Lemma expf_B0_xb0_x_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) xb0 x_1.