Section SubstitutionTransformations.
Variable (X: Const) (n: nat) (s t: exp X) (A: type) (Gamma: ctx).
Hypothesis (Leq: 1 <= n).
Hypothesis (T1:  Gamma ⊢(n) s : A) (T2: Gamma ⊢(n) t : A).
Implicit Types (Delta: ctx) (sigma : fin -> exp X).

Lemma ordertyping_normalise_subst sigma Delta :
Delta ⊩(n) sigma : Gamma -> {tau  | (forall x : fin, sigma x >* tau x) /\
(forall x : nat, x ∈ dom Gamma -> normal (tau x)) /\
Delta ⊩(n) tau : Gamma}.