include "static_2/relocation/drops.ma".
include "basic_2/rt_computation/jsx.ma".
-(* COMPATIBILITY OF STRONG NORMALIZATION FOR UNBOUND RT-TRANSITION **********)
+(* COMPATIBILITY OF STRONG NORMALIZATION FOR EXTENDED RT-TRANSITION *********)
(* Forward lemmas with uniform slicing for local environments ***************)
-lemma jsx_fwd_drops_atom_sn (h) (b) (G):
- ∀L1,L2. G ⊢ L1 ⊒[h] L2 →
- â\88\80f. ð\9d\90\94â¦\83fâ¦\84 â\86\92 â¬\87*[b,f]L1 â\89\98 â\8b\86 â\86\92 â¬\87*[b,f]L2 ≘ ⋆.
-#h #b #G #L1 #L2 #H elim H -L1 -L2
+lemma jsx_fwd_drops_atom_sn (b) (G):
+ ∀L1,L2. G ⊢ L1 ⊒ L2 →
+ â\88\80f. ð\9d\90\94â\9d¨fâ\9d© â\86\92 â\87©*[b,f]L1 â\89\98 â\8b\86 â\86\92 â\87©*[b,f]L2 ≘ ⋆.
+#b #G #L1 #L2 #H elim H -L1 -L2
[ #f #_ #H //
| #I #K1 #K2 #_ #IH #f #Hf #H
| #I #K1 #K2 #V #_ #HV #IH #f #Hf #H
]
qed-.
-lemma jsx_fwd_drops_unit_sn (h) (b) (G):
- ∀L1,L2. G ⊢ L1 ⊒[h] L2 →
- â\88\80f. ð\9d\90\94â¦\83fâ¦\84 â\86\92 â\88\80I,K1. â¬\87*[b,f]L1 â\89\98 K1.â\93¤{I} →
- ∃∃K2. G ⊢ K1 ⊒[h] K2 & ⬇*[b,f]L2 ≘ K2.ⓤ{I}.
-#h #b #G #L1 #L2 #H elim H -L1 -L2
+lemma jsx_fwd_drops_unit_sn (b) (G):
+ ∀L1,L2. G ⊢ L1 ⊒ L2 →
+ â\88\80f. ð\9d\90\94â\9d¨fâ\9d© â\86\92 â\88\80I,K1. â\87©*[b,f]L1 â\89\98 K1.â\93¤[I] →
+ ∃∃K2. G ⊢ K1 ⊒ K2 & ⇩*[b,f]L2 ≘ K2.ⓤ[I].
+#b #G #L1 #L2 #H elim H -L1 -L2
[ #f #_ #J #Y1 #H
lapply (drops_inv_atom1 … H) -H * #H #_ destruct
| #I #K1 #K2 #HK12 #IH #f #Hf #J #Y1 #H
[1,3: #Hf #H destruct -IH /3 width=3 by drops_refl, ex2_intro/
|2,4:
#g #Hg #HK1 #H destruct
- elim (IH … Hg … HK1) -K1 -Hg #Y2 #HY12 #HKY2
+ elim (IH … Hg … HK1) -K1 -Hg #Y2 #HY12 #HKY2
/3 width=3 by drops_drop, ex2_intro/
]
qed-.
-lemma jsx_fwd_drops_pair_sn (h) (b) (G):
- ∀L1,L2. G ⊢ L1 ⊒[h] L2 →
- â\88\80f. ð\9d\90\94â¦\83fâ¦\84 â\86\92 â\88\80I,K1,V. â¬\87*[b,f]L1 â\89\98 K1.â\93\91{I}V →
- ∨∨ ∃∃K2. G ⊢ K1 ⊒[h] K2 & ⬇*[b,f]L2 ≘ K2.ⓑ{I}V
- | ∃∃K2. G ⊢ K1 ⊒[h] K2 & ⬇*[b,f]L2 ≘ K2.ⓧ & G ⊢ ⬈*[h,V] 𝐒⦃K2⦄.
-#h #b #G #L1 #L2 #H elim H -L1 -L2
+lemma jsx_fwd_drops_pair_sn (b) (G):
+ ∀L1,L2. G ⊢ L1 ⊒ L2 →
+ â\88\80f. ð\9d\90\94â\9d¨fâ\9d© â\86\92 â\88\80I,K1,V. â\87©*[b,f]L1 â\89\98 K1.â\93\91[I]V →
+ ∨∨ ∃∃K2. G ⊢ K1 ⊒ K2 & ⇩*[b,f]L2 ≘ K2.ⓑ[I]V
+ | ∃∃K2. G ⊢ K1 ⊒ K2 & ⇩*[b,f]L2 ≘ K2.ⓧ & G ⊢ ⬈*𝐒[V] K2.
+#b #G #L1 #L2 #H elim H -L1 -L2
[ #f #_ #J #Y1 #X1 #H
lapply (drops_inv_atom1 … H) -H * #H #_ destruct
| #I #K1 #K2 #HK12 #IH #f #Hf #J #Y1 #X1 #H