Section Unifiability.
Definition unifies sigma s t := sigma • s = sigma • t.
Definition Unifies sigma E := forall e, e ∈ E -> unifies sigma (fst e) (snd e).
Global Instance unifies_equiv sigma: Equivalence (unifies sigma).

Lemma Unifies_cons sigma e E:
Unifies sigma (e :: E) <-> unifies sigma (fst e) (snd e) /\ Unifies sigma E.