stabilizer_eq_bot — Mathlib

English

For an unramified w, the stabilizer is trivial.

Русский

Для неразмороженного w стабилизатор тривиален.

LaTeX

$$$Stab w = \\{1\\}$$$

Lean4

theorem stabilizer_eq_bot (h : IsUnramified k w) : Stab w = ⊥ :=
  by
  rw [eq_bot_iff, ← mk_embedding w, SetLike.le_def]
  simp only [mem_stabilizer_mk_iff, Subgroup.mem_bot, forall_eq_or_imp, true_and]
  exact fun σ hσ ↦ hσ.isUnramified_mk_iff.mp ((mk_embedding w).symm ▸ h)

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