include "static_2/s_computation/fqus.ma".
include "basic_2/rt_computation/csx_lsubr.ma".
-(* STRONGLY NORMALIZING TERMS FOR UNBOUND PARALLEL RT-TRANSITION ************)
+(* STRONGLY NORMALIZING TERMS FOR EXTENDED PARALLEL RT-TRANSITION ***********)
(* Properties with extended supclosure **************************************)
-lemma csx_fqu_conf: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ →
- ⦃G1, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ → ⦃G2, L2⦄ ⊢ ⬈*[h, o] 𝐒⦃T2⦄.
-#h #o #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
-[ /3 width=5 by csx_inv_lref_pair, drops_refl/
+lemma csx_fqu_conf (b):
+ ∀G1,G2,L1,L2,T1,T2. ❨G1,L1,T1❩ ⬂[b] ❨G2,L2,T2❩ →
+ ❨G1,L1❩ ⊢ ⬈*𝐒 T1 → ❨G2,L2❩ ⊢ ⬈*𝐒 T2.
+#b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
+[ /3 width=5 by csx_inv_lref_pair_drops, drops_refl/
| /2 width=3 by csx_fwd_pair_sn/
| /2 width=2 by csx_fwd_bind_dx/
| /2 width=4 by csx_fwd_bind_dx_unit/
]
qed-.
-lemma csx_fquq_conf: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮[b] ⦃G2, L2, T2⦄ →
- ⦃G1, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ → ⦃G2, L2⦄ ⊢ ⬈*[h, o] 𝐒⦃T2⦄.
-#h #o #b #G1 #G2 #L1 #L2 #T1 #T2 * /2 width=6 by csx_fqu_conf/
+lemma csx_fquq_conf (b):
+ ∀G1,G2,L1,L2,T1,T2. ❨G1,L1,T1❩ ⬂⸮[b] ❨G2,L2,T2❩ →
+ ❨G1,L1❩ ⊢ ⬈*𝐒 T1 → ❨G2,L2❩ ⊢ ⬈*𝐒 T2.
+#b #G1 #G2 #L1 #L2 #T1 #T2 * /2 width=6 by csx_fqu_conf/
* #HG #HL #HT destruct //
qed-.
-lemma csx_fqup_conf: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ →
- ⦃G1, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ → ⦃G2, L2⦄ ⊢ ⬈*[h, o] 𝐒⦃T2⦄.
-#h #o #b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
+lemma csx_fqup_conf (b):
+ ∀G1,G2,L1,L2,T1,T2. ❨G1,L1,T1❩ ⬂+[b] ❨G2,L2,T2❩ →
+ ❨G1,L1❩ ⊢ ⬈*𝐒 T1 → ❨G2,L2❩ ⊢ ⬈*𝐒 T2.
+#b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
/3 width=6 by csx_fqu_conf/
qed-.
-lemma csx_fqus_conf: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐*[b] ⦃G2, L2, T2⦄ →
- ⦃G1, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ → ⦃G2, L2⦄ ⊢ ⬈*[h, o] 𝐒⦃T2⦄.
-#h #o #b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqus_ind … H) -H
+lemma csx_fqus_conf (b):
+ ∀G1,G2,L1,L2,T1,T2. ❨G1,L1,T1❩ ⬂*[b] ❨G2,L2,T2❩ →
+ ❨G1,L1❩ ⊢ ⬈*𝐒 T1 → ❨G2,L2❩ ⊢ ⬈*𝐒 T2.
+#b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqus_ind … H) -H
/3 width=6 by csx_fquq_conf/
qed-.