Lemma expf_B0_CS_2_a_III: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 x_1 t -> expf (B m zero x) z t.