Section CompatibilityProperties.
Global Instance equiv_lam_proper:
Proper (equiv step ++> equiv step) (@lam X).
Global Instance equiv_app_proper:
Proper (equiv step ++> equiv step ++> equiv step) (@app X).
Global Instance ren_equiv_proper:
Proper (eq ++> equiv step ++> equiv step) (@ren X).

Lemma subst_equiv s t sigma:
s ≡ t -> sigma • s ≡ sigma • t.