coeff_ne_zero — Mathlib

English

If y is in mem, and near x, then coefficients stabilize on d ≤ c.

Русский

Если y в mem и близко к x, коэффициенты стабилизируются при d ≤ c.

LaTeX

$$$ coeff\_eq\_of\_mem(f, x, c)(hy) $$$

Lean4

/-- `f.val x` has a non-zero coefficient at the position of the Archimedean class of `x`. -/
theorem coeff_ne_zero [IsOrderedAddMonoid R] [Archimedean R] {x : f.val.domain} (hx0 : x.val ≠ 0) :
    (ofLex (f.val x)).coeff (FiniteArchimedeanClass.mk x.val hx0) ≠ 0 :=
  HahnSeries.coeff_orderTop_ne <| f.orderTop_eq_finiteArchimedeanClassMk hx0

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