Definition planar(m:fmap):= genus m = 0.

Lemma expf_planar_L0: forall (m:fmap)(x y:dart), inv_qhmap m -> planar m -> prec_Lq m di0 x y -> let mc:= clos m in (~eqc mc x y \/ expf mc (A_1 mc di1 x) y) -> planar (L m di0 x y).