Theorem expf_not_expf_B0: forall (m:fmap)(x:dart), inv_hmap m -> succ m zero x -> let x_1:= cA_1 m one x in let x0 := cA m zero x in let xb0 := bottom m zero x in (expf (B m zero x) x_1 x0 <-> ~expf m x0 xb0).