proposition: Lemma T2_invariant: forall x y, power 2 T x y -> fst x < fst y /\ snd x < fst y \/ snd x < snd y /\ fst x < snd y \/ fst x < fst y /\ snd x < snd y.
proof: Proof. intros x y T2. destruct T2 as (z,(Txz,(z0,(Tzz0,Zeq)))). unfold T in *. simpl in Zeq. destruct Txz as [T1 | T2]; destruct Tzz0 as [S1 | S2]; subst z0. right; left; lia. left; lia. right; left; lia. right; right; lia. Defined.
imports: Coq(Relations Lia) AlmostFull.PropBounded(AlmostFull) AlmostFull.PropBounded(AlmostFullInduction) AlmostFull.PropBounded(AFConstructions)