- lapply (IH … HYK … H3) -IH -H3 -HYK
- [1,3: // | skip ]
- #H lapply (frees_sort … H)
-
- ]
-
-
- elim (coafter_inv_xxp … H3) -H3 [1,3: * |*: // ]
- [ #g #g1 #Hf2 #H #H0 destruct
- elim (drops_inv_skip1 … H1) -H1 #K #V #HLK #_ #H destruct
- | #g #Hf2 #H destruct
- lapply (drops_inv_drop1 … H1) -H1
- ] /3 width=4 by frees_sort/
-
-|
-|
-|
+ lapply (IH … HYK … H3) -IH -H3 -HYK [1,3: // | skip ]
+ /3 width=5 by drops_isuni_fwd_drop2, frees_sort_pushs/
+| #f1 #I #K #V #_ #IH #Hf1 #f #L #H1 #U #H2 #f2 #H3
+ lapply (isfin_inv_next … Hf1 ??) -Hf1 [3: |*: // ] #Hf1
+ lapply (lifts_inv_lref1 … H2) -H2 * #j #Hf #H destruct
+ elim (drops_split_trans_pair2 … H1) -H1 [ |*: // ] #Y #W #HLY #HYK #HVW
+ elim (coafter_fwd_xnx_pushs … H3) [ |*: // ] #g2 #H2 destruct
+ lapply (coafter_tls_succ … H3 ??) -H3 [3: |*: // ]
+ <tls_S in ⊢ (???%→?); <tls_pushs <tl_next_rew <tl_next_rew #H3
+ lapply (IH … HYK … HVW … H3) -IH -H3 -HYK -HVW //
+ /2 width=5 by frees_lref_pair/
+| #f1 #I #K #V #i #_ #IH #Hf1 #f #L #H1 #U #H2 #f2 #H3
+ lapply (isfin_fwd_push … Hf1 ??) -Hf1 [3: |*: // ] #Hf1
+ lapply (lifts_inv_lref1 … H2) -H2 * #x #Hf #H destruct
+ elim (at_inv_nxx … Hf) -Hf [ |*: // ] #j #Hf #H destruct
+ elim (drops_split_trans_pair2 … H1) -H1 [ |*: // ] #Y #W #HLY #HYK #_
+ elim (coafter_fwd_xpx_pushs … H3) [ |*: // ] #g2 #H2 destruct
+ lapply (coafter_tls_succ … H3 ??) -H3 [3: |*: // ] <tls_pushs #H3
+ lapply (drops_isuni_fwd_drop2 … HLY) -HLY // #HLY
+ lapply (IH … HYK … H3) -IH -H3 -HYK [4: |*: /2 width=2 by lifts_lref/ ]
+ >plus_S1 /2 width=3 by frees_lref_pushs/ (**) (* full auto fails *)
+| #f1 #I #K #V #l #_ #IH #Hf1 #f #L #H1 #U #H2 #f2 #H3
+ lapply (isfin_fwd_push … Hf1 ??) -Hf1 [3: |*: // ] #Hf1
+ lapply (lifts_inv_gref1 … H2) -H2 #H destruct
+ elim (drops_split_trans_pair2 … H1) -H1 [ |*: // ] #Y #W #HLY #HYK #_
+ elim (coafter_fwd_xpx_pushs … H3) [ |*: // ] #g2 #H2 destruct
+ lapply (coafter_tls_succ … H3 ??) -H3 [3: |*: // ] #H3
+ lapply (IH … HYK … H3) -IH -H3 -HYK [1,3: // | skip ]
+ /3 width=5 by drops_isuni_fwd_drop2, frees_gref_pushs/