addOppositeEquiv_leadingCoeff — Mathlib

English

The leading coefficient of the opposite Hahn series relates to the original leading coefficient via unop.

Русский

ПреleadingCoeff противоположной Hahn-серии относится к исходному через unop.

LaTeX

$$$$ (addOppositeEquiv x).unop.leadingCoeff = x.leadingCoeff.unop. $$$$

Lean4

@[simp]
theorem addOppositeEquiv_leadingCoeff (x : HahnSeries Γ Rᵃᵒᵖ) :
    (addOppositeEquiv x).unop.leadingCoeff = x.leadingCoeff.unop := by
  classical
  obtain rfl | hx := eq_or_ne x 0
  · simp
  simp only [ne_eq, AddOpposite.unop_eq_zero_iff, EmbeddingLike.map_eq_zero_iff, hx, not_false_eq_true,
    leadingCoeff_of_ne_zero, addOppositeEquiv_orderTop]
  simp [addOppositeEquiv]

Похожие утверждения