(* SUPCLOSURE ***************************************************************)
-(* Inversion lemmas with context-free degree-based equivalence for terms ****)
+(* Inversion lemmas with context-free sort-irrelevant equivalence for terms *)
-fact fqu_inv_tdeq_aux: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ →
- G1 = G2 → |L1| = |L2| → T1 ≛[h, o] T2 → ⊥.
-#h #o #b #G1 #G2 #L1 #L2 #T1 #T2 * -G1 -G2 -L1 -L2 -T1 -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)
|6: #I #G #L #T #U #_ #_ #H elim (succ_inv_refl_sn … H)
]
qed-.
(* Basic_2A1: uses: fqu_inv_eq *)
-lemma fqu_inv_tdeq: ∀h,o,b,G,L1,L2,T1,T2. ⦃G, L1, T1⦄ ⊐[b] ⦃G, L2, T2⦄ →
- |L1| = |L2| → T1 ≛[h, o] T2 → ⊥.
-#h #o #b #G #L1 #L2 #T1 #T2 #H
+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 *)
qed-.