let rec p_closed xs = function
| Papp(_,ts) -> List.for_all (e_closed xs) ts
| Ptrue | Pfalse -> true
| Pimplies(p,q) | Pand(p,q) | Por(p,q) | Piff(p,q) ->
p_closed xs p && p_closed xs q
| Pif(t,p,q) ->
e_closed xs t && p_closed xs p && p_closed xs q
| Pnot p | Pnamed(_,p) -> p_closed xs p
| Pforall(x,p) | Pexists(x,p) -> p_closed (x::xs) p
| Plet(x,a,p) ->
e_closed xs a && p_closed (x::xs) p