(** A Generalisation of Newmann's Lemma : Subsection 4.2 *)
Section StarWf.
Variable X: Set.
Variable S: relation X.
Variable TX: relation X.
Hypothesis HS: local_commute TX S.
Hypothesis Hwf: well_founded (trans (comp (plus S) (plus TX))).
Section Gen.
Variable Y: Type.
Variable R: relation2 X Y.
Variable TY: relation Y.
Let SR := comp (star S) R.
Hypothesis HR: diagram TX R (star TY) SR.

(** Lemma 4.5 *)
Lemma diagram_star_wf_1: diagram (star TX) SR (star TY) SR.
Variables X' Y': Type.