Notation sem_imp v rho A phi :=
    ((forall psi, psi el A -> ksat v rho psi) -> ksat v rho phi).(** ** Connection to Tarski Semantics *)

Instance interp_kripke {domain eta} (I : interp domain eta) : kmodel  eta :=
  {| nodes := unit ; reachable u v := True |}.Definition ksatis b (phi : form b) :=
  exists domain eta (M : @kmodel domain eta) u rho, ksat eta M u rho phi.

(* Specifications: *)
Lemma kvalid_valid b (phi : form b) : kvalid phi -> valid phi.
Lemma ksatis_satis b (phi : form b) : satis phi -> ksatis phi.