Global Instance IB : interp (string bool) (fun _ => []) :=
{|
i_f b s := b :: s ;
i_e := nil;
i_P u v := derivable R u v ;
i_Q := BPCP' R
|}.

Lemma IB_drv rho t1 t2 :
rho ⊨ (Pr t1 t2) <-> derivable R (eval rho t1) (eval rho t2).