Section APD.
Variable X V R : Ensf.
Variable S' : Elt.
Hypothesis Gram : isGram X V R S'.
apply isGram4 with S'.
exact Gram.
Qed.
Let P := union X V.
Let f_R_d (a : Elt) :=
couple (word (cons (first a) nil)) (couple (eps X) (second a)).
Let f_X_d (x : Elt) := couple (word (cons x nil)) (couple x (word nil)).
Let d := union (map f_R_d R) (map f_X_d X).
Let wd := cons S' nil.
Let wa := nil.

Lemma Trans : Transition X P d.