Local Notation simp := (Monoid.Theory.simpm, oppr0).Fact matrix_key : unit.Definition matrix_of_fun k := locked_with k matrix_of_fun_def.

(* Specifications: *)
Lemma mxE k F : matrix_of_fun k F =2 F.
Lemma matrixP (A B : matrix) : A =2 B <-> A = B.