replicateCol_injective — Mathlib

English

If the index type ι is nonempty, the column-replication map replicateCol ι: (m → α) → Matrix m ι α is injective.

Русский

Если множество индексов ι непустое, отображение копирования столбца injective: replicateCol ι : (m → α) → Matrix m ι α.

LaTeX

$$$$ \\text{Injective}(\\mathrm{replicateCol}\\; ι) $$$$

Lean4

theorem replicateCol_injective [Nonempty ι] : Function.Injective (replicateCol ι : (m → α) → Matrix m ι α) :=
  by
  inhabit ι
  exact fun _x _y h => funext fun i => congr_fun₂ h i default

Похожие утверждения