Definition predta_produit_4_def (d0 : preDTA) : Prop :=
forall (a a0 : ad) (s s0 : state),
MapGet state (preDTA_produit_r a0 s0 d0) a = Some s ->
exists a1 : ad,
(exists a2 : ad,
(exists s1 : state,
(exists s2 : state,
a = iad_conv a1 a2 /\
MapGet state (M1 state a0 s0) a2 = Some s1 /\
MapGet state d0 a1 = Some s2))).

Lemma predta_produit_4 :
forall (d0 : preDTA) (a a0 : ad) (s s0 : state),
MapGet state (preDTA_produit_r a0 s0 d0) a = Some s ->
exists a1 : ad,
(exists a2 : ad,
(exists s1 : state,
(exists s2 : state,
a = iad_conv a1 a2 /\
MapGet state (M1 state a0 s0) a2 = Some s1 /\
MapGet state d0 a1 = Some s2))).