apply preuve_compilation.
intros e V ML_b s C Trad_b hab CV Eq.
inversion_clear ML_b.
exists (val (elem b)).
split.
exact (Eqbool b).
inversion_clear Trad_b.
intro s0.
exact (QUO s0 CV (elem b)).
Qed.
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(*                  Case where E is an integer                               *)
(*****************************************************************************)

Lemma Proof_int : forall n : nat, compilation (Num n).
intro n.