ofMatrix_matrix — Mathlib

English

If a RingCon c is specified, then the ofMatrix construction gives an isomorphism-like behavior with matrix entries: ofMatrix (matrix n c) = c for nonempty index set and DecidableEq n.

Русский

Для RingCon c конструкция ofMatrix (matrix n c) действует подобно изоморфизму по записям матриц: ofMatrix (matrix n c) = c при непустом множестве индексов и DecidableEq n.

LaTeX

$$ofMatrix_matrix : ofMatrix (matrix n c) = c$$

Lean4

@[simp]
theorem ofMatrix_matrix [DecidableEq n] [Nonempty n] (c : RingCon R) : ofMatrix (matrix n c) = c :=
  by
  ext x y
  classical
  constructor
  · intro h
    inhabit n
    simpa using h default default default default
  · intro h i j
    rwa [matrix_apply_single]

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