Section FirstOrderDecidable.
Variable (X: Const).
Implicit Types (Gamma: ctx) (n: nat) (sigma tau: fin -> exp X) (s t: exp X)
(E: list (exp X * exp X)).
Let free (k: nat) (x: nat) := x >= k.
Instance dec_free k: Dec1 (free k).

Lemma firstorder_decidable' (I: orduni 1 X):
ord' Gamma₀ <= 1 -> ord A₀ <= 2 ->
normal s₀ -> normal t₀ -> Dec (NOU 1 I).