Lemma expf_xb0_xh0_1:forall (m:fmap)(x:dart), inv_hmap m -> exd m 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 xb0 xh0_1.