(* RENAMING of MF.between: *)

Definition betweenf:= MF.between.

Theorem expf_L0_CNS:forall (m:fmap)(x y z t:dart), inv_hmap (L m zero x y) -> exd m z -> (expf (L m zero x y) z t <-> let x0 := cA m zero x in let x_1 := cA_1 m one x in let y_0:= cA_1 m zero y in let y_0_1 := cA_1 m one y_0 in (if expf_dec m x_1 y then betweenf m x_1 z y /\ betweenf m x_1 t y \/ betweenf m y_0_1 z x0 /\ betweenf m y_0_1 t x0 \/ ~ expf m x_1 z /\ expf m z t else expf m z t \/ expf m z y /\ expf m t x0 \/ expf m t y /\ expf m z x0)).