Section Retyping.
Variable (X: Const).
Arguments s₀ {_} {_} _.
Arguments t₀ {_} {_} _.
Arguments Gamma₀ {_} {_} _.
Arguments A₀ {_} {_} _.
Definition retype_ctx (n: nat) (Gamma : ctx) :=
map (fun A => if dec2 le (ord A) n then A else alpha) Gamma.

Lemma retype_ctx_ord n Gamma: 1 <= n -> ord' (retype_ctx n Gamma) <= n.