(* Inversion lemmas with context-free sort-irrelevant equivalence for terms *)
-fact fqu_inv_tdeq_aux: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ →
+fact fqu_inv_tdeq_aux: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⊐[b] ⦃G2,L2,T2⦄ →
G1 = G2 → |L1| = |L2| → T1 ≛ T2 → ⊥.
#b #G1 #G2 #L1 #L2 #T1 #T2 * -G1 -G2 -L1 -L2 -T1 -T2
[1: #I #G #L #V #_ #H elim (succ_inv_refl_sn … H)
qed-.
(* Basic_2A1: uses: fqu_inv_eq *)
-lemma fqu_inv_tdeq: ∀b,G,L1,L2,T1,T2. ⦃G, L1, T1⦄ ⊐[b] ⦃G, L2, T2⦄ →
+lemma fqu_inv_tdeq: ∀b,G,L1,L2,T1,T2. ⦃G,L1,T1⦄ ⊐[b] ⦃G,L2,T2⦄ →
|L1| = |L2| → T1 ≛ T2 → ⊥.
#b #G #L1 #L2 #T1 #T2 #H
@(fqu_inv_tdeq_aux … H) // (**) (* full auto fails *)