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 gradexpinv_clos_trans : forall A B C, GradExpInv A B C <->
clos_refl_trans_1n Tpoint (fun X Y => Midpoint X A Y) B C.