-fact lift_frsupp_trans_aux: ∀L2,U0. (
- ∀L,K,U1,U2. ⦃L, U1⦄ ⧁+ ⦃L @@ K, U2⦄ →
- ∀T1,d,e. ⇧[d, e] T1 ≡ U1 →
- #{L, U1} < #{L2, U0} →
- ∃T2. ⇧[d + |K|, e] T2 ≡ U2
- ) →
- ∀L1,K,U1,U2. ⦃L1, U1⦄ ⧁+ ⦃L2 @@ K, U2⦄ →
- ∀T1,d,e. ⇧[d, e] T1 ≡ U1 →
- L2 = L1 → U0 = U1 →
- ∃T2. ⇧[d + |K|, e] T2 ≡ U2.
-#L2 #U0 #IH #L1 #X #U1 #U2 #H @(frsupp_ind_dx … H) -L1 -U1 /2 width=5 by lift_frsup_trans/
-#L1 #L #U1 #U #HL1 #HL2 #_ #T1 #d #e #HTU1 #H1 #H2 destruct
-elim (frsup_fwd_append … HL1) #K1 #H destruct
-elim (frsupp_fwd_append … HL2) #K >append_assoc #H
-elim (append_inj_dx … H ?) -H // #_ #H destruct
-<append_assoc in HL2; #HL2
-elim (lift_frsup_trans … HTU1 … HL1) -T1 #T #HTU
-lapply (frsup_fwd_fw … HL1) -HL1 #HL1
-elim (IH … HL2 … HTU ?) -IH -HL2 -T // -L1 -U1 -U /2 width=2/
-qed-.
-