Inductive GradExpInv : Tpoint -> Tpoint -> Tpoint -> Prop :=
gradexpinv_init : forall A B, GradExpInv A B B
| gradexpinv_stab : forall A B B' C, Bet A B' B -> Cong A B' B' B -> GradExpInv A B C ->
GradExpInv A B' C.

Lemma reach__ex_gradexp_lt : forall A B P Q, A <> B -> Reach P Q A B ->
exists C, GradExp A C B /\ Lt A C P Q.