normalizer_mono — Mathlib

English

The pair of operations N ↦ [⊤,N] and N ↦ N.normalizer forms a Galois connection between LieSubmodules.

Русский

Пара отображений N ↦ [⊤,N] и N ↦ N.normalizer образует Галуа-отношение между подмодулями Ли.

LaTeX

$$$ \\text{GaloisConnection}\\left(\\lambda N. [\\top, N],\\ \\lambda N. N.normalizer\\right) $$$

Lean4

@[gcongr, mono]
theorem normalizer_mono (h : N₁ ≤ N₂) : normalizer N₁ ≤ normalizer N₂ :=
  by
  intro m hm
  rw [mem_normalizer] at hm ⊢
  exact fun x ↦ h (hm x)

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