Section CompatibilityProperties.
Global Instance lam_proper: Proper (star step ++> star step) lam.
Global Instance ren_step_proper:
Proper (eq ++> step ++> step) (@ren X).
Global Instance ren_steps_proper:
Proper (eq ++> star step ++> star step) (@ren X).

Lemma subst_steps s t sigma:
s >* t -> sigma • s >* sigma • t.