Notation sem_imp v rho A phi :=
((forall psi, psi el A -> ksat v rho psi) -> ksat v rho phi).

(* Specifications: *)
Lemma impl_ksat {b} u A rho (phi : form b) :
ksat u rho (A ==> phi) <-> (forall v, reachable u v -> sem_imp v rho A phi).
Lemma impl_ksat' {b} u A rho (phi : form b) :
ksat u rho (A ==> phi) -> (forall v, reachable u v -> sem_imp v rho A phi).