Lemma expf_B0_CS_1_a_prel2:forall (m:fmap)(x z:dart), inv_hmap m -> succ m zero x -> let x0 := cA m zero x in let xb0 := bottom m zero x in let x_1 := cA_1 m one x in expf m x0 xb0 -> betweenf m x_1 z xb0 -> expf (B m zero x) x_1 z.