Section Evaluation.
Variable (M : model).
Fixpoint eval (ρ : nat -> tpred) (s : poly_type) : tpred :=
match s with
| poly_var n => Var M (ρ n)
| poly_arr s t => Arr M (eval ρ s) (eval ρ t)
| poly_abs s => All M (fun d => eval (d .: ρ) s)
end.
Instance eval_ext :
Proper (pointwise_relation _ pw_iff ==> eq ==> pw_iff) eval.

Lemma eval_ren ξ s ρ :
eval ρ (ren_poly_type ξ s) == eval (ξ >> ρ) s.