(* Advanced inversion lemmas ************************************************)
-lemma fqus_inv_gen: â\88\80G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\83* ⦃G2, L2, T2⦄ →
- â¦\83G1, L1, T1â¦\84 â\8a\83+ ⦃G2, L2, T2⦄ ∨ (∧∧ G1 = G2 & L1 = L2 & T1 = T2).
+lemma fqus_inv_gen: â\88\80G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\90* ⦃G2, L2, T2⦄ →
+ â¦\83G1, L1, T1â¦\84 â\8a\90+ ⦃G2, L2, T2⦄ ∨ (∧∧ G1 = G2 & L1 = L2 & T1 = T2).
#G1 #G2 #L1 #L2 #T1 #T2 #H @(fqus_ind … H) -G2 -L2 -T2 //
#G #G2 #L #L2 #T #T2 #_ #H2 * elim (fquq_inv_gen … H2) -H2
[ /3 width=5 by fqup_strap1, or_introl/
(* Advanced properties ******************************************************)
-lemma fqus_strap1_fqu: â\88\80G1,G,G2,L1,L,L2,T1,T,T2. â¦\83G1, L1, T1â¦\84 â\8a\83* â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G, L, Tâ¦\84 â\8a\83 ⦃G2, L2, T2⦄ →
- â¦\83G1, L1, T1â¦\84 â\8a\83+ ⦃G2, L2, T2⦄.
+lemma fqus_strap1_fqu: â\88\80G1,G,G2,L1,L,L2,T1,T,T2. â¦\83G1, L1, T1â¦\84 â\8a\90* â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G, L, Tâ¦\84 â\8a\90 ⦃G2, L2, T2⦄ →
+ â¦\83G1, L1, T1â¦\84 â\8a\90+ ⦃G2, L2, T2⦄.
#G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2 elim (fqus_inv_gen … H1) -H1
[ /2 width=5 by fqup_strap1/
| * #HG #HL #HT destruct /2 width=1 by fqu_fqup/
]
qed-.
-lemma fqus_strap2_fqu: â\88\80G1,G,G2,L1,L,L2,T1,T,T2. â¦\83G1, L1, T1â¦\84 â\8a\83 â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G, L, Tâ¦\84 â\8a\83* ⦃G2, L2, T2⦄ →
- â¦\83G1, L1, T1â¦\84 â\8a\83+ ⦃G2, L2, T2⦄.
+lemma fqus_strap2_fqu: â\88\80G1,G,G2,L1,L,L2,T1,T,T2. â¦\83G1, L1, T1â¦\84 â\8a\90 â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G, L, Tâ¦\84 â\8a\90* ⦃G2, L2, T2⦄ →
+ â¦\83G1, L1, T1â¦\84 â\8a\90+ ⦃G2, L2, T2⦄.
#G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2 elim (fqus_inv_gen … H2) -H2
[ /2 width=5 by fqup_strap2/
| * #HG #HL #HT destruct /2 width=1 by fqu_fqup/
]
qed-.
-lemma fqus_fqup_trans: â\88\80G1,G,G2,L1,L,L2,T1,T,T2. â¦\83G1, L1, T1â¦\84 â\8a\83* â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G, L, Tâ¦\84 â\8a\83+ ⦃G2, L2, T2⦄ →
- â¦\83G1, L1, T1â¦\84 â\8a\83+ ⦃G2, L2, T2⦄.
+lemma fqus_fqup_trans: â\88\80G1,G,G2,L1,L,L2,T1,T,T2. â¦\83G1, L1, T1â¦\84 â\8a\90* â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G, L, Tâ¦\84 â\8a\90+ ⦃G2, L2, T2⦄ →
+ â¦\83G1, L1, T1â¦\84 â\8a\90+ ⦃G2, L2, T2⦄.
#G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2 @(fqup_ind … H2) -H2 -G2 -L2 -T2
/2 width=5 by fqus_strap1_fqu, fqup_strap1/
qed-.
-lemma fqup_fqus_trans: â\88\80G1,G,G2,L1,L,L2,T1,T,T2. â¦\83G1, L1, T1â¦\84 â\8a\83+ ⦃G, L, T⦄ →
- â¦\83G, L, Tâ¦\84 â\8a\83* â¦\83G2, L2, T2â¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 â\8a\83+ ⦃G2, L2, T2⦄.
+lemma fqup_fqus_trans: â\88\80G1,G,G2,L1,L,L2,T1,T,T2. â¦\83G1, L1, T1â¦\84 â\8a\90+ ⦃G, L, T⦄ →
+ â¦\83G, L, Tâ¦\84 â\8a\90* â¦\83G2, L2, T2â¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 â\8a\90+ ⦃G2, L2, T2⦄.
#G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 @(fqup_ind_dx … H1) -H1 -G1 -L1 -T1
/3 width=5 by fqus_strap2_fqu, fqup_strap2/
qed-.