(* The following lemma also lives under the name KSI in other versions of this proof *)
Axiom
EXTE :
forall (D : Set) (x y : D -> proc), (forall d : D, x d = y d) -> x = y.
Section BPA.
Variable x y z : proc.

(* Specifications: *)
Axiom A1 : alt x y = alt y x.
Axiom A2 : alt x (alt y z) = alt (alt x y) z.
Axiom A3 : x = alt x x.
Axiom A4 : alt (seq x z) (seq y z) = seq (alt x y) z.
Axiom A5 : seq x (seq y z) = seq (seq x y) z.
Axiom A6 : x = alt x Delta.
Axiom A7 : Delta = seq Delta x.
End BPA.