(* FINALLY, THE (GREAT) RESULT: *)

Theorem expf_B0_CNS:forall (m:fmap)(x z t:dart),
inv_hmap m -> succ m zero x ->
(expf (B m zero x) z t <->
let x0 := cA m zero x in
let xb0 := bottom m zero x in
let x_1 := cA_1 m one x in
let xh0 := top m zero x in
let xh0_1 := cA_1 m one xh0 in
(if expf_dec m x0 xb0
then
betweenf m x_1 z xb0 /\ betweenf m x_1 t xb0
\/ betweenf m xh0_1 z x0 /\ betweenf m xh0_1 t x0
\/ ~ expf m x_1 z /\ expf m z t
else
expf m xb0 z /\ expf m x0 t
\/ expf m xb0 t /\ expf m x0 z
\/ expf m z t)).