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 normalise_subst Delta sigma:
Delta ⊩ sigma : Gamma ->
{ tau | (forall x, sigma x >* tau x) /\
(forall x, x ∈ dom Gamma -> normal (tau x)) /\ Delta ⊩ tau : Gamma}.