Fact genmx_key : unit.Definition genmx := locked_with genmx_key genmx_def.Fact addsmx_key : unit.Definition addsmx := locked_with addsmx_key addsmx_def.Fact capmx_key : unit.Definition capmx := locked_with capmx_key capmx_def.Fact diffmx_key : unit.Definition diffmx := locked_with diffmx_key diffmx_def.Local Notation GaussE := Gaussian_elimination.

Lemma ltmx_trans m n : transitive (@ltmx m m n).