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).
End SubstitutionTransformations.
Variable (X: Const).
Arguments sᵤ {_} _.
Arguments tᵤ {_} _.
Arguments Gammaᵤ {_} _.
Arguments Aᵤ {_} _.

Lemma U_reduction (I I': uni X):
sᵤ I ≡ sᵤ I' -> tᵤ I ≡ tᵤ I' ->
Gammaᵤ I = Gammaᵤ I' -> Aᵤ I = Aᵤ I' ->
U X I -> U X I'.