Section EncodingLemmas.
Variable (C: list X) (n: nat).
Hypothesis (O: ord' (map (ctype X) C) < n).

Lemma remove_constants_ordertypingSubst Delta sigma Gamma :
Delta ⊩(n) sigma : Gamma ->
(forall x c, c ∈ consts (sigma x) -> R' c = None -> c ∈ C) ->
enc_ctx C Delta ⊩(n) enc_subst C sigma : enc_ctx C Gamma.