Lemma nf_L0L1_III:forall (m:fmap)(x y x' y':dart), let m1:=L (L m zero x y) one x' y' in let m2:=L (L m one x' y') zero x y in inv_hmap m1 -> let x_1 := cA_1 m one x in let y_0 := cA_1 m zero y in let y'0 := cA m zero y' in let x'1 := cA m one x' in let y'0b := cA (L m zero x y) zero y' in let x_1b := cA_1 (L m one x' y') one x in expf m x_1 y -> ~ expf m x' y'0 -> expf (L m one x' y') x_1b y -> expf (L m zero x y) x' y'0b -> False.