From Undecidability.L Require Import Util.L_facts.
Notation "A '.[' i  ']'" := (elAt A i) (no associativity, at level 50).
Fixpoint appCross A B :=
match A with
| nil => nil
| a :: A => map (app a) B ++ appCross A B
end.
Fixpoint T n :=
match n with
| 0 => [#n]
| S n => let A := T n in A ++ [#(S n)] ++ filter (fun x => Dec (~ x el A)) ( map lam A ++ appCross A A )
end.

Lemma T_S s n m : T n .[ m ] = Some s -> T (S n).[ m ] = Some s.