elim inv_R_prod with e A B C D; auto with arith pts.
elim inv_R_prod with e A B C D; auto with arith pts.
Qed.
End Head_Normal_Products.
Section Algo_Conversion.
Let f (tr : env * (term * term)) :=
match tr with
| (e, (t1, t2)) => (e, t1)
end.

(* Specifications: *)
Theorem CR_WHNF_convert_hn :
forall (e : env) (x y : term),
sn (ctxt R) e x -> sn (ctxt R) e y -> decide (conv_hn_inv e x y).