(* OK: 4 USEFUL LEMMAS (IN FACT, 3 ARE ENOUGH) *)

(* Specifications: *)
Lemma expf_B0_CS_2_a_I:forall (m:fmap)(x z t:dart),
inv_hmap m -> succ m zero x ->
let x0 := cA m zero x in
let x_1:= cA_1 m one x in
let xb0:= bottom m zero x in
let xh0:= top m zero x in
let xh0_1:= cA_1 m one xh0 in
~expf m x0 xb0 ->
expf m x_1 z -> expf m x_1 t
-> expf (B m zero x) z t.
Lemma expf_B0_CS_2_a_II:forall (m:fmap)(x z t:dart),
inv_hmap m -> succ m zero x ->
let x0 := cA m zero x in
let x_1:= cA_1 m one x in
let xb0:= bottom m zero x in
let xh0:= top m zero x in
let xh0_1:= cA_1 m one xh0 in
~expf m x0 xb0 ->
expf m xh0_1 z -> expf m xh0_1 t
-> expf (B m zero x) z t.