(* PARTIAL UNFOLD ON TERMS **************************************************)
-(* Advanced properties ******************************************************)
+(* Advanced inversion lemmas ************************************************)
-lemma tpss_tps: ∀L,T1,T2,d. L ⊢ T1 ▶* [d, 1] T2 → L ⊢ T1 ▶ [d, 1] T2.
+lemma tpss_inv_SO2: ∀L,T1,T2,d. L ⊢ T1 ▶* [d, 1] T2 → L ⊢ T1 ▶ [d, 1] T2.
#L #T1 #T2 #d #H @(tpss_ind … H) -T2 //
#T #T2 #_ #HT2 #IHT1
lapply (tps_trans_ge … IHT1 … HT2 ?) //
-qed.
+qed-.
+
+(* Advanced properties ******************************************************)
lemma tpss_strip_eq: ∀L,T0,T1,d1,e1. L ⊢ T0 ▶* [d1, e1] T1 →
∀T2,d2,e2. L ⊢ T0 ▶ [d2, e2] T2 →