(* "HINGES" AFTER B0: *)

Lemma expf_B0_x0_xh0_1:forall (m:fmap)(x: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 (B m zero x) x0 xh0_1.