(* Inversion lemmas on negated relocation ***********************************)
lemma cpy_fwd_nlift2_ge: ∀G,L,U1,U2,d,e. ⦃G, L⦄ ⊢ U1 ▶[d, e] U2 →
- â\88\80i. d â\89¤ yinj i â\86\92 (â\88\80T2. â\87§[i, 1] T2 ≡ U2 → ⊥) →
- (â\88\80T1. â\87§[i, 1] T1 ≡ U1 → ⊥) ∨
- â\88\83â\88\83I,K,W,j. d â\89¤ yinj j & j < i & â\87©[j]L ≡ K.ⓑ{I}W &
- (â\88\80V. â\87§[i-j-1, 1] V â\89¡ W â\86\92 â\8a¥) & (â\88\80T1. â\87§[j, 1] T1 ≡ U1 → ⊥).
+ â\88\80i. d â\89¤ yinj i â\86\92 (â\88\80T2. â¬\86[i, 1] T2 ≡ U2 → ⊥) →
+ (â\88\80T1. â¬\86[i, 1] T1 ≡ U1 → ⊥) ∨
+ â\88\83â\88\83I,K,W,j. d â\89¤ yinj j & j < i & â¬\87[j]L ≡ K.ⓑ{I}W &
+ (â\88\80V. â¬\86[i-j-1, 1] V â\89¡ W â\86\92 â\8a¥) & (â\88\80T1. â¬\86[j, 1] T1 ≡ U1 → ⊥).
#G #L #U1 #U2 #d #e #H elim H -G -L -U1 -U2 -d -e
[ /3 width=2 by or_introl/
| #I #G #L #K #V #W #j #d #e #Hdj #Hjde #HLK #HVW #i #Hdi #HnW