(* OK: *)

Lemma ring1_ring3_connect:
forall(m:fmap)(x x' xs xs':dart)(l:list),
let l1:= cons x x' (cons xs xs' l) in
let y  := cA m zero x in
let y' := cA m zero x' in
inv_hmap m -> planar m ->
double_link_list m l1 ->
pre_ring1 m l1 -> pre_ring3 m l1 ->
~ expf m y y'.