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.

(* Specifications: *)
Lemma ltmx_trans m n : transitive (@ltmx m m n).
Lemma ltmx_irrefl m n : irreflexive (@ltmx m m n).
Lemma row_full_inj m n p A : row_full A -> injective (@mulmx _ m n p A).
Lemma row_free_inj m n p A : row_free A -> injective ((@mulmx _ m n p)^~ A).
Lemma addsmxSl : (A <= A + B)%MS.
Lemma addsmxSr : (B <= A + B)%MS.