Local Notation simp := (Monoid.Theory.simpm, oppr0).Implicit Types m n p r : nat.Fact Gaussian_elimination_key : unit.Notation "\rank A" := (mxrank A) : nat_scope.Notation "''Z' ( R )" := (center_mx R) : matrix_set_scope.Fact submx_key : unit.Definition submx := locked_with submx_key submx_def.

(* Specifications: *)
Lemma ltmxE : (A < B)%MS = ((A <= B)%MS && ~~ (B <= A)%MS).
Lemma ltmxW : (A < B)%MS -> (A <= B)%MS.