(* interpretation is invariant under context weakening *)
(* under assumption that the interpreted term is well-formed *)
Definition wf i t :=
match t with
Pts n _ => n < size (keyx i)
| Var n => n < size (varx i)
end.

Lemma sc_interp i j ts :
sub_ctx i j -> all (wf i) ts -> interp i ts = interp j ts.