| #T #T2 #_ #HT2 #IHT <(tps_inv_refl_O2 … HT2) -HT2 //
]
qed-.
+
+(* Basic forward lemmas *****************************************************)
+
+lemma tpss_fwd_tw: ∀L,T1,T2,d,e. L ⊢ T1 [d, e] ▶* T2 → #[T1] ≤ #[T2].
+#L #T1 #T2 #d #e #H @(tpss_ind … H) -T2 //
+#T #T2 #_ #HT2 #IHT1
+lapply (tps_fwd_tw … HT2) -HT2 #HT2
+@(transitive_le … IHT1) //
+qed-.