(* CN_1: BY INDUCTION ON i: OK!, TEDIOUS *)

Lemma expf_L0_CN_1:forall (m:fmap)(x y z:dart)(i:nat),
inv_hmap (L m zero x y) -> exd m z ->
let x0 := cA m zero x in
let x_1 := cA_1 m one x in
let y_0:= cA_1 m zero y in
let y_0_1 := cA_1 m one y_0 in
let t:= Iter (cF (L m zero x y)) i z in
expf m x_1 y ->
(betweenf m x_1 z y /\ betweenf m x_1 t y
\/ betweenf m y_0_1 z x0 /\ betweenf m y_0_1 t x0
\/ ~ expf m x_1 z /\ expf m z t).