(* FINALLY, THE RESULT ABOUT THE DEGREES: *)

Theorem degree_L1_merge_summary: forall (m:fmap)(x y z:dart),
let y0 := cA m zero y in
let m1 := L m one x y in
inv_hmap m1 -> exd m z ->
~expf m x y0 ->
let dx:= MF.degree m x in
let dy0:= MF.degree m y0 in
MF.degree m1 z =
if expf_dec m x z then dx + dy0
else if expf_dec m y0 z then dx + dy0
else MF.degree m z.