(* Properties on relocation *************************************************)
lemma da_lift: ∀h,g,G,L1,T1,l. ⦃G, L1⦄ ⊢ T1 ▪[h, g] l →
- â\88\80L2,s,d,e. â\87©[s, d, e] L2 â\89¡ L1 â\86\92 â\88\80T2. â\87§[d, e] T1 ≡ T2 →
+ â\88\80L2,s,d,e. â¬\87[s, d, e] L2 â\89¡ L1 â\86\92 â\88\80T2. â¬\86[d, e] T1 ≡ T2 →
⦃G, L2⦄ ⊢ T2 ▪[h, g] l.
#h #g #G #L1 #T1 #l #H elim H -G -L1 -T1 -l
[ #G #L1 #k #l #Hkl #L2 #s #d #e #_ #X #H
(* Inversion lemmas on relocation *******************************************)
lemma da_inv_lift: ∀h,g,G,L2,T2,l. ⦃G, L2⦄ ⊢ T2 ▪[h, g] l →
- â\88\80L1,s,d,e. â\87©[s, d, e] L2 â\89¡ L1 â\86\92 â\88\80T1. â\87§[d, e] T1 ≡ T2 →
+ â\88\80L1,s,d,e. â¬\87[s, d, e] L2 â\89¡ L1 â\86\92 â\88\80T1. â¬\86[d, e] T1 ≡ T2 →
⦃G, L1⦄ ⊢ T1 ▪[h, g] l.
#h #g #G #L2 #T2 #l #H elim H -G -L2 -T2 -l
[ #G #L2 #k #l #Hkl #L1 #s #d #e #_ #X #H