+record pre_f_algebra (K:ordered_field_ch0) : Type ≝
+ { fa_archimedean_riesz_space:> archimedean_riesz_space K;
+ fa_algebra_:> algebra K;
+ fa_with: a_vector_space ? fa_algebra_ = rs_vector_space ? fa_archimedean_riesz_space
+ }.
+
+lemma fa_algebra: ∀K:ordered_field_ch0.pre_f_algebra K → algebra K.
+ intros (K A);
+ apply mk_algebra;
+ [ apply (rs_vector_space ? A)
+ | elim daemon
+ | elim daemon
+ | elim daemon
+ ]
+ qed.
+
+coercion cic:/matita/integration_algebras/fa_algebra.con.
+
+record is_f_algebra (K) (A:pre_f_algebra K) : Prop ≝