef, if_neg hx]

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