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 ≘ ⋆.
+ 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
[ #f #_ #H //
| #I #K1 #K2 #_ #IH #f #Hf #H
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 ≘ K1.ⓤ{I} →
- â\88\83â\88\83K2. G â\8a¢ K1 â\8a\92[h] K2 & â¬\87*[b,f]L2 ≘ K2.ⓤ{I}.
+ â\88\80f. ð\9d\90\94â¦\83fâ¦\84 â\86\92 â\88\80I,K1. â\87©*[b,f]L1 ≘ K1.ⓤ{I} →
+ â\88\83â\88\83K2. G â\8a¢ K1 â\8a\92[h] K2 & â\87©*[b,f]L2 ≘ K2.ⓤ{I}.
#h #b #G #L1 #L2 #H elim H -L1 -L2
[ #f #_ #J #Y1 #H
lapply (drops_inv_atom1 … H) -H * #H #_ destruct
[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 ≘ K1.ⓑ{I}V →
- â\88¨â\88¨ â\88\83â\88\83K2. G â\8a¢ K1 â\8a\92[h] K2 & â¬\87*[b,f]L2 ≘ K2.ⓑ{I}V
- | â\88\83â\88\83K2. G â\8a¢ K1 â\8a\92[h] K2 & â¬\87*[b,f]L2 ≘ K2.ⓧ & G ⊢ ⬈*[h,V] 𝐒⦃K2⦄.
+ â\88\80f. ð\9d\90\94â¦\83fâ¦\84 â\86\92 â\88\80I,K1,V. â\87©*[b,f]L1 ≘ K1.ⓑ{I}V →
+ â\88¨â\88¨ â\88\83â\88\83K2. G â\8a¢ K1 â\8a\92[h] K2 & â\87©*[b,f]L2 ≘ K2.ⓑ{I}V
+ | â\88\83â\88\83K2. G â\8a¢ K1 â\8a\92[h] K2 & â\87©*[b,f]L2 ≘ K2.ⓧ & G ⊢ ⬈*[h,V] 𝐒⦃K2⦄.
#h #b #G #L1 #L2 #H elim H -L1 -L2
[ #f #_ #J #Y1 #X1 #H
lapply (drops_inv_atom1 … H) -H * #H #_ destruct