Section DowncastLemmas.
Implicit Types (s t: exp X) (Gamma: ctx)  (A: type).
Variable (n: nat).
Hypothesis (Leq: 1 <= n).

Lemma ordertyping_from_basetyping Sigma u B:
(forall c, c ∈ consts u -> ord (ctype X c) <= S n) ->
Sigma ⊢ u : B -> normal u -> ord B <= S n -> ord' Sigma <= n ->
Sigma ⊢(n) u : B.