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