(* Alternative definition with plus-iterated supclosure *********************)
-lemma fqup_fqus: â\88\80b,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â¬\82+[b] â¦\83G2,L2,T2â¦\84 â\86\92 â¦\83G1,L1,T1â¦\84 â¬\82*[b] â¦\83G2,L2,T2â¦\84.
+lemma fqup_fqus: â\88\80b,G1,G2,L1,L2,T1,T2. â\9d¨G1,L1,T1â\9d© â¬\82+[b] â\9d¨G2,L2,T2â\9d© â\86\92 â\9d¨G1,L1,T1â\9d© â¬\82*[b] â\9d¨G2,L2,T2â\9d©.
#b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
/3 width=5 by fqus_strap1, fquq_fqus, fqu_fquq/
qed.
(* Basic_2A1: was: fqus_inv_gen *)
-lemma fqus_inv_fqup: â\88\80b,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â¬\82*[b] â¦\83G2,L2,T2â¦\84 →
- â¦\83G1,L1,T1â¦\84 â¬\82+[b] â¦\83G2,L2,T2â¦\84 ∨ (∧∧ G1 = G2 & L1 = L2 & T1 = T2).
+lemma fqus_inv_fqup: â\88\80b,G1,G2,L1,L2,T1,T2. â\9d¨G1,L1,T1â\9d© â¬\82*[b] â\9d¨G2,L2,T2â\9d© →
+ â\9d¨G1,L1,T1â\9d© â¬\82+[b] â\9d¨G2,L2,T2â\9d© ∨ (∧∧ G1 = G2 & L1 = L2 & T1 = T2).
#b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqus_ind … H) -G2 -L2 -T2 //
#G #G2 #L #L2 #T #T2 #_ *
[ #H2 * /3 width=5 by fqup_strap1, or_introl/
(* Advanced properties ******************************************************)
-lemma fqus_strap1_fqu: â\88\80b,G1,G,G2,L1,L,L2,T1,T,T2. â¦\83G1,L1,T1â¦\84 â¬\82*[b] â¦\83G,L,Tâ¦\84 â\86\92 â¦\83G,L,Tâ¦\84 â¬\82[b] â¦\83G2,L2,T2â¦\84 →
- â¦\83G1,L1,T1â¦\84 â¬\82+[b] â¦\83G2,L2,T2â¦\84.
+lemma fqus_strap1_fqu: â\88\80b,G1,G,G2,L1,L,L2,T1,T,T2. â\9d¨G1,L1,T1â\9d© â¬\82*[b] â\9d¨G,L,Tâ\9d© â\86\92 â\9d¨G,L,Tâ\9d© â¬\82[b] â\9d¨G2,L2,T2â\9d© →
+ â\9d¨G1,L1,T1â\9d© â¬\82+[b] â\9d¨G2,L2,T2â\9d©.
#b #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2 elim (fqus_inv_fqup … H1) -H1
[ /2 width=5 by fqup_strap1/
| * /2 width=1 by fqu_fqup/
]
qed-.
-lemma fqus_strap2_fqu: â\88\80b,G1,G,G2,L1,L,L2,T1,T,T2. â¦\83G1,L1,T1â¦\84 â¬\82[b] â¦\83G,L,Tâ¦\84 â\86\92 â¦\83G,L,Tâ¦\84 â¬\82*[b] â¦\83G2,L2,T2â¦\84 →
- â¦\83G1,L1,T1â¦\84 â¬\82+[b] â¦\83G2,L2,T2â¦\84.
+lemma fqus_strap2_fqu: â\88\80b,G1,G,G2,L1,L,L2,T1,T,T2. â\9d¨G1,L1,T1â\9d© â¬\82[b] â\9d¨G,L,Tâ\9d© â\86\92 â\9d¨G,L,Tâ\9d© â¬\82*[b] â\9d¨G2,L2,T2â\9d© →
+ â\9d¨G1,L1,T1â\9d© â¬\82+[b] â\9d¨G2,L2,T2â\9d©.
#b #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2 elim (fqus_inv_fqup … H2) -H2
[ /2 width=5 by fqup_strap2/
| * /2 width=1 by fqu_fqup/
]
qed-.
-lemma fqus_fqup_trans: â\88\80b,G1,G,G2,L1,L,L2,T1,T,T2. â¦\83G1,L1,T1â¦\84 â¬\82*[b] â¦\83G,L,Tâ¦\84 â\86\92 â¦\83G,L,Tâ¦\84 â¬\82+[b] â¦\83G2,L2,T2â¦\84 →
- â¦\83G1,L1,T1â¦\84 â¬\82+[b] â¦\83G2,L2,T2â¦\84.
+lemma fqus_fqup_trans: â\88\80b,G1,G,G2,L1,L,L2,T1,T,T2. â\9d¨G1,L1,T1â\9d© â¬\82*[b] â\9d¨G,L,Tâ\9d© â\86\92 â\9d¨G,L,Tâ\9d© â¬\82+[b] â\9d¨G2,L2,T2â\9d© →
+ â\9d¨G1,L1,T1â\9d© â¬\82+[b] â\9d¨G2,L2,T2â\9d©.
#b #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\80b,G1,G,G2,L1,L,L2,T1,T,T2. â¦\83G1,L1,T1â¦\84 â¬\82+[b] â¦\83G,L,Tâ¦\84 →
- â¦\83G,L,Tâ¦\84 â¬\82*[b] â¦\83G2,L2,T2â¦\84 â\86\92 â¦\83G1,L1,T1â¦\84 â¬\82+[b] â¦\83G2,L2,T2â¦\84.
+lemma fqup_fqus_trans: â\88\80b,G1,G,G2,L1,L,L2,T1,T,T2. â\9d¨G1,L1,T1â\9d© â¬\82+[b] â\9d¨G,L,Tâ\9d© →
+ â\9d¨G,L,Tâ\9d© â¬\82*[b] â\9d¨G2,L2,T2â\9d© â\86\92 â\9d¨G1,L1,T1â\9d© â¬\82+[b] â\9d¨G2,L2,T2â\9d©.
#b #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-.
(* Advanced inversion lemmas for plus-iterated supclosure *******************)
-lemma fqup_inv_step_sn: â\88\80b,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â¬\82+[b] â¦\83G2,L2,T2â¦\84 →
- â\88\83â\88\83G,L,T. â¦\83G1,L1,T1â¦\84 â¬\82[b] â¦\83G,L,Tâ¦\84 & â¦\83G,L,Tâ¦\84 â¬\82*[b] â¦\83G2,L2,T2â¦\84.
+lemma fqup_inv_step_sn: â\88\80b,G1,G2,L1,L2,T1,T2. â\9d¨G1,L1,T1â\9d© â¬\82+[b] â\9d¨G2,L2,T2â\9d© →
+ â\88\83â\88\83G,L,T. â\9d¨G1,L1,T1â\9d© â¬\82[b] â\9d¨G,L,Tâ\9d© & â\9d¨G,L,Tâ\9d© â¬\82*[b] â\9d¨G2,L2,T2â\9d©.
#b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind_dx … H) -G1 -L1 -T1 /2 width=5 by ex2_3_intro/
#G1 #G #L1 #L #T1 #T #H1 #_ * /4 width=9 by fqus_strap2, fqu_fquq, ex2_3_intro/
qed-.