(* THEN, WE HAVE (OK!): *)

Lemma bottom_B0_quad: forall(m:fmap)(z v:dart)(j:nat),
inv_hmap m -> exd m z -> ~pred m zero z ->
let m0 := B m zero v in
let t := Iter (MA0.f m) j z in
(j < MA0.Iter_upb m z)%nat ->
~MA0.expo m z v ->
bottom m0 zero t = bottom m zero t.