mapGL_inj — Mathlib

English

Same as previous: mapGL is injective under the usual assumptions.

Русский

Аналогично: mapGL инъективна при обычных предположениях.

LaTeX

$$Injective(\\mathrm{mapGL})$$

Lean4

@[simp]
theorem mapGL_inj [FaithfulSMul R S] (g g' : SpecialLinearGroup n R) : mapGL S g = mapGL S g' ↔ g = g' :=
  by
  refine ⟨fun h ↦ ?_, by tauto⟩
  apply SpecialLinearGroup.ext
  simpa [mapGL, toGL_inj, ext_iff, (FaithfulSMul.algebraMap_injective R S).eq_iff] using h

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